licenses
listlengths 1
3
| version
stringclasses 677
values | tree_hash
stringlengths 40
40
| path
stringclasses 1
value | type
stringclasses 2
values | size
stringlengths 2
8
| text
stringlengths 25
67.1M
| package_name
stringlengths 2
41
| repo
stringlengths 33
86
|
|---|---|---|---|---|---|---|---|---|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 16078 | """
The extensible freely-jointed chain (EFJC) model thermodynamics in the isotensional ensemble approximated using a reduced asymptotic approach and a Legendre transformation.
"""
module Legendre
using DocStringExtensions
using .........Polymers: PROJECT_ROOT
import ........Physics: BOLTZMANN_CONSTANT
"""
The structure of the thermodynamics of the EFJC model in the isotensional ensemble approximated using a reduced asymptotic approach and a Legendre transformation.
$(FIELDS)
"""
struct EFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The stiffness of each link in the chain ``k_0`` in units of J/(mol⋅nm^2).
"""
link_stiffness::Float64
"""
The Helmholtz free energy ``\\psi`` as a function of the applied force ``f`` and temperature ``T``.
"""
helmholtz_free_energy::Function
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
helmholtz_free_energy_per_link::Function
"""
The relative helmholtz free energy ``\\Delta\\psi\\equiv\\psi(f,T)-\\psi(0,T)`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_helmholtz_free_energy::Function
"""
The relative helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_helmholtz_free_energy_per_link::Function
"""
The nondimensional helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy::Function
"""
The nondimensional helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy_per_link::Function
"""
The nondimensional relative helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_helmholtz_free_energy::Function
"""
The nondimensional relative helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_helmholtz_free_energy_per_link::Function
end
"""
The Helmholtz free energy ``\\psi`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and link stiffness ``k_0``.
```math
\\psi(f, T) \\sim \\varphi(f, T) + f \\xi(f, T) \\quad \\text{for } N_b\\gg 1.
```
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_efjc_thermodynamics_isotensional_asymptotic_reduced_legendre_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
)
end
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, hinge_mass_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_efjc_thermodynamics_isotensional_asymptotic_reduced_legendre_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
)
end
"""
The relative Helmholtz free energy ``\\Delta\\psi\\equiv\\psi(f,T)-\\psi(0,T)`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, link_stiffness_i, force_i, temperature_i) ->
ccall(
(
:physics_single_chain_efjc_thermodynamics_isotensional_asymptotic_reduced_legendre_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The relative Helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_efjc_thermodynamics_isotensional_asymptotic_reduced_legendre_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The nondimensional Helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_efjc_thermodynamics_isotensional_asymptotic_reduced_legendre_nondimensional_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_force,
temperature,
)
end
"""
The nondimensional Helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_efjc_thermodynamics_isotensional_asymptotic_reduced_legendre_nondimensional_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
),
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_force,
temperature,
)
end
"""
The nondimensional relative Helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b`` and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_link_stiffness_i, nondimensional_force_i) ->
ccall(
(
:physics_single_chain_efjc_thermodynamics_isotensional_asymptotic_reduced_legendre_nondimensional_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta``
parameterized by the nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(nondimensional_link_stiffness_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_efjc_thermodynamics_isotensional_asymptotic_reduced_legendre_nondimensional_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
Initializes and returns an instance of the thermodynamics of the EFJC model in the isotensional ensemble approximated using a reduced asymptotic approach and a Legendre transformation.
$(TYPEDSIGNATURES)
"""
function EFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
)
BOLTZMANN_CONSTANT::Float64 = 8.314462618
return EFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
(force, temperature) -> helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
),
(force, temperature) -> helmholtz_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
),
(force, temperature) -> relative_helmholtz_free_energy(
number_of_links,
link_length,
link_stiffness,
force,
temperature,
),
(force, temperature) -> relative_helmholtz_free_energy_per_link(
link_length,
link_stiffness,
force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) ->
nondimensional_helmholtz_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) ->
nondimensional_relative_helmholtz_free_energy(
number_of_links,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(nondimensional_force, temperature) ->
nondimensional_relative_helmholtz_free_energy_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 30833 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ZERO, parameters
using Polymers.Physics.SingleChain.Efjc.Thermodynamics.Isotensional.Asymptotic.Reduced.Legendre:
EFJC
@testset "physics::single_chain::efjc::thermodynamics::isotensional::asymptotic::reduced::legendre::test::base::init" begin
@test isa(
EFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
),
Any,
)
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::asymptotic::reduced::legendre::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test EFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::asymptotic::reduced::legendre::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test EFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::asymptotic::reduced::legendre::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test EFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.link_stiffness_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::asymptotic::reduced::legendre::test::base::link_stiffness" begin
for _ = 1:parameters.number_of_loops
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test EFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
link_stiffness,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::asymptotic::reduced::legendre::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test all(
EFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).number_of_links == number_of_links &&
EFJC(number_of_links, link_length, hinge_mass, link_stiffness).link_length ==
link_length &&
EFJC(number_of_links, link_length, hinge_mass, link_stiffness).hinge_mass ==
hinge_mass &&
EFJC(number_of_links, link_length, hinge_mass, link_stiffness).link_stiffness ==
link_stiffness,
)
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::asymptotic::reduced::legendre::test::nondimensional::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy =
model.nondimensional_helmholtz_free_energy(nondimensional_force, temperature)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy = model.helmholtz_free_energy(force, temperature)
residual_abs =
helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::asymptotic::reduced::legendre::test::nondimensional::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(force, temperature)
residual_abs =
helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::asymptotic::reduced::legendre::test::nondimensional::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(force, temperature)
residual_abs =
relative_helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::asymptotic::reduced::legendre::test::nondimensional::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(force, temperature)
residual_abs =
relative_helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::asymptotic::reduced::legendre::test::per_link::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy = model.helmholtz_free_energy(force, temperature)
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(force, temperature)
residual_abs =
helmholtz_free_energy / number_of_links - helmholtz_free_energy_per_link
residual_rel = residual_abs / helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::asymptotic::reduced::legendre::test::per_link::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(force, temperature)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(force, temperature)
residual_abs =
relative_helmholtz_free_energy / number_of_links -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::asymptotic::reduced::legendre::test::per_link::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy =
model.nondimensional_helmholtz_free_energy(nondimensional_force, temperature)
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy / number_of_links -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::asymptotic::reduced::legendre::test::per_link::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy / number_of_links -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::asymptotic::reduced::legendre::test::relative::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy = model.helmholtz_free_energy(force, temperature)
helmholtz_free_energy_0 = model.helmholtz_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(force, temperature)
residual_abs =
helmholtz_free_energy - helmholtz_free_energy_0 - relative_helmholtz_free_energy
residual_rel = residual_abs / helmholtz_free_energy_0
@test abs(residual_abs) <=
BOLTZMANN_CONSTANT * temperature * number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::asymptotic::reduced::legendre::test::relative::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(force, temperature)
helmholtz_free_energy_per_link_0 = model.helmholtz_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(force, temperature)
residual_abs =
helmholtz_free_energy_per_link - helmholtz_free_energy_per_link_0 -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / helmholtz_free_energy_per_link_0
@test abs(residual_abs) <= BOLTZMANN_CONSTANT * temperature * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::asymptotic::reduced::legendre::test::relative::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy =
model.nondimensional_helmholtz_free_energy(nondimensional_force, temperature)
nondimensional_helmholtz_free_energy_0 =
model.nondimensional_helmholtz_free_energy(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy - nondimensional_helmholtz_free_energy_0 -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_0
@test abs(residual_abs) <= number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::asymptotic::reduced::legendre::test::relative::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_helmholtz_free_energy_per_link_0 =
model.nondimensional_helmholtz_free_energy_per_link(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy_per_link -
nondimensional_helmholtz_free_energy_per_link_0 -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link_0
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::asymptotic::reduced::legendre::test::zero::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_0 = model.relative_helmholtz_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature * number_of_links
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::asymptotic::reduced::legendre::test::zero::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_per_link_0 =
model.relative_helmholtz_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::asymptotic::reduced::legendre::test::zero::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_0 =
model.nondimensional_relative_helmholtz_free_energy(ZERO, temperature)
@test abs(nondimensional_relative_helmholtz_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::asymptotic::reduced::legendre::test::zero::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_per_link_0 =
model.nondimensional_relative_helmholtz_free_energy_per_link(ZERO, temperature)
@test abs(nondimensional_relative_helmholtz_free_energy_per_link_0) <= ZERO
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 15820 | """
The extensible freely-jointed chain (EFJC) model thermodynamics in the isotensional ensemble approximated using a Legendre transformation.
"""
module Legendre
using DocStringExtensions
using .......Polymers: PROJECT_ROOT
import ......Physics: BOLTZMANN_CONSTANT
"""
The structure of the thermodynamics of the EFJC model in the isotensional ensemble approximated using a Legendre transformation.
$(FIELDS)
"""
struct EFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The stiffness of each link in the chain ``k_0`` in units of J/(mol⋅nm^2).
"""
link_stiffness::Float64
"""
The Helmholtz free energy ``\\psi`` as a function of the applied force ``f`` and temperature ``T``.
"""
helmholtz_free_energy::Function
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
helmholtz_free_energy_per_link::Function
"""
The relative helmholtz free energy ``\\Delta\\psi\\equiv\\psi(f,T)-\\psi(0,T)`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_helmholtz_free_energy::Function
"""
The relative helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_helmholtz_free_energy_per_link::Function
"""
The nondimensional helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy::Function
"""
The nondimensional helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy_per_link::Function
"""
The nondimensional relative helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_helmholtz_free_energy::Function
"""
The nondimensional relative helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_helmholtz_free_energy_per_link::Function
end
"""
The Helmholtz free energy ``\\psi`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and link stiffness ``k_0``.
```math
\\psi(f, T) \\sim \\varphi(f, T) + f \\xi(f, T) \\quad \\text{for } N_b\\gg 1.
```
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_efjc_thermodynamics_isotensional_legendre_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
)
end
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, hinge_mass_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_efjc_thermodynamics_isotensional_legendre_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
)
end
"""
The relative Helmholtz free energy ``\\Delta\\psi\\equiv\\psi(f,T)-\\psi(0,T)`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, link_stiffness_i, force_i, temperature_i) ->
ccall(
(
:physics_single_chain_efjc_thermodynamics_isotensional_legendre_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The relative Helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_efjc_thermodynamics_isotensional_legendre_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The nondimensional Helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_efjc_thermodynamics_isotensional_legendre_nondimensional_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_force,
temperature,
)
end
"""
The nondimensional Helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_efjc_thermodynamics_isotensional_legendre_nondimensional_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
),
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_force,
temperature,
)
end
"""
The nondimensional relative Helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b`` and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_link_stiffness_i, nondimensional_force_i) ->
ccall(
(
:physics_single_chain_efjc_thermodynamics_isotensional_legendre_nondimensional_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta``
parameterized by the nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(nondimensional_link_stiffness_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_efjc_thermodynamics_isotensional_legendre_nondimensional_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
Initializes and returns an instance of the thermodynamics of the EFJC model in the isotensional ensemble approximated using a Legendre transformation.
$(TYPEDSIGNATURES)
"""
function EFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
)
BOLTZMANN_CONSTANT::Float64 = 8.314462618
return EFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
(force, temperature) -> helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
),
(force, temperature) -> helmholtz_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
),
(force, temperature) -> relative_helmholtz_free_energy(
number_of_links,
link_length,
link_stiffness,
force,
temperature,
),
(force, temperature) -> relative_helmholtz_free_energy_per_link(
link_length,
link_stiffness,
force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) ->
nondimensional_helmholtz_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) ->
nondimensional_relative_helmholtz_free_energy(
number_of_links,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(nondimensional_force, temperature) ->
nondimensional_relative_helmholtz_free_energy_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 30347 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ZERO, parameters
using Polymers.Physics.SingleChain.Efjc.Thermodynamics.Isotensional.Legendre: EFJC
@testset "physics::single_chain::efjc::thermodynamics::isotensional::legendre::test::base::init" begin
@test isa(
EFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
),
Any,
)
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::legendre::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test EFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::legendre::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test EFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::legendre::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test EFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.link_stiffness_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::legendre::test::base::link_stiffness" begin
for _ = 1:parameters.number_of_loops
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test EFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
link_stiffness,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::legendre::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test all(
EFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).number_of_links == number_of_links &&
EFJC(number_of_links, link_length, hinge_mass, link_stiffness).link_length ==
link_length &&
EFJC(number_of_links, link_length, hinge_mass, link_stiffness).hinge_mass ==
hinge_mass &&
EFJC(number_of_links, link_length, hinge_mass, link_stiffness).link_stiffness ==
link_stiffness,
)
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::legendre::test::nondimensional::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy =
model.nondimensional_helmholtz_free_energy(nondimensional_force, temperature)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy = model.helmholtz_free_energy(force, temperature)
residual_abs =
helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::legendre::test::nondimensional::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(force, temperature)
residual_abs =
helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::legendre::test::nondimensional::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(force, temperature)
residual_abs =
relative_helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::legendre::test::nondimensional::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(force, temperature)
residual_abs =
relative_helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::legendre::test::per_link::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy = model.helmholtz_free_energy(force, temperature)
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(force, temperature)
residual_abs =
helmholtz_free_energy / number_of_links - helmholtz_free_energy_per_link
residual_rel = residual_abs / helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::legendre::test::per_link::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(force, temperature)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(force, temperature)
residual_abs =
relative_helmholtz_free_energy / number_of_links -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::legendre::test::per_link::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy =
model.nondimensional_helmholtz_free_energy(nondimensional_force, temperature)
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy / number_of_links -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::legendre::test::per_link::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy / number_of_links -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::legendre::test::relative::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy = model.helmholtz_free_energy(force, temperature)
helmholtz_free_energy_0 = model.helmholtz_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(force, temperature)
residual_abs =
helmholtz_free_energy - helmholtz_free_energy_0 - relative_helmholtz_free_energy
residual_rel = residual_abs / helmholtz_free_energy_0
@test abs(residual_abs) <=
BOLTZMANN_CONSTANT * temperature * number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::legendre::test::relative::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(force, temperature)
helmholtz_free_energy_per_link_0 = model.helmholtz_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(force, temperature)
residual_abs =
helmholtz_free_energy_per_link - helmholtz_free_energy_per_link_0 -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / helmholtz_free_energy_per_link_0
@test abs(residual_abs) <= BOLTZMANN_CONSTANT * temperature * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::legendre::test::relative::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy =
model.nondimensional_helmholtz_free_energy(nondimensional_force, temperature)
nondimensional_helmholtz_free_energy_0 =
model.nondimensional_helmholtz_free_energy(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy - nondimensional_helmholtz_free_energy_0 -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_0
@test abs(residual_abs) <= number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::legendre::test::relative::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_helmholtz_free_energy_per_link_0 =
model.nondimensional_helmholtz_free_energy_per_link(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy_per_link -
nondimensional_helmholtz_free_energy_per_link_0 -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link_0
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::legendre::test::zero::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_0 = model.relative_helmholtz_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature * number_of_links
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::legendre::test::zero::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_per_link_0 =
model.relative_helmholtz_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::legendre::test::zero::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_0 =
model.nondimensional_relative_helmholtz_free_energy(ZERO, temperature)
@test abs(nondimensional_relative_helmholtz_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::efjc::thermodynamics::isotensional::legendre::test::zero::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_per_link_0 =
model.nondimensional_relative_helmholtz_free_energy_per_link(ZERO, temperature)
@test abs(nondimensional_relative_helmholtz_free_energy_per_link_0) <= ZERO
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 967 | """
The freely-jointed chain (FJC) single-chain model.
"""
module Fjc
using DocStringExtensions
include("thermodynamics/mod.jl")
"""
The structure of the FJC model.
$(FIELDS)
"""
struct FJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The thermodynamic functions of the model.
"""
thermodynamics::Any
end
"""
Initializes and returns an instance of the FJC model.
$(TYPEDSIGNATURES)
"""
function FJC(number_of_links::UInt8, link_length::Float64, hinge_mass::Float64)
return FJC(
number_of_links,
link_length,
hinge_mass,
Thermodynamics.FJC(number_of_links, link_length, hinge_mass),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 2474 | module Test
using Test
using Polymers.Physics.SingleChain: parameters
using Polymers.Physics.SingleChain.Fjc: FJC
@testset "physics::single_chain::fjc::test::base::init" begin
@test isa(
FJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
),
Any,
)
end
@testset "physics::single_chain::fjc::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test FJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::fjc::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test FJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::fjc::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test FJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::fjc::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test all(
FJC(number_of_links, link_length, hinge_mass).number_of_links ==
number_of_links &&
FJC(number_of_links, link_length, hinge_mass).link_length == link_length &&
FJC(number_of_links, link_length, hinge_mass).hinge_mass == hinge_mass,
)
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 1494 | """
The freely-jointed chain (FJC) model thermodynamics.
"""
module Thermodynamics
using DocStringExtensions
include("isometric/mod.jl")
include("isotensional/mod.jl")
include("modified_canonical/mod.jl")
"""
The structure of the thermodynamics of the FJC model.
$(FIELDS)
"""
struct FJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The thermodynamic functions of the model in the isometric ensemble.
"""
isometric::Any
"""
The thermodynamic functions of the model in the isotensional ensemble.
"""
isotensional::Any
"""
The thermodynamic functions of the model in the modified canonical ensemble.
"""
modified_canonical::Any
end
"""
Initializes and returns an instance of the thermodynamics of the FJC model.
$(TYPEDSIGNATURES)
"""
function FJC(number_of_links::UInt8, link_length::Float64, hinge_mass::Float64)
return FJC(
number_of_links,
link_length,
hinge_mass,
Isometric.FJC(number_of_links, link_length, hinge_mass),
Isotensional.FJC(number_of_links, link_length, hinge_mass),
ModifiedCanonical.FJC(number_of_links, link_length, hinge_mass),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 182134 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT, PLANCK_CONSTANT
using Polymers.Physics.SingleChain: ZERO, POINTS, integrate, parameters
using Polymers.Physics.SingleChain.Fjc.Thermodynamics: FJC
@testset "physics::single_chain::fjc::thermodynamics::test::base::init" begin
@test isa(
FJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
),
Any,
)
end
@testset "physics::single_chain::fjc::thermodynamics::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test FJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test FJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test FJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test all(
FJC(number_of_links, link_length, hinge_mass).number_of_links ==
number_of_links &&
FJC(number_of_links, link_length, hinge_mass).link_length == link_length &&
FJC(number_of_links, link_length, hinge_mass).hinge_mass == hinge_mass,
)
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::legendre::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.isotensional.end_to_end_length(force, temperature)
force_out = model.isometric.legendre.force(end_to_end_length, temperature)
residual_abs = force - force_out
residual_rel = residual_abs / force
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::legendre::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
nondimensional_force_out = model.isometric.legendre.nondimensional_force(
nondimensional_end_to_end_length_per_link,
)
residual_abs = nondimensional_force - nondimensional_force_out
residual_rel = residual_abs / nondimensional_force
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::legendre::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.isotensional.end_to_end_length(force, temperature)
helmholtz_free_energy_legendre =
model.isotensional.gibbs_free_energy(force, temperature) +
force * end_to_end_length
helmholtz_free_energy_legendre_out =
model.isometric.legendre.helmholtz_free_energy(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy_legendre - helmholtz_free_energy_legendre_out +
BOLTZMANN_CONSTANT *
temperature *
log(
8.0 * pi^2 * hinge_mass * link_length^2 * BOLTZMANN_CONSTANT * temperature /
PLANCK_CONSTANT^2,
)
residual_rel = residual_abs / helmholtz_free_energy_legendre
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::legendre::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.isotensional.end_to_end_length(force, temperature)
end_to_end_length_per_link =
model.isotensional.end_to_end_length_per_link(force, temperature)
helmholtz_free_energy_per_link_legendre =
model.isotensional.gibbs_free_energy_per_link(force, temperature) +
force * end_to_end_length_per_link
helmholtz_free_energy_per_link_legendre_out =
model.isometric.legendre.helmholtz_free_energy_per_link(
end_to_end_length,
temperature,
)
residual_abs =
helmholtz_free_energy_per_link_legendre -
helmholtz_free_energy_per_link_legendre_out +
BOLTZMANN_CONSTANT *
temperature *
log(
8.0 * pi^2 * hinge_mass * link_length^2 * BOLTZMANN_CONSTANT * temperature /
PLANCK_CONSTANT^2,
) / number_of_links
residual_rel = residual_abs / helmholtz_free_energy_per_link_legendre
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::legendre::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.isotensional.end_to_end_length(force, temperature)
relative_helmholtz_free_energy_legendre =
model.isotensional.relative_gibbs_free_energy(force, temperature) +
force * end_to_end_length
relative_helmholtz_free_energy_legendre_out =
model.isometric.legendre.relative_helmholtz_free_energy(
end_to_end_length,
temperature,
)
residual_abs =
relative_helmholtz_free_energy_legendre -
relative_helmholtz_free_energy_legendre_out
residual_rel = residual_abs / relative_helmholtz_free_energy_legendre
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::legendre::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.isotensional.end_to_end_length(force, temperature)
end_to_end_length_per_link =
model.isotensional.end_to_end_length_per_link(force, temperature)
relative_helmholtz_free_energy_per_link_legendre =
model.isotensional.relative_gibbs_free_energy_per_link(force, temperature) +
force * end_to_end_length_per_link
relative_helmholtz_free_energy_per_link_legendre_out =
model.isometric.legendre.relative_helmholtz_free_energy_per_link(
end_to_end_length,
temperature,
)
residual_abs =
relative_helmholtz_free_energy_per_link_legendre -
relative_helmholtz_free_energy_per_link_legendre_out
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link_legendre
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::legendre::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_end_to_end_length =
model.isotensional.nondimensional_end_to_end_length(nondimensional_force)
nondimensional_end_to_end_length_per_link =
model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
nondimensional_helmholtz_free_energy_legendre =
model.isotensional.nondimensional_gibbs_free_energy(
nondimensional_force,
temperature,
) + nondimensional_force * nondimensional_end_to_end_length
nondimensional_helmholtz_free_energy_legendre_out =
model.isometric.legendre.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy_legendre -
nondimensional_helmholtz_free_energy_legendre_out + log(
8.0 * pi^2 * hinge_mass * link_length^2 * BOLTZMANN_CONSTANT * temperature /
PLANCK_CONSTANT^2,
)
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_legendre
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::legendre::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
nondimensional_helmholtz_free_energy_per_link_legendre =
model.isotensional.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
) + nondimensional_force * nondimensional_end_to_end_length_per_link
nondimensional_helmholtz_free_energy_per_link_legendre_out =
model.isometric.legendre.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy_per_link_legendre -
nondimensional_helmholtz_free_energy_per_link_legendre_out +
log(
8.0 * pi^2 * hinge_mass * link_length^2 * BOLTZMANN_CONSTANT * temperature /
PLANCK_CONSTANT^2,
) / number_of_links
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link_legendre
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::legendre::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length =
model.isotensional.nondimensional_end_to_end_length(nondimensional_force)
nondimensional_end_to_end_length_per_link =
model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
nondimensional_relative_helmholtz_free_energy_legendre =
model.isotensional.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
) + nondimensional_force * nondimensional_end_to_end_length
nondimensional_relative_helmholtz_free_energy_legendre_out =
model.isometric.legendre.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy_legendre -
nondimensional_relative_helmholtz_free_energy_legendre_out
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_legendre
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::legendre::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
nondimensional_relative_helmholtz_free_energy_per_link_legendre =
model.isotensional.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
) + nondimensional_force * nondimensional_end_to_end_length_per_link
nondimensional_relative_helmholtz_free_energy_per_link_legendre_out =
model.isometric.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy_per_link_legendre -
nondimensional_relative_helmholtz_free_energy_per_link_legendre_out
residual_rel =
residual_abs / nondimensional_relative_helmholtz_free_energy_per_link_legendre
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
force = model.isometric.force(end_to_end_length, temperature)
end_to_end_length_out = model.isotensional.end_to_end_length(force, temperature)
residual_abs = end_to_end_length - end_to_end_length_out
residual_rel = residual_abs / end_to_end_length
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
force = model.isometric.force(end_to_end_length, temperature)
end_to_end_length_per_link = nondimensional_end_to_end_length_per_link * link_length
end_to_end_length_per_link_out =
model.isotensional.end_to_end_length_per_link(force, temperature)
residual_abs = end_to_end_length_per_link - end_to_end_length_per_link_out
residual_rel = residual_abs / end_to_end_length_per_link
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
nondimensional_force =
model.isometric.nondimensional_force(nondimensional_end_to_end_length_per_link)
nondimensional_end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links
nondimensional_end_to_end_length_out =
model.isotensional.nondimensional_end_to_end_length(nondimensional_force)
residual_abs =
nondimensional_end_to_end_length - nondimensional_end_to_end_length_out
residual_rel = residual_abs / nondimensional_end_to_end_length
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::nondimensional_end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
nondimensional_force =
model.isometric.nondimensional_force(nondimensional_end_to_end_length_per_link)
nondimensional_end_to_end_length_per_link_out =
model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
residual_abs =
nondimensional_end_to_end_length_per_link -
nondimensional_end_to_end_length_per_link_out
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::force" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.isotensional.end_to_end_length(force, temperature)
force_out = model.isometric.force(end_to_end_length, temperature)
residual_abs = force - force_out
residual_rel = residual_abs / force
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
nondimensional_force_out =
model.isometric.nondimensional_force(nondimensional_end_to_end_length_per_link)
residual_abs = nondimensional_force - nondimensional_force_out
residual_rel = residual_abs / nondimensional_force
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
force = model.isometric.force(end_to_end_length, temperature)
helmholtz_free_energy =
model.isometric.helmholtz_free_energy(end_to_end_length, temperature)
helmholtz_free_energy_out =
model.isotensional.gibbs_free_energy(force, temperature) +
force * end_to_end_length
residual_abs = helmholtz_free_energy - helmholtz_free_energy_out
residual_rel = residual_abs / helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
end_to_end_length_per_link = nondimensional_end_to_end_length_per_link * link_length
force = model.isometric.force(end_to_end_length, temperature)
helmholtz_free_energy_per_link =
model.isometric.helmholtz_free_energy_per_link(end_to_end_length, temperature)
helmholtz_free_energy_per_link_out =
model.isotensional.gibbs_free_energy_per_link(force, temperature) +
force * end_to_end_length_per_link
residual_abs = helmholtz_free_energy_per_link - helmholtz_free_energy_per_link_out
residual_rel = residual_abs / helmholtz_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
force = model.isometric.force(end_to_end_length, temperature)
relative_helmholtz_free_energy =
model.isometric.relative_helmholtz_free_energy(end_to_end_length, temperature)
relative_helmholtz_free_energy_out =
model.isotensional.relative_gibbs_free_energy(force, temperature) +
force * end_to_end_length
residual_abs = relative_helmholtz_free_energy - relative_helmholtz_free_energy_out
residual_rel = residual_abs / relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
end_to_end_length_per_link = nondimensional_end_to_end_length_per_link * link_length
force = model.isometric.force(end_to_end_length, temperature)
relative_helmholtz_free_energy_per_link =
model.isometric.relative_helmholtz_free_energy_per_link(
end_to_end_length,
temperature,
)
relative_helmholtz_free_energy_per_link_out =
model.isotensional.relative_gibbs_free_energy_per_link(force, temperature) +
force * end_to_end_length_per_link
residual_abs =
relative_helmholtz_free_energy_per_link -
relative_helmholtz_free_energy_per_link_out
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links
nondimensional_force =
model.isometric.nondimensional_force(nondimensional_end_to_end_length_per_link)
nondimensional_helmholtz_free_energy =
model.isometric.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_out =
model.isotensional.nondimensional_gibbs_free_energy(
nondimensional_force,
temperature,
) + nondimensional_force * nondimensional_end_to_end_length
residual_abs =
nondimensional_helmholtz_free_energy - nondimensional_helmholtz_free_energy_out
residual_rel = residual_abs / nondimensional_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
model.isometric.nondimensional_force(nondimensional_end_to_end_length_per_link)
nondimensional_helmholtz_free_energy_per_link =
model.isometric.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_per_link_out =
model.isotensional.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
) + nondimensional_force * nondimensional_end_to_end_length_per_link
residual_abs =
nondimensional_helmholtz_free_energy_per_link -
nondimensional_helmholtz_free_energy_per_link_out
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
nondimensional_end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links
nondimensional_force =
model.isometric.nondimensional_force(nondimensional_end_to_end_length_per_link)
nondimensional_relative_helmholtz_free_energy =
model.isometric.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
)
nondimensional_relative_helmholtz_free_energy_out =
model.isotensional.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
) + nondimensional_force * nondimensional_end_to_end_length
residual_abs =
nondimensional_relative_helmholtz_free_energy -
nondimensional_relative_helmholtz_free_energy_out
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
nondimensional_force =
model.isometric.nondimensional_force(nondimensional_end_to_end_length_per_link)
nondimensional_relative_helmholtz_free_energy_per_link =
model.isometric.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
)
nondimensional_relative_helmholtz_free_energy_per_link_out =
model.isotensional.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
) + nondimensional_force * nondimensional_end_to_end_length_per_link
residual_abs =
nondimensional_relative_helmholtz_free_energy_per_link -
nondimensional_relative_helmholtz_free_energy_per_link_out
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.isotensional.end_to_end_length(force, temperature)
gibbs_free_energy = model.isotensional.gibbs_free_energy(force, temperature)
gibbs_free_energy_out =
model.isometric.helmholtz_free_energy(end_to_end_length, temperature) -
force * end_to_end_length
residual_abs = gibbs_free_energy - gibbs_free_energy_out
residual_rel = residual_abs / gibbs_free_energy
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.isotensional.end_to_end_length(force, temperature)
end_to_end_length_per_link = end_to_end_length / number_of_links
gibbs_free_energy_per_link =
model.isotensional.gibbs_free_energy_per_link(force, temperature)
gibbs_free_energy_per_link_out =
model.isometric.helmholtz_free_energy_per_link(end_to_end_length, temperature) -
force * end_to_end_length_per_link
residual_abs = gibbs_free_energy_per_link - gibbs_free_energy_per_link_out
residual_rel = residual_abs / gibbs_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.isotensional.end_to_end_length(force, temperature)
relative_gibbs_free_energy =
model.isotensional.relative_gibbs_free_energy(force, temperature)
relative_gibbs_free_energy_out =
model.isometric.relative_helmholtz_free_energy(end_to_end_length, temperature) -
force * end_to_end_length
residual_abs = relative_gibbs_free_energy - relative_gibbs_free_energy_out
residual_rel = residual_abs / relative_gibbs_free_energy
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.isotensional.end_to_end_length(force, temperature)
end_to_end_length_per_link = end_to_end_length / number_of_links
relative_gibbs_free_energy_per_link =
model.isotensional.relative_gibbs_free_energy_per_link(force, temperature)
relative_gibbs_free_energy_per_link_out =
model.isometric.relative_helmholtz_free_energy_per_link(
end_to_end_length,
temperature,
) - force * end_to_end_length_per_link
residual_abs =
relative_gibbs_free_energy_per_link - relative_gibbs_free_energy_per_link_out
residual_rel = residual_abs / relative_gibbs_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
nondimensional_end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links
nondimensional_gibbs_free_energy =
model.isotensional.nondimensional_gibbs_free_energy(
nondimensional_force,
temperature,
)
nondimensional_gibbs_free_energy_out =
model.isometric.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length
residual_abs =
nondimensional_gibbs_free_energy - nondimensional_gibbs_free_energy_out
residual_rel = residual_abs / nondimensional_gibbs_free_energy
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::nondimensional_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
nondimensional_gibbs_free_energy_per_link =
model.isotensional.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_gibbs_free_energy_per_link_out =
model.isometric.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length_per_link
residual_abs =
nondimensional_gibbs_free_energy_per_link -
nondimensional_gibbs_free_energy_per_link_out
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
nondimensional_end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links
nondimensional_relative_gibbs_free_energy =
model.isotensional.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
)
nondimensional_relative_gibbs_free_energy_out =
model.isometric.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
) - nondimensional_force * nondimensional_end_to_end_length
residual_abs =
nondimensional_relative_gibbs_free_energy -
nondimensional_relative_gibbs_free_energy_out
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::nondimensional_relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
nondimensional_relative_gibbs_free_energy_per_link =
model.isotensional.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
)
nondimensional_relative_gibbs_free_energy_per_link_out =
model.isometric.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
) - nondimensional_force * nondimensional_end_to_end_length_per_link
residual_abs =
nondimensional_relative_gibbs_free_energy_per_link -
nondimensional_relative_gibbs_free_energy_per_link_out
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_strong_potential_isometric::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(end_to_end_length)
return (
model.modified_canonical.force(
end_to_end_length,
potential_stiffness,
temperature,
) - model.isometric.force(end_to_end_length, temperature)
)^2
end
function integrand_denominator(end_to_end_length)
return model.modified_canonical.force(
end_to_end_length,
potential_stiffness,
temperature,
)^2
end
numerator = integrate(
integrand_numerator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_strong_potential_isometric::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_end_to_end_length_per_link)
return (
model.modified_canonical.nondimensional_force(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
) - model.isometric.nondimensional_force(
nondimensional_end_to_end_length_per_link,
)
)^2
end
function integrand_denominator(nondimensional_end_to_end_length_per_link)
return model.modified_canonical.nondimensional_force(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
)^2
end
numerator = integrate(
integrand_numerator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_strong_potential_isometric::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(end_to_end_length)
return (
model.modified_canonical.relative_helmholtz_free_energy(
end_to_end_length,
potential_stiffness,
temperature,
) - model.isometric.relative_helmholtz_free_energy(
end_to_end_length,
temperature,
)
)^2
end
function integrand_denominator(end_to_end_length)
return model.modified_canonical.relative_helmholtz_free_energy(
end_to_end_length,
potential_stiffness,
temperature,
)^2
end
numerator = integrate(
integrand_numerator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_strong_potential_isometric::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(end_to_end_length)
return (
model.modified_canonical.relative_helmholtz_free_energy_per_link(
end_to_end_length,
potential_stiffness,
temperature,
) - model.isometric.relative_helmholtz_free_energy_per_link(
end_to_end_length,
temperature,
)
)^2
end
function integrand_denominator(end_to_end_length)
return model.modified_canonical.relative_helmholtz_free_energy_per_link(
end_to_end_length,
potential_stiffness,
temperature,
)^2
end
numerator = integrate(
integrand_numerator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_strong_potential_isometric::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_end_to_end_length_per_link)
return (
model.modified_canonical.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
) - model.isometric.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
)
)^2
end
function integrand_denominator(nondimensional_end_to_end_length_per_link)
return model.modified_canonical.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
)^2
end
numerator = integrate(
integrand_numerator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_strong_potential_isometric::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_end_to_end_length_per_link)
return (
model.modified_canonical.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
) -
model.isometric.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
)
)^2
end
function integrand_denominator(nondimensional_end_to_end_length_per_link)
return model.modified_canonical.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
)^2
end
numerator = integrate(
integrand_numerator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_weak_potential_isotensional::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
force = model.modified_canonical.force(
potential_distance,
potential_stiffness,
temperature,
)
return (
model.modified_canonical.end_to_end_length(
potential_distance,
potential_stiffness,
temperature,
) - model.isotensional.end_to_end_length(force, temperature)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return model.modified_canonical.end_to_end_length(
potential_distance,
potential_stiffness,
temperature,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_weak_potential_isotensional::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
force = model.modified_canonical.force(
potential_distance,
potential_stiffness,
temperature,
)
return (
model.modified_canonical.end_to_end_length_per_link(
potential_distance,
potential_stiffness,
temperature,
) - model.isotensional.end_to_end_length_per_link(force, temperature)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return model.modified_canonical.end_to_end_length_per_link(
potential_distance,
potential_stiffness,
temperature,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_weak_potential_isotensional::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_potential_distance)
nondimensional_force = model.modified_canonical.nondimensional_force(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
return (
model.modified_canonical.nondimensional_end_to_end_length(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
) - model.isotensional.nondimensional_end_to_end_length(
nondimensional_force,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
return model.modified_canonical.nondimensional_end_to_end_length(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_weak_potential_isotensional::nondimensional_end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_potential_distance)
nondimensional_force = model.modified_canonical.nondimensional_force(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
return (
model.modified_canonical.nondimensional_end_to_end_length_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
) - model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
return model.modified_canonical.nondimensional_end_to_end_length_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_weak_potential_isotensional::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance_ref =
parameters.nondimensional_potential_distance_large_1 *
number_of_links *
link_length
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
force_ref = model.modified_canonical.force(
potential_distance_ref,
potential_stiffness,
temperature,
)
function integrand_numerator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
force = model.modified_canonical.force(
potential_distance,
potential_stiffness,
temperature,
)
return (
model.modified_canonical.gibbs_free_energy(
potential_distance,
potential_stiffness,
temperature,
) - model.modified_canonical.gibbs_free_energy(
potential_distance_ref,
potential_stiffness,
temperature,
) - model.isotensional.gibbs_free_energy(force, temperature) +
model.isotensional.gibbs_free_energy(force_ref, temperature)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return (
model.modified_canonical.gibbs_free_energy(
potential_distance,
potential_stiffness,
temperature,
) - model.modified_canonical.gibbs_free_energy(
potential_distance_ref,
potential_stiffness,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_weak_potential_isotensional::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance_ref =
parameters.nondimensional_potential_distance_large_1 *
number_of_links *
link_length
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
force_ref = model.modified_canonical.force(
potential_distance_ref,
potential_stiffness,
temperature,
)
function integrand_numerator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
force = model.modified_canonical.force(
potential_distance,
potential_stiffness,
temperature,
)
return (
model.modified_canonical.gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
) - model.modified_canonical.gibbs_free_energy_per_link(
potential_distance_ref,
potential_stiffness,
temperature,
) - model.isotensional.gibbs_free_energy_per_link(force, temperature) +
model.isotensional.gibbs_free_energy_per_link(force_ref, temperature)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return (
model.modified_canonical.gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
) - model.modified_canonical.gibbs_free_energy_per_link(
potential_distance_ref,
potential_stiffness,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_weak_potential_isotensional::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
force = model.modified_canonical.force(
potential_distance,
potential_stiffness,
temperature,
)
return (
model.modified_canonical.relative_gibbs_free_energy(
potential_distance,
potential_stiffness,
temperature,
) - model.isotensional.relative_gibbs_free_energy(force, temperature)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return model.modified_canonical.relative_gibbs_free_energy(
potential_distance,
potential_stiffness,
temperature,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_weak_potential_isotensional::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
force = model.modified_canonical.force(
potential_distance,
potential_stiffness,
temperature,
)
return (
model.modified_canonical.relative_gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
) - model.isotensional.relative_gibbs_free_energy_per_link(
force,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return model.modified_canonical.relative_gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_weak_potential_isotensional::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_potential_distance_ref =
parameters.nondimensional_potential_distance_large_1
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
nondimensional_force_ref = model.modified_canonical.nondimensional_force(
nondimensional_potential_distance_ref,
nondimensional_potential_stiffness,
)
function integrand_numerator(nondimensional_potential_distance)
nondimensional_force = model.modified_canonical.nondimensional_force(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
return (
model.modified_canonical.nondimensional_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
) - model.modified_canonical.nondimensional_gibbs_free_energy(
nondimensional_potential_distance_ref,
nondimensional_potential_stiffness,
temperature,
) - model.isotensional.nondimensional_gibbs_free_energy(
nondimensional_force,
temperature,
) + model.isotensional.nondimensional_gibbs_free_energy(
nondimensional_force_ref,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
return (
model.modified_canonical.nondimensional_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
) - model.modified_canonical.nondimensional_gibbs_free_energy(
nondimensional_potential_distance_ref,
nondimensional_potential_stiffness,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_weak_potential_isotensional::nondimensional_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_potential_distance_ref =
parameters.nondimensional_potential_distance_large_1
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
nondimensional_force_ref = model.modified_canonical.nondimensional_force(
nondimensional_potential_distance_ref,
nondimensional_potential_stiffness,
)
function integrand_numerator(nondimensional_potential_distance)
nondimensional_force = model.modified_canonical.nondimensional_force(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
return (
model.modified_canonical.nondimensional_gibbs_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
) -
model.modified_canonical.nondimensional_gibbs_free_energy_per_link(
nondimensional_potential_distance_ref,
nondimensional_potential_stiffness,
temperature,
) - model.isotensional.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
) + model.isotensional.nondimensional_gibbs_free_energy_per_link(
nondimensional_force_ref,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
return (
model.modified_canonical.nondimensional_gibbs_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
) - model.modified_canonical.nondimensional_gibbs_free_energy_per_link(
nondimensional_potential_distance_ref,
nondimensional_potential_stiffness,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_weak_potential_isotensional::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_potential_distance)
nondimensional_force = model.modified_canonical.nondimensional_force(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
return (
model.modified_canonical.nondimensional_relative_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
) - model.isotensional.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
return model.modified_canonical.nondimensional_relative_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_weak_potential_isotensional::nondimensional_relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_potential_distance)
nondimensional_force = model.modified_canonical.nondimensional_force(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
return (
model.modified_canonical.nondimensional_relative_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
) - model.isotensional.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
return model.modified_canonical.nondimensional_relative_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_strong_potential_isometric::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(end_to_end_length)
return (
model.isometric.force(end_to_end_length, temperature) -
model.modified_canonical.asymptotic.strong_potential.force(
end_to_end_length,
potential_stiffness,
temperature,
)
)^2
end
function integrand_denominator(end_to_end_length)
return model.isometric.force(end_to_end_length, temperature)^2
end
numerator = integrate(
integrand_numerator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_strong_potential_isometric::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_end_to_end_length_per_link)
return (
model.isometric.nondimensional_force(
nondimensional_end_to_end_length_per_link,
) -
model.modified_canonical.asymptotic.strong_potential.nondimensional_force(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
)
)^2
end
function integrand_denominator(nondimensional_end_to_end_length_per_link)
return model.isometric.nondimensional_force(
nondimensional_end_to_end_length_per_link,
)^2
end
numerator = integrate(
integrand_numerator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_strong_potential_isometric::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(end_to_end_length)
return (
model.isometric.helmholtz_free_energy(end_to_end_length, temperature) -
model.isometric.helmholtz_free_energy(
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
temperature,
) -
model.modified_canonical.asymptotic.strong_potential.helmholtz_free_energy(
end_to_end_length,
potential_stiffness,
temperature,
) +
model.modified_canonical.asymptotic.strong_potential.helmholtz_free_energy(
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
potential_stiffness,
temperature,
)
)^2
end
function integrand_denominator(end_to_end_length)
return (
model.isometric.helmholtz_free_energy(end_to_end_length, temperature) -
model.isometric.helmholtz_free_energy(
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_strong_potential_isometric::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(end_to_end_length)
return (
model.isometric.helmholtz_free_energy_per_link(
end_to_end_length,
temperature,
) - model.isometric.helmholtz_free_energy_per_link(
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
temperature,
) -
model.modified_canonical.asymptotic.strong_potential.helmholtz_free_energy_per_link(
end_to_end_length,
potential_stiffness,
temperature,
) +
model.modified_canonical.asymptotic.strong_potential.helmholtz_free_energy_per_link(
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
potential_stiffness,
temperature,
)
)^2
end
function integrand_denominator(end_to_end_length)
return (
model.isometric.helmholtz_free_energy_per_link(
end_to_end_length,
temperature,
) - model.isometric.helmholtz_free_energy_per_link(
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_strong_potential_isometric::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(end_to_end_length)
return (
model.isometric.relative_helmholtz_free_energy(
end_to_end_length,
temperature,
) -
model.modified_canonical.asymptotic.strong_potential.relative_helmholtz_free_energy(
end_to_end_length,
potential_stiffness,
temperature,
)
)^2
end
function integrand_denominator(end_to_end_length)
return model.isometric.relative_helmholtz_free_energy(
end_to_end_length,
temperature,
)^2
end
numerator = integrate(
integrand_numerator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_strong_potential_isometric::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(end_to_end_length)
return (
model.isometric.relative_helmholtz_free_energy_per_link(
end_to_end_length,
temperature,
) -
model.modified_canonical.asymptotic.strong_potential.relative_helmholtz_free_energy_per_link(
end_to_end_length,
potential_stiffness,
temperature,
)
)^2
end
function integrand_denominator(end_to_end_length)
return model.isometric.relative_helmholtz_free_energy_per_link(
end_to_end_length,
temperature,
)^2
end
numerator = integrate(
integrand_numerator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_strong_potential_isometric::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_end_to_end_length_per_link)
return (
model.isometric.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
) - model.isometric.nondimensional_helmholtz_free_energy(
parameters.nondimensional_potential_distance_small,
temperature,
) -
model.modified_canonical.asymptotic.strong_potential.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
temperature,
) +
model.modified_canonical.asymptotic.strong_potential.nondimensional_helmholtz_free_energy(
parameters.nondimensional_potential_distance_small,
nondimensional_potential_stiffness,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_end_to_end_length_per_link)
return (
model.isometric.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
) - model.isometric.nondimensional_helmholtz_free_energy(
parameters.nondimensional_potential_distance_small,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_strong_potential_isometric::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_end_to_end_length_per_link)
return (
model.isometric.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
) - model.isometric.nondimensional_helmholtz_free_energy_per_link(
parameters.nondimensional_potential_distance_small,
temperature,
) -
model.modified_canonical.asymptotic.strong_potential.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
temperature,
) +
model.modified_canonical.asymptotic.strong_potential.nondimensional_helmholtz_free_energy_per_link(
parameters.nondimensional_potential_distance_small,
nondimensional_potential_stiffness,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_end_to_end_length_per_link)
return (
model.isometric.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
) - model.isometric.nondimensional_helmholtz_free_energy_per_link(
parameters.nondimensional_potential_distance_small,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_strong_potential_isometric::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_end_to_end_length_per_link)
return (
model.isometric.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
) -
model.modified_canonical.asymptotic.strong_potential.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
)
)^2
end
function integrand_denominator(nondimensional_end_to_end_length_per_link)
return model.isometric.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
)^2
end
numerator = integrate(
integrand_numerator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_strong_potential_isometric::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_end_to_end_length_per_link)
return (
model.isometric.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
) -
model.modified_canonical.asymptotic.strong_potential.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
)
)^2
end
function integrand_denominator(nondimensional_end_to_end_length_per_link)
return model.isometric.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
)^2
end
numerator = integrate(
integrand_numerator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_weak_potential_isotensional::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
force = model.modified_canonical.asymptotic.weak_potential.force(
potential_distance,
potential_stiffness,
)
return (
model.modified_canonical.asymptotic.weak_potential.end_to_end_length(
potential_distance,
potential_stiffness,
temperature,
) - model.isotensional.end_to_end_length(force, temperature)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return model.modified_canonical.asymptotic.weak_potential.end_to_end_length(
potential_distance,
potential_stiffness,
temperature,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_weak_potential_isotensional::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
force = model.modified_canonical.asymptotic.weak_potential.force(
potential_distance,
potential_stiffness,
)
return (
model.modified_canonical.asymptotic.weak_potential.end_to_end_length_per_link(
potential_distance,
potential_stiffness,
temperature,
) - model.isotensional.end_to_end_length_per_link(force, temperature)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return model.modified_canonical.asymptotic.weak_potential.end_to_end_length_per_link(
potential_distance,
potential_stiffness,
temperature,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_weak_potential_isotensional::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_potential_distance)
nondimensional_force =
model.modified_canonical.asymptotic.weak_potential.nondimensional_force(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
return (
model.modified_canonical.asymptotic.weak_potential.nondimensional_end_to_end_length(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
) - model.isotensional.nondimensional_end_to_end_length(
nondimensional_force,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
return model.modified_canonical.asymptotic.weak_potential.nondimensional_end_to_end_length(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_weak_potential_isotensional::nondimensional_end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_potential_distance)
nondimensional_force =
model.modified_canonical.asymptotic.weak_potential.nondimensional_force(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
return (
model.modified_canonical.asymptotic.weak_potential.nondimensional_end_to_end_length_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
) - model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
return model.modified_canonical.asymptotic.weak_potential.nondimensional_end_to_end_length_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_weak_potential_isotensional::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance_ref =
parameters.nondimensional_potential_distance_large_1 *
number_of_links *
link_length
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
force_ref = model.modified_canonical.asymptotic.weak_potential.force(
potential_distance_ref,
potential_stiffness,
)
function integrand_numerator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
force = model.modified_canonical.asymptotic.weak_potential.force(
potential_distance,
potential_stiffness,
)
return (
model.modified_canonical.asymptotic.weak_potential.gibbs_free_energy(
potential_distance,
potential_stiffness,
temperature,
) -
model.modified_canonical.asymptotic.weak_potential.gibbs_free_energy(
potential_distance_ref,
potential_stiffness,
temperature,
) - model.isotensional.gibbs_free_energy(force, temperature) +
model.isotensional.gibbs_free_energy(force_ref, temperature)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return (
model.modified_canonical.asymptotic.weak_potential.gibbs_free_energy(
potential_distance,
potential_stiffness,
temperature,
) -
model.modified_canonical.asymptotic.weak_potential.gibbs_free_energy(
potential_distance_ref,
potential_stiffness,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_weak_potential_isotensional::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance_ref =
parameters.nondimensional_potential_distance_large_1 *
number_of_links *
link_length
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
force_ref = model.modified_canonical.asymptotic.weak_potential.force(
potential_distance_ref,
potential_stiffness,
)
function integrand_numerator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
force = model.modified_canonical.asymptotic.weak_potential.force(
potential_distance,
potential_stiffness,
)
return (
model.modified_canonical.asymptotic.weak_potential.gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
) -
model.modified_canonical.asymptotic.weak_potential.gibbs_free_energy_per_link(
potential_distance_ref,
potential_stiffness,
temperature,
) - model.isotensional.gibbs_free_energy_per_link(force, temperature) +
model.isotensional.gibbs_free_energy_per_link(force_ref, temperature)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return (
model.modified_canonical.asymptotic.weak_potential.gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
) -
model.modified_canonical.asymptotic.weak_potential.gibbs_free_energy_per_link(
potential_distance_ref,
potential_stiffness,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_weak_potential_isotensional::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
force = model.modified_canonical.asymptotic.weak_potential.force(
potential_distance,
potential_stiffness,
)
return (
model.modified_canonical.asymptotic.weak_potential.relative_gibbs_free_energy(
potential_distance,
potential_stiffness,
temperature,
) - model.isotensional.relative_gibbs_free_energy(force, temperature)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return model.modified_canonical.asymptotic.weak_potential.relative_gibbs_free_energy(
potential_distance,
potential_stiffness,
temperature,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_weak_potential_isotensional::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
force = model.modified_canonical.asymptotic.weak_potential.force(
potential_distance,
potential_stiffness,
)
return (
model.modified_canonical.asymptotic.weak_potential.relative_gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
) - model.isotensional.relative_gibbs_free_energy_per_link(
force,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return model.modified_canonical.asymptotic.weak_potential.relative_gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_weak_potential_isotensional::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_potential_distance_ref =
parameters.nondimensional_potential_distance_large_1
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
nondimensional_force_ref =
model.modified_canonical.asymptotic.weak_potential.nondimensional_force(
nondimensional_potential_distance_ref,
nondimensional_potential_stiffness,
)
function integrand_numerator(nondimensional_potential_distance)
nondimensional_force =
model.modified_canonical.asymptotic.weak_potential.nondimensional_force(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
return (
model.modified_canonical.asymptotic.weak_potential.nondimensional_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
) -
model.modified_canonical.asymptotic.weak_potential.nondimensional_gibbs_free_energy(
nondimensional_potential_distance_ref,
nondimensional_potential_stiffness,
temperature,
) - model.isotensional.nondimensional_gibbs_free_energy(
nondimensional_force,
temperature,
) + model.isotensional.nondimensional_gibbs_free_energy(
nondimensional_force_ref,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
return (
model.modified_canonical.asymptotic.weak_potential.nondimensional_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
) -
model.modified_canonical.asymptotic.weak_potential.nondimensional_gibbs_free_energy(
nondimensional_potential_distance_ref,
nondimensional_potential_stiffness,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_weak_potential_isotensional::nondimensional_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_potential_distance_ref =
parameters.nondimensional_potential_distance_large_1
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
nondimensional_force_ref =
model.modified_canonical.asymptotic.weak_potential.nondimensional_force(
nondimensional_potential_distance_ref,
nondimensional_potential_stiffness,
)
function integrand_numerator(nondimensional_potential_distance)
nondimensional_force =
model.modified_canonical.asymptotic.weak_potential.nondimensional_force(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
return (
model.modified_canonical.asymptotic.weak_potential.nondimensional_gibbs_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
) -
model.modified_canonical.asymptotic.weak_potential.nondimensional_gibbs_free_energy_per_link(
nondimensional_potential_distance_ref,
nondimensional_potential_stiffness,
temperature,
) - model.isotensional.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
) + model.isotensional.nondimensional_gibbs_free_energy_per_link(
nondimensional_force_ref,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
return (
model.modified_canonical.asymptotic.weak_potential.nondimensional_gibbs_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
) -
model.modified_canonical.asymptotic.weak_potential.nondimensional_gibbs_free_energy_per_link(
nondimensional_potential_distance_ref,
nondimensional_potential_stiffness,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_weak_potential_isotensional::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_potential_distance)
nondimensional_force =
model.modified_canonical.asymptotic.weak_potential.nondimensional_force(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
return (
model.modified_canonical.asymptotic.weak_potential.nondimensional_relative_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
) - model.isotensional.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
return model.modified_canonical.asymptotic.weak_potential.nondimensional_relative_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_weak_potential_isotensional::nondimensional_relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_potential_distance)
nondimensional_force =
model.modified_canonical.asymptotic.weak_potential.nondimensional_force(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
return (
model.modified_canonical.asymptotic.weak_potential.nondimensional_relative_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
) - model.isotensional.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
return model.modified_canonical.asymptotic.weak_potential.nondimensional_relative_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 27065 | """
The freely-jointed chain (FJC) model thermodynamics in the isometric ensemble.
"""
module Isometric
using DocStringExtensions
using ......Polymers: PROJECT_ROOT
include("legendre/mod.jl")
"""
The structure of the thermodynamics of the FJC model in the isometric ensemble.
$(FIELDS)
"""
struct FJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The thermodynamic functions of the model in the isometric ensemble approximated using a Legendre transformation.
"""
legendre::Any
"""
The expected force ``f`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
force::Function
"""
The expected nondimensional force ``\\eta`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``.
"""
nondimensional_force::Function
"""
The Helmholtz free energy ``\\psi`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
helmholtz_free_energy::Function
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
helmholtz_free_energy_per_link::Function
"""
The relative Helmholtz free energy ``\\Delta\\psi\\equiv\\psi(\\xi,T)-\\psi(0,T)`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
relative_helmholtz_free_energy::Function
"""
The relative Helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
relative_helmholtz_free_energy_per_link::Function
"""
The nondimensional Helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy::Function
"""
The nondimensional Helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy_per_link::Function
"""
The nondimensional relative Helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``.
"""
nondimensional_relative_helmholtz_free_energy::Function
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``.
"""
nondimensional_relative_helmholtz_free_energy_per_link::Function
"""
The equilibrium probability density of end-to-end vectors ``P_\\mathrm{eq}`` as a function of the end-to-end length ``\\xi``.
"""
equilibrium_distribution::Function
"""
The nondimensional equilibrium probability density of end-to-end vectors ``\\mathscr{P}_\\mathrm{eq}`` as a function of the nondimensional end-to-end length per link ``\\gamma``.
"""
nondimensional_equilibrium_distribution::Function
"""
The equilibrium probability density of end-to-end lengths ``g_\\mathrm{eq}`` as a function of the end-to-end length ``\\xi``.
"""
equilibrium_radial_distribution::Function
"""
The nondimensional equilibrium probability density of end-to-end lengths ``\\mathscr{g}_\\mathrm{eq}`` as a function of the nondimensional end-to-end length per link ``\\gamma``.
"""
nondimensional_equilibrium_radial_distribution::Function
end
"""
The expected force ``f`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``,
```math
f(\\xi, T) = \\frac{\\partial \\psi}{\\partial\\xi} = \\frac{kT}{\\xi} + \\frac{kT}{\\ell_b}\\left(\\frac{1}{2} - \\frac{1}{N_b}\\right)\\frac{\\sum_{s=0}^{s_\\mathrm{max}}(-1)^s\\binom{N_b}{s}\\left(m - \\frac{s}{N_b}\\right)^{N_b - 3}}{\\sum_{s=0}^{s_\\mathrm{max}}(-1)^s\\binom{N_b}{s}\\left(m - \\frac{s}{N_b}\\right)^{N_b - 2}},
```
where ``m\\equiv(1 - \\xi/N_b\\ell_b)/2`` and ``s_\\mathrm{max}/N_b\\leq m\\leq (s_\\mathrm{max}+1)/N_b``.
$(TYPEDSIGNATURES)
"""
function force(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, end_to_end_length_i, temperature_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_force,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
end_to_end_length,
temperature,
)
end
"""
The expected nondimensional force ``\\eta`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``,
parameterized by the number of links ``N_b``,
```math
\\eta(\\gamma) = \\frac{\\partial\\vartheta}{\\partial\\gamma} = \\frac{1}{N_b\\gamma} + \\left(\\frac{1}{2} - \\frac{1}{N_b}\\right)\\frac{\\sum_{s=0}^{s_\\mathrm{max}}(-1)^s\\binom{N_b}{s}\\left(m - \\frac{s}{N_b}\\right)^{N_b - 3}}{\\sum_{s=0}^{s_\\mathrm{max}}(-1)^s\\binom{N_b}{s}\\left(m - \\frac{s}{N_b}\\right)^{N_b - 2}},
```
where ``m\\equiv(1 - \\gamma)/2`` and ``s_\\mathrm{max}/N_b\\leq m\\leq (s_\\mathrm{max}+1)/N_b``.
$(TYPEDSIGNATURES)
"""
function nondimensional_force(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_end_to_end_length_per_link_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_nondimensional_force,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64),
number_of_links_i,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
nondimensional_end_to_end_length_per_link,
)
end
"""
The Helmholtz free energy ``\\psi`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``,
```math
\\psi(\\xi, T) = -kT\\ln Q(\\xi, T).
```
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
end_to_end_length,
temperature,
)
end
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
end_to_end_length,
temperature,
)
end
"""
The relative Helmholtz free energy ``\\Delta\\psi\\equiv\\psi(\\xi,T)-\\psi(0,T)`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``,
```math
\\Delta\\psi(\\xi, T) = kT\\ln\\left[\\frac{P_\\mathrm{eq}(0)}{P_\\mathrm{eq}(\\xi)}\\right].
```
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, end_to_end_length_i, temperature_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
end_to_end_length,
temperature,
)
end
"""
The relative Helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, end_to_end_length_i, temperature_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
end_to_end_length,
temperature,
)
end
"""
The nondimensional Helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_nondimensional_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_end_to_end_length_per_link,
temperature,
)
end
"""
The nondimensional Helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_nondimensional_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_end_to_end_length_per_link,
temperature,
)
end
"""
The nondimensional relative Helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``,
parameterized by the number of links ``N_b``,
```math
\\beta\\Delta\\psi(\\gamma) = \\ln\\left[\\frac{\\mathscr{P}_\\mathrm{eq}(0)}{\\mathscr{P}_\\mathrm{eq}(\\gamma)}\\right].
```
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_end_to_end_length_per_link_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_nondimensional_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64),
number_of_links_i,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
nondimensional_end_to_end_length_per_link,
)
end
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``,
parameterized by the number of links ``N_b``,
```math
\\Delta\\vartheta(\\gamma) = \\ln\\left[\\frac{\\mathscr{P}_\\mathrm{eq}(0)}{\\mathscr{P}_\\mathrm{eq}(\\gamma)}\\right]^{1/N_b}.
```
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_end_to_end_length_per_link_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_nondimensional_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64),
number_of_links_i,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
nondimensional_end_to_end_length_per_link,
)
end
"""
The equilibrium probability density of end-to-end vectors ``P_\\mathrm{eq}`` as a function of the end-to-end length ``\\xi``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``,
```math
P_\\mathrm{eq}(\\xi) = \\frac{e^{-\\beta\\psi(\\xi, T)}}{4\\pi\\int e^{-\\beta\\psi(\\xi', T)} \\,{\\xi'}{}^2 d\\xi'} = \\frac{1}{8\\pi\\ell_b^2\\xi}\\frac{N_b^{N_b - 2}}{(N_b - 2)!}\\sum_{s=0}^{s_\\mathrm{max}}(-1)^s\\binom{N_b}{s}\\left(m - \\frac{s}{N_b}\\right)^{N_b - 2},
```
where ``m\\equiv(1 - \\xi/N_b\\ell_b)/2`` and ``s_\\mathrm{max}/N_b\\leq m\\leq (s_\\mathrm{max}+1)/N_b``.
$(TYPEDSIGNATURES)
"""
function equilibrium_distribution(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, end_to_end_length_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_equilibrium_distribution,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
link_length_i,
end_to_end_length_i,
),
number_of_links,
link_length,
end_to_end_length,
)
end
"""
The nondimensional equilibrium probability density of nondimensional end-to-end vectors per link ``\\mathscr{P}_\\mathrm{eq}`` as a function of the nondimensional end-to-end length per link ``\\gamma``,
parameterized by the number of links ``N_b``,
```math
\\mathscr{P}_\\mathrm{eq}(\\gamma) = \\frac{e^{-\\Delta\\vartheta(\\gamma)}}{4\\pi\\int e^{-\\Delta\\vartheta(\\gamma')} \\,{\\gamma'}{}^2 d\\gamma'} = \\frac{1}{8\\pi\\gamma}\\frac{N_b^{N_b}}{(N_b - 2)!}\\sum_{s=0}^{s_\\mathrm{max}}(-1)^s\\binom{N_b}{s}\\left(m - \\frac{s}{N_b}\\right)^{N_b - 2},
```
where ``m\\equiv(1 - \\gamma)/2`` and ``s_\\mathrm{max}/N_b\\leq m\\leq (s_\\mathrm{max}+1)/N_b``.
$(TYPEDSIGNATURES)
"""
function nondimensional_equilibrium_distribution(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_end_to_end_length_per_link_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_nondimensional_equilibrium_distribution,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64),
number_of_links_i,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
nondimensional_end_to_end_length_per_link,
)
end
"""
The equilibrium probability density of end-to-end lengths ``g_\\mathrm{eq}`` as a function of the end-to-end length ``\\xi``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``,
given by [Treloar](https://global.oup.com/academic/product/the-physics-of-rubber-elasticity-9780198570271) as
```math
g_\\mathrm{eq}(\\xi) = 4\\pi\\xi^2 P_\\mathrm{eq}(\\xi) = \\frac{\\xi}{2\\ell_b^2}\\frac{N_b^{N_b-2}}{(N_b - 2)!}\\sum_{s=0}^{s_\\mathrm{max}}(-1)^s\\binom{N_b}{s}\\left(m - \\frac{s}{N_b}\\right)^{N_b - 2},
```
where ``m\\equiv(1 - \\xi/N_b\\ell_b)/2`` and ``s_\\mathrm{max}/N_b\\leq m\\leq (s_\\mathrm{max}+1)/N_b``.
$(TYPEDSIGNATURES)
"""
function equilibrium_radial_distribution(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, end_to_end_length_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_equilibrium_radial_distribution,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
link_length_i,
end_to_end_length_i,
),
number_of_links,
link_length,
end_to_end_length,
)
end
"""
The nondimensional equilibrium probability density of nondimensional end-to-end lenghts per link ``\\mathscr{g}_\\mathrm{eq}`` as a function of the nondimensional end-to-end length per link ``\\gamma``,
parameterized by the number of links ``N_b``,
```math
\\mathscr{g}_\\mathrm{eq}(\\gamma) = 4\\pi\\gamma^2 \\mathscr{P}_\\mathrm{eq}(\\gamma) = \\frac{\\gamma}{2}\\frac{N_b^{N_b}}{(N_b - 2)!}\\sum_{s=0}^{s_\\mathrm{max}}(-1)^s\\binom{N_b}{s}\\left(m - \\frac{s}{N_b}\\right)^{N_b - 2},
```
where ``m\\equiv(1 - \\gamma)/2`` and ``s_\\mathrm{max}/N_b\\leq m\\leq (s_\\mathrm{max}+1)/N_b``.
$(TYPEDSIGNATURES)
"""
function nondimensional_equilibrium_radial_distribution(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_end_to_end_length_per_link_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_nondimensional_equilibrium_radial_distribution,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64),
number_of_links_i,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
nondimensional_end_to_end_length_per_link,
)
end
"""
Initializes and returns an instance of the thermodynamics of the FJC model in the isometric ensemble.
$(TYPEDSIGNATURES)
"""
function FJC(number_of_links::UInt8, link_length::Float64, hinge_mass::Float64)
return FJC(
number_of_links,
link_length,
hinge_mass,
Legendre.FJC(number_of_links, link_length, hinge_mass),
(end_to_end_length, temperature) ->
force(number_of_links, link_length, end_to_end_length, temperature),
(nondimensional_end_to_end_length_per_link) -> nondimensional_force(
number_of_links,
nondimensional_end_to_end_length_per_link,
),
(end_to_end_length, temperature) -> helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> helmholtz_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> relative_helmholtz_free_energy(
number_of_links,
link_length,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> relative_helmholtz_free_energy_per_link(
number_of_links,
link_length,
end_to_end_length,
temperature,
),
(nondimensional_end_to_end_length_per_link, temperature) ->
nondimensional_helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
nondimensional_end_to_end_length_per_link,
temperature,
),
(nondimensional_end_to_end_length_per_link, temperature) ->
nondimensional_helmholtz_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
nondimensional_end_to_end_length_per_link,
temperature,
),
(nondimensional_end_to_end_length_per_link) ->
nondimensional_relative_helmholtz_free_energy(
number_of_links,
nondimensional_end_to_end_length_per_link,
),
(nondimensional_end_to_end_length_per_link) ->
nondimensional_relative_helmholtz_free_energy_per_link(
number_of_links,
nondimensional_end_to_end_length_per_link,
),
(end_to_end_length) ->
equilibrium_distribution(number_of_links, link_length, end_to_end_length),
(nondimensional_end_to_end_length_per_link) ->
nondimensional_equilibrium_distribution(
number_of_links,
nondimensional_end_to_end_length_per_link,
),
(end_to_end_length) -> equilibrium_radial_distribution(
number_of_links,
link_length,
end_to_end_length,
),
(nondimensional_end_to_end_length_per_link) ->
nondimensional_equilibrium_radial_distribution(
number_of_links,
nondimensional_end_to_end_length_per_link,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 83905 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ONE, ZERO, POINTS, integrate, parameters
using Polymers.Physics.SingleChain.Fjc.Thermodynamics.Isometric: FJC
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::base::init" begin
@test isa(
FJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
),
Any,
)
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test FJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test FJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test FJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test all(
FJC(number_of_links, link_length, hinge_mass).number_of_links ==
number_of_links &&
FJC(number_of_links, link_length, hinge_mass).link_length == link_length &&
FJC(number_of_links, link_length, hinge_mass).hinge_mass == hinge_mass,
)
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::normalization::equilibrium_distribution" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
normalization = integrate(
end_to_end_length ->
4.0 *
pi *
end_to_end_length^2 *
model.equilibrium_distribution(end_to_end_length),
ZERO,
ONE * number_of_links * link_length,
POINTS,
)
@test abs(normalization - 1.0) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::normalization::equilibrium_radial_distribution" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
normalization = integrate(
end_to_end_length ->
model.equilibrium_radial_distribution(end_to_end_length),
ZERO,
ONE * number_of_links * link_length,
POINTS,
)
@test abs(normalization - 1.0) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::normalization::nondimensional_equilibrium_distribution" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
normalization = integrate(
nondimensional_end_to_end_length_per_link ->
4.0 *
pi *
nondimensional_end_to_end_length_per_link^2 *
model.nondimensional_equilibrium_distribution(
nondimensional_end_to_end_length_per_link,
),
ZERO,
ONE,
POINTS,
)
@test abs(normalization - 1.0) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::normalization::nondimensional_equilibrium_radial_distribution" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
normalization = integrate(
nondimensional_end_to_end_length_per_link ->
model.nondimensional_equilibrium_radial_distribution(
nondimensional_end_to_end_length_per_link,
),
ZERO,
ONE,
POINTS,
)
@test abs(normalization - 1.0) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::nondimensional::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
model.nondimensional_force(nondimensional_end_to_end_length_per_link)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
force = model.force(end_to_end_length, temperature)
residual_abs =
force / BOLTZMANN_CONSTANT / temperature * link_length - nondimensional_force
residual_rel = residual_abs / nondimensional_force
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::nondimensional::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy = model.helmholtz_free_energy(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::nondimensional::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::nondimensional::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(end_to_end_length, temperature)
residual_abs =
relative_helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::nondimensional::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
relative_helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::per_link::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy = model.helmholtz_free_energy(end_to_end_length, temperature)
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy / number_of_links - helmholtz_free_energy_per_link
residual_rel = residual_abs / helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::per_link::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(end_to_end_length, temperature)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
relative_helmholtz_free_energy / number_of_links -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::per_link::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy / number_of_links -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::per_link::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy / number_of_links -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::relative::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy = model.helmholtz_free_energy(end_to_end_length, temperature)
helmholtz_free_energy_0 =
model.helmholtz_free_energy(ZERO * number_of_links * link_length, temperature)
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy - helmholtz_free_energy_0 - relative_helmholtz_free_energy
residual_rel = residual_abs / relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::relative::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(end_to_end_length, temperature)
helmholtz_free_energy_per_link_0 = model.helmholtz_free_energy_per_link(
ZERO * number_of_links * link_length,
temperature,
)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy_per_link - helmholtz_free_energy_per_link_0 -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::relative::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_0 =
model.nondimensional_helmholtz_free_energy(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
)
residual_abs =
nondimensional_helmholtz_free_energy - nondimensional_helmholtz_free_energy_0 -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::relative::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_per_link_0 =
model.nondimensional_helmholtz_free_energy_per_link(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
)
residual_abs =
nondimensional_helmholtz_free_energy_per_link -
nondimensional_helmholtz_free_energy_per_link_0 -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::zero::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_0 = model.relative_helmholtz_free_energy(
ZERO * number_of_links * link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_0) <=
ZERO * number_of_links * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::zero::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_per_link_0 =
model.relative_helmholtz_free_energy_per_link(
ZERO * number_of_links * link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::zero::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_relative_helmholtz_free_energy_0 =
model.nondimensional_relative_helmholtz_free_energy(ZERO)
@test abs(nondimensional_relative_helmholtz_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::zero::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_relative_helmholtz_free_energy_per_link_0 =
model.nondimensional_relative_helmholtz_free_energy_per_link(ZERO)
@test abs(nondimensional_relative_helmholtz_free_energy_per_link_0) <= ZERO
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::zero::equilibrium_radial_distribution" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
equilibrium_radial_distribution_0 =
model.equilibrium_radial_distribution(ZERO * number_of_links * link_length)
@test abs(equilibrium_radial_distribution_0) <= ZERO
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::zero::nondimensional_equilibrium_radial_distribution" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_equilibrium_radial_distribution_0 =
model.equilibrium_radial_distribution(ZERO)
@test abs(nondimensional_equilibrium_radial_distribution_0) <= ZERO
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::connection::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
force = model.force(end_to_end_length, temperature)
h = parameters.rel_tol * number_of_links * link_length
force_from_derivative =
(
model.relative_helmholtz_free_energy(
end_to_end_length + 0.5 * h,
temperature,
) - model.relative_helmholtz_free_energy(
end_to_end_length - 0.5 * h,
temperature,
)
) / h
residual_abs = force - force_from_derivative
residual_rel = residual_abs / force
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::connection::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
model.nondimensional_force(nondimensional_end_to_end_length_per_link)
h = parameters.rel_tol
nondimensional_force_from_derivative =
(
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link + 0.5 * h,
) - model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link - 0.5 * h,
)
) / h
residual_abs = nondimensional_force - nondimensional_force_from_derivative
residual_rel = residual_abs / nondimensional_force
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::connection::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(end_to_end_length, temperature)
relative_helmholtz_free_energy_from_connection =
BOLTZMANN_CONSTANT *
temperature *
log((
model.equilibrium_distribution(ZERO * number_of_links * link_length) /
model.equilibrium_distribution(end_to_end_length)
))
residual_abs =
relative_helmholtz_free_energy - relative_helmholtz_free_energy_from_connection
residual_rel = residual_abs / relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::connection::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
)
nondimensional_relative_helmholtz_free_energy_from_connection = log((
model.nondimensional_equilibrium_distribution(ZERO) /
model.nondimensional_equilibrium_distribution(
nondimensional_end_to_end_length_per_link,
)
))
residual_abs =
nondimensional_relative_helmholtz_free_energy -
nondimensional_relative_helmholtz_free_energy_from_connection
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::legendre::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
force = model.force(end_to_end_length, temperature)
helmholtz_free_energy = model.helmholtz_free_energy(end_to_end_length, temperature)
helmholtz_free_energy_legendre =
model.legendre.gibbs_free_energy(end_to_end_length, temperature) +
force * end_to_end_length
residual_abs = helmholtz_free_energy - helmholtz_free_energy_legendre
residual_rel = residual_abs / helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::legendre::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
end_to_end_length_per_link = nondimensional_end_to_end_length_per_link * link_length
force = model.force(end_to_end_length, temperature)
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(end_to_end_length, temperature)
helmholtz_free_energy_per_link_legendre =
model.legendre.gibbs_free_energy_per_link(end_to_end_length, temperature) +
force * end_to_end_length_per_link
residual_abs =
helmholtz_free_energy_per_link - helmholtz_free_energy_per_link_legendre
residual_rel = residual_abs / helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::legendre::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
force = model.force(end_to_end_length, temperature)
force_0 = model.force(ZERO * number_of_links * link_length, temperature)
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(end_to_end_length, temperature)
relative_helmholtz_free_energy_legendre =
model.legendre.relative_gibbs_free_energy(end_to_end_length, temperature) +
force * end_to_end_length - force_0 * ZERO * number_of_links * link_length
residual_abs =
relative_helmholtz_free_energy - relative_helmholtz_free_energy_legendre
residual_rel = residual_abs / relative_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::legendre::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
end_to_end_length_per_link = nondimensional_end_to_end_length_per_link * link_length
force = model.force(end_to_end_length, temperature)
force_0 = model.force(ZERO * number_of_links * link_length, temperature)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(end_to_end_length, temperature)
relative_helmholtz_free_energy_per_link_legendre =
model.legendre.relative_gibbs_free_energy_per_link(
end_to_end_length,
temperature,
) + force * end_to_end_length_per_link - force_0 * ZERO * link_length
residual_abs =
relative_helmholtz_free_energy_per_link -
relative_helmholtz_free_energy_per_link_legendre
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::legendre::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links
nondimensional_force =
model.nondimensional_force(nondimensional_end_to_end_length_per_link)
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_legendre =
model.legendre.nondimensional_gibbs_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
) + nondimensional_force * nondimensional_end_to_end_length
residual_abs =
nondimensional_helmholtz_free_energy -
nondimensional_helmholtz_free_energy_legendre
residual_rel = residual_abs / nondimensional_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::legendre::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
model.nondimensional_force(nondimensional_end_to_end_length_per_link)
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_per_link_legendre =
model.legendre.nondimensional_gibbs_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
) + nondimensional_force * nondimensional_end_to_end_length_per_link
residual_abs =
nondimensional_helmholtz_free_energy_per_link -
nondimensional_helmholtz_free_energy_per_link_legendre
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::legendre::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
nondimensional_end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links
nondimensional_force =
model.nondimensional_force(nondimensional_end_to_end_length_per_link)
nondimensional_force_0 = model.nondimensional_force(ZERO)
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
)
nondimensional_relative_helmholtz_free_energy_legendre =
model.legendre.nondimensional_relative_gibbs_free_energy(
nondimensional_end_to_end_length_per_link,
) + nondimensional_force * nondimensional_end_to_end_length -
nondimensional_force_0 * ZERO * number_of_links
residual_abs =
nondimensional_relative_helmholtz_free_energy -
nondimensional_relative_helmholtz_free_energy_legendre
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::legendre::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
nondimensional_force =
model.nondimensional_force(nondimensional_end_to_end_length_per_link)
nondimensional_force_0 = model.nondimensional_force(ZERO)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
)
nondimensional_relative_helmholtz_free_energy_per_link_legendre =
model.legendre.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
) + nondimensional_force * nondimensional_end_to_end_length_per_link -
nondimensional_force_0 * ZERO
residual_abs =
nondimensional_relative_helmholtz_free_energy_per_link -
nondimensional_relative_helmholtz_free_energy_per_link_legendre
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::legendre_connection::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
h = parameters.rel_tol * number_of_links * link_length
end_to_end_length_from_derivative =
-(
model.legendre.relative_gibbs_free_energy(
end_to_end_length + 0.5 * h,
temperature,
) - model.legendre.relative_gibbs_free_energy(
end_to_end_length - 0.5 * h,
temperature,
)
) / (
model.force(end_to_end_length + 0.5 * h, temperature) -
model.force(end_to_end_length - 0.5 * h, temperature)
)
residual_abs = end_to_end_length - end_to_end_length_from_derivative
residual_rel = residual_abs / end_to_end_length
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::legendre_connection::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
end_to_end_length_per_link = nondimensional_end_to_end_length_per_link * link_length
h = parameters.rel_tol * number_of_links * link_length
end_to_end_length_per_link_from_derivative =
-(
model.legendre.relative_gibbs_free_energy_per_link(
end_to_end_length + 0.5 * h,
temperature,
) - model.legendre.relative_gibbs_free_energy_per_link(
end_to_end_length - 0.5 * h,
temperature,
)
) / (
model.force(end_to_end_length + 0.5 * h, temperature) -
model.force(end_to_end_length - 0.5 * h, temperature)
)
residual_abs =
end_to_end_length_per_link - end_to_end_length_per_link_from_derivative
residual_rel = residual_abs / end_to_end_length_per_link
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::legendre_connection::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
nondimensional_end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links
h = parameters.rel_tol
nondimensional_end_to_end_length_from_derivative =
-(
model.legendre.nondimensional_relative_gibbs_free_energy(
nondimensional_end_to_end_length_per_link + 0.5 * h,
) - model.legendre.nondimensional_relative_gibbs_free_energy(
nondimensional_end_to_end_length_per_link - 0.5 * h,
)
) / (
model.nondimensional_force(
nondimensional_end_to_end_length_per_link + 0.5 * h,
) - model.nondimensional_force(
nondimensional_end_to_end_length_per_link - 0.5 * h,
)
)
residual_abs =
nondimensional_end_to_end_length -
nondimensional_end_to_end_length_from_derivative
residual_rel = residual_abs / nondimensional_end_to_end_length
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::legendre_connection::nondimensional_end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
h = parameters.rel_tol
nondimensional_end_to_end_length_per_link_from_derivative =
-(
model.legendre.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_end_to_end_length_per_link + 0.5 * h,
) - model.legendre.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_end_to_end_length_per_link - 0.5 * h,
)
) / (
model.nondimensional_force(
nondimensional_end_to_end_length_per_link + 0.5 * h,
) - model.nondimensional_force(
nondimensional_end_to_end_length_per_link - 0.5 * h,
)
)
residual_abs =
nondimensional_end_to_end_length_per_link -
nondimensional_end_to_end_length_per_link_from_derivative
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::thermodynamic_limit::force" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
force = model.force(end_to_end_length, temperature)
force_legendre = model.legendre.force(end_to_end_length, temperature)
residual_abs = force - force_legendre
residual_rel = residual_abs / force
@test abs(residual_rel) <= 1.0 / sqrt(number_of_links)
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::thermodynamic_limit::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
nondimensional_force =
model.nondimensional_force(nondimensional_end_to_end_length_per_link)
nondimensional_force_legendre =
model.legendre.nondimensional_force(nondimensional_end_to_end_length_per_link)
residual_abs = nondimensional_force - nondimensional_force_legendre
residual_rel = residual_abs / nondimensional_force
@test abs(residual_rel) <= 1.0 / sqrt(number_of_links)
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::thermodynamic_limit::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy = model.helmholtz_free_energy(end_to_end_length, temperature)
helmholtz_free_energy_legendre =
model.legendre.helmholtz_free_energy(end_to_end_length, temperature)
residual_abs = helmholtz_free_energy - helmholtz_free_energy_legendre
residual_rel = residual_abs / helmholtz_free_energy
@test abs(residual_rel) <= 1.0 / sqrt(number_of_links)
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::thermodynamic_limit::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(end_to_end_length, temperature)
force_legendre =
model.legendre.helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs = helmholtz_free_energy_per_link - force_legendre
residual_rel = residual_abs / helmholtz_free_energy_per_link
@test abs(residual_rel) <= 1.0 / sqrt(number_of_links)
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::thermodynamic_limit::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(end_to_end_length, temperature)
relative_helmholtz_free_energy_legendre =
model.legendre.relative_helmholtz_free_energy(end_to_end_length, temperature)
residual_abs =
relative_helmholtz_free_energy - relative_helmholtz_free_energy_legendre
residual_rel = residual_abs / relative_helmholtz_free_energy
@test abs(residual_rel) <= 1.0 / sqrt(number_of_links)
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::thermodynamic_limit::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(end_to_end_length, temperature)
force_legendre = model.legendre.relative_helmholtz_free_energy_per_link(
end_to_end_length,
temperature,
)
residual_abs = relative_helmholtz_free_energy_per_link - force_legendre
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_rel) <= 1.0 / sqrt(number_of_links)
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::thermodynamic_limit::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_legendre =
model.legendre.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy -
nondimensional_helmholtz_free_energy_legendre
residual_rel = residual_abs / nondimensional_helmholtz_free_energy
@test abs(residual_rel) <= 1.0 / sqrt(number_of_links)
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::thermodynamic_limit::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_per_link_legendre =
model.legendre.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy_per_link -
nondimensional_helmholtz_free_energy_per_link_legendre
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_rel) <= 1.0 / sqrt(number_of_links)
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::thermodynamic_limit::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
)
nondimensional_relative_helmholtz_free_energy_legendre =
model.legendre.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy -
nondimensional_relative_helmholtz_free_energy_legendre
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_rel) <= 1.0 / sqrt(number_of_links)
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::thermodynamic_limit::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
)
nondimensional_relative_helmholtz_free_energy_per_link_legendre =
model.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy_per_link -
nondimensional_relative_helmholtz_free_energy_per_link_legendre
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_rel) <= 1.0 / sqrt(number_of_links)
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::thermodynamic_limit::equilibrium_distribution" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
equilibrium_distribution = model.equilibrium_distribution(end_to_end_length)
equilibrium_distribution_legendre =
model.legendre.equilibrium_distribution(end_to_end_length)
residual_abs = equilibrium_distribution - equilibrium_distribution_legendre
residual_rel = residual_abs / equilibrium_distribution
@test abs(residual_abs) <= 1.0 / sqrt(number_of_links) ||
abs(residual_rel) <= 1.0 / sqrt(number_of_links)
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::thermodynamic_limit::nondimensional_equilibrium_distribution" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
nondimensional_equilibrium_distribution =
model.nondimensional_equilibrium_distribution(
nondimensional_end_to_end_length_per_link,
)
nondimensional_equilibrium_distribution_legendre =
model.legendre.nondimensional_equilibrium_distribution(
nondimensional_end_to_end_length_per_link,
)
residual_abs =
nondimensional_equilibrium_distribution -
nondimensional_equilibrium_distribution_legendre
residual_rel = residual_abs / nondimensional_equilibrium_distribution
@test abs(residual_abs) <= 1.0 / sqrt(number_of_links) ||
abs(residual_rel) <= 1.0 / sqrt(number_of_links)
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::thermodynamic_limit::equilibrium_radial_distribution" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
equilibrium_radial_distribution =
model.equilibrium_radial_distribution(end_to_end_length)
equilibrium_radial_distribution_legendre =
model.legendre.equilibrium_radial_distribution(end_to_end_length)
residual_abs =
equilibrium_radial_distribution - equilibrium_radial_distribution_legendre
residual_rel = residual_abs / equilibrium_radial_distribution
@test abs(residual_abs) <= 1.0 / sqrt(number_of_links) ||
abs(residual_rel) <= 1.0 / sqrt(number_of_links)
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::test::thermodynamic_limit::nondimensional_equilibrium_radial_distribution" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
nondimensional_equilibrium_radial_distribution =
model.nondimensional_equilibrium_radial_distribution(
nondimensional_end_to_end_length_per_link,
)
nondimensional_equilibrium_radial_distribution_legendre =
model.legendre.nondimensional_equilibrium_radial_distribution(
nondimensional_end_to_end_length_per_link,
)
residual_abs =
nondimensional_equilibrium_radial_distribution -
nondimensional_equilibrium_radial_distribution_legendre
residual_rel = residual_abs / nondimensional_equilibrium_radial_distribution
@test abs(residual_abs) <= 1.0 / sqrt(number_of_links) ||
abs(residual_rel) <= 1.0 / sqrt(number_of_links)
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 41341 | """
The freely-jointed chain (FJC) model thermodynamics in the isometric ensemble approximated using a Legendre transformation.
"""
module Legendre
using DocStringExtensions
using .......Polymers: PROJECT_ROOT
using .....SingleChain: ONE, ZERO, POINTS, integrate
"""
The structure of the thermodynamics of the FJC model in the isometric ensemble approximated using a Legendre transformation.
$(FIELDS)
"""
struct FJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
normalization_nondimensional_equilibrium_distribution::Float64
"""
The expected force ``f`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
force::Function
"""
The expected nondimensional force ``\\eta`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``.
"""
nondimensional_force::Function
"""
The Helmholtz free energy ``\\psi`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
helmholtz_free_energy::Function
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
helmholtz_free_energy_per_link::Function
"""
The relative Helmholtz free energy ``\\Delta\\psi\\equiv\\psi(\\xi,T)-\\psi(0,T)`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
relative_helmholtz_free_energy::Function
"""
The relative Helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
relative_helmholtz_free_energy_per_link::Function
"""
The nondimensional Helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy::Function
"""
The nondimensional Helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy_per_link::Function
"""
The nondimensional relative Helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``.
"""
nondimensional_relative_helmholtz_free_energy::Function
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``
"""
nondimensional_relative_helmholtz_free_energy_per_link::Function
"""
The equilibrium probability density of end-to-end vectors ``P_\\mathrm{eq}`` as a function of the end-to-end length ``\\xi``.
"""
equilibrium_distribution::Function
"""
The nondimensional equilibrium probability density of end-to-end vectors ``\\mathscr{P}_\\mathrm{eq}`` as a function of the nondimensional end-to-end length per link ``\\gamma``.
"""
nondimensional_equilibrium_distribution::Function
"""
The equilibrium probability density of end-to-end lengths ``g_\\mathrm{eq}`` as a function of the end-to-end length ``\\xi``.
"""
equilibrium_radial_distribution::Function
"""
The nondimensional equilibrium probability density of end-to-end lengths ``\\mathscr{g}_\\mathrm{eq}`` as a function of the nondimensional end-to-end length per link ``\\gamma``.
"""
nondimensional_equilibrium_radial_distribution::Function
"""
The Gibbs free energy ``\\varphi`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
gibbs_free_energy::Function
"""
The Gibbs free energy per link ``\\varphi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
gibbs_free_energy_per_link::Function
"""
The relative Gibbs free energy ``\\Delta\\varphi`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
relative_gibbs_free_energy::Function
"""
The relative Gibbs free energy per link ``\\Delta\\varphi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
relative_gibbs_free_energy_per_link::Function
"""
The nondimensional Gibbs free energy ``N_b\\varrho=\\beta\\varphi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``.
"""
nondimensional_gibbs_free_energy::Function
"""
The nondimensional Gibbs free energy per link ``\\varrho\\equiv\\beta\\varphi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``.
"""
nondimensional_gibbs_free_energy_per_link::Function
"""
The nondimensional relative Gibbs free energy ``N_b\\Delta\\varrho=\\beta\\Delta\\varphi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``.
"""
nondimensional_relative_gibbs_free_energy::Function
"""
The nondimensional relative Gibbs free energy per link ``\\Delta\\varrho\\equiv\\beta\\Delta\\varphi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``
"""
nondimensional_relative_gibbs_free_energy_per_link::Function
end
"""
The expected force as a function ``f`` of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``,
```math
f(\\xi, T) \\sim \\frac{kT}{\\ell_b}\\,\\mathcal{L}^{-1}\\left(\\frac{\\xi}{N_b\\ell_b}\\right) \\quad \\text{for } N_b\\gg 1,
```
where ``\\mathcal{L}(x)=\\coth(x)-1/x`` is the Langevin function.
$(TYPEDSIGNATURES)
"""
function force(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, end_to_end_length_i, temperature_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_legendre_force,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
end_to_end_length,
temperature,
)
end
"""
The expected nondimensional force as a function ``\\eta`` of the applied nondimensional end-to-end length per link ``\\gamma``,
```math
\\eta(\\gamma) \\sim \\mathcal{L}^{-1}(\\gamma) \\quad \\text{for } N_b\\gg 1,
```
where ``\\mathcal{L}(x)=\\coth(x)-1/x`` is the Langevin function.
$(TYPEDSIGNATURES)
"""
function nondimensional_force(
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
nondimensional_end_to_end_length_per_link_i -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_legendre_nondimensional_force,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64,),
nondimensional_end_to_end_length_per_link_i,
),
nondimensional_end_to_end_length_per_link,
)
end
"""
The Helmholtz free energy ``\\psi`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``,
```math
\\psi(\\xi, T) \\sim \\varphi\\left[f(\\xi, T)\\right] + \\xi f(\\xi, T) \\quad \\text{for } N_b\\gg 1,
```
where ``f(\\xi, T)`` is given by the Legendre transformation approximation above.
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_legendre_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
end_to_end_length,
temperature,
)
end
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_legendre_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
end_to_end_length,
temperature,
)
end
"""
The relative Helmholtz free energy ``\\Delta\\psi\\equiv\\psi(\\xi,T)-\\psi(0,T)`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, end_to_end_length_i, temperature_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_legendre_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
end_to_end_length,
temperature,
)
end
"""
The relative Helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, end_to_end_length_i, temperature_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_legendre_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
end_to_end_length,
temperature,
)
end
"""
The nondimensional Helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_legendre_nondimensional_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_end_to_end_length_per_link,
temperature,
)
end
"""
The nondimensional Helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``,
given by [Buche and Silberstein](https://doi.org/10.1103/PhysRevE.102.012501) as
```math
\\vartheta(\\gamma, T) \\sim \\varphi\\left[\\mathcal{L}^{-1}(\\gamma), T\\right] + \\gamma\\mathcal{L}^{-1}(\\gamma) \\quad \\text{for } N_b\\gg 1,
```
where ``\\mathcal{L}(x)=\\coth(x)-1/x`` is the Langevin function.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_legendre_nondimensional_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_end_to_end_length_per_link,
temperature,
)
end
"""
The nondimensional relative Helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the number of links ``N_b``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_end_to_end_length_per_link_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_legendre_nondimensional_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64),
number_of_links_i,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
nondimensional_end_to_end_length_per_link,
)
end
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
given by [Buche and Silberstein](https://doi.org/10.1016/j.jmps.2021.104593) as
```math
\\Delta\\vartheta(\\gamma) \\sim \\gamma\\mathcal{L}^{-1}(\\gamma) + \\ln\\left\\{\\frac{\\mathcal{L}^{-1}(\\gamma)}{\\sinh[\\mathcal{L}^{-1}(\\gamma)]}\\right\\} \\quad \\text{for } N_b\\gg 1,
```
where ``\\mathcal{L}(x)=\\coth(x)-1/x`` is the Langevin function.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
nondimensional_end_to_end_length_per_link_i -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_legendre_nondimensional_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64,),
nondimensional_end_to_end_length_per_link_i,
),
nondimensional_end_to_end_length_per_link,
)
end
"""
The equilibrium probability density of end-to-end vectors ``P_\\mathrm{eq}`` as a function of the end-to-end length ``\\xi``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``,
```math
P_\\mathrm{eq}(\\xi) = \\frac{e^{-\\beta\\psi(\\xi, T)}}{4\\pi\\int e^{-\\beta\\psi(\\xi', T)} \\,{\\xi'}{}^2 d\\xi'}.
```
$(TYPEDSIGNATURES)
"""
function equilibrium_distribution(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
normalization_nondimensional_equilibrium_distribution::Float64,
end_to_end_length::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, end_to_end_length_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_legendre_equilibrium_distribution,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
normalization_nondimensional_equilibrium_distribution,
end_to_end_length_i,
),
number_of_links,
link_length,
end_to_end_length,
)
end
"""
The nondimensional equilibrium probability density of nondimensional end-to-end vectors per link ``\\mathscr{P}_\\mathrm{eq}`` as a function of the nondimensional end-to-end length per link ``\\gamma``,
parameterized by the number of links ``N_b``,
```math
\\mathscr{P}_\\mathrm{eq}(\\gamma) = \\frac{e^{-\\Delta\\vartheta(\\gamma)}}{4\\pi\\int e^{-\\Delta\\vartheta(\\gamma')} \\,{\\gamma'}{}^2 d\\gamma'}.
```
$(TYPEDSIGNATURES)
"""
function nondimensional_equilibrium_distribution(
number_of_links::Union{UInt8,Vector,Matrix,Array},
normalization_nondimensional_equilibrium_distribution::Float64,
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_end_to_end_length_per_link_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_legendre_nondimensional_equilibrium_distribution,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
normalization_nondimensional_equilibrium_distribution,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
nondimensional_end_to_end_length_per_link,
)
end
"""
The equilibrium probability density of end-to-end lengths ``g_\\mathrm{eq}`` as a function of the end-to-end length ``\\xi``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``,
```math
g_\\mathrm{eq}(\\xi) = 4\\pi\\xi^2 P_\\mathrm{eq}(\\xi).
```
$(TYPEDSIGNATURES)
"""
function equilibrium_radial_distribution(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
normalization_nondimensional_equilibrium_distribution::Float64,
end_to_end_length::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, end_to_end_length_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_legendre_equilibrium_radial_distribution,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
normalization_nondimensional_equilibrium_distribution,
end_to_end_length_i,
),
number_of_links,
link_length,
end_to_end_length,
)
end
"""
The nondimensional equilibrium probability density of nondimensional end-to-end lenghts per link ``\\mathscr{g}_\\mathrm{eq}`` as a function of the nondimensional end-to-end length per link ``\\gamma``,
parameterized by the number of links ``N_b``,
```math
\\mathscr{g}_\\mathrm{eq}(\\gamma) = 4\\pi\\gamma^2 \\mathscr{P}_\\mathrm{eq}(\\gamma).
```
$(TYPEDSIGNATURES)
"""
function nondimensional_equilibrium_radial_distribution(
number_of_links::Union{UInt8,Vector,Matrix,Array},
normalization_nondimensional_equilibrium_distribution::Float64,
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_end_to_end_length_per_link_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_legendre_nondimensional_equilibrium_radial_distribution,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
normalization_nondimensional_equilibrium_distribution,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
nondimensional_end_to_end_length_per_link,
)
end
"""
The Gibbs free energy ``\\varphi`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``,
```math
\\varphi(\\xi, T) \\sim \\psi(\\xi, T) - \\xi f(\\xi, T) \\quad \\text{for } N_b\\gg 1,
```
where ``f(\\xi, T)`` is given by the Legendre transformation approximation above.
$(TYPEDSIGNATURES)
"""
function gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_legendre_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
end_to_end_length,
temperature,
)
end
"""
The Gibbs free energy per link ``\\varphi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function gibbs_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_legendre_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
end_to_end_length,
temperature,
)
end
"""
The relative Helmholtz free energy ``\\Delta\\varphi\\equiv\\varphi(\\xi,T)-\\varphi(0,T)`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, end_to_end_length_i, temperature_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_legendre_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
end_to_end_length,
temperature,
)
end
"""
The relative Gibbs free energy per link ``\\Delta\\varphi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, end_to_end_length_i, temperature_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_legendre_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
end_to_end_length,
temperature,
)
end
"""
The nondimensional Gibbs free energy ``N_b\\varrho=\\beta\\varphi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_legendre_nondimensional_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_end_to_end_length_per_link,
temperature,
)
end
"""
The nondimensional Gibbs free energy per link ``\\varrho\\equiv\\beta\\varphi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_gibbs_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_legendre_nondimensional_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_end_to_end_length_per_link,
temperature,
)
end
"""
The nondimensional relative Gibbs free energy ``N_b\\Delta\\varrho=\\beta\\Delta\\varphi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the number of links ``N_b``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_end_to_end_length_per_link_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_legendre_nondimensional_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64),
number_of_links_i,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
nondimensional_end_to_end_length_per_link,
)
end
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\varrho\\equiv\\beta\\Delta\\varphi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the number of links ``N_b``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_end_to_end_length_per_link_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isometric_legendre_nondimensional_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64),
number_of_links_i,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
nondimensional_end_to_end_length_per_link,
)
end
"""
Initializes and returns an instance of the thermodynamics of the FJC model in the isometric ensemble approximated using a Legendre transformation.
$(TYPEDSIGNATURES)
"""
function FJC(number_of_links::UInt8, link_length::Float64, hinge_mass::Float64)
normalization_nondimensional_equilibrium_distribution = integrate(
nondimensional_end_to_end_length_per_link ->
nondimensional_equilibrium_radial_distribution(
number_of_links,
1.0,
nondimensional_end_to_end_length_per_link,
),
ZERO,
ONE,
POINTS,
)
return FJC(
number_of_links,
link_length,
hinge_mass,
normalization_nondimensional_equilibrium_distribution,
(end_to_end_length, temperature) ->
force(number_of_links, link_length, end_to_end_length, temperature),
(nondimensional_end_to_end_length_per_link) ->
nondimensional_force(nondimensional_end_to_end_length_per_link),
(end_to_end_length, temperature) -> helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> helmholtz_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> relative_helmholtz_free_energy(
number_of_links,
link_length,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> relative_helmholtz_free_energy_per_link(
number_of_links,
link_length,
end_to_end_length,
temperature,
),
(nondimensional_end_to_end_length_per_link, temperature) ->
nondimensional_helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
nondimensional_end_to_end_length_per_link,
temperature,
),
(nondimensional_end_to_end_length_per_link, temperature) ->
nondimensional_helmholtz_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
nondimensional_end_to_end_length_per_link,
temperature,
),
(nondimensional_end_to_end_length_per_link) ->
nondimensional_relative_helmholtz_free_energy(
number_of_links,
nondimensional_end_to_end_length_per_link,
),
(nondimensional_end_to_end_length_per_link) ->
nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
),
(end_to_end_length) -> equilibrium_distribution(
number_of_links,
link_length,
normalization_nondimensional_equilibrium_distribution,
end_to_end_length,
),
(nondimensional_end_to_end_length_per_link) ->
nondimensional_equilibrium_distribution(
number_of_links,
normalization_nondimensional_equilibrium_distribution,
nondimensional_end_to_end_length_per_link,
),
(end_to_end_length) -> equilibrium_radial_distribution(
number_of_links,
link_length,
normalization_nondimensional_equilibrium_distribution,
end_to_end_length,
),
(nondimensional_end_to_end_length_per_link) ->
nondimensional_equilibrium_radial_distribution(
number_of_links,
normalization_nondimensional_equilibrium_distribution,
nondimensional_end_to_end_length_per_link,
),
(end_to_end_length, temperature) -> gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> gibbs_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> relative_gibbs_free_energy(
number_of_links,
link_length,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> relative_gibbs_free_energy_per_link(
number_of_links,
link_length,
end_to_end_length,
temperature,
),
(nondimensional_end_to_end_length_per_link, temperature) ->
nondimensional_gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
nondimensional_end_to_end_length_per_link,
temperature,
),
(nondimensional_end_to_end_length_per_link, temperature) ->
nondimensional_gibbs_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
nondimensional_end_to_end_length_per_link,
temperature,
),
(nondimensional_end_to_end_length_per_link) ->
nondimensional_relative_gibbs_free_energy(
number_of_links,
nondimensional_end_to_end_length_per_link,
),
(nondimensional_end_to_end_length_per_link) ->
nondimensional_relative_gibbs_free_energy_per_link(
number_of_links,
nondimensional_end_to_end_length_per_link,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 66494 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ONE, ZERO, POINTS, integrate, parameters
using Polymers.Physics.SingleChain.Fjc.Thermodynamics.Isometric.Legendre: FJC
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::base::init" begin
@test isa(
FJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
),
Any,
)
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test FJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test FJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test FJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test all(
FJC(number_of_links, link_length, hinge_mass).number_of_links ==
number_of_links &&
FJC(number_of_links, link_length, hinge_mass).link_length == link_length &&
FJC(number_of_links, link_length, hinge_mass).hinge_mass == hinge_mass,
)
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::normalization::equilibrium_distribution" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
normalization = integrate(
end_to_end_length ->
4.0 *
pi *
end_to_end_length^2 *
model.equilibrium_distribution(end_to_end_length),
ZERO,
ONE * number_of_links * link_length,
POINTS,
)
@test abs(normalization - 1.0) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::normalization::equilibrium_radial_distribution" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
normalization = integrate(
end_to_end_length ->
model.equilibrium_radial_distribution(end_to_end_length),
ZERO,
ONE * number_of_links * link_length,
POINTS,
)
@test abs(normalization - 1.0) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::normalization::nondimensional_equilibrium_distribution" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
normalization = integrate(
nondimensional_end_to_end_length_per_link ->
4.0 *
pi *
nondimensional_end_to_end_length_per_link^2 *
model.nondimensional_equilibrium_distribution(
nondimensional_end_to_end_length_per_link,
),
ZERO,
ONE,
POINTS,
)
@test abs(normalization - 1.0) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::normalization::nondimensional_equilibrium_radial_distribution" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
normalization = integrate(
nondimensional_end_to_end_length_per_link ->
model.nondimensional_equilibrium_radial_distribution(
nondimensional_end_to_end_length_per_link,
),
ZERO,
ONE,
POINTS,
)
@test abs(normalization - 1.0) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::nondimensional::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
model.nondimensional_force(nondimensional_end_to_end_length_per_link)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
force = model.force(end_to_end_length, temperature)
residual_abs =
force / BOLTZMANN_CONSTANT / temperature * link_length - nondimensional_force
residual_rel = residual_abs / nondimensional_force
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::nondimensional::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy = model.helmholtz_free_energy(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::nondimensional::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::nondimensional::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(end_to_end_length, temperature)
residual_abs =
relative_helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::nondimensional::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
relative_helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::nondimensional::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_gibbs_free_energy = model.nondimensional_gibbs_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
gibbs_free_energy = model.gibbs_free_energy(end_to_end_length, temperature)
residual_abs =
gibbs_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_gibbs_free_energy
residual_rel = residual_abs / nondimensional_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::nondimensional::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
gibbs_free_energy_per_link =
model.gibbs_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
gibbs_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::nondimensional::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_end_to_end_length_per_link,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_gibbs_free_energy =
model.relative_gibbs_free_energy(end_to_end_length, temperature)
residual_abs =
relative_gibbs_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_gibbs_free_energy
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::nondimensional::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
relative_gibbs_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::per_link::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy = model.helmholtz_free_energy(end_to_end_length, temperature)
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy / number_of_links - helmholtz_free_energy_per_link
residual_rel = residual_abs / helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::per_link::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(end_to_end_length, temperature)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
relative_helmholtz_free_energy / number_of_links -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::per_link::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy / number_of_links -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::per_link::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy / number_of_links -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::per_link::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
gibbs_free_energy = model.gibbs_free_energy(end_to_end_length, temperature)
gibbs_free_energy_per_link =
model.gibbs_free_energy_per_link(end_to_end_length, temperature)
residual_abs = gibbs_free_energy / number_of_links - gibbs_free_energy_per_link
residual_rel = residual_abs / gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::per_link::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_gibbs_free_energy =
model.relative_gibbs_free_energy(end_to_end_length, temperature)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
relative_gibbs_free_energy / number_of_links -
relative_gibbs_free_energy_per_link
residual_rel = residual_abs / relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::per_link::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_gibbs_free_energy = model.nondimensional_gibbs_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_gibbs_free_energy / number_of_links -
nondimensional_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::per_link::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_end_to_end_length_per_link,
)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
)
residual_abs =
nondimensional_relative_gibbs_free_energy / number_of_links -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::relative::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy = model.helmholtz_free_energy(end_to_end_length, temperature)
helmholtz_free_energy_0 =
model.helmholtz_free_energy(ZERO * number_of_links * link_length, temperature)
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy - helmholtz_free_energy_0 - relative_helmholtz_free_energy
residual_rel = residual_abs / relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::relative::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(end_to_end_length, temperature)
helmholtz_free_energy_per_link_0 = model.helmholtz_free_energy_per_link(
ZERO * number_of_links * link_length,
temperature,
)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy_per_link - helmholtz_free_energy_per_link_0 -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::relative::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_0 =
model.nondimensional_helmholtz_free_energy(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
)
residual_abs =
nondimensional_helmholtz_free_energy - nondimensional_helmholtz_free_energy_0 -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::relative::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_per_link_0 =
model.nondimensional_helmholtz_free_energy_per_link(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
)
residual_abs =
nondimensional_helmholtz_free_energy_per_link -
nondimensional_helmholtz_free_energy_per_link_0 -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::relative::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
gibbs_free_energy = model.gibbs_free_energy(end_to_end_length, temperature)
gibbs_free_energy_0 =
model.gibbs_free_energy(ZERO * number_of_links * link_length, temperature)
relative_gibbs_free_energy =
model.relative_gibbs_free_energy(end_to_end_length, temperature)
residual_abs = gibbs_free_energy - gibbs_free_energy_0 - relative_gibbs_free_energy
residual_rel = residual_abs / relative_gibbs_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::relative::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
gibbs_free_energy_per_link =
model.gibbs_free_energy_per_link(end_to_end_length, temperature)
gibbs_free_energy_per_link_0 = model.gibbs_free_energy_per_link(
ZERO * number_of_links * link_length,
temperature,
)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
gibbs_free_energy_per_link - gibbs_free_energy_per_link_0 -
relative_gibbs_free_energy_per_link
residual_rel = residual_abs / relative_gibbs_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::relative::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_gibbs_free_energy = model.nondimensional_gibbs_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_gibbs_free_energy_0 =
model.nondimensional_gibbs_free_energy(ZERO, temperature)
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_end_to_end_length_per_link,
)
residual_abs =
nondimensional_gibbs_free_energy - nondimensional_gibbs_free_energy_0 -
nondimensional_relative_gibbs_free_energy
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::relative::nondimensional_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_gibbs_free_energy_per_link_0 =
model.nondimensional_gibbs_free_energy_per_link(ZERO, temperature)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
)
residual_abs =
nondimensional_gibbs_free_energy_per_link -
nondimensional_gibbs_free_energy_per_link_0 -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::zero::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force_0 = model.force(ZERO * number_of_links * link_length, temperature)
@test abs(force_0) <=
3.1 * ZERO * number_of_links * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::zero::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force_0 = model.nondimensional_force(ZERO)
@test abs(nondimensional_force_0) <= 3.1 * ZERO * number_of_links
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::zero::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_0 = model.relative_helmholtz_free_energy(
ZERO * number_of_links * link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_0) <=
ZERO * number_of_links * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::zero::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_per_link_0 =
model.relative_helmholtz_free_energy_per_link(
ZERO * number_of_links * link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::zero::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_relative_helmholtz_free_energy_0 =
model.nondimensional_relative_helmholtz_free_energy(ZERO)
@test abs(nondimensional_relative_helmholtz_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::zero::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_relative_helmholtz_free_energy_per_link_0 =
model.nondimensional_relative_helmholtz_free_energy_per_link(ZERO)
@test abs(nondimensional_relative_helmholtz_free_energy_per_link_0) <= ZERO
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::zero::equilibrium_radial_distribution" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
equilibrium_radial_distribution_0 =
model.equilibrium_radial_distribution(ZERO * number_of_links * link_length)
@test abs(equilibrium_radial_distribution_0) <= ZERO
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::zero::nondimensional_equilibrium_radial_distribution" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_equilibrium_radial_distribution_0 =
model.equilibrium_radial_distribution(ZERO)
@test abs(nondimensional_equilibrium_radial_distribution_0) <= ZERO
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::zero::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_gibbs_free_energy_0 = model.relative_gibbs_free_energy(
ZERO * number_of_links * link_length,
temperature,
)
@test abs(relative_gibbs_free_energy_0) <=
ZERO * number_of_links * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::zero::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_gibbs_free_energy_per_link_0 = model.relative_gibbs_free_energy_per_link(
ZERO * number_of_links * link_length,
temperature,
)
@test abs(relative_gibbs_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::zero::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_relative_gibbs_free_energy_0 =
model.nondimensional_relative_gibbs_free_energy(ZERO)
@test abs(nondimensional_relative_gibbs_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::zero::nondimensional_relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_relative_gibbs_free_energy_per_link_0 =
model.nondimensional_relative_gibbs_free_energy_per_link(ZERO)
@test abs(nondimensional_relative_gibbs_free_energy_per_link_0) <= ZERO
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::connection::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
force = model.force(end_to_end_length, temperature)
h = parameters.rel_tol * number_of_links * link_length
force_from_derivative =
(
model.relative_helmholtz_free_energy(
end_to_end_length + 0.5 * h,
temperature,
) - model.relative_helmholtz_free_energy(
end_to_end_length - 0.5 * h,
temperature,
)
) / h
residual_abs = force - force_from_derivative
residual_rel = residual_abs / force
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::connection::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
model.nondimensional_force(nondimensional_end_to_end_length_per_link)
h = parameters.rel_tol
nondimensional_force_from_derivative =
(
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link + 0.5 * h,
) - model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link - 0.5 * h,
)
) / h
residual_abs = nondimensional_force - nondimensional_force_from_derivative
residual_rel = residual_abs / nondimensional_force
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::connection::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(end_to_end_length, temperature)
relative_helmholtz_free_energy_from_connection =
BOLTZMANN_CONSTANT *
temperature *
log((
model.equilibrium_distribution(ZERO * number_of_links * link_length) /
model.equilibrium_distribution(end_to_end_length)
))
residual_abs =
relative_helmholtz_free_energy - relative_helmholtz_free_energy_from_connection
residual_rel = residual_abs / relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isometric::legendre::test::connection::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
)
nondimensional_relative_helmholtz_free_energy_from_connection = log((
model.nondimensional_equilibrium_distribution(ZERO) /
model.nondimensional_equilibrium_distribution(
nondimensional_end_to_end_length_per_link,
)
))
residual_abs =
nondimensional_relative_helmholtz_free_energy -
nondimensional_relative_helmholtz_free_energy_from_connection
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 17697 | """
The freely-jointed chain (FJC) model thermodynamics in the isotensional ensemble.
"""
module Isotensional
using DocStringExtensions
using ......Polymers: PROJECT_ROOT
include("legendre/mod.jl")
"""
The structure of the thermodynamics of the FJC model in the isotensional ensemble.
$(FIELDS)
"""
struct FJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The thermodynamic functions of the model in the isotensional ensemble approximated using a Legendre transformation.
"""
legendre::Any
"""
The expected end-to-end length ``\\xi`` as a function of the applied force ``f`` and temperature ``T``.
"""
end_to_end_length::Function
"""
The expected end-to-end length per link ``\\xi/N_b=\\ell_b\\gamma`` as a function of the applied force ``f`` and temperature ``T``.
"""
end_to_end_length_per_link::Function
"""
The expected nondimensional end-to-end length ``N_b\\gamma=\\xi/\\ell_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_end_to_end_length::Function
"""
The expected nondimensional end-to-end length per link ``\\gamma\\equiv\\xi/N_b\\ell_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_end_to_end_length_per_link::Function
"""
The Gibbs free energy ``\\varphi`` as a function of the applied force ``f`` and temperature ``T``.
"""
gibbs_free_energy::Function
"""
The Gibbs free energy per link ``\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
gibbs_free_energy_per_link::Function
"""
The relative Gibbs free energy ``\\Delta\\varphi\\equiv\\varphi(f,T)-\\varphi(0,T)`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_gibbs_free_energy::Function
"""
The relative Gibbs free energy per link ``\\Delta\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_gibbs_free_energy_per_link::Function
"""
The nondimensional Gibbs free energy ``N_b\\varrho=\\beta\\varphi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_gibbs_free_energy::Function
"""
The nondimensional Gibbs free energy per link ``\\varrho\\equiv\\beta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_gibbs_free_energy_per_link::Function
"""
The nondimensional relative Gibbs free energy ``N_b\\Delta\\varrho=\\beta\\Delta\\varphi`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_gibbs_free_energy::Function
"""
The nondimensional relative Gibbs free energy per link ``\\Delta\\varrho\\equiv\\beta\\Delta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_gibbs_free_energy_per_link::Function
end
"""
The expected end-to-end length ``\\xi`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``,
given by [Rubinstein and Colby](https://global.oup.com/academic/product/polymer-physics-9780198520597) as
```math
\\xi(f, T) = -\\frac{\\partial\\varphi}{\\partial f} = N_b \\ell_b \\mathcal{L}(\\beta f\\ell_b),
```
where ``\\mathcal{L}(x)=\\coth(x)-1/x`` is the Langevin function.
$(TYPEDSIGNATURES)
"""
function end_to_end_length(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
force,
temperature,
)
end
"""
The expected end-to-end length per link ``\\xi/N_b=\\ell_b\\gamma`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b``.
$(TYPEDSIGNATURES)
"""
function end_to_end_length_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64),
link_length_i,
force_i,
temperature_i,
),
link_length,
force,
temperature,
)
end
"""
The expected nondimensional end-to-end length ``N_b\\gamma\\equiv\\xi/\\ell_b`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b``.
$(TYPEDSIGNATURES)
"""
function nondimensional_end_to_end_length(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_nondimensional_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64),
number_of_links_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_force,
)
end
"""
The expected nondimensional end-to-end length per link ``\\gamma\\equiv\\xi/N_b\\ell_b`` as a function of the applied nondimensional force ``\\eta``.
$(TYPEDSIGNATURES)
"""
function nondimensional_end_to_end_length_per_link(
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
nondimensional_force_i -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_nondimensional_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64,),
nondimensional_force_i,
),
nondimensional_force,
)
end
"""
The Gibbs free energy ``\\varphi`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``,
```math
\\varphi(f, T) = -kT\\ln Z(f, T).
```
$(TYPEDSIGNATURES)
"""
function gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, hinge_mass_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
force,
temperature,
)
end
"""
The Gibbs free energy per link ``\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, hinge_mass_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
force_i,
temperature_i,
),
link_length,
hinge_mass,
force,
temperature,
)
end
"""
The relative Gibbs free energy ``\\Delta\\varphi\\equiv\\varphi(f,T)-\\varphi(0,T)`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
force,
temperature,
)
end
"""
The relative Gibbs free energy per link ``\\Delta\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64),
link_length_i,
force_i,
temperature_i,
),
link_length,
force,
temperature,
)
end
"""
The nondimensional Gibbs free energy ``N_b\\varrho=\\beta\\varphi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_nondimensional_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_force,
temperature,
)
end
"""
The nondimensional Gibbs free energy per link ``\\varrho\\equiv\\beta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, hinge_mass_i, nondimensional_force_i, temperature_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_nondimensional_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
nondimensional_force_i,
temperature_i,
),
link_length,
hinge_mass,
nondimensional_force,
temperature,
)
end
"""
The nondimensional relative Gibbs free energy ``\\beta\\Delta\\varphi=N_b\\Delta\\varrho`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_nondimensional_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64),
number_of_links_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_force,
)
end
"""
The nondimensional relative Gibbs free energy per link ``\\Delta\\varrho\\equiv\\beta\\Delta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
nondimensional_force_i -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_nondimensional_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64,),
nondimensional_force_i,
),
nondimensional_force,
)
end
"""
Initializes and returns an instance of the thermodynamics of the FJC model in the isotensional ensemble.
$(TYPEDSIGNATURES)
"""
function FJC(number_of_links::UInt8, link_length::Float64, hinge_mass::Float64)
return FJC(
number_of_links,
link_length,
hinge_mass,
Legendre.FJC(number_of_links, link_length, hinge_mass),
(force, temperature) ->
end_to_end_length(number_of_links, link_length, force, temperature),
(force, temperature) -> end_to_end_length_per_link(link_length, force, temperature),
nondimensional_force ->
nondimensional_end_to_end_length(number_of_links, nondimensional_force),
nondimensional_force ->
nondimensional_end_to_end_length_per_link(nondimensional_force),
(force, temperature) ->
gibbs_free_energy(number_of_links, link_length, hinge_mass, force, temperature),
(force, temperature) ->
gibbs_free_energy_per_link(link_length, hinge_mass, force, temperature),
(force, temperature) ->
relative_gibbs_free_energy(number_of_links, link_length, force, temperature),
(force, temperature) ->
relative_gibbs_free_energy_per_link(link_length, force, temperature),
(nondimensional_force, temperature) -> nondimensional_gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_gibbs_free_energy_per_link(
link_length,
hinge_mass,
nondimensional_force,
temperature,
),
nondimensional_force -> nondimensional_relative_gibbs_free_energy(
number_of_links,
nondimensional_force,
),
nondimensional_force ->
nondimensional_relative_gibbs_free_energy_per_link(nondimensional_force),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 57570 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ZERO, parameters
using Polymers.Physics.SingleChain.Fjc.Thermodynamics.Isotensional: FJC
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::base::init" begin
@test isa(
FJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
),
Any,
)
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test FJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test FJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test FJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test all(
FJC(number_of_links, link_length, hinge_mass).number_of_links ==
number_of_links &&
FJC(number_of_links, link_length, hinge_mass).link_length == link_length &&
FJC(number_of_links, link_length, hinge_mass).hinge_mass == hinge_mass,
)
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::nondimensional::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
residual_abs = end_to_end_length / link_length - nondimensional_end_to_end_length
residual_rel = residual_abs / nondimensional_end_to_end_length
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::nondimensional::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(nondimensional_force)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
residual_abs =
end_to_end_length_per_link / link_length -
nondimensional_end_to_end_length_per_link
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::nondimensional::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
residual_abs =
gibbs_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_gibbs_free_energy
residual_rel = residual_abs / nondimensional_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::nondimensional::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
residual_abs =
gibbs_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::nondimensional::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(nondimensional_force)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
residual_abs =
relative_gibbs_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_gibbs_free_energy
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::nondimensional::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(nondimensional_force)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
residual_abs =
relative_gibbs_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::per_link::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
residual_abs = end_to_end_length / number_of_links - end_to_end_length_per_link
residual_rel = residual_abs / end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::per_link::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force)
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(nondimensional_force)
residual_abs =
nondimensional_end_to_end_length / number_of_links -
nondimensional_end_to_end_length_per_link
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::per_link::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
residual_abs = gibbs_free_energy / number_of_links - gibbs_free_energy_per_link
residual_rel = residual_abs / gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::per_link::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
residual_abs =
relative_gibbs_free_energy / number_of_links -
relative_gibbs_free_energy_per_link
residual_rel = residual_abs / relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::per_link::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_gibbs_free_energy / number_of_links -
nondimensional_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::per_link::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(nondimensional_force)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(nondimensional_force)
residual_abs =
nondimensional_relative_gibbs_free_energy / number_of_links -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::relative::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
gibbs_free_energy_0 = model.gibbs_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
residual_abs = gibbs_free_energy - gibbs_free_energy_0 - relative_gibbs_free_energy
residual_rel = residual_abs / gibbs_free_energy_0
@test abs(residual_abs) <=
BOLTZMANN_CONSTANT * temperature * number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::relative::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
gibbs_free_energy_per_link_0 = model.gibbs_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
residual_abs =
gibbs_free_energy_per_link - gibbs_free_energy_per_link_0 -
relative_gibbs_free_energy_per_link
residual_rel = residual_abs / gibbs_free_energy_per_link_0
@test abs(residual_abs) <= BOLTZMANN_CONSTANT * temperature * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::relative::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
nondimensional_gibbs_free_energy_0 =
model.nondimensional_gibbs_free_energy(ZERO, temperature)
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(nondimensional_force)
residual_abs =
nondimensional_gibbs_free_energy - nondimensional_gibbs_free_energy_0 -
nondimensional_relative_gibbs_free_energy
residual_rel = residual_abs / nondimensional_gibbs_free_energy_0
@test abs(residual_abs) <= number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::relative::nondimensional_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_gibbs_free_energy_per_link_0 =
model.nondimensional_gibbs_free_energy_per_link(ZERO, temperature)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(nondimensional_force)
residual_abs =
nondimensional_gibbs_free_energy_per_link -
nondimensional_gibbs_free_energy_per_link_0 -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link_0
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::zero::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length_0 = model.end_to_end_length(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(end_to_end_length_0) <= ZERO * number_of_links * link_length
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::zero::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length_per_link_0 = model.end_to_end_length_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(end_to_end_length_per_link_0) <= ZERO * link_length
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::zero::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_0 = model.nondimensional_end_to_end_length(ZERO)
@test abs(nondimensional_end_to_end_length_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::zero::nondimensional_end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link_0 =
model.nondimensional_end_to_end_length_per_link(ZERO)
@test abs(nondimensional_end_to_end_length_per_link_0) <= ZERO
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::zero::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_gibbs_free_energy_0 = model.relative_gibbs_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_gibbs_free_energy_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature * number_of_links
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::zero::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_gibbs_free_energy_per_link_0 = model.relative_gibbs_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_gibbs_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::zero::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_relative_gibbs_free_energy_0 =
model.nondimensional_relative_gibbs_free_energy(ZERO)
@test abs(nondimensional_relative_gibbs_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::zero::nondimensional_relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_relative_gibbs_free_energy_per_link_0 =
model.nondimensional_relative_gibbs_free_energy_per_link(ZERO)
@test abs(nondimensional_relative_gibbs_free_energy_per_link_0) <= ZERO
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::connection::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
h = parameters.rel_tol * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_from_derivative =
-(
model.relative_gibbs_free_energy(force + 0.5 * h, temperature) -
model.relative_gibbs_free_energy(force - 0.5 * h, temperature)
) / h
residual_abs = end_to_end_length - end_to_end_length_from_derivative
residual_rel = residual_abs / end_to_end_length
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::connection::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
h = parameters.rel_tol * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link_from_derivative =
-(
model.relative_gibbs_free_energy_per_link(force + 0.5 * h, temperature) -
model.relative_gibbs_free_energy_per_link(force - 0.5 * h, temperature)
) / h
residual_abs =
end_to_end_length_per_link - end_to_end_length_per_link_from_derivative
residual_rel = residual_abs / end_to_end_length_per_link
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::connection::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force)
h = parameters.rel_tol
nondimensional_end_to_end_length_from_derivative =
-(
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force + 0.5 * h,
) - model.nondimensional_relative_gibbs_free_energy(
nondimensional_force - 0.5 * h,
)
) / h
residual_abs =
nondimensional_end_to_end_length -
nondimensional_end_to_end_length_from_derivative
residual_rel = residual_abs / nondimensional_end_to_end_length
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::connection::nondimensional_end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(nondimensional_force)
h = parameters.rel_tol
nondimensional_end_to_end_length_per_link_from_derivative =
-(
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force + 0.5 * h,
) - model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force - 0.5 * h,
)
) / h
residual_abs =
nondimensional_end_to_end_length_per_link -
nondimensional_end_to_end_length_per_link_from_derivative
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::legendre::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
gibbs_free_energy_legendre =
model.legendre.helmholtz_free_energy(force, temperature) -
force * end_to_end_length
residual_abs = gibbs_free_energy - gibbs_free_energy_legendre
residual_rel = residual_abs / gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::legendre::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
gibbs_free_energy_per_link_legendre =
model.legendre.helmholtz_free_energy_per_link(force, temperature) -
force * end_to_end_length_per_link
residual_abs = gibbs_free_energy_per_link - gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::legendre::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
end_to_end_length_0 = model.end_to_end_length(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
relative_gibbs_free_energy_legendre =
model.legendre.relative_helmholtz_free_energy(force, temperature) -
force * end_to_end_length +
ZERO * BOLTZMANN_CONSTANT * temperature / link_length * end_to_end_length_0
residual_abs = relative_gibbs_free_energy - relative_gibbs_free_energy_legendre
residual_rel = residual_abs / relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::legendre::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
end_to_end_length_per_link_0 = model.end_to_end_length_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
relative_gibbs_free_energy_per_link_legendre =
model.legendre.relative_helmholtz_free_energy_per_link(force, temperature) -
force * end_to_end_length_per_link +
ZERO * BOLTZMANN_CONSTANT * temperature / link_length *
end_to_end_length_per_link_0
residual_abs =
relative_gibbs_free_energy_per_link -
relative_gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::legendre::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force)
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
nondimensional_gibbs_free_energy_legendre =
model.legendre.nondimensional_helmholtz_free_energy(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length
residual_abs =
nondimensional_gibbs_free_energy - nondimensional_gibbs_free_energy_legendre
residual_rel = residual_abs / nondimensional_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::legendre::nondimensional_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(nondimensional_force)
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_gibbs_free_energy_per_link_legendre =
model.legendre.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length_per_link
residual_abs =
nondimensional_gibbs_free_energy_per_link -
nondimensional_gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::legendre::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force)
nondimensional_end_to_end_length_0 = model.nondimensional_end_to_end_length(ZERO)
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(nondimensional_force)
nondimensional_relative_gibbs_free_energy_legendre =
model.legendre.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
) - nondimensional_force * nondimensional_end_to_end_length +
ZERO * nondimensional_end_to_end_length_0
residual_abs =
nondimensional_relative_gibbs_free_energy -
nondimensional_relative_gibbs_free_energy_legendre
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::legendre::nondimensional_relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(nondimensional_force)
nondimensional_end_to_end_length_per_link_0 =
model.nondimensional_end_to_end_length_per_link(ZERO)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(nondimensional_force)
nondimensional_relative_gibbs_free_energy_per_link_legendre =
model.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
) - nondimensional_force * nondimensional_end_to_end_length_per_link +
ZERO * nondimensional_end_to_end_length_per_link_0
residual_abs =
nondimensional_relative_gibbs_free_energy_per_link -
nondimensional_relative_gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::legendre_connection::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
h = parameters.rel_tol * BOLTZMANN_CONSTANT * temperature / link_length
force_from_derivative =
(
model.legendre.relative_helmholtz_free_energy(
force + 0.5 * h,
temperature,
) -
model.legendre.relative_helmholtz_free_energy(force - 0.5 * h, temperature)
) / (
model.end_to_end_length(force + 0.5 * h, temperature) -
model.end_to_end_length(force - 0.5 * h, temperature)
)
residual_abs = force - force_from_derivative
residual_rel = residual_abs / force
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::test::legendre_connection::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
h = parameters.rel_tol
nondimensional_force_from_derivative =
(
model.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force + 0.5 * h,
) - model.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force - 0.5 * h,
)
) / (
model.nondimensional_end_to_end_length_per_link(
nondimensional_force + 0.5 * h,
) - model.nondimensional_end_to_end_length_per_link(
nondimensional_force - 0.5 * h,
)
)
residual_abs = nondimensional_force - nondimensional_force_from_derivative
residual_rel = residual_abs / nondimensional_force
@test abs(residual_rel) <= h
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 13257 | """
The freely-jointed chain (FJC) model thermodynamics in the isotensional ensemble approximated using a Legendre transformation.
"""
module Legendre
using DocStringExtensions
using .......Polymers: PROJECT_ROOT
"""
The structure of the thermodynamics of the FJC model in the isotensional ensemble approximated using a Legendre transformation.
$(FIELDS)
"""
struct FJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The Helmholtz free energy ``\\psi`` as a function of the applied force ``f`` and temperature ``T``.
"""
helmholtz_free_energy::Function
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
helmholtz_free_energy_per_link::Function
"""
The relative helmholtz free energy ``\\Delta\\psi\\equiv\\psi(f,T)-\\psi(0,T)`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_helmholtz_free_energy::Function
"""
The relative helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_helmholtz_free_energy_per_link::Function
"""
The nondimensional helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy::Function
"""
The nondimensional helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy_per_link::Function
"""
The nondimensional relative helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_helmholtz_free_energy::Function
"""
The nondimensional relative helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_helmholtz_free_energy_per_link::Function
end
"""
The Helmholtz free energy ``\\psi`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
```math
\\psi(f, T) \\sim \\varphi(f, T) + f \\xi(f, T) \\quad \\text{for } N_b\\gg 1.
```
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, hinge_mass_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_legendre_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
force,
temperature,
)
end
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, hinge_mass_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_legendre_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
force_i,
temperature_i,
),
link_length,
hinge_mass,
force,
temperature,
)
end
"""
The relative Helmholtz free energy ``\\Delta\\psi\\equiv\\psi(f,T)-\\psi(0,T)`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_legendre_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
force,
temperature,
)
end
"""
The relative Helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_legendre_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64),
link_length_i,
force_i,
temperature_i,
),
link_length,
force,
temperature,
)
end
"""
The nondimensional Helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_legendre_nondimensional_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_force,
temperature,
)
end
"""
The nondimensional Helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, hinge_mass_i, nondimensional_force_i, temperature_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_legendre_nondimensional_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
nondimensional_force_i,
temperature_i,
),
link_length,
hinge_mass,
nondimensional_force,
temperature,
)
end
"""
The nondimensional relative Helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_legendre_nondimensional_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64),
number_of_links_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_force,
)
end
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
nondimensional_force_i -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_legendre_nondimensional_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64,),
nondimensional_force_i,
),
nondimensional_force,
)
end
"""
Initializes and returns an instance of the thermodynamics of the FJC model in the isotensional ensemble approximated using a Legendre transformation.
$(TYPEDSIGNATURES)
"""
function FJC(number_of_links::UInt8, link_length::Float64, hinge_mass::Float64)
return FJC(
number_of_links,
link_length,
hinge_mass,
(force, temperature) -> helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
force,
temperature,
),
(force, temperature) ->
helmholtz_free_energy_per_link(link_length, hinge_mass, force, temperature),
(force, temperature) -> relative_helmholtz_free_energy(
number_of_links,
link_length,
force,
temperature,
),
(force, temperature) ->
relative_helmholtz_free_energy_per_link(link_length, force, temperature),
(nondimensional_force, temperature) -> nondimensional_helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) ->
nondimensional_helmholtz_free_energy_per_link(
link_length,
hinge_mass,
nondimensional_force,
temperature,
),
nondimensional_force -> nondimensional_relative_helmholtz_free_energy(
number_of_links,
nondimensional_force,
),
nondimensional_force ->
nondimensional_relative_helmholtz_free_energy_per_link(nondimensional_force),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 26009 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ZERO, parameters
using Polymers.Physics.SingleChain.Fjc.Thermodynamics.Isotensional.Legendre: FJC
@testset "physics::single_chain::fjc::thermodynamics::isotensional::legendre::test::base::init" begin
@test isa(
FJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
),
Any,
)
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::legendre::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test FJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::legendre::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test FJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::legendre::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test FJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::legendre::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test all(
FJC(number_of_links, link_length, hinge_mass).number_of_links ==
number_of_links &&
FJC(number_of_links, link_length, hinge_mass).link_length == link_length &&
FJC(number_of_links, link_length, hinge_mass).hinge_mass == hinge_mass,
)
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::legendre::test::nondimensional::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy =
model.nondimensional_helmholtz_free_energy(nondimensional_force, temperature)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy = model.helmholtz_free_energy(force, temperature)
residual_abs =
helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::legendre::test::nondimensional::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(force, temperature)
residual_abs =
helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::legendre::test::nondimensional::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(nondimensional_force)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(force, temperature)
residual_abs =
relative_helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::legendre::test::nondimensional::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(force, temperature)
residual_abs =
relative_helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::legendre::test::per_link::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy = model.helmholtz_free_energy(force, temperature)
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(force, temperature)
residual_abs =
helmholtz_free_energy / number_of_links - helmholtz_free_energy_per_link
residual_rel = residual_abs / helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::legendre::test::per_link::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(force, temperature)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(force, temperature)
residual_abs =
relative_helmholtz_free_energy / number_of_links -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::legendre::test::per_link::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy =
model.nondimensional_helmholtz_free_energy(nondimensional_force, temperature)
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy / number_of_links -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::legendre::test::per_link::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(nondimensional_force)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy / number_of_links -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::legendre::test::relative::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy = model.helmholtz_free_energy(force, temperature)
helmholtz_free_energy_0 = model.helmholtz_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(force, temperature)
residual_abs =
helmholtz_free_energy - helmholtz_free_energy_0 - relative_helmholtz_free_energy
residual_rel = residual_abs / helmholtz_free_energy_0
@test abs(residual_abs) <=
BOLTZMANN_CONSTANT * temperature * number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::legendre::test::relative::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(force, temperature)
helmholtz_free_energy_per_link_0 = model.helmholtz_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(force, temperature)
residual_abs =
helmholtz_free_energy_per_link - helmholtz_free_energy_per_link_0 -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / helmholtz_free_energy_per_link_0
@test abs(residual_abs) <= BOLTZMANN_CONSTANT * temperature * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::legendre::test::relative::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy =
model.nondimensional_helmholtz_free_energy(nondimensional_force, temperature)
nondimensional_helmholtz_free_energy_0 =
model.nondimensional_helmholtz_free_energy(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(nondimensional_force)
residual_abs =
nondimensional_helmholtz_free_energy - nondimensional_helmholtz_free_energy_0 -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_0
@test abs(residual_abs) <= number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::legendre::test::relative::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_helmholtz_free_energy_per_link_0 =
model.nondimensional_helmholtz_free_energy_per_link(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
)
residual_abs =
nondimensional_helmholtz_free_energy_per_link -
nondimensional_helmholtz_free_energy_per_link_0 -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link_0
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::legendre::test::zero::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_0 = model.relative_helmholtz_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature * number_of_links
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::legendre::test::zero::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_per_link_0 =
model.relative_helmholtz_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::legendre::test::zero::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_relative_helmholtz_free_energy_0 =
model.nondimensional_relative_helmholtz_free_energy(ZERO)
@test abs(nondimensional_relative_helmholtz_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::fjc::thermodynamics::isotensional::legendre::test::zero::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_relative_helmholtz_free_energy_per_link_0 =
model.nondimensional_relative_helmholtz_free_energy_per_link(ZERO)
@test abs(nondimensional_relative_helmholtz_free_energy_per_link_0) <= ZERO
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 44881 | """
The freely-jointed chain (FJC) model thermodynamics in the modified canonical ensemble.
"""
module ModifiedCanonical
using DocStringExtensions
using ......Polymers: PROJECT_ROOT
include("asymptotic/mod.jl")
"""
The structure of the thermodynamics of the FJC model in the modified canonical ensemble.
$(FIELDS)
"""
struct FJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The thermodynamic functions of the model in the modified canonical ensemble approximated using an asymptotic approach.
"""
asymptotic::Any
"""
The expected end-to-end length ``\\xi`` as a function of the applied potential distance, potential stiffness, and temperature ``T``.
"""
end_to_end_length::Function
"""
The expected end-to-end length per link ``\\xi/N_b=\\ell_b\\gamma`` as a function of the applied potential distance, potential stiffness, and temperature ``T``.
"""
end_to_end_length_per_link::Function
"""
The expected nondimensional end-to-end length ``N_b\\gamma=\\xi/\\ell_b`` as a function of the applied nondimensional potential distance and nondimensional potential stiffness.
"""
nondimensional_end_to_end_length::Function
"""
The expected nondimensional end-to-end length per link ``\\gamma\\equiv\\xi/N_b\\ell_b`` as a function of the applied nondimensional potential distance and nondimensional potential stiffness.
"""
nondimensional_end_to_end_length_per_link::Function
"""
The expected force ``f`` as a function of the applied potential distance, potential stiffness, and temperature ``T``.
"""
force::Function
"""
The expected nondimensional force ``\\eta`` as a function of the applied nondimensional potential distance and nondimensional potential stiffness.
"""
nondimensional_force::Function
"""
The Helmholtz free energy ``\\psi`` as a function of the applied potential distance, potential stiffness, and temperature ``T``.
"""
helmholtz_free_energy::Function
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied potential distance, potential stiffness, and temperature ``T``.
"""
helmholtz_free_energy_per_link::Function
"""
The relative Helmholtz free energy ``\\Delta\\psi\\equiv\\psi(\\xi,T)-\\psi(0,T)`` as a function of the applied potential distance, potential stiffness, and temperature ``T``.
"""
relative_helmholtz_free_energy::Function
"""
The relative Helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied potential distance, potential stiffness, and temperature ``T``.
"""
relative_helmholtz_free_energy_per_link::Function
"""
The nondimensional Helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional potential distance, nondimensional potential stiffness, and temperature ``T``.
"""
nondimensional_helmholtz_free_energy::Function
"""
The nondimensional Helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional potential distance, nondimensional potential stiffness, and temperature ``T``.
"""
nondimensional_helmholtz_free_energy_per_link::Function
"""
The nondimensional relative Helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional potential distance and nondimensional potential stiffness.
"""
nondimensional_relative_helmholtz_free_energy::Function
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional potential distance and nondimensional potential stiffness.
"""
nondimensional_relative_helmholtz_free_energy_per_link::Function
"""
The Gibbs free energy ``\\varphi`` as a function of the applied potential distance, potential stiffness, and temperature ``T``.
"""
gibbs_free_energy::Function
"""
The Gibbs free energy per link ``\\varphi/N_b`` as a function of the applied potential distance, potential stiffness, and temperature ``T``.
"""
gibbs_free_energy_per_link::Function
"""
The relative Gibbs free energy ``\\Delta\\varphi\\equiv\\varphi(f,T)-\\varphi(0,T)`` as a function of the applied potential distance, potential stiffness, and temperature ``T``.
"""
relative_gibbs_free_energy::Function
"""
The relative Gibbs free energy per link ``\\Delta\\varphi/N_b`` as a function of the applied potential distance, potential stiffness, and temperature ``T``.
"""
relative_gibbs_free_energy_per_link::Function
"""
The nondimensional Gibbs free energy ``N_b\\varrho=\\beta\\varphi`` as a function of the applied nondimensional potential distance, nondimensional potential stiffness, and temperature ``T``.
"""
nondimensional_gibbs_free_energy::Function
"""
The nondimensional Gibbs free energy per link ``\\varrho\\equiv\\beta\\varphi/N_b`` as a function of the applied nondimensional potential distance, nondimensional potential stiffness, and temperature ``T``.
"""
nondimensional_gibbs_free_energy_per_link::Function
"""
The nondimensional relative Gibbs free energy ``N_b\\Delta\\varrho=\\beta\\Delta\\varphi`` as a function of the applied nondimensional potential distance and nondimensional potential stiffness.
"""
nondimensional_relative_gibbs_free_energy::Function
"""
The nondimensional relative Gibbs free energy per link ``\\Delta\\varrho\\equiv\\beta\\Delta\\varphi/N_b`` as a function of the applied nondimensional potential distance and nondimensional potential stiffness.
"""
nondimensional_relative_gibbs_free_energy_per_link::Function
end
"""
The expected end-to-end length ``\\xi`` as a function of the applied potential distance, potential stiffness, and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``.
$(TYPEDSIGNATURES)
"""
function end_to_end_length(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
potential_distance::Union{Float64,Vector,Matrix,Array},
potential_stiffness::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
),
number_of_links,
link_length,
potential_distance,
potential_stiffness,
temperature,
)
end
"""
The expected end-to-end length per link ``\\xi/N_b=\\ell_b\\gamma`` as a function of the applied potential distance, potential stiffness, and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``.
$(TYPEDSIGNATURES)
"""
function end_to_end_length_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
potential_distance::Union{Float64,Vector,Matrix,Array},
potential_stiffness::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
),
number_of_links,
link_length,
potential_distance,
potential_stiffness,
temperature,
)
end
"""
The expected nondimensional end-to-end length ``N_b\\gamma\\equiv\\xi/\\ell_b`` as a function of the applied nondimensional potential distance and nondimensional potential stiffness,
parameterized by the number of links ``N_b``.
$(TYPEDSIGNATURES)
"""
function nondimensional_end_to_end_length(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_potential_distance::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_stiffness::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_nondimensional_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
),
number_of_links,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
end
"""
The expected nondimensional end-to-end length ``\\gamma\\equiv\\xi/N_b\\ell_b`` as a function of the applied nondimensional potential distance and nondimensional potential stiffness,
parameterized by the number of links ``N_b``.
$(TYPEDSIGNATURES)
"""
function nondimensional_end_to_end_length_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_potential_distance::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_stiffness::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_nondimensional_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
),
number_of_links,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
end
"""
The expected force ``f`` as a function of the applied potential distance, potential stiffness, and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``.
$(TYPEDSIGNATURES)
"""
function force(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
potential_distance::Union{Float64,Vector,Matrix,Array},
potential_stiffness::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_force,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
),
number_of_links,
link_length,
potential_distance,
potential_stiffness,
temperature,
)
end
"""
The expected nondimensional force ``\\eta`` as a function of the applied nondimensional potential distance and nondimensional potential stiffness,
parameterized by the number of links ``N_b``.
$(TYPEDSIGNATURES)
"""
function nondimensional_force(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_potential_distance::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_stiffness::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_nondimensional_force,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
),
number_of_links,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
end
"""
The Helmholtz free energy ``\\psi`` as a function of the applied potential distance, potential stiffness, and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
potential_distance::Union{Float64,Vector,Matrix,Array},
potential_stiffness::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
potential_distance,
potential_stiffness,
temperature,
)
end
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied potential distance, potential stiffness, and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
potential_distance::Union{Float64,Vector,Matrix,Array},
potential_stiffness::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
potential_distance,
potential_stiffness,
temperature,
)
end
"""
The relative Helmholtz free energy ``\\Delta\\psi\\equiv\\psi(\\xi,T)-\\psi(0,T)`` as a function of the applied potential distance, potential stiffness, and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
potential_distance::Union{Float64,Vector,Matrix,Array},
potential_stiffness::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
),
number_of_links,
link_length,
potential_distance,
potential_stiffness,
temperature,
)
end
"""
The relative Helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied potential distance, potential stiffness, and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
potential_distance::Union{Float64,Vector,Matrix,Array},
potential_stiffness::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
),
number_of_links,
link_length,
potential_distance,
potential_stiffness,
temperature,
)
end
"""
The nondimensional Helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional potential distance, nondimensional potential stiffness, and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_distance::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_stiffness::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_nondimensional_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
end
"""
The nondimensional Helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional potential distance, nondimensional potential stiffness, and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_distance::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_stiffness::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_nondimensional_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
end
"""
The nondimensional relative Helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional potential distance and nondimensional potential stiffness,
parameterized by the number of links ``N_b``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_potential_distance::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_stiffness::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_nondimensional_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
),
number_of_links,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
end
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional potential distance and nondimensional potential stiffness,
parameterized by the number of links ``N_b``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_potential_distance::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_stiffness::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_nondimensional_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
),
number_of_links,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
end
"""
The gibbs free energy ``\\psi`` as a function of the applied potential distance, potential stiffness, and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
potential_distance::Union{Float64,Vector,Matrix,Array},
potential_stiffness::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
potential_distance,
potential_stiffness,
temperature,
)
end
"""
The gibbs free energy per link ``\\psi/N_b`` as a function of the applied potential distance, potential stiffness, and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function gibbs_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
potential_distance::Union{Float64,Vector,Matrix,Array},
potential_stiffness::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
potential_distance,
potential_stiffness,
temperature,
)
end
"""
The relative gibbs free energy ``\\Delta\\psi\\equiv\\psi(\\xi,T)-\\psi(0,T)`` as a function of the applied potential distance, potential stiffness, and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
potential_distance::Union{Float64,Vector,Matrix,Array},
potential_stiffness::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
),
number_of_links,
link_length,
potential_distance,
potential_stiffness,
temperature,
)
end
"""
The relative gibbs free energy per link ``\\Delta\\psi/N_b`` as a function of the applied potential distance, potential stiffness, and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
potential_distance::Union{Float64,Vector,Matrix,Array},
potential_stiffness::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
),
number_of_links,
link_length,
potential_distance,
potential_stiffness,
temperature,
)
end
"""
The nondimensional gibbs free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional potential distance, nondimensional potential stiffness, and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_distance::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_stiffness::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_nondimensional_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
end
"""
The nondimensional gibbs free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional potential distance, nondimensional potential stiffness, and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_gibbs_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_distance::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_stiffness::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_nondimensional_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
end
"""
The nondimensional relative gibbs free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional potential distance and nondimensional potential stiffness,
parameterized by the number of links ``N_b``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_potential_distance::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_stiffness::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_nondimensional_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
),
number_of_links,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
end
"""
The nondimensional relative gibbs free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional potential distance and nondimensional potential stiffness,
parameterized by the number of links ``N_b``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_potential_distance::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_stiffness::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_nondimensional_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
),
number_of_links,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
end
"""
Initializes and returns an instance of the thermodynamics of the FJC model in the modified canonical ensemble.
$(TYPEDSIGNATURES)
"""
function FJC(number_of_links::UInt8, link_length::Float64, hinge_mass::Float64)
return FJC(
number_of_links,
link_length,
hinge_mass,
Asymptotic.FJC(number_of_links, link_length, hinge_mass),
(potential_distance, potential_stiffness, temperature) -> end_to_end_length(
number_of_links,
link_length,
potential_distance,
potential_stiffness,
temperature,
),
(potential_distance, potential_stiffness, temperature) ->
end_to_end_length_per_link(
number_of_links,
link_length,
potential_distance,
potential_stiffness,
temperature,
),
(nondimensional_potential_distance, nondimensional_potential_stiffness) ->
nondimensional_end_to_end_length(
number_of_links,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
),
(nondimensional_potential_distance, nondimensional_potential_stiffness) ->
nondimensional_end_to_end_length_per_link(
number_of_links,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
),
(potential_distance, potential_stiffness, temperature) -> force(
number_of_links,
link_length,
potential_distance,
potential_stiffness,
temperature,
),
(nondimensional_potential_distance, nondimensional_potential_stiffness) ->
nondimensional_force(
number_of_links,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
),
(potential_distance, potential_stiffness, temperature) -> helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
potential_distance,
potential_stiffness,
temperature,
),
(potential_distance, potential_stiffness, temperature) ->
helmholtz_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
potential_distance,
potential_stiffness,
temperature,
),
(potential_distance, potential_stiffness, temperature) ->
relative_helmholtz_free_energy(
number_of_links,
link_length,
potential_distance,
potential_stiffness,
temperature,
),
(potential_distance, potential_stiffness, temperature) ->
relative_helmholtz_free_energy_per_link(
number_of_links,
link_length,
potential_distance,
potential_stiffness,
temperature,
),
(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
) -> nondimensional_helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
),
(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
) -> nondimensional_helmholtz_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
),
(nondimensional_potential_distance, nondimensional_potential_stiffness) ->
nondimensional_relative_helmholtz_free_energy(
number_of_links,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
),
(nondimensional_potential_distance, nondimensional_potential_stiffness) ->
nondimensional_relative_helmholtz_free_energy_per_link(
number_of_links,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
),
(potential_distance, potential_stiffness, temperature) -> gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
potential_distance,
potential_stiffness,
temperature,
),
(potential_distance, potential_stiffness, temperature) ->
gibbs_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
potential_distance,
potential_stiffness,
temperature,
),
(potential_distance, potential_stiffness, temperature) ->
relative_gibbs_free_energy(
number_of_links,
link_length,
potential_distance,
potential_stiffness,
temperature,
),
(potential_distance, potential_stiffness, temperature) ->
relative_gibbs_free_energy_per_link(
number_of_links,
link_length,
potential_distance,
potential_stiffness,
temperature,
),
(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
) -> nondimensional_gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
),
(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
) -> nondimensional_gibbs_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
),
(nondimensional_potential_distance, nondimensional_potential_stiffness) ->
nondimensional_relative_gibbs_free_energy(
number_of_links,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
),
(nondimensional_potential_distance, nondimensional_potential_stiffness) ->
nondimensional_relative_gibbs_free_energy_per_link(
number_of_links,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 162768 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ZERO, POINTS, integrate, parameters
using Polymers.Physics.SingleChain.Fjc.Thermodynamics.ModifiedCanonical: FJC
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::base::init" begin
@test isa(
FJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
),
Any,
)
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test FJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test FJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test FJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test all(
FJC(number_of_links, link_length, hinge_mass).number_of_links ==
number_of_links &&
FJC(number_of_links, link_length, hinge_mass).link_length == link_length &&
FJC(number_of_links, link_length, hinge_mass).hinge_mass == hinge_mass,
)
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::nondimensional::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_end_to_end_length = model.nondimensional_end_to_end_length(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
end_to_end_length =
model.end_to_end_length(potential_distance, potential_stiffness, temperature)
residual_abs = end_to_end_length / link_length - nondimensional_end_to_end_length
residual_rel = residual_abs / nondimensional_end_to_end_length
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::nondimensional::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
end_to_end_length_per_link = model.end_to_end_length_per_link(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs =
end_to_end_length_per_link / link_length -
nondimensional_end_to_end_length_per_link
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::nondimensional::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_small * (1.0 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force = model.nondimensional_force(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
force = model.force(potential_distance, potential_stiffness, temperature)
residual_abs =
force / BOLTZMANN_CONSTANT / temperature * link_length - nondimensional_force
residual_rel = residual_abs / nondimensional_force
@test abs(residual_abs) <= parameters.abs_tol
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::nondimensional::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_small * (1.0 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
helmholtz_free_energy = model.helmholtz_free_energy(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs =
helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::nondimensional::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_small * (1.0 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
helmholtz_free_energy_per_link = model.helmholtz_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs =
helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::nondimensional::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_small * (1.0 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
relative_helmholtz_free_energy = model.relative_helmholtz_free_energy(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs =
relative_helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::nondimensional::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_small * (1.0 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs =
relative_helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::nondimensional::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_gibbs_free_energy = model.nondimensional_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
gibbs_free_energy =
model.gibbs_free_energy(potential_distance, potential_stiffness, temperature)
residual_abs =
gibbs_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_gibbs_free_energy
residual_rel = residual_abs / nondimensional_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::nondimensional::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs =
gibbs_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::nondimensional::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
relative_gibbs_free_energy = model.relative_gibbs_free_energy(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs =
relative_gibbs_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_gibbs_free_energy
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::nondimensional::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
relative_gibbs_free_energy_per_link = model.relative_gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs =
relative_gibbs_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::per_link::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
end_to_end_length =
model.end_to_end_length(potential_distance, potential_stiffness, temperature)
end_to_end_length_per_link = model.end_to_end_length_per_link(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs = end_to_end_length / number_of_links - end_to_end_length_per_link
residual_rel = residual_abs / end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::per_link::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
nondimensional_end_to_end_length = model.nondimensional_end_to_end_length(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
residual_abs =
nondimensional_end_to_end_length / number_of_links -
nondimensional_end_to_end_length_per_link
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::per_link::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_small * (1.0 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
helmholtz_free_energy = model.helmholtz_free_energy(
potential_distance,
potential_stiffness,
temperature,
)
helmholtz_free_energy_per_link = model.helmholtz_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs =
helmholtz_free_energy / number_of_links - helmholtz_free_energy_per_link
residual_rel = residual_abs / helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::per_link::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_small * (1.0 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
relative_helmholtz_free_energy = model.relative_helmholtz_free_energy(
potential_distance,
potential_stiffness,
temperature,
)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs =
relative_helmholtz_free_energy / number_of_links -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::per_link::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_small * (1.0 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy / number_of_links -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::per_link::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_small * (1.0 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy / number_of_links -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::per_link::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
gibbs_free_energy =
model.gibbs_free_energy(potential_distance, potential_stiffness, temperature)
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs = gibbs_free_energy / number_of_links - gibbs_free_energy_per_link
residual_rel = residual_abs / gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::per_link::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
relative_gibbs_free_energy = model.relative_gibbs_free_energy(
potential_distance,
potential_stiffness,
temperature,
)
relative_gibbs_free_energy_per_link = model.relative_gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs =
relative_gibbs_free_energy / number_of_links -
relative_gibbs_free_energy_per_link
residual_rel = residual_abs / relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::per_link::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_gibbs_free_energy = model.nondimensional_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
residual_abs =
nondimensional_gibbs_free_energy / number_of_links -
nondimensional_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::per_link::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
residual_abs =
nondimensional_relative_gibbs_free_energy / number_of_links -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::relative::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_small * (1.0 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
helmholtz_free_energy = model.helmholtz_free_energy(
potential_distance,
potential_stiffness,
temperature,
)
helmholtz_free_energy_0 = model.helmholtz_free_energy(
ZERO * number_of_links * link_length,
potential_stiffness,
temperature,
)
relative_helmholtz_free_energy = model.relative_helmholtz_free_energy(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs =
helmholtz_free_energy - helmholtz_free_energy_0 - relative_helmholtz_free_energy
residual_rel = residual_abs / relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::relative::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_small * (1.0 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
helmholtz_free_energy_per_link = model.helmholtz_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
)
helmholtz_free_energy_per_link_0 = model.helmholtz_free_energy_per_link(
ZERO * number_of_links * link_length,
potential_stiffness,
temperature,
)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs =
helmholtz_free_energy_per_link - helmholtz_free_energy_per_link_0 -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::relative::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_small * (1.0 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
nondimensional_helmholtz_free_energy_0 = model.nondimensional_helmholtz_free_energy(
ZERO,
nondimensional_potential_stiffness,
temperature,
)
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
residual_abs =
nondimensional_helmholtz_free_energy - nondimensional_helmholtz_free_energy_0 -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::relative::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_small * (1.0 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
nondimensional_helmholtz_free_energy_per_link_0 =
model.nondimensional_helmholtz_free_energy_per_link(
ZERO,
nondimensional_potential_stiffness,
temperature,
)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
residual_abs =
nondimensional_helmholtz_free_energy_per_link -
nondimensional_helmholtz_free_energy_per_link_0 -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::relative::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
gibbs_free_energy =
model.gibbs_free_energy(potential_distance, potential_stiffness, temperature)
gibbs_free_energy_0 = model.gibbs_free_energy(
ZERO * number_of_links * link_length,
potential_stiffness,
temperature,
)
relative_gibbs_free_energy = model.relative_gibbs_free_energy(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs = gibbs_free_energy - gibbs_free_energy_0 - relative_gibbs_free_energy
residual_rel = residual_abs / gibbs_free_energy_0
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::relative::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
)
gibbs_free_energy_per_link_0 = model.gibbs_free_energy_per_link(
ZERO * number_of_links * link_length,
potential_stiffness,
temperature,
)
relative_gibbs_free_energy_per_link = model.relative_gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs =
gibbs_free_energy_per_link - gibbs_free_energy_per_link_0 -
relative_gibbs_free_energy_per_link
residual_rel = residual_abs / gibbs_free_energy_per_link_0
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::relative::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_gibbs_free_energy = model.nondimensional_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
nondimensional_gibbs_free_energy_0 = model.nondimensional_gibbs_free_energy(
ZERO,
nondimensional_potential_stiffness,
temperature,
)
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
residual_abs =
nondimensional_gibbs_free_energy - nondimensional_gibbs_free_energy_0 -
nondimensional_relative_gibbs_free_energy
residual_rel = residual_abs / nondimensional_gibbs_free_energy_0
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::relative::nondimensional_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
nondimensional_gibbs_free_energy_per_link_0 =
model.nondimensional_gibbs_free_energy_per_link(
ZERO,
nondimensional_potential_stiffness,
temperature,
)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
residual_abs =
nondimensional_gibbs_free_energy_per_link -
nondimensional_gibbs_free_energy_per_link_0 -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link_0
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::zero::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
relative_helmholtz_free_energy_0 = model.relative_helmholtz_free_energy(
ZERO * number_of_links * link_length,
potential_stiffness,
temperature,
)
@test abs(relative_helmholtz_free_energy_0) <=
ZERO * number_of_links * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::zero::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
relative_helmholtz_free_energy_per_link_0 =
model.relative_helmholtz_free_energy_per_link(
ZERO * number_of_links * link_length,
potential_stiffness,
temperature,
)
@test abs(relative_helmholtz_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::zero::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_0 =
model.nondimensional_relative_helmholtz_free_energy(
ZERO,
nondimensional_potential_stiffness,
)
@test abs(nondimensional_relative_helmholtz_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::zero::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_per_link_0 =
model.nondimensional_relative_helmholtz_free_energy_per_link(
ZERO,
nondimensional_potential_stiffness,
)
@test abs(nondimensional_relative_helmholtz_free_energy_per_link_0) <= ZERO
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::zero::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
relative_gibbs_free_energy_0 = model.relative_gibbs_free_energy(
ZERO * number_of_links * link_length,
potential_stiffness,
temperature,
)
@test abs(relative_gibbs_free_energy_0) <=
ZERO * number_of_links * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::zero::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
relative_gibbs_free_energy_per_link_0 = model.relative_gibbs_free_energy_per_link(
ZERO * number_of_links * link_length,
potential_stiffness,
temperature,
)
@test abs(relative_gibbs_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::zero::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy_0 =
model.nondimensional_relative_gibbs_free_energy(
ZERO,
nondimensional_potential_stiffness,
)
@test abs(nondimensional_relative_gibbs_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::zero::nondimensional_relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy_per_link_0 =
model.nondimensional_relative_gibbs_free_energy_per_link(
ZERO,
nondimensional_potential_stiffness,
)
@test abs(nondimensional_relative_gibbs_free_energy_per_link_0) <= ZERO
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::connection::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_small
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
force = model.force(potential_distance, potential_stiffness, temperature)
h = parameters.rel_tol * number_of_links * link_length
force_from_derivative =
(
model.relative_helmholtz_free_energy(
potential_distance + 0.5 * h,
potential_stiffness,
temperature,
) - model.relative_helmholtz_free_energy(
potential_distance - 0.5 * h,
potential_stiffness,
temperature,
)
) / h
residual_abs = force - force_from_derivative
residual_rel = residual_abs / force
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::connection::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_small
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force = model.nondimensional_force(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
h = parameters.rel_tol
nondimensional_force_from_derivative =
(
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_potential_distance + 0.5 * h,
nondimensional_potential_stiffness,
) - model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_potential_distance - 0.5 * h,
nondimensional_potential_stiffness,
)
) / h
residual_abs = nondimensional_force - nondimensional_force_from_derivative
residual_rel = residual_abs / nondimensional_force
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::connection::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
end_to_end_length =
model.end_to_end_length(potential_distance, potential_stiffness, temperature)
h = parameters.rel_tol * number_of_links * link_length
end_to_end_length_from_derivative =
-1.0 / potential_stiffness * (
model.relative_gibbs_free_energy(
potential_distance + 0.5 * h,
potential_stiffness,
temperature,
) - model.relative_gibbs_free_energy(
potential_distance - 0.5 * h,
potential_stiffness,
temperature,
)
) / h
residual_abs = end_to_end_length - end_to_end_length_from_derivative
residual_rel = residual_abs / end_to_end_length
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::connection::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
end_to_end_length_per_link = model.end_to_end_length_per_link(
potential_distance,
potential_stiffness,
temperature,
)
h = parameters.rel_tol * number_of_links * link_length
end_to_end_length_per_link_from_derivative =
-1.0 / potential_stiffness * (
model.relative_gibbs_free_energy_per_link(
potential_distance + 0.5 * h,
potential_stiffness,
temperature,
) - model.relative_gibbs_free_energy_per_link(
potential_distance - 0.5 * h,
potential_stiffness,
temperature,
)
) / h
residual_abs =
end_to_end_length_per_link - end_to_end_length_per_link_from_derivative
residual_rel = residual_abs / end_to_end_length_per_link
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::connection::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
nondimensional_end_to_end_length = model.nondimensional_end_to_end_length(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
h = parameters.rel_tol
nondimensional_end_to_end_length_from_derivative =
-1.0 / number_of_links / nondimensional_potential_stiffness * (
model.nondimensional_relative_gibbs_free_energy(
nondimensional_potential_distance + 0.5 * h,
nondimensional_potential_stiffness,
) - model.nondimensional_relative_gibbs_free_energy(
nondimensional_potential_distance - 0.5 * h,
nondimensional_potential_stiffness,
)
) / h
residual_abs =
nondimensional_end_to_end_length -
nondimensional_end_to_end_length_from_derivative
residual_rel = residual_abs / nondimensional_end_to_end_length
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::connection::nondimensional_end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
h = parameters.rel_tol
nondimensional_end_to_end_length_per_link_from_derivative =
-1.0 / number_of_links / nondimensional_potential_stiffness * (
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_potential_distance + 0.5 * h,
nondimensional_potential_stiffness,
) - model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_potential_distance - 0.5 * h,
nondimensional_potential_stiffness,
)
) / h
residual_abs =
nondimensional_end_to_end_length_per_link -
nondimensional_end_to_end_length_per_link_from_derivative
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::strong_potential::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(end_to_end_length)
return (
model.force(end_to_end_length, potential_stiffness, temperature) -
model.asymptotic.strong_potential.force(
end_to_end_length,
potential_stiffness,
temperature,
)
)^2
end
function integrand_denominator(end_to_end_length)
return model.force(end_to_end_length, potential_stiffness, temperature)^2
end
numerator = integrate(
integrand_numerator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope / 2.0 + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::strong_potential::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_end_to_end_length_per_link)
return (
model.nondimensional_force(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
) - model.asymptotic.strong_potential.nondimensional_force(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
)
)^2
end
function integrand_denominator(nondimensional_end_to_end_length_per_link)
return model.nondimensional_force(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
)^2
end
numerator = integrate(
integrand_numerator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope / 2.0 + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::strong_potential::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(end_to_end_length)
return (
model.helmholtz_free_energy(
end_to_end_length,
potential_stiffness,
temperature,
) - model.helmholtz_free_energy(
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
potential_stiffness,
temperature,
) - model.asymptotic.strong_potential.helmholtz_free_energy(
end_to_end_length,
potential_stiffness,
temperature,
) + model.asymptotic.strong_potential.helmholtz_free_energy(
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
potential_stiffness,
temperature,
)
)^2
end
function integrand_denominator(end_to_end_length)
return (
model.helmholtz_free_energy(
end_to_end_length,
potential_stiffness,
temperature,
) - model.helmholtz_free_energy(
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
potential_stiffness,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope / 2.0 + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::strong_potential::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(end_to_end_length)
return (
model.helmholtz_free_energy_per_link(
end_to_end_length,
potential_stiffness,
temperature,
) - model.helmholtz_free_energy_per_link(
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
potential_stiffness,
temperature,
) - model.asymptotic.strong_potential.helmholtz_free_energy_per_link(
end_to_end_length,
potential_stiffness,
temperature,
) + model.asymptotic.strong_potential.helmholtz_free_energy_per_link(
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
potential_stiffness,
temperature,
)
)^2
end
function integrand_denominator(end_to_end_length)
return (
model.helmholtz_free_energy_per_link(
end_to_end_length,
potential_stiffness,
temperature,
) - model.helmholtz_free_energy_per_link(
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
potential_stiffness,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope / 2.0 + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::strong_potential::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(end_to_end_length)
return (
model.relative_helmholtz_free_energy(
end_to_end_length,
potential_stiffness,
temperature,
) - model.relative_helmholtz_free_energy(
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
potential_stiffness,
temperature,
) - model.asymptotic.strong_potential.relative_helmholtz_free_energy(
end_to_end_length,
potential_stiffness,
temperature,
) + model.asymptotic.strong_potential.relative_helmholtz_free_energy(
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
potential_stiffness,
temperature,
)
)^2
end
function integrand_denominator(end_to_end_length)
return (
model.relative_helmholtz_free_energy(
end_to_end_length,
potential_stiffness,
temperature,
) - model.relative_helmholtz_free_energy(
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
potential_stiffness,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope / 2.0 + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::strong_potential::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(end_to_end_length)
return (
model.relative_helmholtz_free_energy_per_link(
end_to_end_length,
potential_stiffness,
temperature,
) - model.relative_helmholtz_free_energy_per_link(
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
potential_stiffness,
temperature,
) -
model.asymptotic.strong_potential.relative_helmholtz_free_energy_per_link(
end_to_end_length,
potential_stiffness,
temperature,
) +
model.asymptotic.strong_potential.relative_helmholtz_free_energy_per_link(
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
potential_stiffness,
temperature,
)
)^2
end
function integrand_denominator(end_to_end_length)
return (
model.relative_helmholtz_free_energy_per_link(
end_to_end_length,
potential_stiffness,
temperature,
) - model.relative_helmholtz_free_energy_per_link(
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
potential_stiffness,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope / 2.0 + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::strong_potential::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_end_to_end_length_per_link)
return (
model.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
temperature,
) - model.nondimensional_helmholtz_free_energy(
parameters.nondimensional_potential_distance_small,
nondimensional_potential_stiffness,
temperature,
) -
model.asymptotic.strong_potential.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
temperature,
) +
model.asymptotic.strong_potential.nondimensional_helmholtz_free_energy(
parameters.nondimensional_potential_distance_small,
nondimensional_potential_stiffness,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_end_to_end_length_per_link)
return (
model.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
temperature,
) - model.nondimensional_helmholtz_free_energy(
parameters.nondimensional_potential_distance_small,
nondimensional_potential_stiffness,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope / 2.0 + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::strong_potential::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_end_to_end_length_per_link)
return (
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
temperature,
) - model.nondimensional_helmholtz_free_energy_per_link(
parameters.nondimensional_potential_distance_small,
nondimensional_potential_stiffness,
temperature,
) -
model.asymptotic.strong_potential.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
temperature,
) +
model.asymptotic.strong_potential.nondimensional_helmholtz_free_energy_per_link(
parameters.nondimensional_potential_distance_small,
nondimensional_potential_stiffness,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_end_to_end_length_per_link)
return (
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
temperature,
) - model.nondimensional_helmholtz_free_energy_per_link(
parameters.nondimensional_potential_distance_small,
nondimensional_potential_stiffness,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope / 2.0 + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::strong_potential::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_end_to_end_length_per_link)
return (
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
) - model.nondimensional_relative_helmholtz_free_energy(
parameters.nondimensional_potential_distance_small,
nondimensional_potential_stiffness,
) -
model.asymptotic.strong_potential.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
) +
model.asymptotic.strong_potential.nondimensional_relative_helmholtz_free_energy(
parameters.nondimensional_potential_distance_small,
nondimensional_potential_stiffness,
)
)^2
end
function integrand_denominator(nondimensional_end_to_end_length_per_link)
return (
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
) - model.nondimensional_relative_helmholtz_free_energy(
parameters.nondimensional_potential_distance_small,
nondimensional_potential_stiffness,
)
)^2
end
numerator = integrate(
integrand_numerator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope / 2.0 + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::strong_potential::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_end_to_end_length_per_link)
return (
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
) - model.nondimensional_relative_helmholtz_free_energy_per_link(
parameters.nondimensional_potential_distance_small,
nondimensional_potential_stiffness,
) -
model.asymptotic.strong_potential.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
) +
model.asymptotic.strong_potential.nondimensional_relative_helmholtz_free_energy_per_link(
parameters.nondimensional_potential_distance_small,
nondimensional_potential_stiffness,
)
)^2
end
function integrand_denominator(nondimensional_end_to_end_length_per_link)
return (
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
) - model.nondimensional_relative_helmholtz_free_energy_per_link(
parameters.nondimensional_potential_distance_small,
nondimensional_potential_stiffness,
)
)^2
end
numerator = integrate(
integrand_numerator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope / 2.0 + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::weak_potential::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return (
model.asymptotic.weak_potential.end_to_end_length(
potential_distance,
potential_stiffness,
temperature,
) - model.end_to_end_length(
potential_distance,
potential_stiffness,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return model.end_to_end_length(
potential_distance,
potential_stiffness,
temperature,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol &&
abs(residual_rel_1) <= parameters.nondimensional_potential_stiffness_small &&
abs(residual_rel_2) <=
parameters.nondimensional_potential_stiffness_small / parameters.log_log_scale
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::weak_potential::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return (
model.asymptotic.weak_potential.end_to_end_length_per_link(
potential_distance,
potential_stiffness,
temperature,
) - model.end_to_end_length_per_link(
potential_distance,
potential_stiffness,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return model.end_to_end_length_per_link(
potential_distance,
potential_stiffness,
temperature,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol &&
abs(residual_rel_1) <= parameters.nondimensional_potential_stiffness_small &&
abs(residual_rel_2) <=
parameters.nondimensional_potential_stiffness_small / parameters.log_log_scale
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::weak_potential::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_potential_distance)
return (
model.asymptotic.weak_potential.nondimensional_end_to_end_length(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
) - model.nondimensional_end_to_end_length(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
return model.nondimensional_end_to_end_length(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol &&
abs(residual_rel_1) <= parameters.nondimensional_potential_stiffness_small &&
abs(residual_rel_2) <=
parameters.nondimensional_potential_stiffness_small / parameters.log_log_scale
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::weak_potential::nondimensional_end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_potential_distance)
return (
model.asymptotic.weak_potential.nondimensional_end_to_end_length_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
) - model.nondimensional_end_to_end_length_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
return model.nondimensional_end_to_end_length_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol &&
abs(residual_rel_1) <= parameters.nondimensional_potential_stiffness_small &&
abs(residual_rel_2) <=
parameters.nondimensional_potential_stiffness_small / parameters.log_log_scale
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::weak_potential::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return (
model.asymptotic.weak_potential.gibbs_free_energy(
potential_distance,
potential_stiffness,
temperature,
) - model.asymptotic.weak_potential.gibbs_free_energy(
number_of_links *
link_length *
parameters.nondimensional_potential_distance_large_1,
potential_stiffness,
temperature,
) - model.gibbs_free_energy(
potential_distance,
potential_stiffness,
temperature,
) + model.gibbs_free_energy(
number_of_links *
link_length *
parameters.nondimensional_potential_distance_large_1,
potential_stiffness,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return (
model.gibbs_free_energy(
potential_distance,
potential_stiffness,
temperature,
) - model.gibbs_free_energy(
number_of_links *
link_length *
parameters.nondimensional_potential_distance_large_1,
potential_stiffness,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol &&
abs(residual_rel_1) <= parameters.nondimensional_potential_stiffness_small &&
abs(residual_rel_2) <=
parameters.nondimensional_potential_stiffness_small / parameters.log_log_scale
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::weak_potential::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return (
model.asymptotic.weak_potential.gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
) - model.asymptotic.weak_potential.gibbs_free_energy_per_link(
number_of_links *
link_length *
parameters.nondimensional_potential_distance_large_1,
potential_stiffness,
temperature,
) - model.gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
) + model.gibbs_free_energy_per_link(
number_of_links *
link_length *
parameters.nondimensional_potential_distance_large_1,
potential_stiffness,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return (
model.gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
) - model.gibbs_free_energy_per_link(
number_of_links *
link_length *
parameters.nondimensional_potential_distance_large_1,
potential_stiffness,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol &&
abs(residual_rel_1) <= parameters.nondimensional_potential_stiffness_small &&
abs(residual_rel_2) <=
parameters.nondimensional_potential_stiffness_small / parameters.log_log_scale
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::weak_potential::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return (
model.asymptotic.weak_potential.relative_gibbs_free_energy(
potential_distance,
potential_stiffness,
temperature,
) - model.asymptotic.weak_potential.relative_gibbs_free_energy(
number_of_links *
link_length *
parameters.nondimensional_potential_distance_large_1,
potential_stiffness,
temperature,
) - model.relative_gibbs_free_energy(
potential_distance,
potential_stiffness,
temperature,
) + model.relative_gibbs_free_energy(
number_of_links *
link_length *
parameters.nondimensional_potential_distance_large_1,
potential_stiffness,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return (
model.relative_gibbs_free_energy(
potential_distance,
potential_stiffness,
temperature,
) - model.relative_gibbs_free_energy(
number_of_links *
link_length *
parameters.nondimensional_potential_distance_large_1,
potential_stiffness,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol &&
abs(residual_rel_1) <= parameters.nondimensional_potential_stiffness_small &&
abs(residual_rel_2) <=
parameters.nondimensional_potential_stiffness_small / parameters.log_log_scale
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::weak_potential::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return (
model.asymptotic.weak_potential.relative_gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
) -
model.asymptotic.weak_potential.relative_gibbs_free_energy_per_link(
number_of_links *
link_length *
parameters.nondimensional_potential_distance_large_1,
potential_stiffness,
temperature,
) - model.relative_gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
) + model.relative_gibbs_free_energy_per_link(
number_of_links *
link_length *
parameters.nondimensional_potential_distance_large_1,
potential_stiffness,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return (
model.relative_gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
) - model.relative_gibbs_free_energy_per_link(
number_of_links *
link_length *
parameters.nondimensional_potential_distance_large_1,
potential_stiffness,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol &&
abs(residual_rel_1) <= parameters.nondimensional_potential_stiffness_small &&
abs(residual_rel_2) <=
parameters.nondimensional_potential_stiffness_small / parameters.log_log_scale
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::weak_potential::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_potential_distance)
return (
model.asymptotic.weak_potential.nondimensional_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
) - model.asymptotic.weak_potential.nondimensional_gibbs_free_energy(
parameters.nondimensional_potential_distance_large_1,
nondimensional_potential_stiffness,
temperature,
) - model.nondimensional_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
) + model.nondimensional_gibbs_free_energy(
parameters.nondimensional_potential_distance_large_1,
nondimensional_potential_stiffness,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
return (
model.nondimensional_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
) - model.nondimensional_gibbs_free_energy(
parameters.nondimensional_potential_distance_large_1,
nondimensional_potential_stiffness,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol &&
abs(residual_rel_1) <= parameters.nondimensional_potential_stiffness_small &&
abs(residual_rel_2) <=
parameters.nondimensional_potential_stiffness_small / parameters.log_log_scale
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::weak_potential::nondimensional_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_potential_distance_ref =
parameters.nondimensional_potential_distance_large_1
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_potential_distance)
nondimensional_force = model.asymptotic.weak_potential.nondimensional_force(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
return (
model.asymptotic.weak_potential.nondimensional_gibbs_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
) -
model.asymptotic.weak_potential.nondimensional_gibbs_free_energy_per_link(
parameters.nondimensional_potential_distance_large_1,
nondimensional_potential_stiffness,
temperature,
) - model.nondimensional_gibbs_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
) + model.nondimensional_gibbs_free_energy_per_link(
parameters.nondimensional_potential_distance_large_1,
nondimensional_potential_stiffness,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
return (
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
) - model.nondimensional_gibbs_free_energy_per_link(
parameters.nondimensional_potential_distance_large_1,
nondimensional_potential_stiffness,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol &&
abs(residual_rel_1) <= parameters.nondimensional_potential_stiffness_small &&
abs(residual_rel_2) <=
parameters.nondimensional_potential_stiffness_small / parameters.log_log_scale
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::weak_potential::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_potential_distance)
return (
model.asymptotic.weak_potential.nondimensional_relative_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
) -
model.asymptotic.weak_potential.nondimensional_relative_gibbs_free_energy(
parameters.nondimensional_potential_distance_large_1,
nondimensional_potential_stiffness,
) - model.nondimensional_relative_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
) + model.nondimensional_relative_gibbs_free_energy(
parameters.nondimensional_potential_distance_large_1,
nondimensional_potential_stiffness,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
return (
model.nondimensional_relative_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
) - model.nondimensional_relative_gibbs_free_energy(
parameters.nondimensional_potential_distance_large_1,
nondimensional_potential_stiffness,
)
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol &&
abs(residual_rel_1) <= parameters.nondimensional_potential_stiffness_small &&
abs(residual_rel_2) <=
parameters.nondimensional_potential_stiffness_small / parameters.log_log_scale
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::test::weak_potential::nondimensional_relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_potential_distance)
return (
model.asymptotic.weak_potential.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
) -
model.asymptotic.weak_potential.nondimensional_relative_gibbs_free_energy_per_link(
parameters.nondimensional_potential_distance_large_1,
nondimensional_potential_stiffness,
) - model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
) + model.nondimensional_relative_gibbs_free_energy_per_link(
parameters.nondimensional_potential_distance_large_1,
nondimensional_potential_stiffness,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
return (
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
) - model.nondimensional_relative_gibbs_free_energy_per_link(
parameters.nondimensional_potential_distance_large_1,
nondimensional_potential_stiffness,
)
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol &&
abs(residual_rel_1) <= parameters.nondimensional_potential_stiffness_small &&
abs(residual_rel_2) <=
parameters.nondimensional_potential_stiffness_small / parameters.log_log_scale
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 1724 | """
The freely-jointed chain (FJC) model thermodynamics in the modified canonical ensemble approximated using an asymptotic approach.
"""
module Asymptotic
using DocStringExtensions
using .......Polymers: PROJECT_ROOT
include("strong_potential/mod.jl")
include("weak_potential/mod.jl")
"""
The structure of the thermodynamics of the FJC model in the modified canonical ensemble approximated using an asymptotic approach.
$(FIELDS)
"""
struct FJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The thermodynamic functions of the model in the modified canonical ensemble approximated using an asymptotic approach approximated using an asymptotic approach valid for strong potentials.
"""
strong_potential::Any
"""
The thermodynamic functions of the model in the modified canonical ensemble approximated using an asymptotic approach approximated using an asymptotic approach valid for weak potentials.
"""
weak_potential::Any
end
"""
Initializes and returns an instance of the thermodynamics of the FJC model in the modified canonical ensemble approximated using an asymptotic approach.
$(TYPEDSIGNATURES)
"""
function FJC(number_of_links::UInt8, link_length::Float64, hinge_mass::Float64)
return FJC(
number_of_links,
link_length,
hinge_mass,
StrongPotential.FJC(number_of_links, link_length, hinge_mass),
WeakPotential.FJC(number_of_links, link_length, hinge_mass),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 2756 | module Test
using Test
using Polymers.Physics.SingleChain: parameters
using Polymers.Physics.SingleChain.Fjc.Thermodynamics.ModifiedCanonical.Asymptotic: FJC
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::test::base::init" begin
@test isa(
FJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
),
Any,
)
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test FJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test FJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test FJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test all(
FJC(number_of_links, link_length, hinge_mass).number_of_links ==
number_of_links &&
FJC(number_of_links, link_length, hinge_mass).link_length == link_length &&
FJC(number_of_links, link_length, hinge_mass).hinge_mass == hinge_mass,
)
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 21386 | """
The freely-jointed chain (FJC) model thermodynamics in the modified canonical ensemble approximated using an asymptotic approach valid for strong potentials.
"""
module StrongPotential
using DocStringExtensions
using ........Polymers: PROJECT_ROOT
"""
The structure of the thermodynamics of the FJC model in the modified canonical ensemble approximated using an asymptotic approach valid for strong potentials.
$(FIELDS)
"""
struct FJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The expected force ``f`` as a function of the applied potential distance, potential stiffness, and temperature ``T``.
"""
force::Function
"""
The expected nondimensional force ``\\eta`` as a function of the applied nondimensional potential distance and nondimensional potential stiffness.
"""
nondimensional_force::Function
"""
The Helmholtz free energy ``\\psi`` as a function of the applied potential distance, potential stiffness, and temperature ``T``.
"""
helmholtz_free_energy::Function
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied potential distance, potential stiffness, and temperature ``T``.
"""
helmholtz_free_energy_per_link::Function
"""
The relative Helmholtz free energy ``\\Delta\\psi\\equiv\\psi(\\xi,T)-\\psi(0,T)`` as a function of the applied potential distance, potential stiffness, and temperature ``T``.
"""
relative_helmholtz_free_energy::Function
"""
The relative Helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied potential distance, potential stiffness, and temperature ``T``.
"""
relative_helmholtz_free_energy_per_link::Function
"""
The nondimensional Helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional potential distance, nondimensional potential stiffness, and temperature ``T``.
"""
nondimensional_helmholtz_free_energy::Function
"""
The nondimensional Helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional potential distance, nondimensional potential stiffness, and temperature ``T``.
"""
nondimensional_helmholtz_free_energy_per_link::Function
"""
The nondimensional relative Helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional potential distance and nondimensional potential stiffness.
"""
nondimensional_relative_helmholtz_free_energy::Function
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional potential distance and nondimensional potential stiffness.
"""
nondimensional_relative_helmholtz_free_energy_per_link::Function
end
"""
The expected force ``f`` as a function of the applied potential distance, potential stiffness, and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``.
$(TYPEDSIGNATURES)
"""
function force(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
potential_distance::Union{Float64,Vector,Matrix,Array},
potential_stiffness::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_asymptotic_strong_potential_force,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
),
number_of_links,
link_length,
potential_distance,
potential_stiffness,
temperature,
)
end
"""
The expected nondimensional force ``\\eta`` as a function of the applied nondimensional potential distance and nondimensional potential stiffness,
parameterized by the number of links ``N_b``.
$(TYPEDSIGNATURES)
"""
function nondimensional_force(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_potential_distance::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_stiffness::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_asymptotic_strong_potential_nondimensional_force,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
),
number_of_links,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
end
"""
The Helmholtz free energy ``\\psi`` as a function of the applied potential distance, potential stiffness, and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
potential_distance::Union{Float64,Vector,Matrix,Array},
potential_stiffness::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_asymptotic_strong_potential_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
potential_distance,
potential_stiffness,
temperature,
)
end
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied potential distance, potential stiffness, and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
potential_distance::Union{Float64,Vector,Matrix,Array},
potential_stiffness::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_asymptotic_strong_potential_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
potential_distance,
potential_stiffness,
temperature,
)
end
"""
The relative Helmholtz free energy ``\\Delta\\psi\\equiv\\psi(\\xi,T)-\\psi(0,T)`` as a function of the applied potential distance, potential stiffness, and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
potential_distance::Union{Float64,Vector,Matrix,Array},
potential_stiffness::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_asymptotic_strong_potential_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
),
number_of_links,
link_length,
potential_distance,
potential_stiffness,
temperature,
)
end
"""
The relative Helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied potential distance, potential stiffness, and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
potential_distance::Union{Float64,Vector,Matrix,Array},
potential_stiffness::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_asymptotic_strong_potential_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
),
number_of_links,
link_length,
potential_distance,
potential_stiffness,
temperature,
)
end
"""
The nondimensional Helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional potential distance, nondimensional potential stiffness, and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_distance::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_stiffness::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_asymptotic_strong_potential_nondimensional_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
end
"""
The nondimensional Helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional potential distance, nondimensional potential stiffness, and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_distance::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_stiffness::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_asymptotic_strong_potential_nondimensional_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
end
"""
The nondimensional relative Helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional potential distance and nondimensional potential stiffness,
parameterized by the number of links ``N_b``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_potential_distance::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_stiffness::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_asymptotic_strong_potential_nondimensional_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
),
number_of_links,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
end
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional potential distance and nondimensional potential stiffness,
parameterized by the number of links ``N_b``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_potential_distance::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_stiffness::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_asymptotic_strong_potential_nondimensional_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
),
number_of_links,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
end
"""
Initializes and returns an instance of the thermodynamics of the FJC model in the modified canonical ensemble approximated using an asymptotic approach valid for strong potentials.
$(TYPEDSIGNATURES)
"""
function FJC(number_of_links::UInt8, link_length::Float64, hinge_mass::Float64)
return FJC(
number_of_links,
link_length,
hinge_mass,
(potential_distance, potential_stiffness, temperature) -> force(
number_of_links,
link_length,
potential_distance,
potential_stiffness,
temperature,
),
(nondimensional_potential_distance, nondimensional_potential_stiffness) ->
nondimensional_force(
number_of_links,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
),
(potential_distance, potential_stiffness, temperature) -> helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
potential_distance,
potential_stiffness,
temperature,
),
(potential_distance, potential_stiffness, temperature) ->
helmholtz_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
potential_distance,
potential_stiffness,
temperature,
),
(potential_distance, potential_stiffness, temperature) ->
relative_helmholtz_free_energy(
number_of_links,
link_length,
potential_distance,
potential_stiffness,
temperature,
),
(potential_distance, potential_stiffness, temperature) ->
relative_helmholtz_free_energy_per_link(
number_of_links,
link_length,
potential_distance,
potential_stiffness,
temperature,
),
(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
) -> nondimensional_helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
),
(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
) -> nondimensional_helmholtz_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
),
(nondimensional_potential_distance, nondimensional_potential_stiffness) ->
nondimensional_relative_helmholtz_free_energy(
number_of_links,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
),
(nondimensional_potential_distance, nondimensional_potential_stiffness) ->
nondimensional_relative_helmholtz_free_energy_per_link(
number_of_links,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 38651 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ZERO, parameters
using Polymers.Physics.SingleChain.Fjc.Thermodynamics.ModifiedCanonical.Asymptotic.StrongPotential:
FJC
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::strong_potential::test::base::init" begin
@test isa(
FJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
),
Any,
)
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::strong_potential::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test FJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::strong_potential::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test FJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::strong_potential::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test FJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::strong_potential::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test all(
FJC(number_of_links, link_length, hinge_mass).number_of_links ==
number_of_links &&
FJC(number_of_links, link_length, hinge_mass).link_length == link_length &&
FJC(number_of_links, link_length, hinge_mass).hinge_mass == hinge_mass,
)
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::strong_potential::test::nondimensional::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_small * (1.0 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force = model.nondimensional_force(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
force = model.force(potential_distance, potential_stiffness, temperature)
residual_abs =
force / BOLTZMANN_CONSTANT / temperature * link_length - nondimensional_force
residual_rel = residual_abs / nondimensional_force
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::strong_potential::test::nondimensional::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_small * (1.0 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
helmholtz_free_energy = model.helmholtz_free_energy(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs =
helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::strong_potential::test::nondimensional::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_small * (1.0 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
helmholtz_free_energy_per_link = model.helmholtz_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs =
helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::strong_potential::test::nondimensional::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_small * (1.0 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
relative_helmholtz_free_energy = model.relative_helmholtz_free_energy(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs =
relative_helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::strong_potential::test::nondimensional::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_small * (1.0 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs =
relative_helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::strong_potential::test::per_link::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_small * (1.0 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
helmholtz_free_energy = model.helmholtz_free_energy(
potential_distance,
potential_stiffness,
temperature,
)
helmholtz_free_energy_per_link = model.helmholtz_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs =
helmholtz_free_energy / number_of_links - helmholtz_free_energy_per_link
residual_rel = residual_abs / helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::strong_potential::test::per_link::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_small * (1.0 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
relative_helmholtz_free_energy = model.relative_helmholtz_free_energy(
potential_distance,
potential_stiffness,
temperature,
)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs =
relative_helmholtz_free_energy / number_of_links -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::strong_potential::test::per_link::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_small * (1.0 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy / number_of_links -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::strong_potential::test::per_link::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_small * (1.0 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy / number_of_links -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::strong_potential::test::relative::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_small * (1.0 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
helmholtz_free_energy = model.helmholtz_free_energy(
potential_distance,
potential_stiffness,
temperature,
)
helmholtz_free_energy_0 = model.helmholtz_free_energy(
ZERO * number_of_links * link_length,
potential_stiffness,
temperature,
)
relative_helmholtz_free_energy = model.relative_helmholtz_free_energy(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs =
helmholtz_free_energy - helmholtz_free_energy_0 - relative_helmholtz_free_energy
residual_rel = residual_abs / relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::strong_potential::test::relative::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_small * (1.0 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
helmholtz_free_energy_per_link = model.helmholtz_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
)
helmholtz_free_energy_per_link_0 = model.helmholtz_free_energy_per_link(
ZERO * number_of_links * link_length,
potential_stiffness,
temperature,
)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs =
helmholtz_free_energy_per_link - helmholtz_free_energy_per_link_0 -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::strong_potential::test::relative::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_small * (1.0 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
nondimensional_helmholtz_free_energy_0 = model.nondimensional_helmholtz_free_energy(
ZERO,
nondimensional_potential_stiffness,
temperature,
)
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
residual_abs =
nondimensional_helmholtz_free_energy - nondimensional_helmholtz_free_energy_0 -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::strong_potential::test::relative::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_small * (1.0 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
nondimensional_helmholtz_free_energy_per_link_0 =
model.nondimensional_helmholtz_free_energy_per_link(
ZERO,
nondimensional_potential_stiffness,
temperature,
)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
residual_abs =
nondimensional_helmholtz_free_energy_per_link -
nondimensional_helmholtz_free_energy_per_link_0 -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::strong_potential::test::zero::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
relative_helmholtz_free_energy_0 = model.relative_helmholtz_free_energy(
ZERO * number_of_links * link_length,
potential_stiffness,
temperature,
)
@test abs(relative_helmholtz_free_energy_0) <=
ZERO * number_of_links * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::strong_potential::test::zero::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
relative_helmholtz_free_energy_per_link_0 =
model.relative_helmholtz_free_energy_per_link(
ZERO * number_of_links * link_length,
potential_stiffness,
temperature,
)
@test abs(relative_helmholtz_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::strong_potential::test::zero::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_0 =
model.nondimensional_relative_helmholtz_free_energy(
ZERO,
nondimensional_potential_stiffness,
)
@test abs(nondimensional_relative_helmholtz_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::strong_potential::test::zero::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_per_link_0 =
model.nondimensional_relative_helmholtz_free_energy_per_link(
ZERO,
nondimensional_potential_stiffness,
)
@test abs(nondimensional_relative_helmholtz_free_energy_per_link_0) <= ZERO
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::strong_potential::test::connection::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_small
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
force = model.force(potential_distance, potential_stiffness, temperature)
h = parameters.rel_tol * number_of_links * link_length
force_from_derivative =
(
model.relative_helmholtz_free_energy(
potential_distance + 0.5 * h,
potential_stiffness,
temperature,
) - model.relative_helmholtz_free_energy(
potential_distance - 0.5 * h,
potential_stiffness,
temperature,
)
) / h
residual_abs = force - force_from_derivative
residual_rel = residual_abs / force
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::strong_potential::test::connection::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_small
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force = model.nondimensional_force(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
h = parameters.rel_tol
nondimensional_force_from_derivative =
(
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_potential_distance + 0.5 * h,
nondimensional_potential_stiffness,
) - model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_potential_distance - 0.5 * h,
nondimensional_potential_stiffness,
)
) / h
residual_abs = nondimensional_force - nondimensional_force_from_derivative
residual_rel = residual_abs / nondimensional_force
@test abs(residual_rel) <= h
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 27865 | """
The freely-jointed chain (FJC) model thermodynamics in the modified canonical ensemble approximated using an asymptotic approach valid for weak potentials.
"""
module WeakPotential
using DocStringExtensions
using ........Polymers: PROJECT_ROOT
"""
The structure of the thermodynamics of the FJC model in the modified canonical ensemble approximated using an asymptotic approach valid for weak potentials.
$(FIELDS)
"""
struct FJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The expected end-to-end length ``\\xi`` as a function of the applied potential distance, potential stiffness, and temperature ``T``.
"""
end_to_end_length::Function
"""
The expected end-to-end length per link ``\\xi/N_b=\\ell_b\\gamma`` as a function of the applied potential distance, potential stiffness, and temperature ``T``.
"""
end_to_end_length_per_link::Function
"""
The expected nondimensional end-to-end length ``N_b\\gamma=\\xi/\\ell_b`` as a function of the applied nondimensional potential distance and nondimensional potential stiffness.
"""
nondimensional_end_to_end_length::Function
"""
The expected nondimensional end-to-end length per link ``\\gamma\\equiv\\xi/N_b\\ell_b`` as a function of the applied nondimensional potential distance and nondimensional potential stiffness.
"""
nondimensional_end_to_end_length_per_link::Function
"""
The expected force ``f`` as a function of the applied potential distance and potential stiffness.
"""
force::Function
"""
The expected nondimensional force ``\\eta`` as a function of the applied nondimensional potential distance and nondimensional potential stiffness.
"""
nondimensional_force::Function
"""
The Gibbs free energy ``\\varphi`` as a function of the applied potential distance, potential stiffness, and temperature ``T``.
"""
gibbs_free_energy::Function
"""
The Gibbs free energy per link ``\\varphi/N_b`` as a function of the applied potential distance, potential stiffness, and temperature ``T``.
"""
gibbs_free_energy_per_link::Function
"""
The relative Gibbs free energy ``\\Delta\\varphi\\equiv\\varphi(f,T)-\\varphi(0,T)`` as a function of the applied potential distance, potential stiffness, and temperature ``T``.
"""
relative_gibbs_free_energy::Function
"""
The relative Gibbs free energy per link ``\\Delta\\varphi/N_b`` as a function of the applied potential distance, potential stiffness, and temperature ``T``.
"""
relative_gibbs_free_energy_per_link::Function
"""
The nondimensional Gibbs free energy ``N_b\\varrho=\\beta\\varphi`` as a function of the applied nondimensional potential distance, nondimensional potential stiffness, and temperature ``T``.
"""
nondimensional_gibbs_free_energy::Function
"""
The nondimensional Gibbs free energy per link ``\\varrho\\equiv\\beta\\varphi/N_b`` as a function of the applied nondimensional potential distance, nondimensional potential stiffness, and temperature ``T``.
"""
nondimensional_gibbs_free_energy_per_link::Function
"""
The nondimensional relative Gibbs free energy ``N_b\\Delta\\varrho=\\beta\\Delta\\varphi`` as a function of the applied nondimensional potential distance and nondimensional potential stiffness.
"""
nondimensional_relative_gibbs_free_energy::Function
"""
The nondimensional relative Gibbs free energy per link ``\\Delta\\varrho\\equiv\\beta\\Delta\\varphi/N_b`` as a function of the applied nondimensional potential distance and nondimensional potential stiffness.
"""
nondimensional_relative_gibbs_free_energy_per_link::Function
end
"""
The expected end-to-end length ``\\xi`` as a function of the applied potential distance, potential stiffness, and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``.
$(TYPEDSIGNATURES)
"""
function end_to_end_length(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
potential_distance::Union{Float64,Vector,Matrix,Array},
potential_stiffness::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_asymptotic_weak_potential_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
),
number_of_links,
link_length,
potential_distance,
potential_stiffness,
temperature,
)
end
"""
The expected end-to-end length per link ``\\xi/N_b=\\ell_b\\gamma`` as a function of the applied potential distance, potential stiffness, and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``.
$(TYPEDSIGNATURES)
"""
function end_to_end_length_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
potential_distance::Union{Float64,Vector,Matrix,Array},
potential_stiffness::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_asymptotic_weak_potential_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
),
number_of_links,
link_length,
potential_distance,
potential_stiffness,
temperature,
)
end
"""
The expected nondimensional end-to-end length ``N_b\\gamma\\equiv\\xi/\\ell_b`` as a function of the applied nondimensional potential distance and nondimensional potential stiffness,
parameterized by the number of links ``N_b``.
$(TYPEDSIGNATURES)
"""
function nondimensional_end_to_end_length(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_potential_distance::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_stiffness::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_asymptotic_weak_potential_nondimensional_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
),
number_of_links,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
end
"""
The expected nondimensional end-to-end length ``\\gamma\\equiv\\xi/N_b\\ell_b`` as a function of the applied nondimensional potential distance and nondimensional potential stiffness,
parameterized by the number of links ``N_b``.
$(TYPEDSIGNATURES)
"""
function nondimensional_end_to_end_length_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_potential_distance::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_stiffness::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_asymptotic_weak_potential_nondimensional_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
),
number_of_links,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
end
"""
The expected force ``f`` as a function of the applied potential distance and potential stiffness.
$(TYPEDSIGNATURES)
"""
function force(
potential_distance::Union{Float64,Vector,Matrix,Array},
potential_stiffness::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(potential_distance_i, potential_stiffness_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_asymptotic_weak_potential_force,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64),
potential_distance_i,
potential_stiffness_i,
),
potential_distance,
potential_stiffness,
)
end
"""
The expected nondimensional force ``\\eta`` as a function of the applied nondimensional potential distance and nondimensional potential stiffness.
$(TYPEDSIGNATURES)
"""
function nondimensional_force(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_potential_distance::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_stiffness::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_asymptotic_weak_potential_nondimensional_force,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
),
number_of_links,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
end
"""
The gibbs free energy ``\\psi`` as a function of the applied potential distance, potential stiffness, and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
potential_distance::Union{Float64,Vector,Matrix,Array},
potential_stiffness::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_asymptotic_weak_potential_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
potential_distance,
potential_stiffness,
temperature,
)
end
"""
The gibbs free energy per link ``\\psi/N_b`` as a function of the applied potential distance, potential stiffness, and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function gibbs_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
potential_distance::Union{Float64,Vector,Matrix,Array},
potential_stiffness::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_asymptotic_weak_potential_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
potential_distance,
potential_stiffness,
temperature,
)
end
"""
The relative gibbs free energy ``\\Delta\\psi\\equiv\\psi(\\xi,T)-\\psi(0,T)`` as a function of the applied potential distance, potential stiffness, and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
potential_distance::Union{Float64,Vector,Matrix,Array},
potential_stiffness::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_asymptotic_weak_potential_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
),
number_of_links,
link_length,
potential_distance,
potential_stiffness,
temperature,
)
end
"""
The relative gibbs free energy per link ``\\Delta\\psi/N_b`` as a function of the applied potential distance, potential stiffness, and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
potential_distance::Union{Float64,Vector,Matrix,Array},
potential_stiffness::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_asymptotic_weak_potential_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
potential_distance_i,
potential_stiffness_i,
temperature_i,
),
number_of_links,
link_length,
potential_distance,
potential_stiffness,
temperature,
)
end
"""
The nondimensional gibbs free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional potential distance, nondimensional potential stiffness, and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_distance::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_stiffness::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_asymptotic_weak_potential_nondimensional_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
end
"""
The nondimensional gibbs free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional potential distance, nondimensional potential stiffness, and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_gibbs_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_distance::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_stiffness::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_asymptotic_weak_potential_nondimensional_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
end
"""
The nondimensional relative gibbs free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional potential distance and nondimensional potential stiffness,
parameterized by the number of links ``N_b``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_potential_distance::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_stiffness::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_asymptotic_weak_potential_nondimensional_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
),
number_of_links,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
end
"""
The nondimensional relative gibbs free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional potential distance and nondimensional potential stiffness,
parameterized by the number of links ``N_b``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_potential_distance::Union{Float64,Vector,Matrix,Array},
nondimensional_potential_stiffness::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_modified_canonical_asymptotic_weak_potential_nondimensional_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_potential_distance_i,
nondimensional_potential_stiffness_i,
),
number_of_links,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
end
"""
Initializes and returns an instance of the thermodynamics of the FJC model in the modified canonical ensemble approximated using an asymptotic approach valid for weak potentials.
$(TYPEDSIGNATURES)
"""
function FJC(number_of_links::UInt8, link_length::Float64, hinge_mass::Float64)
return FJC(
number_of_links,
link_length,
hinge_mass,
(potential_distance, potential_stiffness, temperature) -> end_to_end_length(
number_of_links,
link_length,
potential_distance,
potential_stiffness,
temperature,
),
(potential_distance, potential_stiffness, temperature) ->
end_to_end_length_per_link(
number_of_links,
link_length,
potential_distance,
potential_stiffness,
temperature,
),
(nondimensional_potential_distance, nondimensional_potential_stiffness) ->
nondimensional_end_to_end_length(
number_of_links,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
),
(nondimensional_potential_distance, nondimensional_potential_stiffness) ->
nondimensional_end_to_end_length_per_link(
number_of_links,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
),
(potential_distance, potential_stiffness) ->
force(potential_distance, potential_stiffness),
(nondimensional_potential_distance, nondimensional_potential_stiffness) ->
nondimensional_force(
number_of_links,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
),
(potential_distance, potential_stiffness, temperature) -> gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
potential_distance,
potential_stiffness,
temperature,
),
(potential_distance, potential_stiffness, temperature) ->
gibbs_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
potential_distance,
potential_stiffness,
temperature,
),
(potential_distance, potential_stiffness, temperature) ->
relative_gibbs_free_energy(
number_of_links,
link_length,
potential_distance,
potential_stiffness,
temperature,
),
(potential_distance, potential_stiffness, temperature) ->
relative_gibbs_free_energy_per_link(
number_of_links,
link_length,
potential_distance,
potential_stiffness,
temperature,
),
(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
) -> nondimensional_gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
),
(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
) -> nondimensional_gibbs_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
),
(nondimensional_potential_distance, nondimensional_potential_stiffness) ->
nondimensional_relative_gibbs_free_energy(
number_of_links,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
),
(nondimensional_potential_distance, nondimensional_potential_stiffness) ->
nondimensional_relative_gibbs_free_energy_per_link(
number_of_links,
nondimensional_potential_distance,
nondimensional_potential_stiffness,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 54133 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ZERO, parameters
using Polymers.Physics.SingleChain.Fjc.Thermodynamics.ModifiedCanonical.Asymptotic.WeakPotential:
FJC
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::base::init" begin
@test isa(
FJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
),
Any,
)
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test FJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test FJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test FJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test all(
FJC(number_of_links, link_length, hinge_mass).number_of_links ==
number_of_links &&
FJC(number_of_links, link_length, hinge_mass).link_length == link_length &&
FJC(number_of_links, link_length, hinge_mass).hinge_mass == hinge_mass,
)
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::nondimensional::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_end_to_end_length = model.nondimensional_end_to_end_length(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
end_to_end_length =
model.end_to_end_length(potential_distance, potential_stiffness, temperature)
residual_abs = end_to_end_length / link_length - nondimensional_end_to_end_length
residual_rel = residual_abs / nondimensional_end_to_end_length
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::nondimensional::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
end_to_end_length_per_link = model.end_to_end_length_per_link(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs =
end_to_end_length_per_link / link_length -
nondimensional_end_to_end_length_per_link
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::nondimensional::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force = model.nondimensional_force(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
force = model.force(potential_distance, potential_stiffness)
residual_abs =
force / BOLTZMANN_CONSTANT / temperature * link_length - nondimensional_force
residual_rel = residual_abs / nondimensional_force
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::nondimensional::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_gibbs_free_energy = model.nondimensional_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
gibbs_free_energy =
model.gibbs_free_energy(potential_distance, potential_stiffness, temperature)
residual_abs =
gibbs_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_gibbs_free_energy
residual_rel = residual_abs / nondimensional_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::nondimensional::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs =
gibbs_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::nondimensional::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
relative_gibbs_free_energy = model.relative_gibbs_free_energy(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs =
relative_gibbs_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_gibbs_free_energy
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::nondimensional::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
relative_gibbs_free_energy_per_link = model.relative_gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs =
relative_gibbs_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::per_link::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
end_to_end_length =
model.end_to_end_length(potential_distance, potential_stiffness, temperature)
end_to_end_length_per_link = model.end_to_end_length_per_link(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs = end_to_end_length / number_of_links - end_to_end_length_per_link
residual_rel = residual_abs / end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::per_link::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
nondimensional_end_to_end_length = model.nondimensional_end_to_end_length(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
residual_abs =
nondimensional_end_to_end_length / number_of_links -
nondimensional_end_to_end_length_per_link
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::per_link::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
gibbs_free_energy =
model.gibbs_free_energy(potential_distance, potential_stiffness, temperature)
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs = gibbs_free_energy / number_of_links - gibbs_free_energy_per_link
residual_rel = residual_abs / gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::per_link::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
relative_gibbs_free_energy = model.relative_gibbs_free_energy(
potential_distance,
potential_stiffness,
temperature,
)
relative_gibbs_free_energy_per_link = model.relative_gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs =
relative_gibbs_free_energy / number_of_links -
relative_gibbs_free_energy_per_link
residual_rel = residual_abs / relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::per_link::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_gibbs_free_energy = model.nondimensional_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
residual_abs =
nondimensional_gibbs_free_energy / number_of_links -
nondimensional_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::per_link::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
residual_abs =
nondimensional_relative_gibbs_free_energy / number_of_links -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::relative::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
gibbs_free_energy =
model.gibbs_free_energy(potential_distance, potential_stiffness, temperature)
gibbs_free_energy_0 = model.gibbs_free_energy(
ZERO * number_of_links * link_length,
potential_stiffness,
temperature,
)
relative_gibbs_free_energy = model.relative_gibbs_free_energy(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs = gibbs_free_energy - gibbs_free_energy_0 - relative_gibbs_free_energy
residual_rel = residual_abs / gibbs_free_energy_0
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::relative::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
)
gibbs_free_energy_per_link_0 = model.gibbs_free_energy_per_link(
ZERO * number_of_links * link_length,
potential_stiffness,
temperature,
)
relative_gibbs_free_energy_per_link = model.relative_gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
)
residual_abs =
gibbs_free_energy_per_link - gibbs_free_energy_per_link_0 -
relative_gibbs_free_energy_per_link
residual_rel = residual_abs / gibbs_free_energy_per_link_0
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::relative::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_gibbs_free_energy = model.nondimensional_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
nondimensional_gibbs_free_energy_0 = model.nondimensional_gibbs_free_energy(
ZERO,
nondimensional_potential_stiffness,
temperature,
)
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
residual_abs =
nondimensional_gibbs_free_energy - nondimensional_gibbs_free_energy_0 -
nondimensional_relative_gibbs_free_energy
residual_rel = residual_abs / nondimensional_gibbs_free_energy_0
@test abs(residual_abs) <= number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::relative::nondimensional_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
)
nondimensional_gibbs_free_energy_per_link_0 =
model.nondimensional_gibbs_free_energy_per_link(
ZERO,
nondimensional_potential_stiffness,
temperature,
)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
residual_abs =
nondimensional_gibbs_free_energy_per_link -
nondimensional_gibbs_free_energy_per_link_0 -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link_0
@test abs(residual_abs) <= number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::zero::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
force_0 = model.force(ZERO, potential_stiffness)
@test abs(force_0) <= potential_stiffness * ZERO
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::zero::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
nondimensional_force_0 =
model.nondimensional_force(ZERO, nondimensional_potential_stiffness)
@test abs(nondimensional_force_0) <=
number_of_links * nondimensional_potential_stiffness * ZERO
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::zero::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
relative_gibbs_free_energy_0 = model.relative_gibbs_free_energy(
ZERO * number_of_links * link_length,
potential_stiffness,
temperature,
)
@test abs(relative_gibbs_free_energy_0) <= ZERO
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::zero::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
relative_gibbs_free_energy_per_link_0 = model.relative_gibbs_free_energy_per_link(
ZERO * number_of_links * link_length,
potential_stiffness,
temperature,
)
@test abs(relative_gibbs_free_energy_per_link_0) <= ZERO
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::zero::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy_0 =
model.nondimensional_relative_gibbs_free_energy(
ZERO,
nondimensional_potential_stiffness,
)
@test abs(nondimensional_relative_gibbs_free_energy_0) <= ZERO
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::zero::nondimensional_relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy_per_link_0 =
model.nondimensional_relative_gibbs_free_energy_per_link(
ZERO,
nondimensional_potential_stiffness,
)
@test abs(nondimensional_relative_gibbs_free_energy_per_link_0) <= ZERO
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::connection::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
end_to_end_length =
model.end_to_end_length(potential_distance, potential_stiffness, temperature)
h = parameters.rel_tol * number_of_links * link_length
end_to_end_length_from_derivative =
-1.0 / potential_stiffness * (
model.relative_gibbs_free_energy(
potential_distance + 0.5 * h,
potential_stiffness,
temperature,
) - model.relative_gibbs_free_energy(
potential_distance - 0.5 * h,
potential_stiffness,
temperature,
)
) / h
residual_abs = end_to_end_length - end_to_end_length_from_derivative
residual_rel = residual_abs / end_to_end_length
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::connection::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance =
nondimensional_potential_distance * number_of_links * link_length
potential_stiffness =
nondimensional_potential_stiffness / link_length^2 *
BOLTZMANN_CONSTANT *
temperature
end_to_end_length_per_link = model.end_to_end_length_per_link(
potential_distance,
potential_stiffness,
temperature,
)
h = parameters.rel_tol * number_of_links * link_length
end_to_end_length_per_link_from_derivative =
-1.0 / potential_stiffness * (
model.relative_gibbs_free_energy_per_link(
potential_distance + 0.5 * h,
potential_stiffness,
temperature,
) - model.relative_gibbs_free_energy_per_link(
potential_distance - 0.5 * h,
potential_stiffness,
temperature,
)
) / h
residual_abs =
end_to_end_length_per_link - end_to_end_length_per_link_from_derivative
residual_rel = residual_abs / end_to_end_length_per_link
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::connection::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
nondimensional_end_to_end_length = model.nondimensional_end_to_end_length(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
h = parameters.rel_tol
nondimensional_end_to_end_length_from_derivative =
-1.0 / nondimensional_potential_stiffness / number_of_links * (
model.nondimensional_relative_gibbs_free_energy(
nondimensional_potential_distance + 0.5 * h,
nondimensional_potential_stiffness,
) - model.nondimensional_relative_gibbs_free_energy(
nondimensional_potential_distance - 0.5 * h,
nondimensional_potential_stiffness,
)
) / h
residual_abs =
nondimensional_end_to_end_length -
nondimensional_end_to_end_length_from_derivative
residual_rel = residual_abs / nondimensional_end_to_end_length
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::fjc::thermodynamics::modified_canonical::asymptotic::weak_potential::test::connection::nondimensional_end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_potential_distance =
parameters.nondimensional_potential_distance_reference +
parameters.nondimensional_potential_distance_scale * (0.5 - rand())
nondimensional_potential_stiffness =
parameters.nondimensional_potential_stiffness_reference +
parameters.nondimensional_potential_stiffness_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
h = parameters.rel_tol
nondimensional_end_to_end_length_per_link_from_derivative =
-1.0 / nondimensional_potential_stiffness / number_of_links * (
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_potential_distance + 0.5 * h,
nondimensional_potential_stiffness,
) - model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_potential_distance - 0.5 * h,
nondimensional_potential_stiffness,
)
) / h
residual_abs =
nondimensional_end_to_end_length_per_link -
nondimensional_end_to_end_length_per_link_from_derivative
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_rel) <= h
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 972 | """
The ideal single-chain model.
"""
module Ideal
using DocStringExtensions
include("thermodynamics/mod.jl")
"""
The structure of the ideal chain model.
$(FIELDS)
"""
struct IDEAL
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The thermodynamic functions of the model.
"""
thermodynamics::Any
end
"""
Initializes and returns an instance of the ideal chain model.
$(TYPEDSIGNATURES)
"""
function IDEAL(number_of_links::UInt8, link_length::Float64, hinge_mass::Float64)
return IDEAL(
number_of_links,
link_length,
hinge_mass,
Thermodynamics.IDEAL(number_of_links, link_length, hinge_mass),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 2502 | module Test
using Test
using Polymers.Physics.SingleChain: parameters
using Polymers.Physics.SingleChain.Ideal: IDEAL
@testset "physics::single_chain::ideal::test::base::init" begin
@test isa(
IDEAL(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
),
Any,
)
end
@testset "physics::single_chain::ideal::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test IDEAL(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ideal::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test IDEAL(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ideal::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test IDEAL(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ideal::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test all(
IDEAL(number_of_links, link_length, hinge_mass).number_of_links ==
number_of_links &&
IDEAL(number_of_links, link_length, hinge_mass).link_length == link_length &&
IDEAL(number_of_links, link_length, hinge_mass).hinge_mass == hinge_mass,
)
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 1264 | """
The ideal chain model thermodynamics.
"""
module Thermodynamics
using DocStringExtensions
include("isometric/mod.jl")
include("isotensional/mod.jl")
"""
The structure of the thermodynamics of the ideal chain model.
$(FIELDS)
"""
struct IDEAL
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The thermodynamic functions of the model in the isometric ensemble.
"""
isometric::Any
"""
The thermodynamic functions of the model in the isotensional ensemble.
"""
isotensional::Any
end
"""
Initializes and returns an instance of the thermodynamics of the ideal chain model.
$(TYPEDSIGNATURES)
"""
function IDEAL(number_of_links::UInt8, link_length::Float64, hinge_mass::Float64)
return IDEAL(
number_of_links,
link_length,
hinge_mass,
Isometric.IDEAL(number_of_links, link_length, hinge_mass),
Isotensional.IDEAL(number_of_links, link_length, hinge_mass),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 2597 | module Test
using Test
using Polymers.Physics.SingleChain: parameters
using Polymers.Physics.SingleChain.Ideal.Thermodynamics: IDEAL
@testset "physics::single_chain::ideal::thermodynamics::test::base::init" begin
@test isa(
IDEAL(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
),
Any,
)
end
@testset "physics::single_chain::ideal::thermodynamics::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test IDEAL(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ideal::thermodynamics::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test IDEAL(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ideal::thermodynamics::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test IDEAL(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ideal::thermodynamics::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test all(
IDEAL(number_of_links, link_length, hinge_mass).number_of_links ==
number_of_links &&
IDEAL(number_of_links, link_length, hinge_mass).link_length == link_length &&
IDEAL(number_of_links, link_length, hinge_mass).hinge_mass == hinge_mass,
)
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 24693 | """
The ideal chain model thermodynamics in the isometric ensemble.
"""
module Isometric
using DocStringExtensions
using ......Polymers: PROJECT_ROOT
"""
The structure of the thermodynamics of the ideal chain model in the isometric ensemble.
$(FIELDS)
"""
struct IDEAL
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The expected force ``f`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
force::Function
"""
The expected nondimensional force ``\\eta`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``.
"""
nondimensional_force::Function
"""
The Helmholtz free energy ``\\psi`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
helmholtz_free_energy::Function
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
helmholtz_free_energy_per_link::Function
"""
The relative Helmholtz free energy ``\\Delta\\psi\\equiv\\psi(\\xi,T)-\\psi(0,T)`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
relative_helmholtz_free_energy::Function
"""
The relative Helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
relative_helmholtz_free_energy_per_link::Function
"""
The nondimensional Helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy::Function
"""
The nondimensional Helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy_per_link::Function
"""
The nondimensional relative Helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``.
"""
nondimensional_relative_helmholtz_free_energy::Function
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``.
"""
nondimensional_relative_helmholtz_free_energy_per_link::Function
"""
The equilibrium probability density of end-to-end vectors ``P_\\mathrm{eq}`` as a function of the end-to-end length ``\\xi``.
"""
equilibrium_distribution::Function
"""
The nondimensional equilibrium probability density of end-to-end vectors ``\\mathscr{P}_\\mathrm{eq}`` as a function of the nondimensional end-to-end length per link ``\\gamma``.
"""
nondimensional_equilibrium_distribution::Function
"""
The equilibrium probability density of end-to-end lengths ``g_\\mathrm{eq}`` as a function of the end-to-end length ``\\xi``.
"""
equilibrium_radial_distribution::Function
"""
The nondimensional equilibrium probability density of end-to-end lengths ``\\mathscr{g}_\\mathrm{eq}`` as a function of the nondimensional end-to-end length per link ``\\gamma``.
"""
nondimensional_equilibrium_radial_distribution::Function
end
"""
The expected force ``f`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``,
```math
f(\\xi, T) = \\frac{\\partial\\psi}{\\partial\\xi} = \\frac{3kT\\xi}{N_b\\ell_b^2}.
```
$(TYPEDSIGNATURES)
"""
function force(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, end_to_end_length_i, temperature_i) -> ccall(
(
:physics_single_chain_ideal_thermodynamics_isometric_force,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
end_to_end_length,
temperature,
)
end
"""
The expected nondimensional force ``\\eta`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``,
```math
\\eta(\\gamma) = \\frac{\\partial\\vartheta}{\\partial\\gamma} = 3\\gamma.
```
$(TYPEDSIGNATURES)
"""
function nondimensional_force(
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
nondimensional_end_to_end_length_per_link_i -> ccall(
(
:physics_single_chain_ideal_thermodynamics_isometric_nondimensional_force,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64,),
nondimensional_end_to_end_length_per_link_i,
),
nondimensional_end_to_end_length_per_link,
)
end
"""
The Helmholtz free energy ``\\psi`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``,
```math
\\psi(\\xi, T) = -kT\\ln Q(\\xi, T).
```
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ideal_thermodynamics_isometric_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
end_to_end_length,
temperature,
)
end
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ideal_thermodynamics_isometric_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
end_to_end_length,
temperature,
)
end
"""
The relative Helmholtz free energy ``\\Delta\\psi\\equiv\\psi(\\xi,T)-\\psi(0,T)`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``,
```math
\\Delta\\psi(\\xi, T) = kT\\ln\\left[\\frac{P_\\mathrm{eq}(0)}{P_\\mathrm{eq}(\\xi)}\\right] = \\frac{3kT\\xi^2}{2N_b\\ell_b^2}.
```
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, end_to_end_length_i, temperature_i) -> ccall(
(
:physics_single_chain_ideal_thermodynamics_isometric_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
end_to_end_length,
temperature,
)
end
"""
The relative Helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, end_to_end_length_i, temperature_i) -> ccall(
(
:physics_single_chain_ideal_thermodynamics_isometric_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
end_to_end_length,
temperature,
)
end
"""
The nondimensional Helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ideal_thermodynamics_isometric_nondimensional_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_end_to_end_length_per_link,
temperature,
)
end
"""
The nondimensional Helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
link_length_i,
hinge_mass_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ideal_thermodynamics_isometric_nondimensional_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
),
link_length,
hinge_mass,
nondimensional_end_to_end_length_per_link,
temperature,
)
end
"""
The nondimensional relative Helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``,
parameterized by the number of links ``N_b``,
```math
\\beta\\Delta\\psi(\\gamma) = \\ln\\left[\\frac{\\mathscr{P}_\\mathrm{eq}(0)}{\\mathscr{P}_\\mathrm{eq}(\\gamma)}\\right] = \\frac{3}{2}\\,N_b\\gamma^2.
```
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_end_to_end_length_per_link_i) -> ccall(
(
:physics_single_chain_ideal_thermodynamics_isometric_nondimensional_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64),
number_of_links_i,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
nondimensional_end_to_end_length_per_link,
)
end
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``,
parameterized by the number of links ``N_b``,
```math
\\Delta\\vartheta(\\gamma) = \\ln\\left[\\frac{\\mathscr{P}_\\mathrm{eq}(0)}{\\mathscr{P}_\\mathrm{eq}(\\gamma)}\\right]^{1/N_b} = \\frac{3}{2}\\,\\gamma^2.
```
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
nondimensional_end_to_end_length_per_link_i -> ccall(
(
:physics_single_chain_ideal_thermodynamics_isometric_nondimensional_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64,),
nondimensional_end_to_end_length_per_link_i,
),
nondimensional_end_to_end_length_per_link,
)
end
"""
The equilibrium probability density of end-to-end vectors ``P_\\mathrm{eq}`` as a function of the end-to-end length ``\\xi``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``,
```math
P_\\mathrm{eq}(\\xi) = \\frac{e^{-\\beta\\psi(\\xi, T)}}{4\\pi\\int e^{-\\beta\\psi(\\xi', T)} \\,{\\xi'}{}^2 d\\xi'} = \\left(\\frac{3}{2\\pi N_b\\ell_b^2}\\right)^{3/2}\\exp\\left(-\\frac{3\\xi^2}{2N_b\\ell_b^2}\\right).
```
$(TYPEDSIGNATURES)
"""
function equilibrium_distribution(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, end_to_end_length_i) -> ccall(
(
:physics_single_chain_ideal_thermodynamics_isometric_equilibrium_distribution,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
link_length_i,
end_to_end_length_i,
),
number_of_links,
link_length,
end_to_end_length,
)
end
"""
The nondimensional equilibrium probability density of nondimensional end-to-end vectors per link ``\\mathscr{P}_\\mathrm{eq}`` as a function of the nondimensional end-to-end length per link ``\\gamma``,
parameterized by the number of links ``N_b``,
```math
\\mathscr{P}_\\mathrm{eq}(\\gamma) = \\frac{e^{-\\Delta\\vartheta(\\gamma)}}{4\\pi\\int e^{-\\Delta\\vartheta(\\gamma')} \\,{\\gamma'}{}^2 d\\gamma'} = \\left(\\frac{3}{2\\pi N_b}\\right)^{3/2}\\exp\\left(-\\frac{3}{2}\\,N_b\\gamma^2\\right).
```
$(TYPEDSIGNATURES)
"""
function nondimensional_equilibrium_distribution(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_end_to_end_length_per_link_i) -> ccall(
(
:physics_single_chain_ideal_thermodynamics_isometric_nondimensional_equilibrium_distribution,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64),
number_of_links_i,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
nondimensional_end_to_end_length_per_link,
)
end
"""
The equilibrium probability density of end-to-end lengths ``g_\\mathrm{eq}`` as a function of the end-to-end length ``\\xi``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``,
```math
g_\\mathrm{eq}(\\xi) = 4\\pi\\xi^2 P_\\mathrm{eq}(\\xi).
```
$(TYPEDSIGNATURES)
"""
function equilibrium_radial_distribution(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, end_to_end_length_i) -> ccall(
(
:physics_single_chain_ideal_thermodynamics_isometric_equilibrium_radial_distribution,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
link_length_i,
end_to_end_length_i,
),
number_of_links,
link_length,
end_to_end_length,
)
end
"""
The nondimensional equilibrium probability density of nondimensional end-to-end lenghts per link ``\\mathscr{g}_\\mathrm{eq}`` as a function of the nondimensional end-to-end length per link ``\\gamma``,
parameterized by the number of links ``N_b``,
```math
\\mathscr{g}_\\mathrm{eq}(\\gamma) = 4\\pi\\gamma^2 \\mathscr{P}_\\mathrm{eq}(\\gamma).
```
$(TYPEDSIGNATURES)
"""
function nondimensional_equilibrium_radial_distribution(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_end_to_end_length_per_link_i) -> ccall(
(
:physics_single_chain_ideal_thermodynamics_isometric_nondimensional_equilibrium_radial_distribution,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64),
number_of_links_i,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
nondimensional_end_to_end_length_per_link,
)
end
"""
Initializes and returns an instance of the thermodynamics of the ideal chain model in the isometric ensemble.
$(TYPEDSIGNATURES)
"""
function IDEAL(number_of_links::UInt8, link_length::Float64, hinge_mass::Float64)
return IDEAL(
number_of_links,
link_length,
hinge_mass,
(end_to_end_length, temperature) ->
force(number_of_links, link_length, end_to_end_length, temperature),
(nondimensional_end_to_end_length_per_link) ->
nondimensional_force(nondimensional_end_to_end_length_per_link),
(end_to_end_length, temperature) -> helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> helmholtz_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> relative_helmholtz_free_energy(
number_of_links,
link_length,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> relative_helmholtz_free_energy_per_link(
number_of_links,
link_length,
end_to_end_length,
temperature,
),
(nondimensional_end_to_end_length_per_link, temperature) ->
nondimensional_helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
nondimensional_end_to_end_length_per_link,
temperature,
),
(nondimensional_end_to_end_length_per_link, temperature) ->
nondimensional_helmholtz_free_energy_per_link(
link_length,
hinge_mass,
nondimensional_end_to_end_length_per_link,
temperature,
),
(nondimensional_end_to_end_length_per_link) ->
nondimensional_relative_helmholtz_free_energy(
number_of_links,
nondimensional_end_to_end_length_per_link,
),
(nondimensional_end_to_end_length_per_link) ->
nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
),
(end_to_end_length) ->
equilibrium_distribution(number_of_links, link_length, end_to_end_length),
(nondimensional_end_to_end_length_per_link) ->
nondimensional_equilibrium_distribution(
number_of_links,
nondimensional_end_to_end_length_per_link,
),
(end_to_end_length) -> equilibrium_radial_distribution(
number_of_links,
link_length,
end_to_end_length,
),
(nondimensional_end_to_end_length_per_link) ->
nondimensional_equilibrium_radial_distribution(
number_of_links,
nondimensional_end_to_end_length_per_link,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 40767 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ONE, ZERO, POINTS, integrate, parameters
using Polymers.Physics.SingleChain.Ideal.Thermodynamics.Isometric: IDEAL
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::base::init" begin
@test isa(
IDEAL(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
),
Any,
)
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test IDEAL(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test IDEAL(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test IDEAL(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test all(
IDEAL(number_of_links, link_length, hinge_mass).number_of_links ==
number_of_links &&
IDEAL(number_of_links, link_length, hinge_mass).link_length == link_length &&
IDEAL(number_of_links, link_length, hinge_mass).hinge_mass == hinge_mass,
)
end
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::normalization::equilibrium_distribution" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
normalization = integrate(
end_to_end_length ->
4.0 *
pi *
end_to_end_length^2 *
model.equilibrium_distribution(end_to_end_length),
ZERO,
5e0 * number_of_links * link_length,
POINTS,
)
@test normalization - 1.0 <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::normalization::equilibrium_radial_distribution" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
normalization = integrate(
end_to_end_length ->
model.equilibrium_radial_distribution(end_to_end_length),
ZERO,
5e0 * number_of_links * link_length,
POINTS,
)
@test normalization - 1.0 <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::normalization::nondimensional_equilibrium_distribution" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
normalization = integrate(
nondimensional_end_to_end_length_per_link ->
4.0 *
pi *
nondimensional_end_to_end_length_per_link^2 *
model.nondimensional_equilibrium_distribution(
nondimensional_end_to_end_length_per_link,
),
ZERO,
5e0,
POINTS,
)
@test normalization - 1.0 <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::normalization::nondimensional_equilibrium_radial_distribution" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
normalization = integrate(
nondimensional_end_to_end_length_per_link ->
model.nondimensional_equilibrium_radial_distribution(
nondimensional_end_to_end_length_per_link,
),
ZERO,
5e0,
POINTS,
)
@test normalization - 1.0 <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::nondimensional::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
model.nondimensional_force(nondimensional_end_to_end_length_per_link)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
force = model.force(end_to_end_length, temperature)
residual_abs =
force / BOLTZMANN_CONSTANT / temperature * link_length - nondimensional_force
residual_rel = residual_abs / nondimensional_force
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::nondimensional::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy = model.helmholtz_free_energy(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::nondimensional::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::nondimensional::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(end_to_end_length, temperature)
residual_abs =
relative_helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::nondimensional::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
relative_helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::per_link::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy = model.helmholtz_free_energy(end_to_end_length, temperature)
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy / number_of_links - helmholtz_free_energy_per_link
residual_rel = residual_abs / helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::per_link::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(end_to_end_length, temperature)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
relative_helmholtz_free_energy / number_of_links -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::per_link::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy / number_of_links -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::per_link::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy / number_of_links -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::relative::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy = model.helmholtz_free_energy(end_to_end_length, temperature)
helmholtz_free_energy_0 =
model.helmholtz_free_energy(ZERO * number_of_links * link_length, temperature)
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy - helmholtz_free_energy_0 - relative_helmholtz_free_energy
residual_rel = residual_abs / relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::relative::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(end_to_end_length, temperature)
helmholtz_free_energy_per_link_0 = model.helmholtz_free_energy_per_link(
ZERO * number_of_links * link_length,
temperature,
)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy_per_link - helmholtz_free_energy_per_link_0 -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::relative::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_0 =
model.nondimensional_helmholtz_free_energy(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
)
residual_abs =
nondimensional_helmholtz_free_energy - nondimensional_helmholtz_free_energy_0 -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::relative::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_per_link_0 =
model.nondimensional_helmholtz_free_energy_per_link(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
)
residual_abs =
nondimensional_helmholtz_free_energy_per_link -
nondimensional_helmholtz_free_energy_per_link_0 -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::zero::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_0 = model.relative_helmholtz_free_energy(
ZERO * number_of_links * link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_0) <=
ZERO * number_of_links * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::zero::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_per_link_0 =
model.relative_helmholtz_free_energy_per_link(
ZERO * number_of_links * link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::zero::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
nondimensional_relative_helmholtz_free_energy_0 =
model.nondimensional_relative_helmholtz_free_energy(ZERO)
@test abs(nondimensional_relative_helmholtz_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::zero::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
nondimensional_relative_helmholtz_free_energy_per_link_0 =
model.nondimensional_relative_helmholtz_free_energy_per_link(ZERO)
@test abs(nondimensional_relative_helmholtz_free_energy_per_link_0) <= ZERO
end
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::zero::equilibrium_radial_distribution" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
equilibrium_radial_distribution_0 =
model.equilibrium_radial_distribution(ZERO * number_of_links * link_length)
@test abs(equilibrium_radial_distribution_0) <= ZERO
end
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::zero::nondimensional_equilibrium_radial_distribution" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
nondimensional_equilibrium_radial_distribution_0 =
model.equilibrium_radial_distribution(ZERO)
@test abs(nondimensional_equilibrium_radial_distribution_0) <= ZERO
end
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::connection::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
force = model.force(end_to_end_length, temperature)
h = parameters.rel_tol * number_of_links * link_length
force_from_derivative =
(
model.relative_helmholtz_free_energy(
end_to_end_length + 0.5 * h,
temperature,
) - model.relative_helmholtz_free_energy(
end_to_end_length - 0.5 * h,
temperature,
)
) / h
residual_abs = force - force_from_derivative
residual_rel = residual_abs / force
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::connection::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
model.nondimensional_force(nondimensional_end_to_end_length_per_link)
h = parameters.rel_tol
nondimensional_force_from_derivative =
(
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link + 0.5 * h,
) - model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link - 0.5 * h,
)
) / h
residual_abs = nondimensional_force - nondimensional_force_from_derivative
residual_rel = residual_abs / nondimensional_force
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::connection::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(end_to_end_length, temperature)
relative_helmholtz_free_energy_from_connection =
BOLTZMANN_CONSTANT *
temperature *
log((
model.equilibrium_distribution(ZERO * number_of_links * link_length) /
model.equilibrium_distribution(end_to_end_length)
))
residual_abs =
relative_helmholtz_free_energy - relative_helmholtz_free_energy_from_connection
residual_rel = residual_abs / relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isometric::test::connection::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
)
nondimensional_relative_helmholtz_free_energy_from_connection = log((
model.nondimensional_equilibrium_distribution(ZERO) /
model.nondimensional_equilibrium_distribution(
nondimensional_end_to_end_length_per_link,
)
))
residual_abs =
nondimensional_relative_helmholtz_free_energy -
nondimensional_relative_helmholtz_free_energy_from_connection
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 18016 | """
The ideal chain model thermodynamics in the isotensional ensemble.
"""
module Isotensional
using DocStringExtensions
using ......Polymers: PROJECT_ROOT
"""
The structure of the thermodynamics of the ideal chain model in the isotensional ensemble.
$(FIELDS)
"""
struct IDEAL
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The expected end-to-end length ``\\xi`` as a function of the applied force ``f`` and temperature ``T``.
"""
end_to_end_length::Function
"""
The expected end-to-end length per link ``\\xi/N_b=\\ell_b\\gamma`` as a function of the applied force ``f`` and temperature ``T``.
"""
end_to_end_length_per_link::Function
"""
The expected nondimensional end-to-end length ``N_b\\gamma=\\xi/\\ell_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_end_to_end_length::Function
"""
The expected nondimensional end-to-end length per link ``\\gamma\\equiv\\xi/N_b\\ell_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_end_to_end_length_per_link::Function
"""
The Gibbs free energy ``\\varphi`` as a function of the applied force ``f`` and temperature ``T``.
"""
gibbs_free_energy::Function
"""
The Gibbs free energy per link ``\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
gibbs_free_energy_per_link::Function
"""
The relative Gibbs free energy ``\\Delta\\varphi\\equiv\\varphi(f,T)-\\varphi(0,T)`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_gibbs_free_energy::Function
"""
The relative Gibbs free energy per link ``\\Delta\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_gibbs_free_energy_per_link::Function
"""
The nondimensional Gibbs free energy ``N_b\\varrho=\\beta\\varphi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_gibbs_free_energy::Function
"""
The nondimensional Gibbs free energy per link ``\\varrho\\equiv\\beta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_gibbs_free_energy_per_link::Function
"""
The nondimensional relative Gibbs free energy ``N_b\\Delta\\varrho=\\beta\\Delta\\varphi`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_gibbs_free_energy::Function
"""
The nondimensional relative Gibbs free energy per link ``\\Delta\\varrho\\equiv\\beta\\Delta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_gibbs_free_energy_per_link::Function
end
"""
The expected end-to-end length ``\\xi`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``,
```math
\\xi(f, T) = -\\frac{\\partial\\varphi}{\\partial f} = \\frac{N_b\\ell_b^2f}{3kT}.
```
$(TYPEDSIGNATURES)
"""
function end_to_end_length(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ideal_thermodynamics_isotensional_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
force,
temperature,
)
end
"""
The expected end-to-end length per link ``\\xi/N_b=\\ell_b\\gamma`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b``.
$(TYPEDSIGNATURES)
"""
function end_to_end_length_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ideal_thermodynamics_isotensional_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64),
link_length_i,
force_i,
temperature_i,
),
link_length,
force,
temperature,
)
end
"""
The expected nondimensional end-to-end length ``N_b\\gamma\\equiv\\xi/\\ell_b`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b``.
$(TYPEDSIGNATURES)
"""
function nondimensional_end_to_end_length(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_ideal_thermodynamics_isotensional_nondimensional_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64),
number_of_links_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_force,
)
end
"""
The expected nondimensional end-to-end length per link ``\\gamma\\equiv\\xi/N_b\\ell_b`` as a function of the applied nondimensional force ``\\eta``,
```math
\\gamma(\\eta) = -\\frac{\\partial\\varrho}{\\partial\\eta} = \\frac{\\eta}{3}.
```
$(TYPEDSIGNATURES)
"""
function nondimensional_end_to_end_length_per_link(
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
nondimensional_force_i -> ccall(
(
:physics_single_chain_ideal_thermodynamics_isotensional_nondimensional_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64,),
nondimensional_force_i,
),
nondimensional_force,
)
end
"""
The Gibbs free energy ``\\varphi`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``,
```math
\\varphi(f, T) = -kT\\ln Z(f, T).
```
$(TYPEDSIGNATURES)
"""
function gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, hinge_mass_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ideal_thermodynamics_isotensional_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
force,
temperature,
)
end
"""
The Gibbs free energy per link ``\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, hinge_mass_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ideal_thermodynamics_isotensional_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
force_i,
temperature_i,
),
link_length,
hinge_mass,
force,
temperature,
)
end
"""
The relative Gibbs free energy ``\\Delta\\varphi\\equiv\\varphi(f,T)-\\varphi(0,T)`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``,
```math
\\Delta\\varphi(f, T) = -\\frac{N_b\\ell_b^2f^2}{6kT}.
```
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ideal_thermodynamics_isotensional_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
force,
temperature,
)
end
"""
The relative Gibbs free energy per link ``\\Delta\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ideal_thermodynamics_isotensional_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64),
link_length_i,
force_i,
temperature_i,
),
link_length,
force,
temperature,
)
end
"""
The nondimensional Gibbs free energy ``N_b\\varrho=\\beta\\varphi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ideal_thermodynamics_isotensional_nondimensional_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_force,
temperature,
)
end
"""
The nondimensional Gibbs free energy per link ``\\varrho\\equiv\\beta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, hinge_mass_i, nondimensional_force_i, temperature_i) -> ccall(
(
:physics_single_chain_ideal_thermodynamics_isotensional_nondimensional_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
nondimensional_force_i,
temperature_i,
),
link_length,
hinge_mass,
nondimensional_force,
temperature,
)
end
"""
The nondimensional relative Gibbs free energy ``\\beta\\Delta\\varphi=N_b\\Delta\\varrho`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_ideal_thermodynamics_isotensional_nondimensional_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64),
number_of_links_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_force,
)
end
"""
The nondimensional relative Gibbs free energy per link ``\\Delta\\varrho\\equiv\\beta\\Delta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta``,
```math
\\Delta\\varrho(\\eta) = -\\frac{\\eta^2}{6}.
```
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
nondimensional_force_i -> ccall(
(
:physics_single_chain_ideal_thermodynamics_isotensional_nondimensional_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64,),
nondimensional_force_i,
),
nondimensional_force,
)
end
"""
Initializes and returns an instance of the thermodynamics of the ideal chain model in the isotensional ensemble.
$(TYPEDSIGNATURES)
"""
function IDEAL(number_of_links::UInt8, link_length::Float64, hinge_mass::Float64)
return IDEAL(
number_of_links,
link_length,
hinge_mass,
(force, temperature) ->
end_to_end_length(number_of_links, link_length, force, temperature),
(force, temperature) -> end_to_end_length_per_link(link_length, force, temperature),
nondimensional_force ->
nondimensional_end_to_end_length(number_of_links, nondimensional_force),
nondimensional_force ->
nondimensional_end_to_end_length_per_link(nondimensional_force),
(force, temperature) ->
gibbs_free_energy(number_of_links, link_length, hinge_mass, force, temperature),
(force, temperature) ->
gibbs_free_energy_per_link(link_length, hinge_mass, force, temperature),
(force, temperature) ->
relative_gibbs_free_energy(number_of_links, link_length, force, temperature),
(force, temperature) ->
relative_gibbs_free_energy_per_link(link_length, force, temperature),
(nondimensional_force, temperature) -> nondimensional_gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_gibbs_free_energy_per_link(
link_length,
hinge_mass,
nondimensional_force,
temperature,
),
nondimensional_force -> nondimensional_relative_gibbs_free_energy(
number_of_links,
nondimensional_force,
),
nondimensional_force ->
nondimensional_relative_gibbs_free_energy_per_link(nondimensional_force),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 39893 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: parameters
using Polymers.Physics.SingleChain.Ideal.Thermodynamics.Isotensional: IDEAL
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::base::init" begin
@test isa(
IDEAL(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
),
Any,
)
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test IDEAL(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test IDEAL(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test IDEAL(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test all(
IDEAL(number_of_links, link_length, hinge_mass).number_of_links ==
number_of_links &&
IDEAL(number_of_links, link_length, hinge_mass).link_length == link_length &&
IDEAL(number_of_links, link_length, hinge_mass).hinge_mass == hinge_mass,
)
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::nondimensional::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
residual_abs = end_to_end_length / link_length - nondimensional_end_to_end_length
residual_rel = residual_abs / nondimensional_end_to_end_length
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::nondimensional::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(nondimensional_force)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
residual_abs =
end_to_end_length_per_link / link_length -
nondimensional_end_to_end_length_per_link
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::nondimensional::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
residual_abs =
gibbs_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_gibbs_free_energy
residual_rel = residual_abs / nondimensional_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::nondimensional::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
residual_abs =
gibbs_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::nondimensional::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(nondimensional_force)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
residual_abs =
relative_gibbs_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_gibbs_free_energy
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::nondimensional::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(nondimensional_force)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
residual_abs =
relative_gibbs_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::per_link::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
residual_abs = end_to_end_length / number_of_links - end_to_end_length_per_link
residual_rel = residual_abs / end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::per_link::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force)
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(nondimensional_force)
residual_abs =
nondimensional_end_to_end_length / number_of_links -
nondimensional_end_to_end_length_per_link
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::per_link::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
residual_abs = gibbs_free_energy / number_of_links - gibbs_free_energy_per_link
residual_rel = residual_abs / gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::per_link::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
residual_abs =
relative_gibbs_free_energy / number_of_links -
relative_gibbs_free_energy_per_link
residual_rel = residual_abs / relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::per_link::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_gibbs_free_energy / number_of_links -
nondimensional_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::per_link::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(nondimensional_force)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(nondimensional_force)
residual_abs =
nondimensional_relative_gibbs_free_energy / number_of_links -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::relative::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
gibbs_free_energy_0 = model.gibbs_free_energy(0.0, temperature)
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
residual_abs = gibbs_free_energy - gibbs_free_energy_0 - relative_gibbs_free_energy
residual_rel = residual_abs / gibbs_free_energy
@test abs(residual_abs) <=
BOLTZMANN_CONSTANT * temperature * number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::relative::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
gibbs_free_energy_per_link_0 = model.gibbs_free_energy_per_link(0.0, temperature)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
residual_abs =
gibbs_free_energy_per_link - gibbs_free_energy_per_link_0 -
relative_gibbs_free_energy_per_link
residual_rel = residual_abs / gibbs_free_energy_per_link
@test abs(residual_abs) <= BOLTZMANN_CONSTANT * temperature * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::relative::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
nondimensional_gibbs_free_energy_0 =
model.nondimensional_gibbs_free_energy(0.0, temperature)
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(nondimensional_force)
residual_abs =
nondimensional_gibbs_free_energy - nondimensional_gibbs_free_energy_0 -
nondimensional_relative_gibbs_free_energy
residual_rel = residual_abs / nondimensional_gibbs_free_energy
@test abs(residual_abs) <= number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::relative::nondimensional_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_gibbs_free_energy_per_link_0 =
model.nondimensional_gibbs_free_energy_per_link(0.0, temperature)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(nondimensional_force)
residual_abs =
nondimensional_gibbs_free_energy_per_link -
nondimensional_gibbs_free_energy_per_link_0 -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::zero::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length_0 = model.end_to_end_length(0.0, temperature)
@test abs(end_to_end_length_0) <=
3.0 * BOLTZMANN_CONSTANT * temperature * number_of_links * 0.0
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::zero::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length_per_link_0 = model.end_to_end_length_per_link(0.0, temperature)
@test abs(end_to_end_length_per_link_0) <=
3.0 * BOLTZMANN_CONSTANT * temperature * 0.0
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::zero::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_0 = model.nondimensional_end_to_end_length(0.0)
@test abs(nondimensional_end_to_end_length_0) <= 3.0 * number_of_links * 0.0
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::zero::nondimensional_end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link_0 =
model.nondimensional_end_to_end_length_per_link(0.0)
@test abs(nondimensional_end_to_end_length_per_link_0) <= 3.0 * 0.0
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::zero::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_gibbs_free_energy_0 = model.relative_gibbs_free_energy(0.0, temperature)
@test abs(relative_gibbs_free_energy_0) <= 0.0
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::zero::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_gibbs_free_energy_per_link_0 =
model.relative_gibbs_free_energy_per_link(0.0, temperature)
@test abs(relative_gibbs_free_energy_per_link_0) <= 0.0
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::zero::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
nondimensional_relative_gibbs_free_energy_0 =
model.nondimensional_relative_gibbs_free_energy(0.0)
@test abs(nondimensional_relative_gibbs_free_energy_0) <= 0.0
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::zero::nondimensional_relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
nondimensional_relative_gibbs_free_energy_per_link_0 =
model.nondimensional_relative_gibbs_free_energy_per_link(0.0)
@test abs(nondimensional_relative_gibbs_free_energy_per_link_0) <= 0.0
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::connection::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
h = parameters.rel_tol * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_from_derivative =
-(
model.relative_gibbs_free_energy(force + 0.5 * h, temperature) -
model.relative_gibbs_free_energy(force - 0.5 * h, temperature)
) / h
residual_abs = end_to_end_length - end_to_end_length_from_derivative
residual_rel = residual_abs / end_to_end_length
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::connection::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
h = parameters.rel_tol * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link_from_derivative =
-(
model.relative_gibbs_free_energy_per_link(force + 0.5 * h, temperature) -
model.relative_gibbs_free_energy_per_link(force - 0.5 * h, temperature)
) / h
residual_abs =
end_to_end_length_per_link - end_to_end_length_per_link_from_derivative
residual_rel = residual_abs / end_to_end_length_per_link
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::connection::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force)
h = parameters.rel_tol
nondimensional_end_to_end_length_from_derivative =
-(
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force + 0.5 * h,
) - model.nondimensional_relative_gibbs_free_energy(
nondimensional_force - 0.5 * h,
)
) / h
residual_abs =
nondimensional_end_to_end_length -
nondimensional_end_to_end_length_from_derivative
residual_rel = residual_abs / nondimensional_end_to_end_length
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ideal::thermodynamics::isotensional::test::connection::nondimensional_end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = IDEAL(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(nondimensional_force)
h = parameters.rel_tol
nondimensional_end_to_end_length_per_link_from_derivative =
-(
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force + 0.5 * h,
) - model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force - 0.5 * h,
)
) / h
residual_abs =
nondimensional_end_to_end_length_per_link -
nondimensional_end_to_end_length_per_link_from_derivative
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_rel) <= h
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 1165 | """
The square-well freely-jointed chain (SWFJC) single-chain model.
"""
module Swfjc
using DocStringExtensions
include("thermodynamics/mod.jl")
"""
The structure of the SWFJC model.
$(FIELDS)
"""
struct SWFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The width of the well ``w`` in units of nm.
"""
well_width::Float64
"""
The thermodynamic functions of the model.
"""
thermodynamics::Any
end
"""
Initializes and returns an instance of the SWFJC model.
$(TYPEDSIGNATURES)
"""
function SWFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
well_width::Float64,
)
return SWFJC(
number_of_links,
link_length,
hinge_mass,
well_width,
Thermodynamics.SWFJC(number_of_links, link_length, hinge_mass, well_width),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 3444 | module Test
using Test
using Polymers.Physics.SingleChain: parameters
using Polymers.Physics.SingleChain.Swfjc: SWFJC
@testset "physics::single_chain::swfjc::test::base::init" begin
@test isa(
SWFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.well_width_reference,
),
Any,
)
end
@testset "physics::single_chain::swfjc::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test SWFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.well_width_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::swfjc::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test SWFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.well_width_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::swfjc::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test SWFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.well_width_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::swfjc::test::base::well_width" begin
for _ = 1:parameters.number_of_loops
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
@test SWFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
well_width,
).well_width == well_width
end
end
@testset "physics::single_chain::swfjc::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
@test all(
SWFJC(number_of_links, link_length, hinge_mass, well_width).number_of_links ==
number_of_links &&
SWFJC(number_of_links, link_length, hinge_mass, well_width).link_length ==
link_length &&
SWFJC(number_of_links, link_length, hinge_mass, well_width).hinge_mass ==
hinge_mass &&
SWFJC(number_of_links, link_length, hinge_mass, well_width).well_width ==
well_width,
)
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 1463 | """
The square-well freely-jointed chain (SWFJC) model thermodynamics.
"""
module Thermodynamics
using DocStringExtensions
include("isometric/mod.jl")
include("isotensional/mod.jl")
"""
The structure of the thermodynamics of the SWFJC model.
$(FIELDS)
"""
struct SWFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The width of the well ``w`` in units of nm.
"""
well_width::Float64
"""
The thermodynamic functions of the model in the isometric ensemble.
"""
isometric::Any
"""
The thermodynamic functions of the model in the isotensional ensemble.
"""
isotensional::Any
end
"""
Initializes and returns an instance of the thermodynamics of the SWFJC model.
$(TYPEDSIGNATURES)
"""
function SWFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
well_width::Float64,
)
return SWFJC(
number_of_links,
link_length,
hinge_mass,
well_width,
Isometric.SWFJC(number_of_links, link_length, hinge_mass, well_width),
Isotensional.SWFJC(number_of_links, link_length, hinge_mass, well_width),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 23253 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT, PLANCK_CONSTANT
using Polymers.Physics.SingleChain: parameters
using Polymers.Physics.SingleChain.Swfjc.Thermodynamics: SWFJC
@testset "physics::single_chain::swfjc::thermodynamics::test::base::init" begin
@test isa(
SWFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.well_width_reference,
),
Any,
)
end
@testset "physics::single_chain::swfjc::thermodynamics::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test SWFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.well_width_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::swfjc::thermodynamics::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test SWFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.well_width_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::swfjc::thermodynamics::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test SWFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.well_width_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::swfjc::thermodynamics::test::base::well_width" begin
for _ = 1:parameters.number_of_loops
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
@test SWFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
well_width,
).well_width == well_width
end
end
@testset "physics::single_chain::swfjc::thermodynamics::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
@test all(
SWFJC(number_of_links, link_length, hinge_mass, well_width).number_of_links ==
number_of_links &&
SWFJC(number_of_links, link_length, hinge_mass, well_width).link_length ==
link_length &&
SWFJC(number_of_links, link_length, hinge_mass, well_width).hinge_mass ==
hinge_mass &&
SWFJC(number_of_links, link_length, hinge_mass, well_width).well_width ==
well_width,
)
end
end
@testset "physics::single_chain::swfjc::thermodynamics::test::legendre::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.isotensional.end_to_end_length(force, temperature)
force_out = model.isometric.legendre.force(end_to_end_length, temperature)
residual_abs = force - force_out
residual_rel = residual_abs / force
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::test::legendre::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
nondimensional_force_out = model.isometric.legendre.nondimensional_force(
nondimensional_end_to_end_length_per_link,
)
residual_abs = nondimensional_force - nondimensional_force_out
residual_rel = residual_abs / nondimensional_force
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::test::legendre::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.isotensional.end_to_end_length(force, temperature)
helmholtz_free_energy_legendre =
model.isotensional.gibbs_free_energy(force, temperature) +
force * end_to_end_length
helmholtz_free_energy_legendre_out =
model.isometric.legendre.helmholtz_free_energy(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy_legendre - helmholtz_free_energy_legendre_out +
BOLTZMANN_CONSTANT *
temperature *
log(
8.0 * pi^2 * hinge_mass * link_length^2 * BOLTZMANN_CONSTANT * temperature /
PLANCK_CONSTANT^2,
)
residual_rel = residual_abs / helmholtz_free_energy_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::test::legendre::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.isotensional.end_to_end_length(force, temperature)
end_to_end_length_per_link =
model.isotensional.end_to_end_length_per_link(force, temperature)
helmholtz_free_energy_per_link_legendre =
model.isotensional.gibbs_free_energy_per_link(force, temperature) +
force * end_to_end_length_per_link
helmholtz_free_energy_per_link_legendre_out =
model.isometric.legendre.helmholtz_free_energy_per_link(
end_to_end_length,
temperature,
)
residual_abs =
helmholtz_free_energy_per_link_legendre -
helmholtz_free_energy_per_link_legendre_out +
BOLTZMANN_CONSTANT *
temperature *
log(
8.0 * pi^2 * hinge_mass * link_length^2 * BOLTZMANN_CONSTANT * temperature /
PLANCK_CONSTANT^2,
) / number_of_links
residual_rel = residual_abs / helmholtz_free_energy_per_link_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::test::legendre::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.isotensional.end_to_end_length(force, temperature)
relative_helmholtz_free_energy_legendre =
model.isotensional.relative_gibbs_free_energy(force, temperature) +
force * end_to_end_length
relative_helmholtz_free_energy_legendre_out =
model.isometric.legendre.relative_helmholtz_free_energy(
end_to_end_length,
temperature,
)
residual_abs =
relative_helmholtz_free_energy_legendre -
relative_helmholtz_free_energy_legendre_out
residual_rel = residual_abs / relative_helmholtz_free_energy_legendre
@test abs(residual_abs) <= 3e1 * parameters.abs_tol ||
abs(residual_rel) <= 3e1 * parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::test::legendre::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.isotensional.end_to_end_length(force, temperature)
end_to_end_length_per_link =
model.isotensional.end_to_end_length_per_link(force, temperature)
relative_helmholtz_free_energy_per_link_legendre =
model.isotensional.relative_gibbs_free_energy_per_link(force, temperature) +
force * end_to_end_length_per_link
relative_helmholtz_free_energy_per_link_legendre_out =
model.isometric.legendre.relative_helmholtz_free_energy_per_link(
end_to_end_length,
temperature,
)
residual_abs =
relative_helmholtz_free_energy_per_link_legendre -
relative_helmholtz_free_energy_per_link_legendre_out
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link_legendre
@test abs(residual_abs) <= 3e1 * parameters.abs_tol ||
abs(residual_rel) <= 3e1 * parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::test::legendre::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_end_to_end_length =
model.isotensional.nondimensional_end_to_end_length(nondimensional_force)
nondimensional_end_to_end_length_per_link =
model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
nondimensional_helmholtz_free_energy_legendre =
model.isotensional.nondimensional_gibbs_free_energy(
nondimensional_force,
temperature,
) + nondimensional_force * nondimensional_end_to_end_length
nondimensional_helmholtz_free_energy_legendre_out =
model.isometric.legendre.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy_legendre -
nondimensional_helmholtz_free_energy_legendre_out + log(
8.0 * pi^2 * hinge_mass * link_length^2 * BOLTZMANN_CONSTANT * temperature /
PLANCK_CONSTANT^2,
)
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::test::legendre::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
nondimensional_helmholtz_free_energy_per_link_legendre =
model.isotensional.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
) + nondimensional_force * nondimensional_end_to_end_length_per_link
nondimensional_helmholtz_free_energy_per_link_legendre_out =
model.isometric.legendre.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy_per_link_legendre -
nondimensional_helmholtz_free_energy_per_link_legendre_out +
log(
8.0 * pi^2 * hinge_mass * link_length^2 * BOLTZMANN_CONSTANT * temperature /
PLANCK_CONSTANT^2,
) / number_of_links
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::test::legendre::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length =
model.isotensional.nondimensional_end_to_end_length(nondimensional_force)
nondimensional_end_to_end_length_per_link =
model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
nondimensional_relative_helmholtz_free_energy_legendre =
model.isotensional.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
) + nondimensional_force * nondimensional_end_to_end_length
nondimensional_relative_helmholtz_free_energy_legendre_out =
model.isometric.legendre.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy_legendre -
nondimensional_relative_helmholtz_free_energy_legendre_out
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_legendre
@test abs(residual_abs) <= 3e1 * parameters.abs_tol ||
abs(residual_rel) <= 3e1 * parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::test::legendre::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
nondimensional_relative_helmholtz_free_energy_per_link_legendre =
model.isotensional.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
) + nondimensional_force * nondimensional_end_to_end_length_per_link
nondimensional_relative_helmholtz_free_energy_per_link_legendre_out =
model.isometric.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy_per_link_legendre -
nondimensional_relative_helmholtz_free_energy_per_link_legendre_out
residual_rel =
residual_abs / nondimensional_relative_helmholtz_free_energy_per_link_legendre
@test abs(residual_abs) <= 3e1 * parameters.abs_tol ||
abs(residual_rel) <= 3e1 * parameters.rel_tol
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 1382 | """
The square-well freely-jointed chain (SWFJC) model thermodynamics in the isometric ensemble.
"""
module Isometric
using DocStringExtensions
using ......Polymers: PROJECT_ROOT
include("legendre/mod.jl")
"""
The structure of the thermodynamics of the SWFJC model in the isometric ensemble.
$(FIELDS)
"""
struct SWFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The width of the well ``w`` in units of nm.
"""
well_width::Float64
"""
The thermodynamic functions of the model in the isometric ensemble approximated using a Legendre transformation.
"""
legendre::Any
end
"""
Initializes and returns an instance of the thermodynamics of the SWFJC model in the isometric ensemble.
$(TYPEDSIGNATURES)
"""
function SWFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
well_width::Float64,
)
return SWFJC(
number_of_links,
link_length,
hinge_mass,
well_width,
Legendre.SWFJC(number_of_links, link_length, hinge_mass, well_width),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 3681 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ZERO, parameters
using Polymers.Physics.SingleChain.Swfjc.Thermodynamics.Isometric: SWFJC
@testset "physics::single_chain::swfjc::thermodynamics::isometric::test::base::init" begin
@test isa(
SWFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.well_width_reference,
),
Any,
)
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test SWFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.well_width_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test SWFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.well_width_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test SWFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.well_width_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::test::base::well_width" begin
for _ = 1:parameters.number_of_loops
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
@test SWFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
well_width,
).well_width == well_width
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
@test all(
SWFJC(number_of_links, link_length, hinge_mass, well_width).number_of_links ==
number_of_links &&
SWFJC(number_of_links, link_length, hinge_mass, well_width).link_length ==
link_length &&
SWFJC(number_of_links, link_length, hinge_mass, well_width).hinge_mass ==
hinge_mass &&
SWFJC(number_of_links, link_length, hinge_mass, well_width).well_width ==
well_width,
)
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 30059 | """
The square-well freely-jointed chain (SWFJC) model thermodynamics in the isometric ensemble approximated using a Legendre transformation.
"""
module Legendre
using DocStringExtensions
using .......Polymers: PROJECT_ROOT
using .....SingleChain: ONE, ZERO, POINTS, integrate
"""
The structure of the thermodynamics of the SWFJC model in the isometric ensemble approximated using a Legendre transformation.
$(FIELDS)
"""
struct SWFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The width of the well ``w`` in units of nm.
"""
well_width::Float64
normalization_nondimensional_equilibrium_distribution::Float64
"""
The expected force ``f`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
force::Function
"""
The expected nondimensional force ``\\eta`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``.
"""
nondimensional_force::Function
"""
The Helmholtz free energy ``\\psi`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
helmholtz_free_energy::Function
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
helmholtz_free_energy_per_link::Function
"""
The relative Helmholtz free energy ``\\Delta\\psi\\equiv\\psi(\\xi,T)-\\psi(0,T)`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
relative_helmholtz_free_energy::Function
"""
The relative Helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
relative_helmholtz_free_energy_per_link::Function
"""
The nondimensional Helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy::Function
"""
The nondimensional Helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy_per_link::Function
"""
The nondimensional relative Helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``.
"""
nondimensional_relative_helmholtz_free_energy::Function
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``
"""
nondimensional_relative_helmholtz_free_energy_per_link::Function
"""
The equilibrium probability density of end-to-end vectors ``P_\\mathrm{eq}`` as a function of the end-to-end length ``\\xi``.
"""
equilibrium_distribution::Function
"""
The nondimensional equilibrium probability density of end-to-end vectors ``\\mathscr{P}_\\mathrm{eq}`` as a function of the nondimensional end-to-end length per link ``\\gamma``.
"""
nondimensional_equilibrium_distribution::Function
"""
The equilibrium probability density of end-to-end lengths ``g_\\mathrm{eq}`` as a function of the end-to-end length ``\\xi``.
"""
equilibrium_radial_distribution::Function
"""
The nondimensional equilibrium probability density of end-to-end lengths ``\\mathscr{g}_\\mathrm{eq}`` as a function of the nondimensional end-to-end length per link ``\\gamma``.
"""
nondimensional_equilibrium_radial_distribution::Function
end
"""
The expected force as a function ``f`` of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and well width ``w``.
$(TYPEDSIGNATURES)
"""
function force(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
well_width_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isometric_legendre_force,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
well_width_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
well_width,
end_to_end_length,
temperature,
)
end
"""
The expected nondimensional force as a function ``\\eta`` of the applied nondimensional end-to-end length per link ``\\gamma``,
parameterized by the link length ``\\ell_b`` and well width ``w``.
$(TYPEDSIGNATURES)
"""
function nondimensional_force(
link_length::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, well_width_i, nondimensional_end_to_end_length_per_link_i) ->
ccall(
(
:physics_single_chain_swfjc_thermodynamics_isometric_legendre_nondimensional_force,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64),
link_length_i,
well_width_i,
nondimensional_end_to_end_length_per_link_i,
),
link_length,
well_width,
nondimensional_end_to_end_length_per_link,
)
end
"""
The Helmholtz free energy ``\\psi`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, well width ``w``, and hinge mass ``m``,
```math
\\psi(\\xi, T) \\sim \\varphi\\left[f(\\xi, T)\\right] + \\xi f(\\xi, T) \\quad \\text{for } N_b\\gg 1,
```
where ``f(\\xi, T)`` is given by the Legendre transformation approximation above.
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
well_width_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isometric_legendre_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
well_width_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
well_width,
end_to_end_length,
temperature,
)
end
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, well width ``w``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
well_width_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isometric_legendre_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
well_width_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
well_width,
end_to_end_length,
temperature,
)
end
"""
The relative Helmholtz free energy ``\\Delta\\psi\\equiv\\psi(\\xi,T)-\\psi(0,T)`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and well width ``w``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
well_width_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isometric_legendre_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
well_width_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
well_width,
end_to_end_length,
temperature,
)
end
"""
The relative Helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and well width ``w``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
well_width_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isometric_legendre_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
well_width_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
well_width,
end_to_end_length,
temperature,
)
end
"""
The nondimensional Helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, well width ``w``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
well_width_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isometric_legendre_nondimensional_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
well_width_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
well_width,
nondimensional_end_to_end_length_per_link,
temperature,
)
end
"""
The nondimensional Helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, well width ``w``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
well_width_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isometric_legendre_nondimensional_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
well_width_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
well_width,
nondimensional_end_to_end_length_per_link,
temperature,
)
end
"""
The nondimensional relative Helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and well width ``w``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
well_width_i,
nondimensional_end_to_end_length_per_link_i,
) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isometric_legendre_nondimensional_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
well_width_i,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
link_length,
well_width,
nondimensional_end_to_end_length_per_link,
)
end
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and well width ``w``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, well_width_i, nondimensional_end_to_end_length_per_link_i) ->
ccall(
(
:physics_single_chain_swfjc_thermodynamics_isometric_legendre_nondimensional_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64),
link_length_i,
well_width_i,
nondimensional_end_to_end_length_per_link_i,
),
link_length,
well_width,
nondimensional_end_to_end_length_per_link,
)
end
"""
The equilibrium probability density of end-to-end vectors ``P_\\mathrm{eq}`` as a function of the end-to-end length ``\\xi``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and well width ``w``,
```math
P_\\mathrm{eq}(\\xi) = \\frac{e^{-\\beta\\psi(\\xi, T)}}{4\\pi\\int e^{-\\beta\\psi(\\xi', T)} \\,{\\xi'}{}^2 d\\xi'}.
```
$(TYPEDSIGNATURES)
"""
function equilibrium_distribution(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
normalization_nondimensional_equilibrium_distribution::Float64,
end_to_end_length::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, well_width_i, end_to_end_length_i) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isometric_legendre_equilibrium_distribution,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
well_width_i,
normalization_nondimensional_equilibrium_distribution,
end_to_end_length_i,
),
number_of_links,
link_length,
well_width,
end_to_end_length,
)
end
"""
The nondimensional equilibrium probability density of nondimensional end-to-end vectors per link ``\\mathscr{P}_\\mathrm{eq}`` as a function of the nondimensional end-to-end length per link ``\\gamma``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and well width ``w``,
```math
\\mathscr{P}_\\mathrm{eq}(\\gamma) = \\frac{e^{-\\Delta\\vartheta(\\gamma)}}{4\\pi\\int e^{-\\Delta\\vartheta(\\gamma')} \\,{\\gamma'}{}^2 d\\gamma'}.
```
$(TYPEDSIGNATURES)
"""
function nondimensional_equilibrium_distribution(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
normalization_nondimensional_equilibrium_distribution::Float64,
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
well_width_i,
nondimensional_end_to_end_length_per_link_i,
) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isometric_legendre_nondimensional_equilibrium_distribution,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
well_width_i,
normalization_nondimensional_equilibrium_distribution,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
link_length,
well_width,
nondimensional_end_to_end_length_per_link,
)
end
"""
The equilibrium probability density of end-to-end lengths ``g_\\mathrm{eq}`` as a function of the end-to-end length ``\\xi``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and well width ``w``,
```math
g_\\mathrm{eq}(\\xi) = 4\\pi\\xi^2 P_\\mathrm{eq}(\\xi).
```
$(TYPEDSIGNATURES)
"""
function equilibrium_radial_distribution(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
normalization_nondimensional_equilibrium_distribution::Float64,
end_to_end_length::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, well_width_i, end_to_end_length_i) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isometric_legendre_equilibrium_radial_distribution,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
well_width_i,
normalization_nondimensional_equilibrium_distribution,
end_to_end_length_i,
),
number_of_links,
link_length,
well_width,
end_to_end_length,
)
end
"""
The nondimensional equilibrium probability density of nondimensional end-to-end lenghts per link ``\\mathscr{g}_\\mathrm{eq}`` as a function of the nondimensional end-to-end length per link ``\\gamma``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and well width ``w``,
```math
\\mathscr{g}_\\mathrm{eq}(\\gamma) = 4\\pi\\gamma^2 \\mathscr{P}_\\mathrm{eq}(\\gamma).
```
$(TYPEDSIGNATURES)
"""
function nondimensional_equilibrium_radial_distribution(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
normalization_nondimensional_equilibrium_distribution::Float64,
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
well_width_i,
nondimensional_end_to_end_length_per_link_i,
) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isometric_legendre_nondimensional_equilibrium_radial_distribution,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
well_width_i,
normalization_nondimensional_equilibrium_distribution,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
link_length,
well_width,
nondimensional_end_to_end_length_per_link,
)
end
"""
Initializes and returns an instance of the thermodynamics of the SWFJC model in the isometric ensemble approximated using a Legendre transformation.
$(TYPEDSIGNATURES)
"""
function SWFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
well_width::Float64,
)
normalization_nondimensional_equilibrium_distribution = integrate(
nondimensional_end_to_end_length_per_link ->
nondimensional_equilibrium_radial_distribution(
number_of_links,
link_length,
well_width,
1.0,
nondimensional_end_to_end_length_per_link,
),
ZERO,
ONE * (1.0 + well_width / link_length),
POINTS,
)
return SWFJC(
number_of_links,
link_length,
hinge_mass,
well_width,
normalization_nondimensional_equilibrium_distribution,
(end_to_end_length, temperature) ->
force(number_of_links, link_length, well_width, end_to_end_length, temperature),
(nondimensional_end_to_end_length_per_link) -> nondimensional_force(
link_length,
well_width,
nondimensional_end_to_end_length_per_link,
),
(end_to_end_length, temperature) -> helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
well_width,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> helmholtz_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
well_width,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> relative_helmholtz_free_energy(
number_of_links,
link_length,
well_width,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> relative_helmholtz_free_energy_per_link(
number_of_links,
link_length,
well_width,
end_to_end_length,
temperature,
),
(nondimensional_end_to_end_length_per_link, temperature) ->
nondimensional_helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
well_width,
nondimensional_end_to_end_length_per_link,
temperature,
),
(nondimensional_end_to_end_length_per_link, temperature) ->
nondimensional_helmholtz_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
well_width,
nondimensional_end_to_end_length_per_link,
temperature,
),
(nondimensional_end_to_end_length_per_link) ->
nondimensional_relative_helmholtz_free_energy(
number_of_links,
link_length,
well_width,
nondimensional_end_to_end_length_per_link,
),
(nondimensional_end_to_end_length_per_link) ->
nondimensional_relative_helmholtz_free_energy_per_link(
link_length,
well_width,
nondimensional_end_to_end_length_per_link,
),
(end_to_end_length) -> equilibrium_distribution(
number_of_links,
link_length,
well_width,
normalization_nondimensional_equilibrium_distribution,
end_to_end_length,
),
(nondimensional_end_to_end_length_per_link) ->
nondimensional_equilibrium_distribution(
number_of_links,
link_length,
well_width,
normalization_nondimensional_equilibrium_distribution,
nondimensional_end_to_end_length_per_link,
),
(end_to_end_length) -> equilibrium_radial_distribution(
number_of_links,
link_length,
well_width,
normalization_nondimensional_equilibrium_distribution,
end_to_end_length,
),
(nondimensional_end_to_end_length_per_link) ->
nondimensional_equilibrium_radial_distribution(
number_of_links,
link_length,
well_width,
normalization_nondimensional_equilibrium_distribution,
nondimensional_end_to_end_length_per_link,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 47344 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ONE, ZERO, POINTS, integrate, parameters
using Polymers.Physics.SingleChain.Swfjc.Thermodynamics.Isometric.Legendre: SWFJC
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::base::init" begin
@test isa(
SWFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.well_width_reference,
),
Any,
)
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test SWFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.well_width_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test SWFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.well_width_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test SWFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.well_width_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::base::well_width" begin
for _ = 1:parameters.number_of_loops
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
@test SWFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
well_width,
).well_width == well_width
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
@test all(
SWFJC(number_of_links, link_length, hinge_mass, well_width).number_of_links ==
number_of_links &&
SWFJC(number_of_links, link_length, hinge_mass, well_width).link_length ==
link_length &&
SWFJC(number_of_links, link_length, hinge_mass, well_width).hinge_mass ==
hinge_mass &&
SWFJC(number_of_links, link_length, hinge_mass, well_width).well_width ==
well_width,
)
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::normalization::equilibrium_distribution" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
normalization = integrate(
end_to_end_length ->
4.0 *
pi *
end_to_end_length^2 *
model.equilibrium_distribution(end_to_end_length),
ZERO,
ONE * number_of_links * (link_length + well_width),
POINTS,
)
@test abs(normalization - 1.0) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::normalization::equilibrium_radial_distribution" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
normalization = integrate(
end_to_end_length ->
model.equilibrium_radial_distribution(end_to_end_length),
ZERO,
ONE * number_of_links * (link_length + well_width),
POINTS,
)
@test abs(normalization - 1.0) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::normalization::nondimensional_equilibrium_distribution" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
normalization = integrate(
nondimensional_end_to_end_length_per_link ->
4.0 *
pi *
nondimensional_end_to_end_length_per_link^2 *
model.nondimensional_equilibrium_distribution(
nondimensional_end_to_end_length_per_link,
),
ZERO,
ONE * (1.0 + well_width / link_length),
POINTS,
)
@test abs(normalization - 1.0) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::normalization::nondimensional_equilibrium_radial_distribution" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
normalization = integrate(
nondimensional_end_to_end_length_per_link ->
model.nondimensional_equilibrium_radial_distribution(
nondimensional_end_to_end_length_per_link,
),
ZERO,
ONE * (1.0 + well_width / link_length),
POINTS,
)
@test abs(normalization - 1.0) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::nondimensional::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
model.nondimensional_force(nondimensional_end_to_end_length_per_link)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
force = model.force(end_to_end_length, temperature)
residual_abs =
force / BOLTZMANN_CONSTANT / temperature * link_length - nondimensional_force
residual_rel = residual_abs / nondimensional_force
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::nondimensional::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy = model.helmholtz_free_energy(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::nondimensional::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::nondimensional::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(end_to_end_length, temperature)
residual_abs =
relative_helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::nondimensional::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
relative_helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::per_link::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy = model.helmholtz_free_energy(end_to_end_length, temperature)
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy / number_of_links - helmholtz_free_energy_per_link
residual_rel = residual_abs / helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::per_link::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(end_to_end_length, temperature)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
relative_helmholtz_free_energy / number_of_links -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::per_link::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy / number_of_links -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::per_link::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy / number_of_links -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::relative::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy = model.helmholtz_free_energy(end_to_end_length, temperature)
helmholtz_free_energy_0 =
model.helmholtz_free_energy(ZERO * number_of_links * link_length, temperature)
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy - helmholtz_free_energy_0 - relative_helmholtz_free_energy
residual_rel = residual_abs / relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::relative::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(end_to_end_length, temperature)
helmholtz_free_energy_per_link_0 = model.helmholtz_free_energy_per_link(
ZERO * number_of_links * link_length,
temperature,
)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy_per_link - helmholtz_free_energy_per_link_0 -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::relative::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_0 =
model.nondimensional_helmholtz_free_energy(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
)
residual_abs =
nondimensional_helmholtz_free_energy - nondimensional_helmholtz_free_energy_0 -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::relative::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_per_link_0 =
model.nondimensional_helmholtz_free_energy_per_link(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
)
residual_abs =
nondimensional_helmholtz_free_energy_per_link -
nondimensional_helmholtz_free_energy_per_link_0 -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::zero::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force_0 = model.force(ZERO * number_of_links * link_length, temperature)
@test abs(force_0) <=
3.1 * ZERO * number_of_links * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::zero::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_force_0 = model.nondimensional_force(ZERO)
@test abs(nondimensional_force_0) <= 3.1 * ZERO * number_of_links
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::zero::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_0 = model.relative_helmholtz_free_energy(
ZERO * number_of_links * link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_0) <=
ZERO * number_of_links * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::zero::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_per_link_0 =
model.relative_helmholtz_free_energy_per_link(
ZERO * number_of_links * link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::zero::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_relative_helmholtz_free_energy_0 =
model.nondimensional_relative_helmholtz_free_energy(ZERO)
@test abs(nondimensional_relative_helmholtz_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::zero::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_relative_helmholtz_free_energy_per_link_0 =
model.nondimensional_relative_helmholtz_free_energy_per_link(ZERO)
@test abs(nondimensional_relative_helmholtz_free_energy_per_link_0) <= ZERO
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::zero::equilibrium_radial_distribution" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
equilibrium_radial_distribution_0 =
model.equilibrium_radial_distribution(ZERO * number_of_links * link_length)
@test abs(equilibrium_radial_distribution_0) <= ZERO
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::zero::nondimensional_equilibrium_radial_distribution" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_equilibrium_radial_distribution_0 =
model.equilibrium_radial_distribution(ZERO)
@test abs(nondimensional_equilibrium_radial_distribution_0) <= ZERO
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::connection::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
force = model.force(end_to_end_length, temperature)
h = parameters.rel_tol * number_of_links * link_length
force_from_derivative =
(
model.relative_helmholtz_free_energy(
end_to_end_length + 0.5 * h,
temperature,
) - model.relative_helmholtz_free_energy(
end_to_end_length - 0.5 * h,
temperature,
)
) / h
residual_abs = force - force_from_derivative
residual_rel = residual_abs / force
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::connection::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
nondimensional_force =
model.nondimensional_force(nondimensional_end_to_end_length_per_link)
h = parameters.rel_tol
nondimensional_force_from_derivative =
(
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link + 0.5 * h,
) - model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link - 0.5 * h,
)
) / h
residual_abs = nondimensional_force - nondimensional_force_from_derivative
residual_rel = residual_abs / nondimensional_force
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::connection::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(end_to_end_length, temperature)
relative_helmholtz_free_energy_from_connection =
BOLTZMANN_CONSTANT *
temperature *
log((
model.equilibrium_distribution(ZERO * number_of_links * link_length) /
model.equilibrium_distribution(end_to_end_length)
))
residual_abs =
relative_helmholtz_free_energy - relative_helmholtz_free_energy_from_connection
residual_rel = residual_abs / relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isometric::legendre::test::connection::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
)
nondimensional_relative_helmholtz_free_energy_from_connection = log((
model.nondimensional_equilibrium_distribution(ZERO) /
model.nondimensional_equilibrium_distribution(
nondimensional_end_to_end_length_per_link,
)
))
residual_abs =
nondimensional_relative_helmholtz_free_energy -
nondimensional_relative_helmholtz_free_energy_from_connection
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 21607 | """
The square-well freely-jointed chain (SWFJC) model thermodynamics in the isotensional ensemble.
"""
module Isotensional
using DocStringExtensions
using ......Polymers: PROJECT_ROOT
include("legendre/mod.jl")
"""
The structure of the thermodynamics of the SWFJC model in the isotensional ensemble.
$(FIELDS)
"""
struct SWFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The width of the well ``w`` in units of nm.
"""
well_width::Float64
"""
The thermodynamic functions of the model in the isotensional ensemble approximated using a Legendre transformation.
"""
legendre::Any
"""
The expected end-to-end length ``\\xi`` as a function of the applied force ``f`` and temperature ``T``.
"""
end_to_end_length::Function
"""
The expected end-to-end length per link ``\\xi/N_b=\\ell_b\\gamma`` as a function of the applied force ``f`` and temperature ``T``.
"""
end_to_end_length_per_link::Function
"""
The expected nondimensional end-to-end length ``N_b\\gamma=\\xi/\\ell_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_end_to_end_length::Function
"""
The expected nondimensional end-to-end length per link ``\\gamma\\equiv\\xi/N_b\\ell_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_end_to_end_length_per_link::Function
"""
The Gibbs free energy ``\\varphi`` as a function of the applied force ``f`` and temperature ``T``.
"""
gibbs_free_energy::Function
"""
The Gibbs free energy per link ``\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
gibbs_free_energy_per_link::Function
"""
The relative Gibbs free energy ``\\Delta\\varphi\\equiv\\varphi(f,T)-\\varphi(0,T)`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_gibbs_free_energy::Function
"""
The relative Gibbs free energy per link ``\\Delta\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_gibbs_free_energy_per_link::Function
"""
The nondimensional Gibbs free energy ``N_b\\varrho=\\beta\\varphi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_gibbs_free_energy::Function
"""
The nondimensional Gibbs free energy per link ``\\varrho\\equiv\\beta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_gibbs_free_energy_per_link::Function
"""
The nondimensional relative Gibbs free energy ``N_b\\Delta\\varrho=\\beta\\Delta\\varphi`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_gibbs_free_energy::Function
"""
The nondimensional relative Gibbs free energy per link ``\\Delta\\varrho\\equiv\\beta\\Delta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_gibbs_free_energy_per_link::Function
end
"""
The expected end-to-end length ``N_b\\gamma=\\xi/\\ell_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and well width ``w``,
```math
\\xi(f, T) = -\\frac{\\partial\\varphi}{\\partial f}.
```
$(TYPEDSIGNATURES)
"""
function end_to_end_length(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, well_width_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isotensional_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
well_width_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
well_width,
force,
temperature,
)
end
"""
The expected end-to-end length per link ``\\xi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and well width ``w``
$(TYPEDSIGNATURES)
"""
function end_to_end_length_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, well_width_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isotensional_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
well_width_i,
force_i,
temperature_i,
),
link_length,
well_width,
force,
temperature,
)
end
"""
The expected nondimensional end-to-end length ``N_b\\gamma=\\xi/\\ell_b`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and well width ``w``.
$(TYPEDSIGNATURES)
"""
function nondimensional_end_to_end_length(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, well_width_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isotensional_nondimensional_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
well_width_i,
nondimensional_force_i,
),
number_of_links,
link_length,
well_width,
nondimensional_force,
)
end
"""
The expected nondimensional end-to-end length per link ``\\gamma\\equiv \\xi/N_b\\ell_b`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the link length ``\\ell_b`` and well width ``w``,
given by [Buche et al.](https://doi.org/10.1103/PhysRevE.106.024502) as
```math
\\gamma(\\eta) = -\\frac{\\partial\\varrho}{\\partial\\eta} = \\frac{\\varsigma^2\\eta\\sinh(\\varsigma\\eta) - \\eta\\sinh(\\eta)}{y(\\eta,\\varsigma) - y(\\eta,1)},
```
where ``\\varsigma\\equiv 1+w/\\ell_b`` is the nondimensional well width parameter,
and where ``y(\\eta,\\varsigma)\\equiv\\varsigma\\eta\\cosh(\\varsigma\\eta)-\\sinh(\\varsigma\\eta)``.
$(TYPEDSIGNATURES)
"""
function nondimensional_end_to_end_length_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, well_width_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isotensional_nondimensional_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64),
link_length_i,
well_width_i,
nondimensional_force_i,
),
link_length,
well_width,
nondimensional_force,
)
end
"""
The Gibbs free energy ``\\varphi`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and well width ``w``.
```math
\\varphi(f, T) = -kT\\ln Z(f, T).
```
$(TYPEDSIGNATURES)
"""
function gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
well_width_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isotensional_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
well_width_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
well_width,
force,
temperature,
)
end
"""
The Gibbs free energy per link ``\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and well width ``w``.
$(TYPEDSIGNATURES)
"""
function gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, hinge_mass_i, well_width_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isotensional_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
well_width_i,
force_i,
temperature_i,
),
link_length,
hinge_mass,
well_width,
force,
temperature,
)
end
"""
The relative Gibbs free energy ``\\Delta\\varphi\\equiv\\varphi(f,T)-\\varphi(0,T)`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and well width ``w``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, well_width_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isotensional_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
well_width_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
well_width,
force,
temperature,
)
end
"""
The relative Gibbs free energy per link ``\\Delta\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and well width ``w``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, well_width_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isotensional_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
well_width_i,
force_i,
temperature_i,
),
link_length,
well_width,
force,
temperature,
)
end
"""
The nondimensional Gibbs free energy ``N_b\\varrho=\\beta\\varphi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and well width ``w``.
$(TYPEDSIGNATURES)
"""
function nondimensional_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
well_width_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isotensional_nondimensional_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
well_width_i,
nondimensional_force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
well_width,
nondimensional_force,
temperature,
)
end
"""
The nondimensional Gibbs free energy per link ``\\varrho\\equiv\\beta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and well width ``w``.
$(TYPEDSIGNATURES)
"""
function nondimensional_gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
link_length_i,
hinge_mass_i,
well_width_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isotensional_nondimensional_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
well_width_i,
nondimensional_force_i,
temperature_i,
),
link_length,
hinge_mass,
well_width,
nondimensional_force,
temperature,
)
end
"""
The nondimensional relative Gibbs free energy ``N_b\\Delta\\varrho=\\beta\\Delta\\varphi`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and well width ``w``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, well_width_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isotensional_nondimensional_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
well_width_i,
nondimensional_force_i,
),
number_of_links,
link_length,
well_width,
nondimensional_force,
)
end
"""
The nondimensional relative Gibbs free energy per link ``\\Delta\\varrho\\equiv\\beta\\Delta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the link length ``\\ell_b`` and well width ``w``,
given by [Buche et al.](https://doi.org/10.1103/PhysRevE.106.024502) as
```math
\\Delta\\varrho(\\eta) = 3\\ln(\\eta) - \\ln\\left[y(\\eta,\\varsigma) - y(\\eta,1)\\right],
```
where ``\\varsigma\\equiv 1+w/\\ell_b`` is the nondimensional well width parameter,
and where ``y(\\eta,\\varsigma)\\equiv\\varsigma\\eta\\cosh(\\varsigma\\eta)-\\sinh(\\varsigma\\eta)``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, well_width_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isotensional_nondimensional_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64),
link_length_i,
well_width_i,
nondimensional_force_i,
),
link_length,
well_width,
nondimensional_force,
)
end
"""
Initializes and returns an instance of the thermodynamics of the SWFJC model in the isotensional ensemble.
$(TYPEDSIGNATURES)
"""
function SWFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
well_width::Float64,
)
return SWFJC(
number_of_links,
link_length,
hinge_mass,
well_width,
Legendre.SWFJC(number_of_links, link_length, hinge_mass, well_width),
(force, temperature) ->
end_to_end_length(number_of_links, link_length, well_width, force, temperature),
(force, temperature) ->
end_to_end_length_per_link(link_length, well_width, force, temperature),
nondimensional_force -> nondimensional_end_to_end_length(
number_of_links,
link_length,
well_width,
nondimensional_force,
),
nondimensional_force -> nondimensional_end_to_end_length_per_link(
link_length,
well_width,
nondimensional_force,
),
(force, temperature) -> gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
well_width,
force,
temperature,
),
(force, temperature) -> gibbs_free_energy_per_link(
link_length,
hinge_mass,
well_width,
force,
temperature,
),
(force, temperature) -> relative_gibbs_free_energy(
number_of_links,
link_length,
well_width,
force,
temperature,
),
(force, temperature) -> relative_gibbs_free_energy_per_link(
link_length,
well_width,
force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
well_width,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_gibbs_free_energy_per_link(
link_length,
hinge_mass,
well_width,
nondimensional_force,
temperature,
),
nondimensional_force -> nondimensional_relative_gibbs_free_energy(
number_of_links,
link_length,
well_width,
nondimensional_force,
),
nondimensional_force -> nondimensional_relative_gibbs_free_energy_per_link(
link_length,
well_width,
nondimensional_force,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 59555 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ZERO, parameters
using Polymers.Physics.SingleChain.Swfjc.Thermodynamics.Isotensional: SWFJC
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::base::init" begin
@test isa(
SWFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.well_width_reference,
),
Any,
)
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test SWFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.well_width_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test SWFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.well_width_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test SWFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.well_width_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::base::well_width" begin
for _ = 1:parameters.number_of_loops
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
@test SWFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
well_width,
).well_width == well_width
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
@test all(
SWFJC(number_of_links, link_length, hinge_mass, well_width).number_of_links ==
number_of_links &&
SWFJC(number_of_links, link_length, hinge_mass, well_width).link_length ==
link_length &&
SWFJC(number_of_links, link_length, hinge_mass, well_width).hinge_mass ==
hinge_mass &&
SWFJC(number_of_links, link_length, hinge_mass, well_width).well_width ==
well_width,
)
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::nondimensional::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
residual_abs = end_to_end_length / link_length - nondimensional_end_to_end_length
residual_rel = residual_abs / nondimensional_end_to_end_length
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::nondimensional::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(nondimensional_force)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
residual_abs =
end_to_end_length_per_link / link_length -
nondimensional_end_to_end_length_per_link
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::nondimensional::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
residual_abs =
gibbs_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_gibbs_free_energy
residual_rel = residual_abs / nondimensional_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::nondimensional::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
residual_abs =
gibbs_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::nondimensional::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(nondimensional_force)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
residual_abs =
relative_gibbs_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_gibbs_free_energy
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::nondimensional::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(nondimensional_force)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
residual_abs =
relative_gibbs_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::per_link::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
residual_abs = end_to_end_length / number_of_links - end_to_end_length_per_link
residual_rel = residual_abs / end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::per_link::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force)
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(nondimensional_force)
residual_abs =
nondimensional_end_to_end_length / number_of_links -
nondimensional_end_to_end_length_per_link
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::per_link::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
residual_abs = gibbs_free_energy / number_of_links - gibbs_free_energy_per_link
residual_rel = residual_abs / gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::per_link::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
residual_abs =
relative_gibbs_free_energy / number_of_links -
relative_gibbs_free_energy_per_link
residual_rel = residual_abs / relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::per_link::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_gibbs_free_energy / number_of_links -
nondimensional_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::per_link::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(nondimensional_force)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(nondimensional_force)
residual_abs =
nondimensional_relative_gibbs_free_energy / number_of_links -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::relative::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
gibbs_free_energy_0 = model.gibbs_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
residual_abs = gibbs_free_energy - gibbs_free_energy_0 - relative_gibbs_free_energy
residual_rel = residual_abs / gibbs_free_energy_0
@test abs(residual_abs) <=
BOLTZMANN_CONSTANT * temperature * number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::relative::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
gibbs_free_energy_per_link_0 = model.gibbs_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
residual_abs =
gibbs_free_energy_per_link - gibbs_free_energy_per_link_0 -
relative_gibbs_free_energy_per_link
residual_rel = residual_abs / gibbs_free_energy_per_link_0
@test abs(residual_abs) <= BOLTZMANN_CONSTANT * temperature * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::relative::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
nondimensional_gibbs_free_energy_0 =
model.nondimensional_gibbs_free_energy(ZERO, temperature)
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(nondimensional_force)
residual_abs =
nondimensional_gibbs_free_energy - nondimensional_gibbs_free_energy_0 -
nondimensional_relative_gibbs_free_energy
residual_rel = residual_abs / nondimensional_gibbs_free_energy_0
@test abs(residual_abs) <= number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::relative::nondimensional_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_gibbs_free_energy_per_link_0 =
model.nondimensional_gibbs_free_energy_per_link(ZERO, temperature)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(nondimensional_force)
residual_abs =
nondimensional_gibbs_free_energy_per_link -
nondimensional_gibbs_free_energy_per_link_0 -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link_0
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::zero::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_gibbs_free_energy_0 = model.relative_gibbs_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_gibbs_free_energy_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature * number_of_links
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::zero::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_gibbs_free_energy_per_link_0 = model.relative_gibbs_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_gibbs_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::zero::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_relative_gibbs_free_energy_0 =
model.nondimensional_relative_gibbs_free_energy(ZERO)
@test abs(nondimensional_relative_gibbs_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::zero::nondimensional_relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_relative_gibbs_free_energy_per_link_0 =
model.nondimensional_relative_gibbs_free_energy_per_link(ZERO)
@test abs(nondimensional_relative_gibbs_free_energy_per_link_0) <= ZERO
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::connection::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
h = parameters.rel_tol * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_from_derivative =
-(
model.relative_gibbs_free_energy(force + 0.5 * h, temperature) -
model.relative_gibbs_free_energy(force - 0.5 * h, temperature)
) / h
residual_abs = end_to_end_length - end_to_end_length_from_derivative
residual_rel = residual_abs / end_to_end_length
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::connection::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
h = parameters.rel_tol * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link_from_derivative =
-(
model.relative_gibbs_free_energy_per_link(force + 0.5 * h, temperature) -
model.relative_gibbs_free_energy_per_link(force - 0.5 * h, temperature)
) / h
residual_abs =
end_to_end_length_per_link - end_to_end_length_per_link_from_derivative
residual_rel = residual_abs / end_to_end_length_per_link
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::connection::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force)
h = parameters.rel_tol
nondimensional_end_to_end_length_from_derivative =
-(
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force + 0.5 * h,
) - model.nondimensional_relative_gibbs_free_energy(
nondimensional_force - 0.5 * h,
)
) / h
residual_abs =
nondimensional_end_to_end_length -
nondimensional_end_to_end_length_from_derivative
residual_rel = residual_abs / nondimensional_end_to_end_length
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::connection::nondimensional_end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(nondimensional_force)
h = parameters.rel_tol
nondimensional_end_to_end_length_per_link_from_derivative =
-(
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force + 0.5 * h,
) - model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force - 0.5 * h,
)
) / h
residual_abs =
nondimensional_end_to_end_length_per_link -
nondimensional_end_to_end_length_per_link_from_derivative
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::legendre::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
gibbs_free_energy_legendre =
model.legendre.helmholtz_free_energy(force, temperature) -
force * end_to_end_length
residual_abs = gibbs_free_energy - gibbs_free_energy_legendre
residual_rel = residual_abs / gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::legendre::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
gibbs_free_energy_per_link_legendre =
model.legendre.helmholtz_free_energy_per_link(force, temperature) -
force * end_to_end_length_per_link
residual_abs = gibbs_free_energy_per_link - gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::legendre::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
end_to_end_length_0 = model.end_to_end_length(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
relative_gibbs_free_energy_legendre =
model.legendre.relative_helmholtz_free_energy(force, temperature) -
force * end_to_end_length +
ZERO * BOLTZMANN_CONSTANT * temperature / link_length * end_to_end_length_0
residual_abs = relative_gibbs_free_energy - relative_gibbs_free_energy_legendre
residual_rel = residual_abs / relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::legendre::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
end_to_end_length_per_link_0 = model.end_to_end_length_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
relative_gibbs_free_energy_per_link_legendre =
model.legendre.relative_helmholtz_free_energy_per_link(force, temperature) -
force * end_to_end_length_per_link +
ZERO * BOLTZMANN_CONSTANT * temperature / link_length *
end_to_end_length_per_link_0
residual_abs =
relative_gibbs_free_energy_per_link -
relative_gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::legendre::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force)
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
nondimensional_gibbs_free_energy_legendre =
model.legendre.nondimensional_helmholtz_free_energy(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length
residual_abs =
nondimensional_gibbs_free_energy - nondimensional_gibbs_free_energy_legendre
residual_rel = residual_abs / nondimensional_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::legendre::nondimensional_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(nondimensional_force)
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_gibbs_free_energy_per_link_legendre =
model.legendre.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length_per_link
residual_abs =
nondimensional_gibbs_free_energy_per_link -
nondimensional_gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::legendre::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force)
nondimensional_end_to_end_length_0 = model.nondimensional_end_to_end_length(ZERO)
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(nondimensional_force)
nondimensional_relative_gibbs_free_energy_legendre =
model.legendre.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
) - nondimensional_force * nondimensional_end_to_end_length +
ZERO * nondimensional_end_to_end_length_0
residual_abs =
nondimensional_relative_gibbs_free_energy -
nondimensional_relative_gibbs_free_energy_legendre
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::legendre::nondimensional_relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(nondimensional_force)
nondimensional_end_to_end_length_per_link_0 =
model.nondimensional_end_to_end_length_per_link(ZERO)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(nondimensional_force)
nondimensional_relative_gibbs_free_energy_per_link_legendre =
model.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
) - nondimensional_force * nondimensional_end_to_end_length_per_link +
ZERO * nondimensional_end_to_end_length_per_link_0
residual_abs =
nondimensional_relative_gibbs_free_energy_per_link -
nondimensional_relative_gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::legendre_connection::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
h = parameters.rel_tol * BOLTZMANN_CONSTANT * temperature / link_length
force_from_derivative =
(
model.legendre.relative_helmholtz_free_energy(
force + 0.5 * h,
temperature,
) -
model.legendre.relative_helmholtz_free_energy(force - 0.5 * h, temperature)
) / (
model.end_to_end_length(force + 0.5 * h, temperature) -
model.end_to_end_length(force - 0.5 * h, temperature)
)
residual_abs = force - force_from_derivative
residual_rel = residual_abs / force
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::test::legendre_connection::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
h = parameters.rel_tol
nondimensional_force_from_derivative =
(
model.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force + 0.5 * h,
) - model.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force - 0.5 * h,
)
) / (
model.nondimensional_end_to_end_length_per_link(
nondimensional_force + 0.5 * h,
) - model.nondimensional_end_to_end_length_per_link(
nondimensional_force - 0.5 * h,
)
)
residual_abs = nondimensional_force - nondimensional_force_from_derivative
residual_rel = residual_abs / nondimensional_force
@test abs(residual_rel) <= h
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 15033 | """
The square-well freely-jointed chain (SWFJC) model thermodynamics in the isotensional ensemble approximated using a Legendre transformation.
"""
module Legendre
using DocStringExtensions
using .......Polymers: PROJECT_ROOT
"""
The structure of the thermodynamics of the SWFJC model in the isotensional ensemble approximated using a Legendre transformation.
$(FIELDS)
"""
struct SWFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The width of the well ``w`` in units of nm.
"""
well_width::Float64
"""
The Helmholtz free energy ``\\psi`` as a function of the applied force ``f`` and temperature ``T``.
"""
helmholtz_free_energy::Function
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
helmholtz_free_energy_per_link::Function
"""
The relative helmholtz free energy ``\\Delta\\psi\\equiv\\psi(f,T)-\\psi(0,T)`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_helmholtz_free_energy::Function
"""
The relative helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_helmholtz_free_energy_per_link::Function
"""
The nondimensional helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy::Function
"""
The nondimensional helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy_per_link::Function
"""
The nondimensional relative helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_helmholtz_free_energy::Function
"""
The nondimensional relative helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_helmholtz_free_energy_per_link::Function
end
"""
The Helmholtz free energy ``\\psi`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and well width ``w``.
```math
\\psi(f, T) \\sim \\varphi(f, T) + f \\xi(f, T) \\quad \\text{for } N_b\\gg 1.
```
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
well_width_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isotensional_legendre_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
well_width_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
well_width,
force,
temperature,
)
end
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and well width ``w``.
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, hinge_mass_i, well_width_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isotensional_legendre_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
well_width_i,
force_i,
temperature_i,
),
link_length,
hinge_mass,
well_width,
force,
temperature,
)
end
"""
The relative Helmholtz free energy ``\\Delta\\psi\\equiv\\psi(f,T)-\\psi(0,T)`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and well width ``w``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, well_width_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isotensional_legendre_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
well_width_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
well_width,
force,
temperature,
)
end
"""
The relative Helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and well width ``w``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, well_width_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isotensional_legendre_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
well_width_i,
force_i,
temperature_i,
),
link_length,
well_width,
force,
temperature,
)
end
"""
The nondimensional Helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and well width ``w``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
well_width_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isotensional_legendre_nondimensional_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
well_width_i,
nondimensional_force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
well_width,
nondimensional_force,
temperature,
)
end
"""
The nondimensional Helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and well width ``w``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
link_length_i,
hinge_mass_i,
well_width_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isotensional_legendre_nondimensional_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
well_width_i,
nondimensional_force_i,
temperature_i,
),
link_length,
hinge_mass,
well_width,
nondimensional_force,
temperature,
)
end
"""
The nondimensional relative Helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and well width ``w``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, well_width_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isotensional_legendre_nondimensional_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
well_width_i,
nondimensional_force_i,
),
number_of_links,
link_length,
well_width,
nondimensional_force,
)
end
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta``
parameterized by the link length ``\\ell_b`` and well width ``w``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
well_width::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, well_width_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_swfjc_thermodynamics_isotensional_legendre_nondimensional_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64),
link_length_i,
well_width_i,
nondimensional_force_i,
),
link_length,
well_width,
nondimensional_force,
)
end
"""
Initializes and returns an instance of the thermodynamics of the SWFJC model in the isotensional ensemble approximated using a Legendre transformation.
$(TYPEDSIGNATURES)
"""
function SWFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
well_width::Float64,
)
return SWFJC(
number_of_links,
link_length,
hinge_mass,
well_width,
(force, temperature) -> helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
well_width,
force,
temperature,
),
(force, temperature) -> helmholtz_free_energy_per_link(
link_length,
hinge_mass,
well_width,
force,
temperature,
),
(force, temperature) -> relative_helmholtz_free_energy(
number_of_links,
link_length,
well_width,
force,
temperature,
),
(force, temperature) -> relative_helmholtz_free_energy_per_link(
link_length,
well_width,
force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
well_width,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) ->
nondimensional_helmholtz_free_energy_per_link(
link_length,
hinge_mass,
well_width,
nondimensional_force,
temperature,
),
nondimensional_force -> nondimensional_relative_helmholtz_free_energy(
number_of_links,
link_length,
well_width,
nondimensional_force,
),
nondimensional_force -> nondimensional_relative_helmholtz_free_energy_per_link(
link_length,
well_width,
nondimensional_force,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 29099 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ZERO, parameters
using Polymers.Physics.SingleChain.Swfjc.Thermodynamics.Isotensional.Legendre: SWFJC
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::legendre::test::base::init" begin
@test isa(
SWFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.well_width_reference,
),
Any,
)
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::legendre::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test SWFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.well_width_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::legendre::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test SWFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.well_width_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::legendre::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test SWFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.well_width_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::legendre::test::base::well_width" begin
for _ = 1:parameters.number_of_loops
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
@test SWFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
well_width,
).well_width == well_width
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::legendre::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
@test all(
SWFJC(number_of_links, link_length, hinge_mass, well_width).number_of_links ==
number_of_links &&
SWFJC(number_of_links, link_length, hinge_mass, well_width).link_length ==
link_length &&
SWFJC(number_of_links, link_length, hinge_mass, well_width).hinge_mass ==
hinge_mass &&
SWFJC(number_of_links, link_length, hinge_mass, well_width).well_width ==
well_width,
)
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::legendre::test::nondimensional::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy =
model.nondimensional_helmholtz_free_energy(nondimensional_force, temperature)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy = model.helmholtz_free_energy(force, temperature)
residual_abs =
helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::legendre::test::nondimensional::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(force, temperature)
residual_abs =
helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::legendre::test::nondimensional::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(nondimensional_force)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(force, temperature)
residual_abs =
relative_helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::legendre::test::nondimensional::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(force, temperature)
residual_abs =
relative_helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::legendre::test::per_link::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy = model.helmholtz_free_energy(force, temperature)
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(force, temperature)
residual_abs =
helmholtz_free_energy / number_of_links - helmholtz_free_energy_per_link
residual_rel = residual_abs / helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::legendre::test::per_link::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(force, temperature)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(force, temperature)
residual_abs =
relative_helmholtz_free_energy / number_of_links -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::legendre::test::per_link::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy =
model.nondimensional_helmholtz_free_energy(nondimensional_force, temperature)
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy / number_of_links -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::legendre::test::per_link::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(nondimensional_force)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy / number_of_links -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::legendre::test::relative::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy = model.helmholtz_free_energy(force, temperature)
helmholtz_free_energy_0 = model.helmholtz_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(force, temperature)
residual_abs =
helmholtz_free_energy - helmholtz_free_energy_0 - relative_helmholtz_free_energy
residual_rel = residual_abs / helmholtz_free_energy_0
@test abs(residual_abs) <=
BOLTZMANN_CONSTANT * temperature * number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::legendre::test::relative::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(force, temperature)
helmholtz_free_energy_per_link_0 = model.helmholtz_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(force, temperature)
residual_abs =
helmholtz_free_energy_per_link - helmholtz_free_energy_per_link_0 -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / helmholtz_free_energy_per_link_0
@test abs(residual_abs) <= BOLTZMANN_CONSTANT * temperature * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::legendre::test::relative::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy =
model.nondimensional_helmholtz_free_energy(nondimensional_force, temperature)
nondimensional_helmholtz_free_energy_0 =
model.nondimensional_helmholtz_free_energy(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(nondimensional_force)
residual_abs =
nondimensional_helmholtz_free_energy - nondimensional_helmholtz_free_energy_0 -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_0
@test abs(residual_abs) <= number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::legendre::test::relative::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_helmholtz_free_energy_per_link_0 =
model.nondimensional_helmholtz_free_energy_per_link(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
)
residual_abs =
nondimensional_helmholtz_free_energy_per_link -
nondimensional_helmholtz_free_energy_per_link_0 -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link_0
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::legendre::test::zero::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_0 = model.relative_helmholtz_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature * number_of_links
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::legendre::test::zero::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_per_link_0 =
model.relative_helmholtz_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::legendre::test::zero::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_relative_helmholtz_free_energy_0 =
model.nondimensional_relative_helmholtz_free_energy(ZERO)
@test abs(nondimensional_relative_helmholtz_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::swfjc::thermodynamics::isotensional::legendre::test::zero::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
well_width =
parameters.well_width_reference + parameters.well_width_scale * (0.5 - rand())
model = SWFJC(number_of_links, link_length, hinge_mass, well_width)
nondimensional_relative_helmholtz_free_energy_per_link_0 =
model.nondimensional_relative_helmholtz_free_energy_per_link(ZERO)
@test abs(nondimensional_relative_helmholtz_free_energy_per_link_0) <= ZERO
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 199 | """
The arbitrary link potential freely-jointed chain (uFJC) single-chain model.
"""
module Ufjc
include("lennard_jones/mod.jl")
include("log_squared/mod.jl")
include("morse/mod.jl")
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 1370 | """
The Lennard-Jones potential freely-jointed chain (Lennard-Jones-FJC) single-chain model.
"""
module LennardJones
using DocStringExtensions
include("thermodynamics/mod.jl")
"""
The structure of the Lennard-Jones-FJC model.
$(FIELDS)
"""
struct LENNARDJONESFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The stiffness of each link in the chain ``k_0`` in units of J/(mol⋅nm^2).
"""
link_stiffness::Float64
"""
The thermodynamic functions of the model.
"""
thermodynamics::Any
end
"""
Initializes and returns an instance of the Lennard-Jones-FJC model.
$(TYPEDSIGNATURES)
"""
function LENNARDJONESFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
)
return LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
Thermodynamics.LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 4080 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ZERO, parameters
using Polymers.Physics.SingleChain.Ufjc.LennardJones: LENNARDJONESFJC
@testset "physics::single_chain::ufjc::lennard_jones::test::base::init" begin
@test isa(
LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
),
Any,
)
end
@testset "physics::single_chain::ufjc::lennard_jones::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test LENNARDJONESFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ufjc::lennard_jones::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ufjc::lennard_jones::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.link_stiffness_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ufjc::lennard_jones::test::base::link_stiffness" begin
for _ = 1:parameters.number_of_loops
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
link_stiffness,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::lennard_jones::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test all(
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).number_of_links == number_of_links &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_length == link_length &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).hinge_mass == hinge_mass &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_stiffness == link_stiffness,
)
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 1688 | """
The Lennard-Jones potential freely-jointed chain (Lennard-Jones-FJC) single-chain model thermodynamics.
"""
module Thermodynamics
using DocStringExtensions
include("isometric/mod.jl")
include("isotensional/mod.jl")
"""
The structure of the thermodynamics of the Lennard-Jones-FJC model.
$(FIELDS)
"""
struct LENNARDJONESFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The stiffness of each link in the chain ``k_0`` in units of J/(mol⋅nm^2).
"""
link_stiffness::Float64
"""
The thermodynamic functions of the model in the isometric ensemble.
"""
isometric::Any
"""
The thermodynamic functions of the model in the isotensional ensemble.
"""
isotensional::Any
end
"""
Initializes and returns an instance of the thermodynamics of the Lennard-Jones-FJC model.
$(TYPEDSIGNATURES)
"""
function LENNARDJONESFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
)
return LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
Isometric.LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness),
Isotensional.LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 51948 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT, PLANCK_CONSTANT
using Polymers.Physics.SingleChain: parameters
using Polymers.Physics.SingleChain.Ufjc.LennardJones.Thermodynamics: LENNARDJONESFJC
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::test::base::init" begin
@test isa(
LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
),
Any,
)
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test LENNARDJONESFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.link_stiffness_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::test::base::link_stiffness" begin
for _ = 1:parameters.number_of_loops
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
link_stiffness,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test all(
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).number_of_links == number_of_links &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_length == link_length &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).hinge_mass == hinge_mass &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_stiffness == link_stiffness,
)
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::test::legendre_asymptotic::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length =
model.isotensional.asymptotic.end_to_end_length(force, temperature)
force_out =
model.isometric.asymptotic.legendre.force(end_to_end_length, temperature)
residual_abs = force - force_out
residual_rel = residual_abs / force
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::test::legendre_asymptotic::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.isotensional.asymptotic.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_force_out = model.isometric.asymptotic.legendre.nondimensional_force(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs = nondimensional_force - nondimensional_force_out
residual_rel = residual_abs / nondimensional_force
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::test::legendre_asymptotic::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length =
model.isotensional.asymptotic.end_to_end_length(force, temperature)
helmholtz_free_energy_legendre =
model.isotensional.asymptotic.gibbs_free_energy(force, temperature) +
force * end_to_end_length
helmholtz_free_energy_legendre_out =
model.isometric.asymptotic.legendre.helmholtz_free_energy(
end_to_end_length,
temperature,
)
residual_abs =
helmholtz_free_energy_legendre - helmholtz_free_energy_legendre_out +
BOLTZMANN_CONSTANT *
temperature *
(
0.5 * log(2.0 * pi * BOLTZMANN_CONSTANT * temperature / link_stiffness) +
log(
8.0 *
pi^2 *
hinge_mass *
link_length^2 *
BOLTZMANN_CONSTANT *
temperature / PLANCK_CONSTANT^2,
)
)
residual_rel = residual_abs / helmholtz_free_energy_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::test::legendre_asymptotic::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length =
model.isotensional.asymptotic.end_to_end_length(force, temperature)
end_to_end_length_per_link =
model.isotensional.asymptotic.end_to_end_length_per_link(force, temperature)
helmholtz_free_energy_per_link_legendre =
model.isotensional.asymptotic.gibbs_free_energy_per_link(force, temperature) +
force * end_to_end_length_per_link
helmholtz_free_energy_per_link_legendre_out =
model.isometric.asymptotic.legendre.helmholtz_free_energy_per_link(
end_to_end_length,
temperature,
)
residual_abs =
helmholtz_free_energy_per_link_legendre -
helmholtz_free_energy_per_link_legendre_out +
BOLTZMANN_CONSTANT *
temperature *
(
0.5 * log(2.0 * pi * BOLTZMANN_CONSTANT * temperature / link_stiffness) +
log(
8.0 *
pi^2 *
hinge_mass *
link_length^2 *
BOLTZMANN_CONSTANT *
temperature / PLANCK_CONSTANT^2,
)
) / number_of_links
residual_rel = residual_abs / helmholtz_free_energy_per_link_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::test::legendre_asymptotic::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length =
model.isotensional.asymptotic.end_to_end_length(force, temperature)
relative_helmholtz_free_energy_legendre =
model.isotensional.asymptotic.relative_gibbs_free_energy(force, temperature) +
force * end_to_end_length
relative_helmholtz_free_energy_legendre_out =
model.isometric.asymptotic.legendre.relative_helmholtz_free_energy(
end_to_end_length,
temperature,
)
residual_abs =
relative_helmholtz_free_energy_legendre -
relative_helmholtz_free_energy_legendre_out
residual_rel = residual_abs / relative_helmholtz_free_energy_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::test::legendre_asymptotic::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length =
model.isotensional.asymptotic.end_to_end_length(force, temperature)
end_to_end_length_per_link =
model.isotensional.asymptotic.end_to_end_length_per_link(force, temperature)
relative_helmholtz_free_energy_per_link_legendre =
model.isotensional.asymptotic.relative_gibbs_free_energy_per_link(
force,
temperature,
) + force * end_to_end_length_per_link
relative_helmholtz_free_energy_per_link_legendre_out =
model.isometric.asymptotic.legendre.relative_helmholtz_free_energy_per_link(
end_to_end_length,
temperature,
)
residual_abs =
relative_helmholtz_free_energy_per_link_legendre -
relative_helmholtz_free_energy_per_link_legendre_out
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::test::legendre_asymptotic::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.isotensional.asymptotic.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
)
nondimensional_end_to_end_length_per_link =
model.isotensional.asymptotic.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_helmholtz_free_energy_legendre =
model.isotensional.asymptotic.nondimensional_gibbs_free_energy(
nondimensional_force,
temperature,
) + nondimensional_force * nondimensional_end_to_end_length
nondimensional_helmholtz_free_energy_legendre_out =
model.isometric.asymptotic.legendre.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy_legendre -
nondimensional_helmholtz_free_energy_legendre_out + (
0.5 * log(2.0 * pi * BOLTZMANN_CONSTANT * temperature / link_stiffness) +
log(
8.0 *
pi^2 *
hinge_mass *
link_length^2 *
BOLTZMANN_CONSTANT *
temperature / PLANCK_CONSTANT^2,
)
)
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::test::legendre_asymptotic::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.isotensional.asymptotic.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_helmholtz_free_energy_per_link_legendre =
model.isotensional.asymptotic.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
) + nondimensional_force * nondimensional_end_to_end_length_per_link
nondimensional_helmholtz_free_energy_per_link_legendre_out =
model.isometric.asymptotic.legendre.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy_per_link_legendre -
nondimensional_helmholtz_free_energy_per_link_legendre_out +
(
0.5 * log(2.0 * pi * BOLTZMANN_CONSTANT * temperature / link_stiffness) +
log(
8.0 *
pi^2 *
hinge_mass *
link_length^2 *
BOLTZMANN_CONSTANT *
temperature / PLANCK_CONSTANT^2,
)
) / number_of_links
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::test::legendre_asymptotic::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.isotensional.asymptotic.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
)
nondimensional_end_to_end_length_per_link =
model.isotensional.asymptotic.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_relative_helmholtz_free_energy_legendre =
model.isotensional.asymptotic.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
) + nondimensional_force * nondimensional_end_to_end_length
nondimensional_relative_helmholtz_free_energy_legendre_out =
model.isometric.asymptotic.legendre.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy_legendre -
nondimensional_relative_helmholtz_free_energy_legendre_out
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::test::legendre_asymptotic::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.isotensional.asymptotic.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_relative_helmholtz_free_energy_per_link_legendre =
model.isotensional.asymptotic.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
) + nondimensional_force * nondimensional_end_to_end_length_per_link
nondimensional_relative_helmholtz_free_energy_per_link_legendre_out =
model.isometric.asymptotic.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy_per_link_legendre -
nondimensional_relative_helmholtz_free_energy_per_link_legendre_out
residual_rel =
residual_abs / nondimensional_relative_helmholtz_free_energy_per_link_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::test::legendre_asymptotic_reduced::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length =
model.isotensional.asymptotic.reduced.end_to_end_length(force, temperature)
force_out = model.isometric.asymptotic.reduced.legendre.force(
end_to_end_length,
temperature,
)
residual_abs = force - force_out
residual_rel = residual_abs / force
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::test::legendre_asymptotic_reduced::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.isotensional.asymptotic.reduced.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_force_out =
model.isometric.asymptotic.reduced.legendre.nondimensional_force(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs = nondimensional_force - nondimensional_force_out
residual_rel = residual_abs / nondimensional_force
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::test::legendre_asymptotic_reduced::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length =
model.isotensional.asymptotic.reduced.end_to_end_length(force, temperature)
helmholtz_free_energy_legendre =
model.isotensional.asymptotic.reduced.gibbs_free_energy(force, temperature) +
force * end_to_end_length
helmholtz_free_energy_legendre_out =
model.isometric.asymptotic.reduced.legendre.helmholtz_free_energy(
end_to_end_length,
temperature,
)
residual_abs =
helmholtz_free_energy_legendre - helmholtz_free_energy_legendre_out +
BOLTZMANN_CONSTANT *
temperature *
(
0.5 * log(2.0 * pi * BOLTZMANN_CONSTANT * temperature / link_stiffness) +
log(
8.0 *
pi^2 *
hinge_mass *
link_length^2 *
BOLTZMANN_CONSTANT *
temperature / PLANCK_CONSTANT^2,
)
)
residual_rel = residual_abs / helmholtz_free_energy_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::test::legendre_asymptotic_reduced::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length =
model.isotensional.asymptotic.reduced.end_to_end_length(force, temperature)
end_to_end_length_per_link =
model.isotensional.asymptotic.reduced.end_to_end_length_per_link(
force,
temperature,
)
helmholtz_free_energy_per_link_legendre =
model.isotensional.asymptotic.reduced.gibbs_free_energy_per_link(
force,
temperature,
) + force * end_to_end_length_per_link
helmholtz_free_energy_per_link_legendre_out =
model.isometric.asymptotic.reduced.legendre.helmholtz_free_energy_per_link(
end_to_end_length,
temperature,
)
residual_abs =
helmholtz_free_energy_per_link_legendre -
helmholtz_free_energy_per_link_legendre_out +
BOLTZMANN_CONSTANT *
temperature *
(
0.5 * log(2.0 * pi * BOLTZMANN_CONSTANT * temperature / link_stiffness) +
log(
8.0 *
pi^2 *
hinge_mass *
link_length^2 *
BOLTZMANN_CONSTANT *
temperature / PLANCK_CONSTANT^2,
)
) / number_of_links
residual_rel = residual_abs / helmholtz_free_energy_per_link_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::test::legendre_asymptotic_reduced::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length =
model.isotensional.asymptotic.reduced.end_to_end_length(force, temperature)
relative_helmholtz_free_energy_legendre =
model.isotensional.asymptotic.reduced.relative_gibbs_free_energy(
force,
temperature,
) + force * end_to_end_length
relative_helmholtz_free_energy_legendre_out =
model.isometric.asymptotic.reduced.legendre.relative_helmholtz_free_energy(
end_to_end_length,
temperature,
)
residual_abs =
relative_helmholtz_free_energy_legendre -
relative_helmholtz_free_energy_legendre_out
residual_rel = residual_abs / relative_helmholtz_free_energy_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::test::legendre_asymptotic_reduced::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length =
model.isotensional.asymptotic.reduced.end_to_end_length(force, temperature)
end_to_end_length_per_link =
model.isotensional.asymptotic.reduced.end_to_end_length_per_link(
force,
temperature,
)
relative_helmholtz_free_energy_per_link_legendre =
model.isotensional.asymptotic.reduced.relative_gibbs_free_energy_per_link(
force,
temperature,
) + force * end_to_end_length_per_link
relative_helmholtz_free_energy_per_link_legendre_out =
model.isometric.asymptotic.reduced.legendre.relative_helmholtz_free_energy_per_link(
end_to_end_length,
temperature,
)
residual_abs =
relative_helmholtz_free_energy_per_link_legendre -
relative_helmholtz_free_energy_per_link_legendre_out
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::test::legendre_asymptotic_reduced::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.isotensional.asymptotic.reduced.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
)
nondimensional_end_to_end_length_per_link =
model.isotensional.asymptotic.reduced.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_helmholtz_free_energy_legendre =
model.isotensional.asymptotic.reduced.nondimensional_gibbs_free_energy(
nondimensional_force,
temperature,
) + nondimensional_force * nondimensional_end_to_end_length
nondimensional_helmholtz_free_energy_legendre_out =
model.isometric.asymptotic.reduced.legendre.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy_legendre -
nondimensional_helmholtz_free_energy_legendre_out + (
0.5 * log(2.0 * pi * BOLTZMANN_CONSTANT * temperature / link_stiffness) +
log(
8.0 *
pi^2 *
hinge_mass *
link_length^2 *
BOLTZMANN_CONSTANT *
temperature / PLANCK_CONSTANT^2,
)
)
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::test::legendre_asymptotic_reduced::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.isotensional.asymptotic.reduced.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_helmholtz_free_energy_per_link_legendre =
model.isotensional.asymptotic.reduced.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
) + nondimensional_force * nondimensional_end_to_end_length_per_link
nondimensional_helmholtz_free_energy_per_link_legendre_out =
model.isometric.asymptotic.reduced.legendre.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy_per_link_legendre -
nondimensional_helmholtz_free_energy_per_link_legendre_out +
(
0.5 * log(2.0 * pi * BOLTZMANN_CONSTANT * temperature / link_stiffness) +
log(
8.0 *
pi^2 *
hinge_mass *
link_length^2 *
BOLTZMANN_CONSTANT *
temperature / PLANCK_CONSTANT^2,
)
) / number_of_links
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::test::legendre_asymptotic_reduced::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.isotensional.asymptotic.reduced.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
)
nondimensional_end_to_end_length_per_link =
model.isotensional.asymptotic.reduced.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_relative_helmholtz_free_energy_legendre =
model.isotensional.asymptotic.reduced.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
) + nondimensional_force * nondimensional_end_to_end_length
nondimensional_relative_helmholtz_free_energy_legendre_out =
model.isometric.asymptotic.reduced.legendre.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy_legendre -
nondimensional_relative_helmholtz_free_energy_legendre_out
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::test::legendre_asymptotic_reduced::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.isotensional.asymptotic.reduced.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_relative_helmholtz_free_energy_per_link_legendre =
model.isotensional.asymptotic.reduced.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
) + nondimensional_force * nondimensional_end_to_end_length_per_link
nondimensional_relative_helmholtz_free_energy_per_link_legendre_out =
model.isometric.asymptotic.reduced.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy_per_link_legendre -
nondimensional_relative_helmholtz_free_energy_per_link_legendre_out
residual_rel =
residual_abs / nondimensional_relative_helmholtz_free_energy_per_link_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 1584 | """
The Lennard-Jones potential freely-jointed chain (Lennard-Jones-FJC) model thermodynamics in the isometric ensemble.
"""
module Isometric
using DocStringExtensions
using .......Polymers: PROJECT_ROOT
include("asymptotic/mod.jl")
"""
The structure of the thermodynamics of the Lennard-Jones-FJC model in the isometric ensemble.
$(FIELDS)
"""
struct LENNARDJONESFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The stiffness of each link in the chain ``k_0`` in units of J/(mol⋅nm^2).
"""
link_stiffness::Float64
"""
The thermodynamic functions of the model in the isometric ensemble approximated using an asymptotic approach.
"""
asymptotic::Any
end
"""
Initializes and returns an instance of the thermodynamics of the Lennard-Jones-FJC model in the isometric ensemble.
$(TYPEDSIGNATURES)
"""
function LENNARDJONESFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
)
return LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
Asymptotic.LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 4266 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: parameters
using Polymers.Physics.SingleChain.Ufjc.LennardJones.Thermodynamics.Isometric:
LENNARDJONESFJC
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::test::base::init" begin
@test isa(
LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
),
Any,
)
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test LENNARDJONESFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.link_stiffness_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::test::base::link_stiffness" begin
for _ = 1:parameters.number_of_loops
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
link_stiffness,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test all(
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).number_of_links == number_of_links &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_length == link_length &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).hinge_mass == hinge_mass &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_stiffness == link_stiffness,
)
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 1949 | """
The Lennard-Jones potential freely-jointed chain (Lennard-Jones-FJC) model thermodynamics in the isometric ensemble approximated using an asymptotic approach.
"""
module Asymptotic
using DocStringExtensions
using ........Polymers: PROJECT_ROOT
include("reduced/mod.jl")
include("legendre/mod.jl")
"""
The structure of the thermodynamics of the Lennard-Jones-FJC model in the isometric ensemble approximated using an asymptotic approach.
$(FIELDS)
"""
struct LENNARDJONESFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The stiffness of each link in the chain ``k_0`` in units of J/(mol⋅nm^2).
"""
link_stiffness::Float64
"""
The thermodynamic functions of the model in the isometric ensemble approximated using a reduced asymptotic approach.
"""
reduced::Any
"""
The thermodynamic functions of the model in the isometric ensemble approximated using an asymptotic approach and a Legendre transformation.
"""
legendre::Any
end
"""
Initializes and returns an instance of the thermodynamics of the Lennard-Jones-FJC model in the isometric ensemble approximated using an asymptotic approach.
$(TYPEDSIGNATURES)
"""
function LENNARDJONESFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
)
return LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
Reduced.LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness),
Legendre.LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 4349 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: parameters
using Polymers.Physics.SingleChain.Ufjc.LennardJones.Thermodynamics.Isometric.Asymptotic:
LENNARDJONESFJC
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::test::base::init" begin
@test isa(
LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
),
Any,
)
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test LENNARDJONESFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.link_stiffness_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::test::base::link_stiffness" begin
for _ = 1:parameters.number_of_loops
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
link_stiffness,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test all(
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).number_of_links == number_of_links &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_length == link_length &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).hinge_mass == hinge_mass &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_stiffness == link_stiffness,
)
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 22056 | """
The Lennard-Jones potential freely-jointed chain (Lennard-Jones-FJC) model thermodynamics in the isometric ensemble approximated using an asymptotic approach and a Legendre transformation.
"""
module Legendre
using DocStringExtensions
using .........Polymers: PROJECT_ROOT
import ........Physics: BOLTZMANN_CONSTANT
"""
The structure of the thermodynamics of the Lennard-Jones-FJC model in the isometric ensemble approximated using an asymptotic approach and a Legendre transformation.
$(FIELDS)
"""
struct LENNARDJONESFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The stiffness of each link in the chain ``k_0`` in units of J/(mol⋅nm^2).
"""
link_stiffness::Float64
"""
The expected force ``f`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
force::Function
"""
The expected nondimensional force ``\\eta`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``.
"""
nondimensional_force::Function
"""
The Helmholtz free energy ``\\psi`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
helmholtz_free_energy::Function
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
helmholtz_free_energy_per_link::Function
"""
The relative Helmholtz free energy ``\\Delta\\psi\\equiv\\psi(\\xi,T)-\\psi(0,T)`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
relative_helmholtz_free_energy::Function
"""
The relative Helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
relative_helmholtz_free_energy_per_link::Function
"""
The nondimensional Helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy::Function
"""
The nondimensional Helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy_per_link::Function
"""
The nondimensional relative Helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``.
"""
nondimensional_relative_helmholtz_free_energy::Function
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``
"""
nondimensional_relative_helmholtz_free_energy_per_link::Function
end
"""
The expected force as a function ``f`` of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function force(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isometric_asymptotic_legendre_force,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
end_to_end_length,
temperature,
)
end
"""
The expected nondimensional force as a function ``\\eta`` of the applied nondimensional end-to-end length per link ``\\gamma``,
parameterized by the link length ``\\ell_b`` and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_force(
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(nondimensional_link_stiffness_i, nondimensional_end_to_end_length_per_link_i) ->
ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isometric_asymptotic_legendre_nondimensional_force,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
),
nondimensional_link_stiffness,
nondimensional_end_to_end_length_per_link,
)
end
"""
The Helmholtz free energy ``\\psi`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, link stiffness ``k_0``, and hinge mass ``m``,
```math
\\psi(\\xi, T) \\sim \\varphi\\left[f(\\xi, T)\\right] + \\xi f(\\xi, T) \\quad \\text{for } N_b\\gg 1,
```
where ``f(\\xi, T)`` is given by the Legendre transformation approximation above.
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isometric_asymptotic_legendre_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
end_to_end_length,
temperature,
)
end
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, link stiffness ``k_0``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isometric_asymptotic_legendre_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
end_to_end_length,
temperature,
)
end
"""
The relative Helmholtz free energy ``\\Delta\\psi\\equiv\\psi(\\xi,T)-\\psi(0,T)`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isometric_asymptotic_legendre_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
end_to_end_length,
temperature,
)
end
"""
The relative Helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isometric_asymptotic_legendre_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
end_to_end_length,
temperature,
)
end
"""
The nondimensional Helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isometric_asymptotic_legendre_nondimensional_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_end_to_end_length_per_link,
temperature,
)
end
"""
The nondimensional Helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isometric_asymptotic_legendre_nondimensional_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_end_to_end_length_per_link,
temperature,
)
end
"""
The nondimensional relative Helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the number of links ``N_b`` and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isometric_asymptotic_legendre_nondimensional_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_end_to_end_length_per_link,
)
end
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(nondimensional_link_stiffness_i, nondimensional_end_to_end_length_per_link_i) ->
ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isometric_asymptotic_legendre_nondimensional_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
),
nondimensional_link_stiffness,
nondimensional_end_to_end_length_per_link,
)
end
"""
Initializes and returns an instance of the thermodynamics of the Lennard-Jones-FJC model in the isometric ensemble approximated using an asymptotic approach and a Legendre transformation.
$(TYPEDSIGNATURES)
"""
function LENNARDJONESFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
)
BOLTZMANN_CONSTANT::Float64 = 8.314462618
return LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
(end_to_end_length, temperature) -> force(
number_of_links,
link_length,
link_stiffness,
end_to_end_length,
temperature,
),
(nondimensional_end_to_end_length_per_link, temperature) -> nondimensional_force(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_end_to_end_length_per_link,
),
(end_to_end_length, temperature) -> helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> helmholtz_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> relative_helmholtz_free_energy(
number_of_links,
link_length,
link_stiffness,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> relative_helmholtz_free_energy_per_link(
number_of_links,
link_length,
link_stiffness,
end_to_end_length,
temperature,
),
(nondimensional_end_to_end_length_per_link, temperature) ->
nondimensional_helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_end_to_end_length_per_link,
temperature,
),
(nondimensional_end_to_end_length_per_link, temperature) ->
nondimensional_helmholtz_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_end_to_end_length_per_link,
temperature,
),
(nondimensional_end_to_end_length_per_link, temperature) ->
nondimensional_relative_helmholtz_free_energy(
number_of_links,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_end_to_end_length_per_link,
),
(nondimensional_end_to_end_length_per_link, temperature) ->
nondimensional_relative_helmholtz_free_energy_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_end_to_end_length_per_link,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 46101 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ZERO, parameters
using Polymers.Physics.SingleChain.Ufjc.LennardJones.Thermodynamics.Isometric.Asymptotic.Legendre:
LENNARDJONESFJC
using Polymers.Physics.SingleChain.Ufjc.LennardJones.Thermodynamics.Isotensional.Asymptotic:
nondimensional_end_to_end_length_per_link as isotensional_nondimensional_end_to_end_length_per_link
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::legendre::test::base::init" begin
@test isa(
LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
),
Any,
)
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::legendre::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test LENNARDJONESFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::legendre::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::legendre::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.link_stiffness_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::legendre::test::base::link_stiffness" begin
for _ = 1:parameters.number_of_loops
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
link_stiffness,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::legendre::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test all(
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).number_of_links == number_of_links &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_length == link_length &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).hinge_mass == hinge_mass &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_stiffness == link_stiffness,
)
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::legendre::test::nondimensional::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_force = model.nondimensional_force(
nondimensional_end_to_end_length_per_link,
temperature,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
force = model.force(end_to_end_length, temperature)
residual_abs =
force / BOLTZMANN_CONSTANT / temperature * link_length - nondimensional_force
residual_rel = residual_abs / nondimensional_force
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::legendre::test::nondimensional::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy = model.helmholtz_free_energy(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::legendre::test::nondimensional::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::legendre::test::nondimensional::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(end_to_end_length, temperature)
residual_abs =
relative_helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::legendre::test::nondimensional::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
relative_helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::legendre::test::per_link::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy = model.helmholtz_free_energy(end_to_end_length, temperature)
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy / number_of_links - helmholtz_free_energy_per_link
residual_rel = residual_abs / helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::legendre::test::per_link::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(end_to_end_length, temperature)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
relative_helmholtz_free_energy / number_of_links -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::legendre::test::per_link::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy / number_of_links -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::legendre::test::per_link::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy / number_of_links -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::legendre::test::relative::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy = model.helmholtz_free_energy(end_to_end_length, temperature)
helmholtz_free_energy_0 =
model.helmholtz_free_energy(ZERO * number_of_links * link_length, temperature)
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy - helmholtz_free_energy_0 - relative_helmholtz_free_energy
residual_rel = residual_abs / relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::legendre::test::relative::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(end_to_end_length, temperature)
helmholtz_free_energy_per_link_0 = model.helmholtz_free_energy_per_link(
ZERO * number_of_links * link_length,
temperature,
)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy_per_link - helmholtz_free_energy_per_link_0 -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::legendre::test::relative::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_0 =
model.nondimensional_helmholtz_free_energy(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy - nondimensional_helmholtz_free_energy_0 -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::legendre::test::relative::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_per_link_0 =
model.nondimensional_helmholtz_free_energy_per_link(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy_per_link -
nondimensional_helmholtz_free_energy_per_link_0 -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::legendre::test::zero::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force_0 = model.force(ZERO * number_of_links * link_length, temperature)
@test abs(force_0) <=
3.1 * ZERO * number_of_links * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::legendre::test::zero::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_0 = model.nondimensional_force(ZERO, temperature)
@test abs(nondimensional_force_0) <= 3.1 * ZERO
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::legendre::test::zero::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_0 = model.relative_helmholtz_free_energy(
ZERO * number_of_links * link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_0) <=
ZERO * number_of_links * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::legendre::test::zero::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_per_link_0 =
model.relative_helmholtz_free_energy_per_link(
ZERO * number_of_links * link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::legendre::test::zero::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_0 =
model.nondimensional_relative_helmholtz_free_energy(ZERO, temperature)
@test abs(nondimensional_relative_helmholtz_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::legendre::test::zero::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_per_link_0 =
model.nondimensional_relative_helmholtz_free_energy_per_link(ZERO, temperature)
@test abs(nondimensional_relative_helmholtz_free_energy_per_link_0) <= ZERO
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::legendre::test::connection::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
force = model.force(end_to_end_length, temperature)
h = parameters.rel_tol * number_of_links * link_length
force_from_derivative =
(
model.relative_helmholtz_free_energy(
end_to_end_length + 0.5 * h,
temperature,
) - model.relative_helmholtz_free_energy(
end_to_end_length - 0.5 * h,
temperature,
)
) / h
residual_abs = force - force_from_derivative
residual_rel = residual_abs / force
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::legendre::test::connection::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_force = model.nondimensional_force(
nondimensional_end_to_end_length_per_link,
temperature,
)
h = parameters.rel_tol
nondimensional_force_from_derivative =
(
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link + 0.5 * h,
temperature,
) - model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link - 0.5 * h,
temperature,
)
) / h
residual_abs = nondimensional_force - nondimensional_force_from_derivative
residual_rel = residual_abs / nondimensional_force
@test abs(residual_rel) <= h
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 1672 | """
The Lennard-Jones potential freely-jointed chain (Lennard-Jones-FJC) model thermodynamics in the isometric ensemble approximated using an reduced asymptotic approach.
"""
module Reduced
using DocStringExtensions
using .........Polymers: PROJECT_ROOT
include("legendre/mod.jl")
"""
The structure of the thermodynamics of the Lennard-Jones-FJC model in the isometric ensemble approximated using an reduced asymptotic approach.
$(FIELDS)
"""
struct LENNARDJONESFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The stiffness of each link in the chain ``k_0`` in units of J/(mol⋅nm^2).
"""
link_stiffness::Float64
"""
The thermodynamic functions of the model in the isometric ensemble approximated using an reduced asymptotic approach.
"""
legendre::Any
end
"""
Initializes and returns an instance of the thermodynamics of the Lennard-Jones-FJC model in the isometric ensemble approximated using an reduced asymptotic approach.
$(TYPEDSIGNATURES)
"""
function LENNARDJONESFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
)
return LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
Legendre.LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 4411 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: parameters
using Polymers.Physics.SingleChain.Ufjc.LennardJones.Thermodynamics.Isometric.Asymptotic.Reduced:
LENNARDJONESFJC
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::test::base::init" begin
@test isa(
LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
),
Any,
)
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test LENNARDJONESFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.link_stiffness_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::test::base::link_stiffness" begin
for _ = 1:parameters.number_of_loops
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
link_stiffness,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test all(
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).number_of_links == number_of_links &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_length == link_length &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).hinge_mass == hinge_mass &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_stiffness == link_stiffness,
)
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 22159 | """
The Lennard-Jones potential freely-jointed chain (Lennard-Jones-FJC) model thermodynamics in the isometric ensemble approximated using a reduced asymptotic approach and a Legendre transformation.
"""
module Legendre
using DocStringExtensions
using ..........Polymers: PROJECT_ROOT
import .........Physics: BOLTZMANN_CONSTANT
"""
The structure of the thermodynamics of the Lennard-Jones-FJC model in the isometric ensemble approximated using a reduced asymptotic approach and a Legendre transformation.
$(FIELDS)
"""
struct LENNARDJONESFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The stiffness of each link in the chain ``k_0`` in units of J/(mol⋅nm^2).
"""
link_stiffness::Float64
"""
The expected force ``f`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
force::Function
"""
The expected nondimensional force ``\\eta`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``.
"""
nondimensional_force::Function
"""
The Helmholtz free energy ``\\psi`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
helmholtz_free_energy::Function
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
helmholtz_free_energy_per_link::Function
"""
The relative Helmholtz free energy ``\\Delta\\psi\\equiv\\psi(\\xi,T)-\\psi(0,T)`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
relative_helmholtz_free_energy::Function
"""
The relative Helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
relative_helmholtz_free_energy_per_link::Function
"""
The nondimensional Helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy::Function
"""
The nondimensional Helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy_per_link::Function
"""
The nondimensional relative Helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``.
"""
nondimensional_relative_helmholtz_free_energy::Function
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``
"""
nondimensional_relative_helmholtz_free_energy_per_link::Function
end
"""
The expected force as a function ``f`` of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function force(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isometric_asymptotic_reduced_legendre_force,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
end_to_end_length,
temperature,
)
end
"""
The expected nondimensional force as a function ``\\eta`` of the applied nondimensional end-to-end length per link ``\\gamma``,
parameterized by the link length ``\\ell_b`` and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_force(
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(nondimensional_link_stiffness_i, nondimensional_end_to_end_length_per_link_i) ->
ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isometric_asymptotic_reduced_legendre_nondimensional_force,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
),
nondimensional_link_stiffness,
nondimensional_end_to_end_length_per_link,
)
end
"""
The Helmholtz free energy ``\\psi`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, link stiffness ``k_0``, and hinge mass ``m``,
```math
\\psi(\\xi, T) \\sim \\varphi\\left[f(\\xi, T)\\right] + \\xi f(\\xi, T) \\quad \\text{for } N_b\\gg 1,
```
where ``f(\\xi, T)`` is given by the Legendre transformation approximation above.
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isometric_asymptotic_reduced_legendre_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
end_to_end_length,
temperature,
)
end
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, link stiffness ``k_0``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isometric_asymptotic_reduced_legendre_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
end_to_end_length,
temperature,
)
end
"""
The relative Helmholtz free energy ``\\Delta\\psi\\equiv\\psi(\\xi,T)-\\psi(0,T)`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isometric_asymptotic_reduced_legendre_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
end_to_end_length,
temperature,
)
end
"""
The relative Helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isometric_asymptotic_reduced_legendre_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
end_to_end_length,
temperature,
)
end
"""
The nondimensional Helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isometric_asymptotic_reduced_legendre_nondimensional_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_end_to_end_length_per_link,
temperature,
)
end
"""
The nondimensional Helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isometric_asymptotic_reduced_legendre_nondimensional_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_end_to_end_length_per_link,
temperature,
)
end
"""
The nondimensional relative Helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the number of links ``N_b`` and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isometric_asymptotic_reduced_legendre_nondimensional_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_end_to_end_length_per_link,
)
end
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(nondimensional_link_stiffness_i, nondimensional_end_to_end_length_per_link_i) ->
ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isometric_asymptotic_reduced_legendre_nondimensional_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
),
nondimensional_link_stiffness,
nondimensional_end_to_end_length_per_link,
)
end
"""
Initializes and returns an instance of the thermodynamics of the Lennard-Jones-FJC model in the isometric ensemble approximated using a reduced asymptotic approach and a Legendre transformation.
$(TYPEDSIGNATURES)
"""
function LENNARDJONESFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
)
BOLTZMANN_CONSTANT::Float64 = 8.314462618
return LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
(end_to_end_length, temperature) -> force(
number_of_links,
link_length,
link_stiffness,
end_to_end_length,
temperature,
),
(nondimensional_end_to_end_length_per_link, temperature) -> nondimensional_force(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_end_to_end_length_per_link,
),
(end_to_end_length, temperature) -> helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> helmholtz_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> relative_helmholtz_free_energy(
number_of_links,
link_length,
link_stiffness,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> relative_helmholtz_free_energy_per_link(
number_of_links,
link_length,
link_stiffness,
end_to_end_length,
temperature,
),
(nondimensional_end_to_end_length_per_link, temperature) ->
nondimensional_helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_end_to_end_length_per_link,
temperature,
),
(nondimensional_end_to_end_length_per_link, temperature) ->
nondimensional_helmholtz_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_end_to_end_length_per_link,
temperature,
),
(nondimensional_end_to_end_length_per_link, temperature) ->
nondimensional_relative_helmholtz_free_energy(
number_of_links,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_end_to_end_length_per_link,
),
(nondimensional_end_to_end_length_per_link, temperature) ->
nondimensional_relative_helmholtz_free_energy_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_end_to_end_length_per_link,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 46360 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ZERO, parameters
using Polymers.Physics.SingleChain.Ufjc.LennardJones.Thermodynamics.Isometric.Asymptotic.Reduced.Legendre:
LENNARDJONESFJC
using Polymers.Physics.SingleChain.Ufjc.LennardJones.Thermodynamics.Isotensional.Asymptotic.Reduced:
nondimensional_end_to_end_length_per_link as isotensional_nondimensional_end_to_end_length_per_link
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::legendre::test::base::init" begin
@test isa(
LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
),
Any,
)
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::legendre::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test LENNARDJONESFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::legendre::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::legendre::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.link_stiffness_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::legendre::test::base::link_stiffness" begin
for _ = 1:parameters.number_of_loops
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
link_stiffness,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::legendre::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test all(
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).number_of_links == number_of_links &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_length == link_length &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).hinge_mass == hinge_mass &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_stiffness == link_stiffness,
)
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::legendre::test::nondimensional::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_force = model.nondimensional_force(
nondimensional_end_to_end_length_per_link,
temperature,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
force = model.force(end_to_end_length, temperature)
residual_abs =
force / BOLTZMANN_CONSTANT / temperature * link_length - nondimensional_force
residual_rel = residual_abs / nondimensional_force
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::legendre::test::nondimensional::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy = model.helmholtz_free_energy(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::legendre::test::nondimensional::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::legendre::test::nondimensional::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(end_to_end_length, temperature)
residual_abs =
relative_helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::legendre::test::nondimensional::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
relative_helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::legendre::test::per_link::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy = model.helmholtz_free_energy(end_to_end_length, temperature)
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy / number_of_links - helmholtz_free_energy_per_link
residual_rel = residual_abs / helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::legendre::test::per_link::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(end_to_end_length, temperature)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
relative_helmholtz_free_energy / number_of_links -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::legendre::test::per_link::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy / number_of_links -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::legendre::test::per_link::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy / number_of_links -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::legendre::test::relative::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy = model.helmholtz_free_energy(end_to_end_length, temperature)
helmholtz_free_energy_0 =
model.helmholtz_free_energy(ZERO * number_of_links * link_length, temperature)
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy - helmholtz_free_energy_0 - relative_helmholtz_free_energy
residual_rel = residual_abs / relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::legendre::test::relative::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(end_to_end_length, temperature)
helmholtz_free_energy_per_link_0 = model.helmholtz_free_energy_per_link(
ZERO * number_of_links * link_length,
temperature,
)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy_per_link - helmholtz_free_energy_per_link_0 -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::legendre::test::relative::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_0 =
model.nondimensional_helmholtz_free_energy(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy - nondimensional_helmholtz_free_energy_0 -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::legendre::test::relative::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_per_link_0 =
model.nondimensional_helmholtz_free_energy_per_link(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy_per_link -
nondimensional_helmholtz_free_energy_per_link_0 -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::legendre::test::zero::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force_0 = model.force(ZERO * number_of_links * link_length, temperature)
@test abs(force_0) <=
3.1 * ZERO * number_of_links * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::legendre::test::zero::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_0 = model.nondimensional_force(ZERO, temperature)
@test abs(nondimensional_force_0) <= 3.1 * ZERO
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::legendre::test::zero::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_0 = model.relative_helmholtz_free_energy(
ZERO * number_of_links * link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_0) <=
ZERO * number_of_links * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::legendre::test::zero::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_per_link_0 =
model.relative_helmholtz_free_energy_per_link(
ZERO * number_of_links * link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::legendre::test::zero::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_0 =
model.nondimensional_relative_helmholtz_free_energy(ZERO, temperature)
@test abs(nondimensional_relative_helmholtz_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::legendre::test::zero::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_per_link_0 =
model.nondimensional_relative_helmholtz_free_energy_per_link(ZERO, temperature)
@test abs(nondimensional_relative_helmholtz_free_energy_per_link_0) <= ZERO
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::legendre::test::connection::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
force = model.force(end_to_end_length, temperature)
h = parameters.rel_tol * number_of_links * link_length
force_from_derivative =
(
model.relative_helmholtz_free_energy(
end_to_end_length + 0.5 * h,
temperature,
) - model.relative_helmholtz_free_energy(
end_to_end_length - 0.5 * h,
temperature,
)
) / h
residual_abs = force - force_from_derivative
residual_rel = residual_abs / force
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isometric::asymptotic::reduced::legendre::test::connection::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13 / 7)^(1 / 6)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_force = model.nondimensional_force(
nondimensional_end_to_end_length_per_link,
temperature,
)
h = parameters.rel_tol
nondimensional_force_from_derivative =
(
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link + 0.5 * h,
temperature,
) - model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link - 0.5 * h,
temperature,
)
) / h
residual_abs = nondimensional_force - nondimensional_force_from_derivative
residual_rel = residual_abs / nondimensional_force
@test abs(residual_rel) <= h
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 23997 | """
The Lennard-Jones potential freely-jointed chain (Lennard-Jones-FJC) model thermodynamics in the isotensional ensemble.
"""
module Isotensional
using DocStringExtensions
using .......Polymers: PROJECT_ROOT
import ......Physics: BOLTZMANN_CONSTANT
include("asymptotic/mod.jl")
include("legendre/mod.jl")
"""
The structure of the thermodynamics of the Lennard-Jones-FJC model in the isotensional ensemble.
$(FIELDS)
"""
struct LENNARDJONESFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The stiffness of each link in the chain ``k_0`` in units of J/(mol⋅nm^2).
"""
link_stiffness::Float64
"""
The thermodynamic functions of the model in the isotensional ensemble approximated using an asymptotic approach.
"""
asymptotic::Any
"""
The thermodynamic functions of the model in the isotensional ensemble approximated using a Legendre transformation.
"""
legendre::Any
"""
The expected end-to-end length ``\\xi`` as a function of the applied force ``f`` and temperature ``T``.
"""
end_to_end_length::Function
"""
The expected end-to-end length per link ``\\xi/N_b=\\ell_b\\gamma`` as a function of the applied force ``f`` and temperature ``T``.
"""
end_to_end_length_per_link::Function
"""
The expected nondimensional end-to-end length ``N_b\\gamma=\\xi/\\ell_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_end_to_end_length::Function
"""
The expected nondimensional end-to-end length per link ``\\gamma\\equiv\\xi/N_b\\ell_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_end_to_end_length_per_link::Function
"""
The Gibbs free energy ``\\varphi`` as a function of the applied force ``f`` and temperature ``T``.
"""
gibbs_free_energy::Function
"""
The Gibbs free energy per link ``\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
gibbs_free_energy_per_link::Function
"""
The relative Gibbs free energy ``\\Delta\\varphi\\equiv\\varphi(f,T)-\\varphi(0,T)`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_gibbs_free_energy::Function
"""
The relative Gibbs free energy per link ``\\Delta\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_gibbs_free_energy_per_link::Function
"""
The nondimensional Gibbs free energy ``N_b\\varrho=\\beta\\varphi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_gibbs_free_energy::Function
"""
The nondimensional Gibbs free energy per link ``\\varrho\\equiv\\beta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_gibbs_free_energy_per_link::Function
"""
The nondimensional relative Gibbs free energy ``N_b\\Delta\\varrho=\\beta\\Delta\\varphi`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_gibbs_free_energy::Function
"""
The nondimensional relative Gibbs free energy per link ``\\Delta\\varrho\\equiv\\beta\\Delta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_gibbs_free_energy_per_link::Function
end
"""
The expected end-to-end length ``N_b\\gamma=\\xi/\\ell_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``,
```math
\\xi(f, T) = -\\frac{\\partial\\varphi}{\\partial f}.
```
$(TYPEDSIGNATURES)
"""
function end_to_end_length(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, link_stiffness_i, force_i, temperature_i) ->
ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The expected end-to-end length per link ``\\xi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function end_to_end_length_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The expected nondimensional end-to-end length ``N_b\\gamma=\\xi/\\ell_b`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b`` and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_end_to_end_length(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_link_stiffness_i, nondimensional_force_i) ->
ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_nondimensional_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
The expected nondimensional end-to-end length per link ``\\gamma\\equiv \\xi/N_b\\ell_b`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``,
given by [Buche et al.](https://doi.org/10.1103/PhysRevE.106.024502) as
```math
\\gamma(\\eta) = -\\frac{\\partial}{\\partial\\eta}\\,\\ln\\left[\\int \\frac{\\sinh(s\\eta)}{s\\eta}\\,e^{-\\beta u(s)}s^2\\,ds\\right].
```
$(TYPEDSIGNATURES)
"""
function nondimensional_end_to_end_length_per_link(
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(nondimensional_link_stiffness_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_nondimensional_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
The Gibbs free energy ``\\varphi`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and link stiffness ``k_0``.
```math
\\varphi(f, T) = -kT\\ln Z(f, T).
```
$(TYPEDSIGNATURES)
"""
function gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
)
end
"""
The Gibbs free energy per link ``\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, hinge_mass_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
)
end
"""
The relative Gibbs free energy ``\\Delta\\varphi\\equiv\\varphi(f,T)-\\varphi(0,T)`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, link_stiffness_i, force_i, temperature_i) ->
ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The relative Gibbs free energy per link ``\\Delta\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The nondimensional Gibbs free energy ``N_b\\varrho=\\beta\\varphi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_nondimensional_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_force,
temperature,
)
end
"""
The nondimensional Gibbs free energy per link ``\\varrho\\equiv\\beta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_nondimensional_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
),
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_force,
temperature,
)
end
"""
The nondimensional relative Gibbs free energy ``N_b\\Delta\\varrho=\\beta\\Delta\\varphi`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b`` and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_link_stiffness_i, nondimensional_force_i) ->
ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_nondimensional_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
The nondimensional relative Gibbs free energy per link ``\\Delta\\varrho\\equiv\\beta\\Delta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``,
given by [Buche et al.](https://doi.org/10.1103/PhysRevE.106.024502) as
```math
\\Delta\\varrho(\\eta) = \\ln\\left[\\int \\frac{\\sinh(s\\eta)}{s\\eta}\\,e^{-\\beta u(s)}s^2\\,ds\\right] - \\ln\\left[\\int e^{-\\beta u(s)}s^2\\,ds\\right],
```
where the nondimensional link potential ``\\beta u`` is given by [Jones](https://doi.org/10.1098/rspa.1924.0082) as
```math
\\beta u(\\lambda) = \\varepsilon\\left[\\frac{1}{\\lambda^{12}} - \\frac{2}{\\lambda^6}\\right],
```
where ``\\varepsilon\\equiv\\beta u_b=\\kappa/72`` is the nondimensional potential energy scale, ``\\kappa\\equiv\\beta k_b\\ell_b^2`` is the nondimensional link stiffness, and ``\\lambda\\equiv\\ell/\\ell_b`` is the nondimensional link stretch.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(nondimensional_link_stiffness_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_nondimensional_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
Initializes and returns an instance of the thermodynamics of the Lennard-Jones-FJC model in the isotensional ensemble.
$(TYPEDSIGNATURES)
"""
function LENNARDJONESFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
)
BOLTZMANN_CONSTANT::Float64 = 8.314462618
return LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
Asymptotic.LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
),
Legendre.LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness),
(force, temperature) -> end_to_end_length(
number_of_links,
link_length,
link_stiffness,
force,
temperature,
),
(force, temperature) ->
end_to_end_length_per_link(link_length, link_stiffness, force, temperature),
(nondimensional_force, temperature) -> nondimensional_end_to_end_length(
number_of_links,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(nondimensional_force, temperature) -> nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(force, temperature) -> gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
),
(force, temperature) -> gibbs_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
),
(force, temperature) -> relative_gibbs_free_energy(
number_of_links,
link_length,
link_stiffness,
force,
temperature,
),
(force, temperature) -> relative_gibbs_free_energy_per_link(
link_length,
link_stiffness,
force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_gibbs_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_relative_gibbs_free_energy(
number_of_links,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(nondimensional_force, temperature) ->
nondimensional_relative_gibbs_free_energy_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 88132 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ONE, ZERO, POINTS, integrate, parameters
using Polymers.Physics.SingleChain.Ufjc.LennardJones.Thermodynamics.Isotensional:
LENNARDJONESFJC
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::base::init" begin
@test isa(
LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
),
Any,
)
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test LENNARDJONESFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.link_stiffness_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::base::link_stiffness" begin
for _ = 1:parameters.number_of_loops
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
link_stiffness,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test all(
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).number_of_links == number_of_links &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_length == link_length &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).hinge_mass == hinge_mass &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_stiffness == link_stiffness,
)
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::nondimensional::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
residual_abs = end_to_end_length / link_length - nondimensional_end_to_end_length
residual_rel = residual_abs / nondimensional_end_to_end_length
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::nondimensional::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
residual_abs =
end_to_end_length_per_link / link_length -
nondimensional_end_to_end_length_per_link
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::nondimensional::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
residual_abs =
gibbs_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_gibbs_free_energy
residual_rel = residual_abs / nondimensional_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::nondimensional::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
residual_abs =
gibbs_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::nondimensional::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
residual_abs =
relative_gibbs_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_gibbs_free_energy
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::nondimensional::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
residual_abs =
relative_gibbs_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::per_link::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
residual_abs = end_to_end_length / number_of_links - end_to_end_length_per_link
residual_rel = residual_abs / end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::per_link::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_end_to_end_length / number_of_links -
nondimensional_end_to_end_length_per_link
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::per_link::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
residual_abs = gibbs_free_energy / number_of_links - gibbs_free_energy_per_link
residual_rel = residual_abs / gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::per_link::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
residual_abs =
relative_gibbs_free_energy / number_of_links -
relative_gibbs_free_energy_per_link
residual_rel = residual_abs / relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::per_link::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_gibbs_free_energy / number_of_links -
nondimensional_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::per_link::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_relative_gibbs_free_energy / number_of_links -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::relative::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
gibbs_free_energy_0 = model.gibbs_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
residual_abs = gibbs_free_energy - gibbs_free_energy_0 - relative_gibbs_free_energy
residual_rel = residual_abs / gibbs_free_energy_0
@test abs(residual_abs) <=
BOLTZMANN_CONSTANT * temperature * number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::relative::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
gibbs_free_energy_per_link_0 = model.gibbs_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
residual_abs =
gibbs_free_energy_per_link - gibbs_free_energy_per_link_0 -
relative_gibbs_free_energy_per_link
residual_rel = residual_abs / gibbs_free_energy_per_link_0
@test abs(residual_abs) <= BOLTZMANN_CONSTANT * temperature * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::relative::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
nondimensional_gibbs_free_energy_0 =
model.nondimensional_gibbs_free_energy(ZERO, temperature)
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_gibbs_free_energy - nondimensional_gibbs_free_energy_0 -
nondimensional_relative_gibbs_free_energy
residual_rel = residual_abs / nondimensional_gibbs_free_energy_0
@test abs(residual_abs) <= number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::relative::nondimensional_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_gibbs_free_energy_per_link_0 =
model.nondimensional_gibbs_free_energy_per_link(ZERO, temperature)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_gibbs_free_energy_per_link -
nondimensional_gibbs_free_energy_per_link_0 -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link_0
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::zero::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_gibbs_free_energy_0 = model.relative_gibbs_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_gibbs_free_energy_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature * number_of_links
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::zero::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_gibbs_free_energy_per_link_0 = model.relative_gibbs_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_gibbs_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::zero::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy_0 =
model.nondimensional_relative_gibbs_free_energy(ZERO, temperature)
@test abs(nondimensional_relative_gibbs_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::zero::nondimensional_relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy_per_link_0 =
model.nondimensional_relative_gibbs_free_energy_per_link(ZERO, temperature)
@test abs(nondimensional_relative_gibbs_free_energy_per_link_0) <= ZERO
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::connection::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
h = parameters.rel_tol * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_from_derivative =
-(
model.relative_gibbs_free_energy(force + 0.5 * h, temperature) -
model.relative_gibbs_free_energy(force - 0.5 * h, temperature)
) / h
residual_abs = end_to_end_length - end_to_end_length_from_derivative
residual_rel = residual_abs / end_to_end_length
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::connection::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
h = parameters.rel_tol * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link_from_derivative =
-(
model.relative_gibbs_free_energy_per_link(force + 0.5 * h, temperature) -
model.relative_gibbs_free_energy_per_link(force - 0.5 * h, temperature)
) / h
residual_abs =
end_to_end_length_per_link - end_to_end_length_per_link_from_derivative
residual_rel = residual_abs / end_to_end_length_per_link
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::connection::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
h = parameters.rel_tol
nondimensional_end_to_end_length_from_derivative =
-(
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force + 0.5 * h,
temperature,
) - model.nondimensional_relative_gibbs_free_energy(
nondimensional_force - 0.5 * h,
temperature,
)
) / h
residual_abs =
nondimensional_end_to_end_length -
nondimensional_end_to_end_length_from_derivative
residual_rel = residual_abs / nondimensional_end_to_end_length
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::connection::nondimensional_end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
h = parameters.rel_tol
nondimensional_end_to_end_length_per_link_from_derivative =
-(
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force + 0.5 * h,
temperature,
) - model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force - 0.5 * h,
temperature,
)
) / h
residual_abs =
nondimensional_end_to_end_length_per_link -
nondimensional_end_to_end_length_per_link_from_derivative
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::legendre::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
gibbs_free_energy_legendre =
model.legendre.helmholtz_free_energy(force, temperature) -
force * end_to_end_length
residual_abs = gibbs_free_energy - gibbs_free_energy_legendre
residual_rel = residual_abs / gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::legendre::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
gibbs_free_energy_per_link_legendre =
model.legendre.helmholtz_free_energy_per_link(force, temperature) -
force * end_to_end_length_per_link
residual_abs = gibbs_free_energy_per_link - gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::legendre::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
end_to_end_length_0 = model.end_to_end_length(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
relative_gibbs_free_energy_legendre =
model.legendre.relative_helmholtz_free_energy(force, temperature) -
force * end_to_end_length +
ZERO * BOLTZMANN_CONSTANT * temperature / link_length * end_to_end_length_0
residual_abs = relative_gibbs_free_energy - relative_gibbs_free_energy_legendre
residual_rel = residual_abs / relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::legendre::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
end_to_end_length_per_link_0 = model.end_to_end_length_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
relative_gibbs_free_energy_per_link_legendre =
model.legendre.relative_helmholtz_free_energy_per_link(force, temperature) -
force * end_to_end_length_per_link +
ZERO * BOLTZMANN_CONSTANT * temperature / link_length *
end_to_end_length_per_link_0
residual_abs =
relative_gibbs_free_energy_per_link -
relative_gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::legendre::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
nondimensional_gibbs_free_energy_legendre =
model.legendre.nondimensional_helmholtz_free_energy(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length
residual_abs =
nondimensional_gibbs_free_energy - nondimensional_gibbs_free_energy_legendre
residual_rel = residual_abs / nondimensional_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::legendre::nondimensional_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_gibbs_free_energy_per_link_legendre =
model.legendre.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length_per_link
residual_abs =
nondimensional_gibbs_free_energy_per_link -
nondimensional_gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::legendre::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
nondimensional_end_to_end_length_0 =
model.nondimensional_end_to_end_length(ZERO, temperature)
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
)
nondimensional_relative_gibbs_free_energy_legendre =
model.legendre.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length +
ZERO * nondimensional_end_to_end_length_0
residual_abs =
nondimensional_relative_gibbs_free_energy -
nondimensional_relative_gibbs_free_energy_legendre
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::legendre::nondimensional_relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_end_to_end_length_per_link_0 =
model.nondimensional_end_to_end_length_per_link(ZERO, temperature)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_relative_gibbs_free_energy_per_link_legendre =
model.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length_per_link +
ZERO * nondimensional_end_to_end_length_per_link_0
residual_abs =
nondimensional_relative_gibbs_free_energy_per_link -
nondimensional_relative_gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::legendre_connection::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
h = parameters.rel_tol * BOLTZMANN_CONSTANT * temperature / link_length
force_from_derivative =
(
model.legendre.relative_helmholtz_free_energy(
force + 0.5 * h,
temperature,
) -
model.legendre.relative_helmholtz_free_energy(force - 0.5 * h, temperature)
) / (
model.end_to_end_length(force + 0.5 * h, temperature) -
model.end_to_end_length(force - 0.5 * h, temperature)
)
residual_abs = force - force_from_derivative
residual_rel = residual_abs / force
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::legendre_connection::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
h = parameters.rel_tol
nondimensional_force_from_derivative =
(
model.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force + 0.5 * h,
temperature,
) - model.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force - 0.5 * h,
temperature,
)
) / (
model.nondimensional_end_to_end_length_per_link(
nondimensional_force + 0.5 * h,
temperature,
) - model.nondimensional_end_to_end_length_per_link(
nondimensional_force - 0.5 * h,
temperature,
)
)
residual_abs = nondimensional_force - nondimensional_force_from_derivative
residual_rel = residual_abs / nondimensional_force
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::asymptotic::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model =
LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return (
model.end_to_end_length(force, temperature) -
model.asymptotic.end_to_end_length(force, temperature)
)^2
end
function integrand_denominator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return model.end_to_end_length(force, temperature)^2
end
nondimensional_link_stretch_max = (13 / 7)^(1 / 6)
nondimensional_force_max = nondimensional_link_stretch_max
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(5.0 * parameters.nondimensional_link_stiffness_big)
residual_rel_2 = residual_rel(
5.0 * parameters.nondimensional_link_stiffness_big * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(0.5 * log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::asymptotic::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model =
LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return (
model.end_to_end_length_per_link(force, temperature) -
model.asymptotic.end_to_end_length_per_link(force, temperature)
)^2
end
function integrand_denominator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return model.end_to_end_length_per_link(force, temperature)^2
end
nondimensional_link_stretch_max = (13 / 7)^(1 / 6)
nondimensional_force_max = nondimensional_link_stretch_max
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(5.0 * parameters.nondimensional_link_stiffness_big)
residual_rel_2 = residual_rel(
5.0 * parameters.nondimensional_link_stiffness_big * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(0.5 * log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::asymptotic::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model =
LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
return (
model.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
) - model.asymptotic.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_force)
return model.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
)^2
end
nondimensional_link_stretch_max = (13 / 7)^(1 / 6)
nondimensional_force_max = nondimensional_link_stretch_max
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(5.0 * parameters.nondimensional_link_stiffness_big)
residual_rel_2 = residual_rel(
5.0 * parameters.nondimensional_link_stiffness_big * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(0.5 * log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::asymptotic::nondimensional_end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model =
LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
return (
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
) - model.asymptotic.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_force)
return model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)^2
end
nondimensional_link_stretch_max = (13 / 7)^(1 / 6)
nondimensional_force_max = nondimensional_link_stretch_max
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(5.0 * parameters.nondimensional_link_stiffness_big)
residual_rel_2 = residual_rel(
5.0 * parameters.nondimensional_link_stiffness_big * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(0.5 * log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::asymptotic_reduced::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model =
LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return (
model.end_to_end_length(force, temperature) -
model.asymptotic.reduced.end_to_end_length(force, temperature)
)^2
end
function integrand_denominator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return model.end_to_end_length(force, temperature)^2
end
nondimensional_link_stretch_max = (13 / 7)^(1 / 6)
nondimensional_force_max = nondimensional_link_stretch_max
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_link_stiffness_big)
residual_rel_2 = residual_rel(
parameters.nondimensional_link_stiffness_big * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::asymptotic_reduced::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model =
LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return (
model.end_to_end_length_per_link(force, temperature) -
model.asymptotic.reduced.end_to_end_length_per_link(force, temperature)
)^2
end
function integrand_denominator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return model.end_to_end_length_per_link(force, temperature)^2
end
nondimensional_link_stretch_max = (13 / 7)^(1 / 6)
nondimensional_force_max = nondimensional_link_stretch_max
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_link_stiffness_big)
residual_rel_2 = residual_rel(
parameters.nondimensional_link_stiffness_big * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::asymptotic_reduced::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model =
LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
return (
model.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
) - model.asymptotic.reduced.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_force)
return model.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
)^2
end
nondimensional_link_stretch_max = (13 / 7)^(1 / 6)
nondimensional_force_max = nondimensional_link_stretch_max
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_link_stiffness_big)
residual_rel_2 = residual_rel(
parameters.nondimensional_link_stiffness_big * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::test::asymptotic_reduced::nondimensional_end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model =
LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
return (
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
) - model.asymptotic.reduced.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_force)
return model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)^2
end
nondimensional_link_stretch_max = (13 / 7)^(1 / 6)
nondimensional_force_max = nondimensional_link_stretch_max
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_link_stiffness_big)
residual_rel_2 = residual_rel(
parameters.nondimensional_link_stiffness_big * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 24742 | """
The Lennard-Jones potential freely-jointed chain (Lennard-Jones-FJC) model thermodynamics in the isotensional ensemble approximated using an asymptotic approach.
"""
module Asymptotic
using DocStringExtensions
using ........Polymers: PROJECT_ROOT
import .......Physics: BOLTZMANN_CONSTANT
include("reduced/mod.jl")
include("legendre/mod.jl")
"""
The structure of the thermodynamics of the Lennard-Jones-FJC model in the isotensional ensemble approximated using an asymptotic approach.
$(FIELDS)
"""
struct LENNARDJONESFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The stiffness of each link in the chain ``k_0`` in units of J/(mol⋅nm^2).
"""
link_stiffness::Float64
"""
The thermodynamic functions of the model in the isotensional ensemble approximated using a reduced asymptotic approach.
"""
reduced::Any
"""
The thermodynamic functions of the model in the isotensional ensemble approximated using an asymptotic approach and a Legendre transformation.
"""
legendre::Any
"""
The expected end-to-end length ``\\xi`` as a function of the applied force ``f`` and temperature ``T``.
"""
end_to_end_length::Function
"""
The expected end-to-end length per link ``\\xi/N_b=\\ell_b\\gamma`` as a function of the applied force ``f`` and temperature ``T``.
"""
end_to_end_length_per_link::Function
"""
The expected nondimensional end-to-end length ``N_b\\gamma=\\xi/\\ell_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_end_to_end_length::Function
"""
The expected nondimensional end-to-end length per link ``\\gamma\\equiv\\xi/N_b\\ell_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_end_to_end_length_per_link::Function
"""
The Gibbs free energy ``\\varphi`` as a function of the applied force ``f`` and temperature ``T``.
"""
gibbs_free_energy::Function
"""
The Gibbs free energy per link ``\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
gibbs_free_energy_per_link::Function
"""
The relative Gibbs free energy ``\\Delta\\varphi\\equiv\\varphi(f,T)-\\varphi(0,T)`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_gibbs_free_energy::Function
"""
The relative Gibbs free energy per link ``\\Delta\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_gibbs_free_energy_per_link::Function
"""
The nondimensional Gibbs free energy ``N_b\\varrho=\\beta\\varphi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_gibbs_free_energy::Function
"""
The nondimensional Gibbs free energy per link ``\\varrho\\equiv\\beta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_gibbs_free_energy_per_link::Function
"""
The nondimensional relative Gibbs free energy ``N_b\\Delta\\varrho=\\beta\\Delta\\varphi`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_gibbs_free_energy::Function
"""
The nondimensional relative Gibbs free energy per link ``\\Delta\\varrho\\equiv\\beta\\Delta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_gibbs_free_energy_per_link::Function
end
"""
The expected end-to-end length ``N_b\\gamma=\\xi/\\ell_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``,
```math
\\xi(f, T) = -\\frac{\\partial\\varphi}{\\partial f}.
```
$(TYPEDSIGNATURES)
"""
function end_to_end_length(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, link_stiffness_i, force_i, temperature_i) ->
ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The expected end-to-end length per link ``\\xi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function end_to_end_length_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The expected nondimensional end-to-end length ``N_b\\gamma=\\xi/\\ell_b`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b`` and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_end_to_end_length(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_link_stiffness_i, nondimensional_force_i) ->
ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_nondimensional_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
The expected nondimensional end-to-end length per link ``\\gamma\\equiv \\xi/N_b\\ell_b`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``,
given by [Buche et al.](https://doi.org/10.1103/PhysRevE.106.024502) as
```math
\\Delta\\varrho(\\eta) \\sim \\mathcal{L}(\\eta) + \\frac{\\eta}{\\kappa}\\left[\\frac{1 - \\mathcal{L}(\\eta)\\coth(\\eta)}{c + (\\eta/\\kappa)\\coth(\\eta)}\\right] + \\Delta\\lambda(\\eta) \\quad \\text{for } \\varepsilon,\\kappa\\gg 1,
```
where ``\\mathcal{L}(x)=\\coth(x)-1/x`` is the Langevin function, and ``\\Delta\\lambda(\\eta)`` is the incremental link stretch, given by inverting
```math
\\eta(\\lambda) = 12\\varepsilon\\left[\\frac{1}{\\lambda^7} - \\frac{1}{\\lambda^{13}}\\right].
```
$(TYPEDSIGNATURES)
"""
function nondimensional_end_to_end_length_per_link(
nondimensional_link_stiffness_i::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(nondimensional_link_stiffness_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_nondimensional_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
nondimensional_link_stiffness_i,
nondimensional_force,
)
end
"""
The Gibbs free energy ``\\varphi`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and link stiffness ``k_0``.
```math
\\varphi(f, T) = -kT\\ln Z(f, T).
```
$(TYPEDSIGNATURES)
"""
function gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
)
end
"""
The Gibbs free energy per link ``\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, hinge_mass_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
)
end
"""
The relative Gibbs free energy ``\\Delta\\varphi\\equiv\\varphi(f,T)-\\varphi(0,T)`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, link_stiffness_i, force_i, temperature_i) ->
ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The relative Gibbs free energy per link ``\\Delta\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The nondimensional Gibbs free energy ``N_b\\varrho=\\beta\\varphi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_nondimensional_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_force,
temperature,
)
end
"""
The nondimensional Gibbs free energy per link ``\\varrho\\equiv\\beta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_nondimensional_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
),
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_force,
temperature,
)
end
"""
The nondimensional relative Gibbs free energy ``N_b\\Delta\\varrho=\\beta\\Delta\\varphi`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b`` and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_link_stiffness_i, nondimensional_force_i) ->
ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_nondimensional_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
The nondimensional relative Gibbs free energy per link ``\\Delta\\varrho\\equiv\\beta\\Delta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``,
given by [Buche et al.](https://doi.org/10.1103/PhysRevE.106.024502) as
```math
\\Delta\\varrho(\\eta) \\sim \\ln\\left[\\frac{\\eta}{\\sinh(\\eta)}\\right] - \\ln\\left[1 + \\frac{\\eta}{c\\kappa}\\,\\coth(\\eta)\\right] + \\beta u[\\lambda(\\eta)] - \\eta\\Delta\\lambda(\\eta) \\quad \\text{for } \\varepsilon,\\kappa\\gg 1,
```
where the nondimensional link potential ``\\beta u`` is given by [Jones](https://doi.org/10.1098/rspa.1924.0082) as
```math
\\beta u(\\lambda) = \\varepsilon\\left[\\frac{1}{\\lambda^{12}} - \\frac{2}{\\lambda^6}\\right],
```
where ``\\varepsilon\\equiv\\beta u_b=\\kappa/72`` is the nondimensional potential energy scale, ``1/c\\equiv 1-u'''(1)/2u''(1)=23/2`` is related to anharmonicity, ``\\kappa\\equiv\\beta k_b\\ell_b^2`` is the nondimensional link stiffness, and ``\\lambda\\equiv\\ell/\\ell_b`` is the nondimensional link stretch.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(nondimensional_link_stiffness_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_nondimensional_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
Initializes and returns an instance of the thermodynamics of the Lennard-Jones-FJC model in the isotensional ensemble approximated using an asymptotic approach.
$(TYPEDSIGNATURES)
"""
function LENNARDJONESFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
)
BOLTZMANN_CONSTANT::Float64 = 8.314462618
return LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
Reduced.LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness),
Legendre.LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness),
(force, temperature) -> end_to_end_length(
number_of_links,
link_length,
link_stiffness,
force,
temperature,
),
(force, temperature) ->
end_to_end_length_per_link(link_length, link_stiffness, force, temperature),
(nondimensional_force, temperature) -> nondimensional_end_to_end_length(
number_of_links,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(nondimensional_force, temperature) -> nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(force, temperature) -> gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
),
(force, temperature) -> gibbs_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
),
(force, temperature) -> relative_gibbs_free_energy(
number_of_links,
link_length,
link_stiffness,
force,
temperature,
),
(force, temperature) -> relative_gibbs_free_energy_per_link(
link_length,
link_stiffness,
force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_gibbs_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_relative_gibbs_free_energy(
number_of_links,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(nondimensional_force, temperature) ->
nondimensional_relative_gibbs_free_energy_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 80051 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ONE, ZERO, POINTS, integrate, parameters
using Polymers.Physics.SingleChain.Ufjc.LennardJones.Thermodynamics.Isotensional.Asymptotic:
LENNARDJONESFJC
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::base::init" begin
@test isa(
LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
),
Any,
)
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test LENNARDJONESFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.link_stiffness_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::base::link_stiffness" begin
for _ = 1:parameters.number_of_loops
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
link_stiffness,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test all(
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).number_of_links == number_of_links &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_length == link_length &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).hinge_mass == hinge_mass &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_stiffness == link_stiffness,
)
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::nondimensional::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
residual_abs = end_to_end_length / link_length - nondimensional_end_to_end_length
residual_rel = residual_abs / nondimensional_end_to_end_length
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::nondimensional::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
residual_abs =
end_to_end_length_per_link / link_length -
nondimensional_end_to_end_length_per_link
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::nondimensional::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
residual_abs =
gibbs_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_gibbs_free_energy
residual_rel = residual_abs / nondimensional_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::nondimensional::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
residual_abs =
gibbs_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::nondimensional::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
residual_abs =
relative_gibbs_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_gibbs_free_energy
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::nondimensional::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
residual_abs =
relative_gibbs_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::per_link::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
residual_abs = end_to_end_length / number_of_links - end_to_end_length_per_link
residual_rel = residual_abs / end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::per_link::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_end_to_end_length / number_of_links -
nondimensional_end_to_end_length_per_link
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::per_link::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
residual_abs = gibbs_free_energy / number_of_links - gibbs_free_energy_per_link
residual_rel = residual_abs / gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::per_link::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
residual_abs =
relative_gibbs_free_energy / number_of_links -
relative_gibbs_free_energy_per_link
residual_rel = residual_abs / relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::per_link::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_gibbs_free_energy / number_of_links -
nondimensional_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::per_link::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_relative_gibbs_free_energy / number_of_links -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::relative::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
gibbs_free_energy_0 = model.gibbs_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
residual_abs = gibbs_free_energy - gibbs_free_energy_0 - relative_gibbs_free_energy
residual_rel = residual_abs / gibbs_free_energy_0
@test abs(residual_abs) <=
BOLTZMANN_CONSTANT * temperature * number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::relative::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
gibbs_free_energy_per_link_0 = model.gibbs_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
residual_abs =
gibbs_free_energy_per_link - gibbs_free_energy_per_link_0 -
relative_gibbs_free_energy_per_link
residual_rel = residual_abs / gibbs_free_energy_per_link_0
@test abs(residual_abs) <= BOLTZMANN_CONSTANT * temperature * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::relative::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
nondimensional_gibbs_free_energy_0 =
model.nondimensional_gibbs_free_energy(ZERO, temperature)
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_gibbs_free_energy - nondimensional_gibbs_free_energy_0 -
nondimensional_relative_gibbs_free_energy
residual_rel = residual_abs / nondimensional_gibbs_free_energy_0
@test abs(residual_abs) <= number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::relative::nondimensional_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_gibbs_free_energy_per_link_0 =
model.nondimensional_gibbs_free_energy_per_link(ZERO, temperature)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_gibbs_free_energy_per_link -
nondimensional_gibbs_free_energy_per_link_0 -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link_0
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::zero::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_gibbs_free_energy_0 = model.relative_gibbs_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_gibbs_free_energy_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature * number_of_links
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::zero::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_gibbs_free_energy_per_link_0 = model.relative_gibbs_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_gibbs_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::zero::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy_0 =
model.nondimensional_relative_gibbs_free_energy(ZERO, temperature)
@test abs(nondimensional_relative_gibbs_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::zero::nondimensional_relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy_per_link_0 =
model.nondimensional_relative_gibbs_free_energy_per_link(ZERO, temperature)
@test abs(nondimensional_relative_gibbs_free_energy_per_link_0) <= ZERO
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::connection::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
h = parameters.rel_tol * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_from_derivative =
-(
model.relative_gibbs_free_energy(force + 0.5 * h, temperature) -
model.relative_gibbs_free_energy(force - 0.5 * h, temperature)
) / h
residual_abs = end_to_end_length - end_to_end_length_from_derivative
residual_rel = residual_abs / end_to_end_length
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::connection::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
h = parameters.rel_tol * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link_from_derivative =
-(
model.relative_gibbs_free_energy_per_link(force + 0.5 * h, temperature) -
model.relative_gibbs_free_energy_per_link(force - 0.5 * h, temperature)
) / h
residual_abs =
end_to_end_length_per_link - end_to_end_length_per_link_from_derivative
residual_rel = residual_abs / end_to_end_length_per_link
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::connection::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
h = parameters.rel_tol
nondimensional_end_to_end_length_from_derivative =
-(
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force + 0.5 * h,
temperature,
) - model.nondimensional_relative_gibbs_free_energy(
nondimensional_force - 0.5 * h,
temperature,
)
) / h
residual_abs =
nondimensional_end_to_end_length -
nondimensional_end_to_end_length_from_derivative
residual_rel = residual_abs / nondimensional_end_to_end_length
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::connection::nondimensional_end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
h = parameters.rel_tol
nondimensional_end_to_end_length_per_link_from_derivative =
-(
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force + 0.5 * h,
temperature,
) - model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force - 0.5 * h,
temperature,
)
) / h
residual_abs =
nondimensional_end_to_end_length_per_link -
nondimensional_end_to_end_length_per_link_from_derivative
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::legendre::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
gibbs_free_energy_legendre =
model.legendre.helmholtz_free_energy(force, temperature) -
force * end_to_end_length
residual_abs = gibbs_free_energy - gibbs_free_energy_legendre
residual_rel = residual_abs / gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::legendre::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
gibbs_free_energy_per_link_legendre =
model.legendre.helmholtz_free_energy_per_link(force, temperature) -
force * end_to_end_length_per_link
residual_abs = gibbs_free_energy_per_link - gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::legendre::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
end_to_end_length_0 = model.end_to_end_length(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
relative_gibbs_free_energy_legendre =
model.legendre.relative_helmholtz_free_energy(force, temperature) -
force * end_to_end_length +
ZERO * BOLTZMANN_CONSTANT * temperature / link_length * end_to_end_length_0
residual_abs = relative_gibbs_free_energy - relative_gibbs_free_energy_legendre
residual_rel = residual_abs / relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::legendre::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
end_to_end_length_per_link_0 = model.end_to_end_length_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
relative_gibbs_free_energy_per_link_legendre =
model.legendre.relative_helmholtz_free_energy_per_link(force, temperature) -
force * end_to_end_length_per_link +
ZERO * BOLTZMANN_CONSTANT * temperature / link_length *
end_to_end_length_per_link_0
residual_abs =
relative_gibbs_free_energy_per_link -
relative_gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::legendre::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
nondimensional_gibbs_free_energy_legendre =
model.legendre.nondimensional_helmholtz_free_energy(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length
residual_abs =
nondimensional_gibbs_free_energy - nondimensional_gibbs_free_energy_legendre
residual_rel = residual_abs / nondimensional_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::legendre::nondimensional_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_gibbs_free_energy_per_link_legendre =
model.legendre.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length_per_link
residual_abs =
nondimensional_gibbs_free_energy_per_link -
nondimensional_gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::legendre::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
nondimensional_end_to_end_length_0 =
model.nondimensional_end_to_end_length(ZERO, temperature)
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
)
nondimensional_relative_gibbs_free_energy_legendre =
model.legendre.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length +
ZERO * nondimensional_end_to_end_length_0
residual_abs =
nondimensional_relative_gibbs_free_energy -
nondimensional_relative_gibbs_free_energy_legendre
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::legendre::nondimensional_relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_end_to_end_length_per_link_0 =
model.nondimensional_end_to_end_length_per_link(ZERO, temperature)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_relative_gibbs_free_energy_per_link_legendre =
model.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length_per_link +
ZERO * nondimensional_end_to_end_length_per_link_0
residual_abs =
nondimensional_relative_gibbs_free_energy_per_link -
nondimensional_relative_gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::legendre_connection::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
h = parameters.rel_tol * BOLTZMANN_CONSTANT * temperature / link_length
force_from_derivative =
(
model.legendre.relative_helmholtz_free_energy(
force + 0.5 * h,
temperature,
) -
model.legendre.relative_helmholtz_free_energy(force - 0.5 * h, temperature)
) / (
model.end_to_end_length(force + 0.5 * h, temperature) -
model.end_to_end_length(force - 0.5 * h, temperature)
)
residual_abs = force - force_from_derivative
residual_rel = residual_abs / force
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::legendre_connection::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
h = parameters.rel_tol
nondimensional_force_from_derivative =
(
model.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force + 0.5 * h,
temperature,
) - model.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force - 0.5 * h,
temperature,
)
) / (
model.nondimensional_end_to_end_length_per_link(
nondimensional_force + 0.5 * h,
temperature,
) - model.nondimensional_end_to_end_length_per_link(
nondimensional_force - 0.5 * h,
temperature,
)
)
residual_abs = nondimensional_force - nondimensional_force_from_derivative
residual_rel = residual_abs / nondimensional_force
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::asymptotic_reduced::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model =
LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return (
model.end_to_end_length(force, temperature) -
model.reduced.end_to_end_length(force, temperature)
)^2
end
function integrand_denominator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return model.end_to_end_length(force, temperature)^2
end
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(5.0 * parameters.nondimensional_link_stiffness_large)
residual_rel_2 = residual_rel(
5.0 * parameters.nondimensional_link_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(residual_rel_1) <= 5.0 / parameters.nondimensional_link_stiffness_large &&
abs(residual_rel_2) <=
5.0 / parameters.nondimensional_link_stiffness_large /
parameters.log_log_scale &&
abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::asymptotic_reduced::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model =
LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return (
model.end_to_end_length_per_link(force, temperature) -
model.reduced.end_to_end_length_per_link(force, temperature)
)^2
end
function integrand_denominator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return model.end_to_end_length_per_link(force, temperature)^2
end
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(5.0 * parameters.nondimensional_link_stiffness_large)
residual_rel_2 = residual_rel(
5.0 * parameters.nondimensional_link_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(residual_rel_1) <= 5.0 / parameters.nondimensional_link_stiffness_large &&
abs(residual_rel_2) <=
5.0 / parameters.nondimensional_link_stiffness_large /
parameters.log_log_scale &&
abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::asymptotic_reduced::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model =
LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
return (
model.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
) - model.reduced.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_force)
return model.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
)^2
end
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(5.0 * parameters.nondimensional_link_stiffness_large)
residual_rel_2 = residual_rel(
5.0 * parameters.nondimensional_link_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(residual_rel_1) <= 5.0 / parameters.nondimensional_link_stiffness_large &&
abs(residual_rel_2) <=
5.0 / parameters.nondimensional_link_stiffness_large /
parameters.log_log_scale &&
abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::test::asymptotic_reduced::nondimensional_end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model =
LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
return (
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
) - model.reduced.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_force)
return model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)^2
end
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(5.0 * parameters.nondimensional_link_stiffness_large)
residual_rel_2 = residual_rel(
5.0 * parameters.nondimensional_link_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(residual_rel_1) <= 5.0 / parameters.nondimensional_link_stiffness_large &&
abs(residual_rel_2) <=
5.0 / parameters.nondimensional_link_stiffness_large /
parameters.log_log_scale &&
abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 16595 | """
The Lennard-Jones potential freely-jointed chain (Lennard-Jones-FJC) model thermodynamics in the isotensional ensemble approximated using an asymptotic approach and a Legendre transformation.
"""
module Legendre
using DocStringExtensions
using .........Polymers: PROJECT_ROOT
import ........Physics: BOLTZMANN_CONSTANT
"""
The structure of the thermodynamics of the Lennard-Jones-FJC model in the isotensional ensemble approximated using an asymptotic approach and a Legendre transformation.
$(FIELDS)
"""
struct LENNARDJONESFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The stiffness of each link in the chain ``k_0`` in units of J/(mol⋅nm^2).
"""
link_stiffness::Float64
"""
The Helmholtz free energy ``\\psi`` as a function of the applied force ``f`` and temperature ``T``.
"""
helmholtz_free_energy::Function
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
helmholtz_free_energy_per_link::Function
"""
The relative helmholtz free energy ``\\Delta\\psi\\equiv\\psi(f,T)-\\psi(0,T)`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_helmholtz_free_energy::Function
"""
The relative helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_helmholtz_free_energy_per_link::Function
"""
The nondimensional helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy::Function
"""
The nondimensional helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy_per_link::Function
"""
The nondimensional relative helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_helmholtz_free_energy::Function
"""
The nondimensional relative helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_helmholtz_free_energy_per_link::Function
end
"""
The Helmholtz free energy ``\\psi`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and link stiffness ``k_0``.
```math
\\psi(f, T) \\sim \\varphi(f, T) + f \\xi(f, T) \\quad \\text{for } N_b\\gg 1.
```
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_legendre_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
)
end
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, hinge_mass_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_legendre_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
)
end
"""
The relative Helmholtz free energy ``\\Delta\\psi\\equiv\\psi(f,T)-\\psi(0,T)`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, link_stiffness_i, force_i, temperature_i) ->
ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_legendre_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The relative Helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_legendre_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The nondimensional Helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_legendre_nondimensional_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_force,
temperature,
)
end
"""
The nondimensional Helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
link_length_i,
hinge_mass_i,
link_stiffness_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_legendre_nondimensional_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
link_stiffness_i,
nondimensional_force_i,
temperature_i,
),
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_force,
temperature,
)
end
"""
The nondimensional relative Helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b`` and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_link_stiffness_i, nondimensional_force_i) ->
ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_legendre_nondimensional_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta``
parameterized by the nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(nondimensional_link_stiffness_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_legendre_nondimensional_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
Initializes and returns an instance of the thermodynamics of the Lennard-Jones-FJC model in the isotensional ensemble approximated using an asymptotic approach and a Legendre transformation.
$(TYPEDSIGNATURES)
"""
function LENNARDJONESFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
)
BOLTZMANN_CONSTANT::Float64 = 8.314462618
return LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
(force, temperature) -> helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
),
(force, temperature) -> helmholtz_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
),
(force, temperature) -> relative_helmholtz_free_energy(
number_of_links,
link_length,
link_stiffness,
force,
temperature,
),
(force, temperature) -> relative_helmholtz_free_energy_per_link(
link_length,
link_stiffness,
force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) ->
nondimensional_helmholtz_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) ->
nondimensional_relative_helmholtz_free_energy(
number_of_links,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(nondimensional_force, temperature) ->
nondimensional_relative_helmholtz_free_energy_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 32982 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ZERO, parameters
using Polymers.Physics.SingleChain.Ufjc.LennardJones.Thermodynamics.Isotensional.Legendre:
LENNARDJONESFJC
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::legendre::test::base::init" begin
@test isa(
LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
),
Any,
)
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::legendre::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test LENNARDJONESFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::legendre::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::legendre::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.link_stiffness_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::legendre::test::base::link_stiffness" begin
for _ = 1:parameters.number_of_loops
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
link_stiffness,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::legendre::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test all(
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).number_of_links == number_of_links &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_length == link_length &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).hinge_mass == hinge_mass &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_stiffness == link_stiffness,
)
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::legendre::test::nondimensional::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_helmholtz_free_energy =
model.nondimensional_helmholtz_free_energy(nondimensional_force, temperature)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy = model.helmholtz_free_energy(force, temperature)
residual_abs =
helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::legendre::test::nondimensional::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(force, temperature)
residual_abs =
helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::legendre::test::nondimensional::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(force, temperature)
residual_abs =
relative_helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::legendre::test::nondimensional::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(force, temperature)
residual_abs =
relative_helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::legendre::test::per_link::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy = model.helmholtz_free_energy(force, temperature)
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(force, temperature)
residual_abs =
helmholtz_free_energy / number_of_links - helmholtz_free_energy_per_link
residual_rel = residual_abs / helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::legendre::test::per_link::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(force, temperature)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(force, temperature)
residual_abs =
relative_helmholtz_free_energy / number_of_links -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::legendre::test::per_link::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_helmholtz_free_energy =
model.nondimensional_helmholtz_free_energy(nondimensional_force, temperature)
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy / number_of_links -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::legendre::test::per_link::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy / number_of_links -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::legendre::test::relative::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy = model.helmholtz_free_energy(force, temperature)
helmholtz_free_energy_0 = model.helmholtz_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(force, temperature)
residual_abs =
helmholtz_free_energy - helmholtz_free_energy_0 - relative_helmholtz_free_energy
residual_rel = residual_abs / helmholtz_free_energy_0
@test abs(residual_abs) <=
BOLTZMANN_CONSTANT * temperature * number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::legendre::test::relative::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(force, temperature)
helmholtz_free_energy_per_link_0 = model.helmholtz_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(force, temperature)
residual_abs =
helmholtz_free_energy_per_link - helmholtz_free_energy_per_link_0 -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / helmholtz_free_energy_per_link_0
@test abs(residual_abs) <= BOLTZMANN_CONSTANT * temperature * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::legendre::test::relative::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_helmholtz_free_energy =
model.nondimensional_helmholtz_free_energy(nondimensional_force, temperature)
nondimensional_helmholtz_free_energy_0 =
model.nondimensional_helmholtz_free_energy(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy - nondimensional_helmholtz_free_energy_0 -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_0
@test abs(residual_abs) <= number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::legendre::test::relative::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_helmholtz_free_energy_per_link_0 =
model.nondimensional_helmholtz_free_energy_per_link(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy_per_link -
nondimensional_helmholtz_free_energy_per_link_0 -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link_0
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::legendre::test::zero::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_0 = model.relative_helmholtz_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature * number_of_links
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::legendre::test::zero::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_per_link_0 =
model.relative_helmholtz_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::legendre::test::zero::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_0 =
model.nondimensional_relative_helmholtz_free_energy(ZERO, temperature)
@test abs(nondimensional_relative_helmholtz_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::legendre::test::zero::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_per_link_0 =
model.nondimensional_relative_helmholtz_free_energy_per_link(ZERO, temperature)
@test abs(nondimensional_relative_helmholtz_free_energy_per_link_0) <= ZERO
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 24305 | """
The Lennard-Jones potential freely-jointed chain (Lennard-Jones-FJC) model thermodynamics in the isotensional ensemble approximated using an reduced asymptotic approach.
"""
module Reduced
using DocStringExtensions
using .........Polymers: PROJECT_ROOT
import ........Physics: BOLTZMANN_CONSTANT
include("legendre/mod.jl")
"""
The structure of the thermodynamics of the Lennard-Jones-FJC model in the isotensional ensemble approximated using an reduced asymptotic approach.
$(FIELDS)
"""
struct LENNARDJONESFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The stiffness of each link in the chain ``k_0`` in units of J/(mol⋅nm^2).
"""
link_stiffness::Float64
"""
The thermodynamic functions of the model in the isotensional ensemble approximated using an reduced asymptotic approach.
"""
legendre::Any
"""
The expected end-to-end length ``\\xi`` as a function of the applied force ``f`` and temperature ``T``.
"""
end_to_end_length::Function
"""
The expected end-to-end length per link ``\\xi/N_b=\\ell_b\\gamma`` as a function of the applied force ``f`` and temperature ``T``.
"""
end_to_end_length_per_link::Function
"""
The expected nondimensional end-to-end length ``N_b\\gamma=\\xi/\\ell_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_end_to_end_length::Function
"""
The expected nondimensional end-to-end length per link ``\\gamma\\equiv\\xi/N_b\\ell_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_end_to_end_length_per_link::Function
"""
The Gibbs free energy ``\\varphi`` as a function of the applied force ``f`` and temperature ``T``.
"""
gibbs_free_energy::Function
"""
The Gibbs free energy per link ``\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
gibbs_free_energy_per_link::Function
"""
The relative Gibbs free energy ``\\Delta\\varphi\\equiv\\varphi(f,T)-\\varphi(0,T)`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_gibbs_free_energy::Function
"""
The relative Gibbs free energy per link ``\\Delta\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_gibbs_free_energy_per_link::Function
"""
The nondimensional Gibbs free energy ``N_b\\varrho=\\beta\\varphi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_gibbs_free_energy::Function
"""
The nondimensional Gibbs free energy per link ``\\varrho\\equiv\\beta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_gibbs_free_energy_per_link::Function
"""
The nondimensional relative Gibbs free energy ``N_b\\Delta\\varrho=\\beta\\Delta\\varphi`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_gibbs_free_energy::Function
"""
The nondimensional relative Gibbs free energy per link ``\\Delta\\varrho\\equiv\\beta\\Delta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_gibbs_free_energy_per_link::Function
end
"""
The expected end-to-end length ``N_b\\gamma=\\xi/\\ell_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``,
```math
\\xi(f, T) = -\\frac{\\partial\\varphi}{\\partial f}.
```
$(TYPEDSIGNATURES)
"""
function end_to_end_length(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, link_stiffness_i, force_i, temperature_i) ->
ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_reduced_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The expected end-to-end length per link ``\\xi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function end_to_end_length_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_reduced_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The expected nondimensional end-to-end length ``N_b\\gamma=\\xi/\\ell_b`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b`` and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_end_to_end_length(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_link_stiffness_i, nondimensional_force_i) ->
ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_reduced_nondimensional_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
The expected nondimensional end-to-end length per link ``\\gamma\\equiv \\xi/N_b\\ell_b`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``,
given by [Buche et al.](https://doi.org/10.1103/PhysRevE.106.024502) as
```math
\\Delta\\varrho(\\eta) \\sim \\mathcal{L}(\\eta) + \\Delta\\lambda(\\eta) \\quad \\text{for } \\varepsilon,\\kappa\\gg 1,
```
where ``\\mathcal{L}(x)=\\coth(x)-1/x`` is the Langevin function, and ``\\Delta\\lambda(\\eta)`` is the incremental link stretch, given by inverting
```math
\\eta(\\lambda) = 12\\varepsilon\\left[\\frac{1}{\\lambda^7} - \\frac{1}{\\lambda^{13}}\\right].
```
$(TYPEDSIGNATURES)
"""
function nondimensional_end_to_end_length_per_link(
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(nondimensional_link_stiffness_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_reduced_nondimensional_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
The Gibbs free energy ``\\varphi`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and link stiffness ``k_0``.
```math
\\varphi(f, T) = -kT\\ln Z(f, T).
```
$(TYPEDSIGNATURES)
"""
function gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_reduced_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
)
end
"""
The Gibbs free energy per link ``\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, hinge_mass_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_reduced_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
)
end
"""
The relative Gibbs free energy ``\\Delta\\varphi\\equiv\\varphi(f,T)-\\varphi(0,T)`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, link_stiffness_i, force_i, temperature_i) ->
ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_reduced_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The relative Gibbs free energy per link ``\\Delta\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_reduced_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The nondimensional Gibbs free energy ``N_b\\varrho=\\beta\\varphi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_reduced_nondimensional_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_force,
temperature,
)
end
"""
The nondimensional Gibbs free energy per link ``\\varrho\\equiv\\beta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_reduced_nondimensional_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
),
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_force,
temperature,
)
end
"""
The nondimensional relative Gibbs free energy ``N_b\\Delta\\varrho=\\beta\\Delta\\varphi`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b`` and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_link_stiffness_i, nondimensional_force_i) ->
ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_reduced_nondimensional_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
The nondimensional relative Gibbs free energy per link ``\\Delta\\varrho\\equiv\\beta\\Delta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``,
given by [Buche et al.](https://doi.org/10.1103/PhysRevE.106.024502) as
```math
\\Delta\\varrho(\\eta) \\sim \\ln\\left[\\frac{\\eta}{\\sinh(\\eta)}\\right] + \\beta u[\\lambda(\\eta)] - \\eta\\Delta\\lambda(\\eta) \\quad \\text{for } \\varepsilon,\\kappa\\gg 1,
```
where the nondimensional link potential ``\\beta u`` is given by [Jones](https://doi.org/10.1098/rspa.1924.0082) as
```math
\\beta u(\\lambda) = \\varepsilon\\left[\\frac{1}{\\lambda^{12}} - \\frac{2}{\\lambda^6}\\right],
```
where ``\\varepsilon\\equiv\\beta u_b=\\kappa/72`` is the nondimensional potential energy scale, ``\\kappa\\equiv\\beta k_b\\ell_b^2`` is the nondimensional link stiffness, and ``\\lambda\\equiv\\ell/\\ell_b`` is the nondimensional link stretch.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(nondimensional_link_stiffness_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_reduced_nondimensional_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
Initializes and returns an instance of the thermodynamics of the Lennard-Jones-FJC model in the isotensional ensemble approximated using an reduced asymptotic approach.
$(TYPEDSIGNATURES)
"""
function LENNARDJONESFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
)
BOLTZMANN_CONSTANT::Float64 = 8.314462618
return LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
Legendre.LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness),
(force, temperature) -> end_to_end_length(
number_of_links,
link_length,
link_stiffness,
force,
temperature,
),
(force, temperature) ->
end_to_end_length_per_link(link_length, link_stiffness, force, temperature),
(nondimensional_force, temperature) -> nondimensional_end_to_end_length(
number_of_links,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(nondimensional_force, temperature) -> nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(force, temperature) -> gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
),
(force, temperature) -> gibbs_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
),
(force, temperature) -> relative_gibbs_free_energy(
number_of_links,
link_length,
link_stiffness,
force,
temperature,
),
(force, temperature) -> relative_gibbs_free_energy_per_link(
link_length,
link_stiffness,
force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_gibbs_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_relative_gibbs_free_energy(
number_of_links,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(nondimensional_force, temperature) ->
nondimensional_relative_gibbs_free_energy_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 68951 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ZERO, parameters
using Polymers.Physics.SingleChain.Ufjc.LennardJones.Thermodynamics.Isotensional.Asymptotic.Reduced:
LENNARDJONESFJC
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::base::init" begin
@test isa(
LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
),
Any,
)
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test LENNARDJONESFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.link_stiffness_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::base::link_stiffness" begin
for _ = 1:parameters.number_of_loops
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
link_stiffness,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test all(
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).number_of_links == number_of_links &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_length == link_length &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).hinge_mass == hinge_mass &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_stiffness == link_stiffness,
)
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::nondimensional::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
residual_abs = end_to_end_length / link_length - nondimensional_end_to_end_length
residual_rel = residual_abs / nondimensional_end_to_end_length
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::nondimensional::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
residual_abs =
end_to_end_length_per_link / link_length -
nondimensional_end_to_end_length_per_link
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::nondimensional::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
residual_abs =
gibbs_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_gibbs_free_energy
residual_rel = residual_abs / nondimensional_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::nondimensional::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
residual_abs =
gibbs_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::nondimensional::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
residual_abs =
relative_gibbs_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_gibbs_free_energy
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::nondimensional::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
residual_abs =
relative_gibbs_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::per_link::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
residual_abs = end_to_end_length / number_of_links - end_to_end_length_per_link
residual_rel = residual_abs / end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::per_link::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_end_to_end_length / number_of_links -
nondimensional_end_to_end_length_per_link
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::per_link::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
residual_abs = gibbs_free_energy / number_of_links - gibbs_free_energy_per_link
residual_rel = residual_abs / gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::per_link::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
residual_abs =
relative_gibbs_free_energy / number_of_links -
relative_gibbs_free_energy_per_link
residual_rel = residual_abs / relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::per_link::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_gibbs_free_energy / number_of_links -
nondimensional_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::per_link::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_relative_gibbs_free_energy / number_of_links -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::relative::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
gibbs_free_energy_0 = model.gibbs_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
residual_abs = gibbs_free_energy - gibbs_free_energy_0 - relative_gibbs_free_energy
residual_rel = residual_abs / gibbs_free_energy_0
@test abs(residual_abs) <=
BOLTZMANN_CONSTANT * temperature * number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::relative::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
gibbs_free_energy_per_link_0 = model.gibbs_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
residual_abs =
gibbs_free_energy_per_link - gibbs_free_energy_per_link_0 -
relative_gibbs_free_energy_per_link
residual_rel = residual_abs / gibbs_free_energy_per_link_0
@test abs(residual_abs) <= BOLTZMANN_CONSTANT * temperature * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::relative::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
nondimensional_gibbs_free_energy_0 =
model.nondimensional_gibbs_free_energy(ZERO, temperature)
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_gibbs_free_energy - nondimensional_gibbs_free_energy_0 -
nondimensional_relative_gibbs_free_energy
residual_rel = residual_abs / nondimensional_gibbs_free_energy_0
@test abs(residual_abs) <= number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::relative::nondimensional_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_gibbs_free_energy_per_link_0 =
model.nondimensional_gibbs_free_energy_per_link(ZERO, temperature)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_gibbs_free_energy_per_link -
nondimensional_gibbs_free_energy_per_link_0 -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link_0
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::zero::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_gibbs_free_energy_0 = model.relative_gibbs_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_gibbs_free_energy_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature * number_of_links
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::zero::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_gibbs_free_energy_per_link_0 = model.relative_gibbs_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_gibbs_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::zero::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy_0 =
model.nondimensional_relative_gibbs_free_energy(ZERO, temperature)
@test abs(nondimensional_relative_gibbs_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::zero::nondimensional_relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy_per_link_0 =
model.nondimensional_relative_gibbs_free_energy_per_link(ZERO, temperature)
@test abs(nondimensional_relative_gibbs_free_energy_per_link_0) <= ZERO
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::connection::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
h = parameters.rel_tol * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_from_derivative =
-(
model.relative_gibbs_free_energy(force + 0.5 * h, temperature) -
model.relative_gibbs_free_energy(force - 0.5 * h, temperature)
) / h
residual_abs = end_to_end_length - end_to_end_length_from_derivative
residual_rel = residual_abs / end_to_end_length
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::connection::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
h = parameters.rel_tol * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link_from_derivative =
-(
model.relative_gibbs_free_energy_per_link(force + 0.5 * h, temperature) -
model.relative_gibbs_free_energy_per_link(force - 0.5 * h, temperature)
) / h
residual_abs =
end_to_end_length_per_link - end_to_end_length_per_link_from_derivative
residual_rel = residual_abs / end_to_end_length_per_link
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::connection::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
h = parameters.rel_tol
nondimensional_end_to_end_length_from_derivative =
-(
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force + 0.5 * h,
temperature,
) - model.nondimensional_relative_gibbs_free_energy(
nondimensional_force - 0.5 * h,
temperature,
)
) / h
residual_abs =
nondimensional_end_to_end_length -
nondimensional_end_to_end_length_from_derivative
residual_rel = residual_abs / nondimensional_end_to_end_length
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::connection::nondimensional_end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
h = parameters.rel_tol
nondimensional_end_to_end_length_per_link_from_derivative =
-(
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force + 0.5 * h,
temperature,
) - model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force - 0.5 * h,
temperature,
)
) / h
residual_abs =
nondimensional_end_to_end_length_per_link -
nondimensional_end_to_end_length_per_link_from_derivative
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::legendre::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
gibbs_free_energy_legendre =
model.legendre.helmholtz_free_energy(force, temperature) -
force * end_to_end_length
residual_abs = gibbs_free_energy - gibbs_free_energy_legendre
residual_rel = residual_abs / gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::legendre::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
gibbs_free_energy_per_link_legendre =
model.legendre.helmholtz_free_energy_per_link(force, temperature) -
force * end_to_end_length_per_link
residual_abs = gibbs_free_energy_per_link - gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::legendre::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
end_to_end_length_0 = model.end_to_end_length(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
relative_gibbs_free_energy_legendre =
model.legendre.relative_helmholtz_free_energy(force, temperature) -
force * end_to_end_length +
ZERO * BOLTZMANN_CONSTANT * temperature / link_length * end_to_end_length_0
residual_abs = relative_gibbs_free_energy - relative_gibbs_free_energy_legendre
residual_rel = residual_abs / relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::legendre::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
end_to_end_length_per_link_0 = model.end_to_end_length_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
relative_gibbs_free_energy_per_link_legendre =
model.legendre.relative_helmholtz_free_energy_per_link(force, temperature) -
force * end_to_end_length_per_link +
ZERO * BOLTZMANN_CONSTANT * temperature / link_length *
end_to_end_length_per_link_0
residual_abs =
relative_gibbs_free_energy_per_link -
relative_gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::legendre::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
nondimensional_gibbs_free_energy_legendre =
model.legendre.nondimensional_helmholtz_free_energy(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length
residual_abs =
nondimensional_gibbs_free_energy - nondimensional_gibbs_free_energy_legendre
residual_rel = residual_abs / nondimensional_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::legendre::nondimensional_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_gibbs_free_energy_per_link_legendre =
model.legendre.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length_per_link
residual_abs =
nondimensional_gibbs_free_energy_per_link -
nondimensional_gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::legendre::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
nondimensional_end_to_end_length_0 =
model.nondimensional_end_to_end_length(ZERO, temperature)
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
)
nondimensional_relative_gibbs_free_energy_legendre =
model.legendre.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length +
ZERO * nondimensional_end_to_end_length_0
residual_abs =
nondimensional_relative_gibbs_free_energy -
nondimensional_relative_gibbs_free_energy_legendre
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::legendre::nondimensional_relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_end_to_end_length_per_link_0 =
model.nondimensional_end_to_end_length_per_link(ZERO, temperature)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_relative_gibbs_free_energy_per_link_legendre =
model.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length_per_link +
ZERO * nondimensional_end_to_end_length_per_link_0
residual_abs =
nondimensional_relative_gibbs_free_energy_per_link -
nondimensional_relative_gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::legendre_connection::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
h = parameters.rel_tol * BOLTZMANN_CONSTANT * temperature / link_length
force_from_derivative =
(
model.legendre.relative_helmholtz_free_energy(
force + 0.5 * h,
temperature,
) -
model.legendre.relative_helmholtz_free_energy(force - 0.5 * h, temperature)
) / (
model.end_to_end_length(force + 0.5 * h, temperature) -
model.end_to_end_length(force - 0.5 * h, temperature)
)
residual_abs = force - force_from_derivative
residual_rel = residual_abs / force
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::test::legendre_connection::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
h = parameters.rel_tol
nondimensional_force_from_derivative =
(
model.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force + 0.5 * h,
temperature,
) - model.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force - 0.5 * h,
temperature,
)
) / (
model.nondimensional_end_to_end_length_per_link(
nondimensional_force + 0.5 * h,
temperature,
) - model.nondimensional_end_to_end_length_per_link(
nondimensional_force - 0.5 * h,
temperature,
)
)
residual_abs = nondimensional_force - nondimensional_force_from_derivative
residual_rel = residual_abs / nondimensional_force
@test abs(residual_rel) <= h
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 16682 | """
The Lennard-Jones potential freely-jointed chain (Lennard-Jones-FJC) model thermodynamics in the isotensional ensemble approximated using a reduced asymptotic approach and a Legendre transformation.
"""
module Legendre
using DocStringExtensions
using ..........Polymers: PROJECT_ROOT
import .........Physics: BOLTZMANN_CONSTANT
"""
The structure of the thermodynamics of the Lennard-Jones-FJC model in the isotensional ensemble approximated using a reduced asymptotic approach and a Legendre transformation.
$(FIELDS)
"""
struct LENNARDJONESFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The stiffness of each link in the chain ``k_0`` in units of J/(mol⋅nm^2).
"""
link_stiffness::Float64
"""
The Helmholtz free energy ``\\psi`` as a function of the applied force ``f`` and temperature ``T``.
"""
helmholtz_free_energy::Function
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
helmholtz_free_energy_per_link::Function
"""
The relative helmholtz free energy ``\\Delta\\psi\\equiv\\psi(f,T)-\\psi(0,T)`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_helmholtz_free_energy::Function
"""
The relative helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_helmholtz_free_energy_per_link::Function
"""
The nondimensional helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy::Function
"""
The nondimensional helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy_per_link::Function
"""
The nondimensional relative helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_helmholtz_free_energy::Function
"""
The nondimensional relative helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_helmholtz_free_energy_per_link::Function
end
"""
The Helmholtz free energy ``\\psi`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and link stiffness ``k_0``.
```math
\\psi(f, T) \\sim \\varphi(f, T) + f \\xi(f, T) \\quad \\text{for } N_b\\gg 1.
```
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_reduced_legendre_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
)
end
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, hinge_mass_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_reduced_legendre_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
)
end
"""
The relative Helmholtz free energy ``\\Delta\\psi\\equiv\\psi(f,T)-\\psi(0,T)`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, link_stiffness_i, force_i, temperature_i) ->
ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_reduced_legendre_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The relative Helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_reduced_legendre_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The nondimensional Helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_reduced_legendre_nondimensional_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_force,
temperature,
)
end
"""
The nondimensional Helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
link_length_i,
hinge_mass_i,
link_stiffness_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_reduced_legendre_nondimensional_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
link_stiffness_i,
nondimensional_force_i,
temperature_i,
),
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_force,
temperature,
)
end
"""
The nondimensional relative Helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b`` and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_link_stiffness_i, nondimensional_force_i) ->
ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_reduced_legendre_nondimensional_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta``
parameterized by the nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(nondimensional_link_stiffness_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_asymptotic_reduced_legendre_nondimensional_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
Initializes and returns an instance of the thermodynamics of the Lennard-Jones-FJC model in the isotensional ensemble approximated using a reduced asymptotic approach and a Legendre transformation.
$(TYPEDSIGNATURES)
"""
function LENNARDJONESFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
)
BOLTZMANN_CONSTANT::Float64 = 8.314462618
return LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
(force, temperature) -> helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
),
(force, temperature) -> helmholtz_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
),
(force, temperature) -> relative_helmholtz_free_energy(
number_of_links,
link_length,
link_stiffness,
force,
temperature,
),
(force, temperature) -> relative_helmholtz_free_energy_per_link(
link_length,
link_stiffness,
force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) ->
nondimensional_helmholtz_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) ->
nondimensional_relative_helmholtz_free_energy(
number_of_links,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(nondimensional_force, temperature) ->
nondimensional_relative_helmholtz_free_energy_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 33180 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ZERO, parameters
using Polymers.Physics.SingleChain.Ufjc.LennardJones.Thermodynamics.Isotensional.Legendre:
LENNARDJONESFJC
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::legendre::test::base::init" begin
@test isa(
LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
),
Any,
)
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::legendre::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test LENNARDJONESFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::legendre::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::legendre::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.link_stiffness_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::legendre::test::base::link_stiffness" begin
for _ = 1:parameters.number_of_loops
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
link_stiffness,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::legendre::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test all(
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).number_of_links == number_of_links &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_length == link_length &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).hinge_mass == hinge_mass &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_stiffness == link_stiffness,
)
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::legendre::test::nondimensional::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_helmholtz_free_energy =
model.nondimensional_helmholtz_free_energy(nondimensional_force, temperature)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy = model.helmholtz_free_energy(force, temperature)
residual_abs =
helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::legendre::test::nondimensional::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(force, temperature)
residual_abs =
helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::legendre::test::nondimensional::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(force, temperature)
residual_abs =
relative_helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::legendre::test::nondimensional::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(force, temperature)
residual_abs =
relative_helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::legendre::test::per_link::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy = model.helmholtz_free_energy(force, temperature)
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(force, temperature)
residual_abs =
helmholtz_free_energy / number_of_links - helmholtz_free_energy_per_link
residual_rel = residual_abs / helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::legendre::test::per_link::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(force, temperature)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(force, temperature)
residual_abs =
relative_helmholtz_free_energy / number_of_links -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::legendre::test::per_link::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_helmholtz_free_energy =
model.nondimensional_helmholtz_free_energy(nondimensional_force, temperature)
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy / number_of_links -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::legendre::test::per_link::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy / number_of_links -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::legendre::test::relative::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy = model.helmholtz_free_energy(force, temperature)
helmholtz_free_energy_0 = model.helmholtz_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(force, temperature)
residual_abs =
helmholtz_free_energy - helmholtz_free_energy_0 - relative_helmholtz_free_energy
residual_rel = residual_abs / helmholtz_free_energy_0
@test abs(residual_abs) <=
BOLTZMANN_CONSTANT * temperature * number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::legendre::test::relative::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(force, temperature)
helmholtz_free_energy_per_link_0 = model.helmholtz_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(force, temperature)
residual_abs =
helmholtz_free_energy_per_link - helmholtz_free_energy_per_link_0 -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / helmholtz_free_energy_per_link_0
@test abs(residual_abs) <= BOLTZMANN_CONSTANT * temperature * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::legendre::test::relative::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_helmholtz_free_energy =
model.nondimensional_helmholtz_free_energy(nondimensional_force, temperature)
nondimensional_helmholtz_free_energy_0 =
model.nondimensional_helmholtz_free_energy(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy - nondimensional_helmholtz_free_energy_0 -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_0
@test abs(residual_abs) <= number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::legendre::test::relative::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_helmholtz_free_energy_per_link_0 =
model.nondimensional_helmholtz_free_energy_per_link(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy_per_link -
nondimensional_helmholtz_free_energy_per_link_0 -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link_0
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::legendre::test::zero::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_0 = model.relative_helmholtz_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature * number_of_links
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::legendre::test::zero::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_per_link_0 =
model.relative_helmholtz_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::legendre::test::zero::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_0 =
model.nondimensional_relative_helmholtz_free_energy(ZERO, temperature)
@test abs(nondimensional_relative_helmholtz_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::asymptotic::reduced::legendre::test::zero::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_per_link_0 =
model.nondimensional_relative_helmholtz_free_energy_per_link(ZERO, temperature)
@test abs(nondimensional_relative_helmholtz_free_energy_per_link_0) <= ZERO
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 16426 | """
The Lennard-Jones potential freely-jointed chain (Lennard-Jones-FJC) model thermodynamics in the isotensional ensemble approximated using a Legendre transformation.
"""
module Legendre
using DocStringExtensions
using ........Polymers: PROJECT_ROOT
import .......Physics: BOLTZMANN_CONSTANT
"""
The structure of the thermodynamics of the Lennard-Jones-FJC model in the isotensional ensemble approximated using a Legendre transformation.
$(FIELDS)
"""
struct LENNARDJONESFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The stiffness of each link in the chain ``k_0`` in units of J/(mol⋅nm^2).
"""
link_stiffness::Float64
"""
The Helmholtz free energy ``\\psi`` as a function of the applied force ``f`` and temperature ``T``.
"""
helmholtz_free_energy::Function
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
helmholtz_free_energy_per_link::Function
"""
The relative helmholtz free energy ``\\Delta\\psi\\equiv\\psi(f,T)-\\psi(0,T)`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_helmholtz_free_energy::Function
"""
The relative helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_helmholtz_free_energy_per_link::Function
"""
The nondimensional helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy::Function
"""
The nondimensional helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy_per_link::Function
"""
The nondimensional relative helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_helmholtz_free_energy::Function
"""
The nondimensional relative helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_helmholtz_free_energy_per_link::Function
end
"""
The Helmholtz free energy ``\\psi`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and link stiffness ``k_0``.
```math
\\psi(f, T) \\sim \\varphi(f, T) + f \\xi(f, T) \\quad \\text{for } N_b\\gg 1.
```
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_legendre_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
)
end
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, hinge_mass_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_legendre_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
)
end
"""
The relative Helmholtz free energy ``\\Delta\\psi\\equiv\\psi(f,T)-\\psi(0,T)`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, link_stiffness_i, force_i, temperature_i) ->
ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_legendre_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The relative Helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_legendre_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The nondimensional Helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_legendre_nondimensional_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_force,
temperature,
)
end
"""
The nondimensional Helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
link_length_i,
hinge_mass_i,
link_stiffness_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_legendre_nondimensional_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
link_stiffness_i,
nondimensional_force_i,
temperature_i,
),
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_force,
temperature,
)
end
"""
The nondimensional relative Helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b`` and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_link_stiffness_i, nondimensional_force_i) ->
ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_legendre_nondimensional_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta``
parameterized by the nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(nondimensional_link_stiffness_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_ufjc_lennard_jones_thermodynamics_isotensional_legendre_nondimensional_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
Initializes and returns an instance of the thermodynamics of the Lennard-Jones-FJC model in the isotensional ensemble approximated using a Legendre transformation.
$(TYPEDSIGNATURES)
"""
function LENNARDJONESFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
)
BOLTZMANN_CONSTANT::Float64 = 8.314462618
return LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
(force, temperature) -> helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
),
(force, temperature) -> helmholtz_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
),
(force, temperature) -> relative_helmholtz_free_energy(
number_of_links,
link_length,
link_stiffness,
force,
temperature,
),
(force, temperature) -> relative_helmholtz_free_energy_per_link(
link_length,
link_stiffness,
force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) ->
nondimensional_helmholtz_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) ->
nondimensional_relative_helmholtz_free_energy(
number_of_links,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(nondimensional_force, temperature) ->
nondimensional_relative_helmholtz_free_energy_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 32718 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ZERO, parameters
using Polymers.Physics.SingleChain.Ufjc.LennardJones.Thermodynamics.Isotensional.Legendre:
LENNARDJONESFJC
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::legendre::test::base::init" begin
@test isa(
LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
),
Any,
)
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::legendre::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test LENNARDJONESFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::legendre::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::legendre::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.link_stiffness_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::legendre::test::base::link_stiffness" begin
for _ = 1:parameters.number_of_loops
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test LENNARDJONESFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
link_stiffness,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::legendre::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test all(
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).number_of_links == number_of_links &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_length == link_length &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).hinge_mass == hinge_mass &&
LENNARDJONESFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_stiffness == link_stiffness,
)
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::legendre::test::nondimensional::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_helmholtz_free_energy =
model.nondimensional_helmholtz_free_energy(nondimensional_force, temperature)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy = model.helmholtz_free_energy(force, temperature)
residual_abs =
helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::legendre::test::nondimensional::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(force, temperature)
residual_abs =
helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::legendre::test::nondimensional::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(force, temperature)
residual_abs =
relative_helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::legendre::test::nondimensional::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(force, temperature)
residual_abs =
relative_helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::legendre::test::per_link::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy = model.helmholtz_free_energy(force, temperature)
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(force, temperature)
residual_abs =
helmholtz_free_energy / number_of_links - helmholtz_free_energy_per_link
residual_rel = residual_abs / helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::legendre::test::per_link::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(force, temperature)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(force, temperature)
residual_abs =
relative_helmholtz_free_energy / number_of_links -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::legendre::test::per_link::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_helmholtz_free_energy =
model.nondimensional_helmholtz_free_energy(nondimensional_force, temperature)
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy / number_of_links -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::legendre::test::per_link::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy / number_of_links -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::legendre::test::relative::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy = model.helmholtz_free_energy(force, temperature)
helmholtz_free_energy_0 = model.helmholtz_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(force, temperature)
residual_abs =
helmholtz_free_energy - helmholtz_free_energy_0 - relative_helmholtz_free_energy
residual_rel = residual_abs / helmholtz_free_energy_0
@test abs(residual_abs) <=
BOLTZMANN_CONSTANT * temperature * number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::legendre::test::relative::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(force, temperature)
helmholtz_free_energy_per_link_0 = model.helmholtz_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(force, temperature)
residual_abs =
helmholtz_free_energy_per_link - helmholtz_free_energy_per_link_0 -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / helmholtz_free_energy_per_link_0
@test abs(residual_abs) <= BOLTZMANN_CONSTANT * temperature * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::legendre::test::relative::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_helmholtz_free_energy =
model.nondimensional_helmholtz_free_energy(nondimensional_force, temperature)
nondimensional_helmholtz_free_energy_0 =
model.nondimensional_helmholtz_free_energy(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy - nondimensional_helmholtz_free_energy_0 -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_0
@test abs(residual_abs) <= number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::legendre::test::relative::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
lambda_max = (13.0 / 7.0)^(1.0 / 6.0)
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / 6 *
(lambda_max^(-7) - lambda_max^(-13))
nondimensional_force = nondimensional_force_max * rand()
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_helmholtz_free_energy_per_link_0 =
model.nondimensional_helmholtz_free_energy_per_link(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy_per_link -
nondimensional_helmholtz_free_energy_per_link_0 -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link_0
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::legendre::test::zero::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_0 = model.relative_helmholtz_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature * number_of_links
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::legendre::test::zero::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_per_link_0 =
model.relative_helmholtz_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::legendre::test::zero::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_0 =
model.nondimensional_relative_helmholtz_free_energy(ZERO, temperature)
@test abs(nondimensional_relative_helmholtz_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::ufjc::lennard_jones::thermodynamics::isotensional::legendre::test::zero::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LENNARDJONESFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_per_link_0 =
model.nondimensional_relative_helmholtz_free_energy_per_link(ZERO, temperature)
@test abs(nondimensional_relative_helmholtz_free_energy_per_link_0) <= ZERO
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 1352 | """
The log-squared potential freely-jointed chain (log-squared-FJC) single-chain model.
"""
module LogSquared
using DocStringExtensions
include("thermodynamics/mod.jl")
"""
The structure of the log-squared-FJC model.
$(FIELDS)
"""
struct LOGSQUAREDFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The stiffness of each link in the chain ``k_0`` in units of J/(mol⋅nm^2).
"""
link_stiffness::Float64
"""
The thermodynamic functions of the model.
"""
thermodynamics::Any
end
"""
Initializes and returns an instance of the log-squared-FJC model.
$(TYPEDSIGNATURES)
"""
function LOGSQUAREDFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
)
return LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
Thermodynamics.LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 4046 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ZERO, parameters
using Polymers.Physics.SingleChain.Ufjc.LogSquared: LOGSQUAREDFJC
@testset "physics::single_chain::ufjc::log_squared::test::base::init" begin
@test isa(
LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
),
Any,
)
end
@testset "physics::single_chain::ufjc::log_squared::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test LOGSQUAREDFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ufjc::log_squared::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ufjc::log_squared::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.link_stiffness_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ufjc::log_squared::test::base::link_stiffness" begin
for _ = 1:parameters.number_of_loops
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
link_stiffness,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::log_squared::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test all(
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).number_of_links == number_of_links &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_length == link_length &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).hinge_mass == hinge_mass &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_stiffness == link_stiffness,
)
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 1670 | """
The log-squared potential freely-jointed chain (log-squared-FJC) single-chain model thermodynamics.
"""
module Thermodynamics
using DocStringExtensions
include("isometric/mod.jl")
include("isotensional/mod.jl")
"""
The structure of the thermodynamics of the log-squared-FJC model.
$(FIELDS)
"""
struct LOGSQUAREDFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The stiffness of each link in the chain ``k_0`` in units of J/(mol⋅nm^2).
"""
link_stiffness::Float64
"""
The thermodynamic functions of the model in the isometric ensemble.
"""
isometric::Any
"""
The thermodynamic functions of the model in the isotensional ensemble.
"""
isotensional::Any
end
"""
Initializes and returns an instance of the thermodynamics of the log-squared-FJC model.
$(TYPEDSIGNATURES)
"""
function LOGSQUAREDFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
)
return LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
Isometric.LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness),
Isotensional.LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 50114 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT, PLANCK_CONSTANT
using Polymers.Physics.SingleChain: parameters
using Polymers.Physics.SingleChain.Ufjc.LogSquared.Thermodynamics: LOGSQUAREDFJC
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::test::base::init" begin
@test isa(
LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
),
Any,
)
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test LOGSQUAREDFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.link_stiffness_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::test::base::link_stiffness" begin
for _ = 1:parameters.number_of_loops
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
link_stiffness,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test all(
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).number_of_links == number_of_links &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_length == link_length &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).hinge_mass == hinge_mass &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_stiffness == link_stiffness,
)
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::test::legendre_asymptotic::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length =
model.isotensional.asymptotic.end_to_end_length(force, temperature)
force_out =
model.isometric.asymptotic.legendre.force(end_to_end_length, temperature)
residual_abs = force - force_out
residual_rel = residual_abs / force
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::test::legendre_asymptotic::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.isotensional.asymptotic.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_force_out = model.isometric.asymptotic.legendre.nondimensional_force(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs = nondimensional_force - nondimensional_force_out
residual_rel = residual_abs / nondimensional_force
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::test::legendre_asymptotic::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length =
model.isotensional.asymptotic.end_to_end_length(force, temperature)
helmholtz_free_energy_legendre =
model.isotensional.asymptotic.gibbs_free_energy(force, temperature) +
force * end_to_end_length
helmholtz_free_energy_legendre_out =
model.isometric.asymptotic.legendre.helmholtz_free_energy(
end_to_end_length,
temperature,
)
residual_abs =
helmholtz_free_energy_legendre - helmholtz_free_energy_legendre_out +
BOLTZMANN_CONSTANT *
temperature *
(
0.5 * log(2.0 * pi * BOLTZMANN_CONSTANT * temperature / link_stiffness) +
log(
8.0 *
pi^2 *
hinge_mass *
link_length^2 *
BOLTZMANN_CONSTANT *
temperature / PLANCK_CONSTANT^2,
)
)
residual_rel = residual_abs / helmholtz_free_energy_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::test::legendre_asymptotic::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length =
model.isotensional.asymptotic.end_to_end_length(force, temperature)
end_to_end_length_per_link =
model.isotensional.asymptotic.end_to_end_length_per_link(force, temperature)
helmholtz_free_energy_per_link_legendre =
model.isotensional.asymptotic.gibbs_free_energy_per_link(force, temperature) +
force * end_to_end_length_per_link
helmholtz_free_energy_per_link_legendre_out =
model.isometric.asymptotic.legendre.helmholtz_free_energy_per_link(
end_to_end_length,
temperature,
)
residual_abs =
helmholtz_free_energy_per_link_legendre -
helmholtz_free_energy_per_link_legendre_out +
BOLTZMANN_CONSTANT *
temperature *
(
0.5 * log(2.0 * pi * BOLTZMANN_CONSTANT * temperature / link_stiffness) +
log(
8.0 *
pi^2 *
hinge_mass *
link_length^2 *
BOLTZMANN_CONSTANT *
temperature / PLANCK_CONSTANT^2,
)
) / number_of_links
residual_rel = residual_abs / helmholtz_free_energy_per_link_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::test::legendre_asymptotic::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length =
model.isotensional.asymptotic.end_to_end_length(force, temperature)
relative_helmholtz_free_energy_legendre =
model.isotensional.asymptotic.relative_gibbs_free_energy(force, temperature) +
force * end_to_end_length
relative_helmholtz_free_energy_legendre_out =
model.isometric.asymptotic.legendre.relative_helmholtz_free_energy(
end_to_end_length,
temperature,
)
residual_abs =
relative_helmholtz_free_energy_legendre -
relative_helmholtz_free_energy_legendre_out
residual_rel = residual_abs / relative_helmholtz_free_energy_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::test::legendre_asymptotic::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length =
model.isotensional.asymptotic.end_to_end_length(force, temperature)
end_to_end_length_per_link =
model.isotensional.asymptotic.end_to_end_length_per_link(force, temperature)
relative_helmholtz_free_energy_per_link_legendre =
model.isotensional.asymptotic.relative_gibbs_free_energy_per_link(
force,
temperature,
) + force * end_to_end_length_per_link
relative_helmholtz_free_energy_per_link_legendre_out =
model.isometric.asymptotic.legendre.relative_helmholtz_free_energy_per_link(
end_to_end_length,
temperature,
)
residual_abs =
relative_helmholtz_free_energy_per_link_legendre -
relative_helmholtz_free_energy_per_link_legendre_out
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::test::legendre_asymptotic::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.isotensional.asymptotic.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
)
nondimensional_end_to_end_length_per_link =
model.isotensional.asymptotic.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_helmholtz_free_energy_legendre =
model.isotensional.asymptotic.nondimensional_gibbs_free_energy(
nondimensional_force,
temperature,
) + nondimensional_force * nondimensional_end_to_end_length
nondimensional_helmholtz_free_energy_legendre_out =
model.isometric.asymptotic.legendre.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy_legendre -
nondimensional_helmholtz_free_energy_legendre_out + (
0.5 * log(2.0 * pi * BOLTZMANN_CONSTANT * temperature / link_stiffness) +
log(
8.0 *
pi^2 *
hinge_mass *
link_length^2 *
BOLTZMANN_CONSTANT *
temperature / PLANCK_CONSTANT^2,
)
)
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::test::legendre_asymptotic::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.isotensional.asymptotic.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_helmholtz_free_energy_per_link_legendre =
model.isotensional.asymptotic.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
) + nondimensional_force * nondimensional_end_to_end_length_per_link
nondimensional_helmholtz_free_energy_per_link_legendre_out =
model.isometric.asymptotic.legendre.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy_per_link_legendre -
nondimensional_helmholtz_free_energy_per_link_legendre_out +
(
0.5 * log(2.0 * pi * BOLTZMANN_CONSTANT * temperature / link_stiffness) +
log(
8.0 *
pi^2 *
hinge_mass *
link_length^2 *
BOLTZMANN_CONSTANT *
temperature / PLANCK_CONSTANT^2,
)
) / number_of_links
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::test::legendre_asymptotic::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.isotensional.asymptotic.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
)
nondimensional_end_to_end_length_per_link =
model.isotensional.asymptotic.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_relative_helmholtz_free_energy_legendre =
model.isotensional.asymptotic.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
) + nondimensional_force * nondimensional_end_to_end_length
nondimensional_relative_helmholtz_free_energy_legendre_out =
model.isometric.asymptotic.legendre.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy_legendre -
nondimensional_relative_helmholtz_free_energy_legendre_out
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::test::legendre_asymptotic::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.isotensional.asymptotic.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_relative_helmholtz_free_energy_per_link_legendre =
model.isotensional.asymptotic.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
) + nondimensional_force * nondimensional_end_to_end_length_per_link
nondimensional_relative_helmholtz_free_energy_per_link_legendre_out =
model.isometric.asymptotic.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy_per_link_legendre -
nondimensional_relative_helmholtz_free_energy_per_link_legendre_out
residual_rel =
residual_abs / nondimensional_relative_helmholtz_free_energy_per_link_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::test::legendre_asymptotic_reduced::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length =
model.isotensional.asymptotic.reduced.end_to_end_length(force, temperature)
force_out = model.isometric.asymptotic.reduced.legendre.force(
end_to_end_length,
temperature,
)
residual_abs = force - force_out
residual_rel = residual_abs / force
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::test::legendre_asymptotic_reduced::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.isotensional.asymptotic.reduced.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_force_out =
model.isometric.asymptotic.reduced.legendre.nondimensional_force(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs = nondimensional_force - nondimensional_force_out
residual_rel = residual_abs / nondimensional_force
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::test::legendre_asymptotic_reduced::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length =
model.isotensional.asymptotic.reduced.end_to_end_length(force, temperature)
helmholtz_free_energy_legendre =
model.isotensional.asymptotic.reduced.gibbs_free_energy(force, temperature) +
force * end_to_end_length
helmholtz_free_energy_legendre_out =
model.isometric.asymptotic.reduced.legendre.helmholtz_free_energy(
end_to_end_length,
temperature,
)
residual_abs =
helmholtz_free_energy_legendre - helmholtz_free_energy_legendre_out +
BOLTZMANN_CONSTANT *
temperature *
(
0.5 * log(2.0 * pi * BOLTZMANN_CONSTANT * temperature / link_stiffness) +
log(
8.0 *
pi^2 *
hinge_mass *
link_length^2 *
BOLTZMANN_CONSTANT *
temperature / PLANCK_CONSTANT^2,
)
)
residual_rel = residual_abs / helmholtz_free_energy_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::test::legendre_asymptotic_reduced::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length =
model.isotensional.asymptotic.reduced.end_to_end_length(force, temperature)
end_to_end_length_per_link =
model.isotensional.asymptotic.reduced.end_to_end_length_per_link(
force,
temperature,
)
helmholtz_free_energy_per_link_legendre =
model.isotensional.asymptotic.reduced.gibbs_free_energy_per_link(
force,
temperature,
) + force * end_to_end_length_per_link
helmholtz_free_energy_per_link_legendre_out =
model.isometric.asymptotic.reduced.legendre.helmholtz_free_energy_per_link(
end_to_end_length,
temperature,
)
residual_abs =
helmholtz_free_energy_per_link_legendre -
helmholtz_free_energy_per_link_legendre_out +
BOLTZMANN_CONSTANT *
temperature *
(
0.5 * log(2.0 * pi * BOLTZMANN_CONSTANT * temperature / link_stiffness) +
log(
8.0 *
pi^2 *
hinge_mass *
link_length^2 *
BOLTZMANN_CONSTANT *
temperature / PLANCK_CONSTANT^2,
)
) / number_of_links
residual_rel = residual_abs / helmholtz_free_energy_per_link_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::test::legendre_asymptotic_reduced::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length =
model.isotensional.asymptotic.reduced.end_to_end_length(force, temperature)
relative_helmholtz_free_energy_legendre =
model.isotensional.asymptotic.reduced.relative_gibbs_free_energy(
force,
temperature,
) + force * end_to_end_length
relative_helmholtz_free_energy_legendre_out =
model.isometric.asymptotic.reduced.legendre.relative_helmholtz_free_energy(
end_to_end_length,
temperature,
)
residual_abs =
relative_helmholtz_free_energy_legendre -
relative_helmholtz_free_energy_legendre_out
residual_rel = residual_abs / relative_helmholtz_free_energy_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::test::legendre_asymptotic_reduced::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length =
model.isotensional.asymptotic.reduced.end_to_end_length(force, temperature)
end_to_end_length_per_link =
model.isotensional.asymptotic.reduced.end_to_end_length_per_link(
force,
temperature,
)
relative_helmholtz_free_energy_per_link_legendre =
model.isotensional.asymptotic.reduced.relative_gibbs_free_energy_per_link(
force,
temperature,
) + force * end_to_end_length_per_link
relative_helmholtz_free_energy_per_link_legendre_out =
model.isometric.asymptotic.reduced.legendre.relative_helmholtz_free_energy_per_link(
end_to_end_length,
temperature,
)
residual_abs =
relative_helmholtz_free_energy_per_link_legendre -
relative_helmholtz_free_energy_per_link_legendre_out
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::test::legendre_asymptotic_reduced::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.isotensional.asymptotic.reduced.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
)
nondimensional_end_to_end_length_per_link =
model.isotensional.asymptotic.reduced.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_helmholtz_free_energy_legendre =
model.isotensional.asymptotic.reduced.nondimensional_gibbs_free_energy(
nondimensional_force,
temperature,
) + nondimensional_force * nondimensional_end_to_end_length
nondimensional_helmholtz_free_energy_legendre_out =
model.isometric.asymptotic.reduced.legendre.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy_legendre -
nondimensional_helmholtz_free_energy_legendre_out + (
0.5 * log(2.0 * pi * BOLTZMANN_CONSTANT * temperature / link_stiffness) +
log(
8.0 *
pi^2 *
hinge_mass *
link_length^2 *
BOLTZMANN_CONSTANT *
temperature / PLANCK_CONSTANT^2,
)
)
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::test::legendre_asymptotic_reduced::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.isotensional.asymptotic.reduced.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_helmholtz_free_energy_per_link_legendre =
model.isotensional.asymptotic.reduced.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
) + nondimensional_force * nondimensional_end_to_end_length_per_link
nondimensional_helmholtz_free_energy_per_link_legendre_out =
model.isometric.asymptotic.reduced.legendre.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy_per_link_legendre -
nondimensional_helmholtz_free_energy_per_link_legendre_out +
(
0.5 * log(2.0 * pi * BOLTZMANN_CONSTANT * temperature / link_stiffness) +
log(
8.0 *
pi^2 *
hinge_mass *
link_length^2 *
BOLTZMANN_CONSTANT *
temperature / PLANCK_CONSTANT^2,
)
) / number_of_links
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::test::legendre_asymptotic_reduced::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.isotensional.asymptotic.reduced.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
)
nondimensional_end_to_end_length_per_link =
model.isotensional.asymptotic.reduced.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_relative_helmholtz_free_energy_legendre =
model.isotensional.asymptotic.reduced.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
) + nondimensional_force * nondimensional_end_to_end_length
nondimensional_relative_helmholtz_free_energy_legendre_out =
model.isometric.asymptotic.reduced.legendre.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy_legendre -
nondimensional_relative_helmholtz_free_energy_legendre_out
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::test::legendre_asymptotic_reduced::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.isotensional.asymptotic.reduced.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_relative_helmholtz_free_energy_per_link_legendre =
model.isotensional.asymptotic.reduced.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
) + nondimensional_force * nondimensional_end_to_end_length_per_link
nondimensional_relative_helmholtz_free_energy_per_link_legendre_out =
model.isometric.asymptotic.reduced.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy_per_link_legendre -
nondimensional_relative_helmholtz_free_energy_per_link_legendre_out
residual_rel =
residual_abs / nondimensional_relative_helmholtz_free_energy_per_link_legendre
@test abs(residual_abs) <= parameters.abs_tol ||
abs(residual_rel) <= parameters.rel_tol
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 1504 | """
The log-squared potential freely-jointed chain (log-squared-FJC) model thermodynamics in the isometric ensemble.
"""
module Isometric
using DocStringExtensions
using .......Polymers: PROJECT_ROOT
include("asymptotic/mod.jl")
"""
The structure of the thermodynamics of the log-squared-FJC model in the isometric ensemble.
$(FIELDS)
"""
struct LOGSQUAREDFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The stiffness of each link in the chain ``k_0`` in units of J/(mol⋅nm^2).
"""
link_stiffness::Float64
"""
The thermodynamic functions of the model in the isometric ensemble approximated using an asymptotic approach.
"""
asymptotic::Any
end
"""
Initializes and returns an instance of the thermodynamics of the log-squared-FJC model in the isometric ensemble.
$(TYPEDSIGNATURES)
"""
function LOGSQUAREDFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
)
return LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
Asymptotic.LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 4183 | module Test
using Test
using Polymers.Physics.SingleChain: parameters
using Polymers.Physics.SingleChain.Ufjc.LogSquared.Thermodynamics.Isometric: LOGSQUAREDFJC
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::test::base::init" begin
@test isa(
LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
),
Any,
)
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test LOGSQUAREDFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.link_stiffness_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::test::base::link_stiffness" begin
for _ = 1:parameters.number_of_loops
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
link_stiffness,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test all(
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).number_of_links == number_of_links &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_length == link_length &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).hinge_mass == hinge_mass &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_stiffness == link_stiffness,
)
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 1931 | """
The log-squared potential freely-jointed chain (log-squared-FJC) model thermodynamics in the isometric ensemble approximated using an asymptotic approach.
"""
module Asymptotic
using DocStringExtensions
using ........Polymers: PROJECT_ROOT
include("reduced/mod.jl")
include("legendre/mod.jl")
"""
The structure of the thermodynamics of the log-squared-FJC model in the isometric ensemble approximated using an asymptotic approach.
$(FIELDS)
"""
struct LOGSQUAREDFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The stiffness of each link in the chain ``k_0`` in units of J/(mol⋅nm^2).
"""
link_stiffness::Float64
"""
The thermodynamic functions of the model in the isometric ensemble approximated using a reduced asymptotic approach.
"""
reduced::Any
"""
The thermodynamic functions of the model in the isometric ensemble approximated using an asymptotic approach and a Legendre transformation.
"""
legendre::Any
end
"""
Initializes and returns an instance of the thermodynamics of the log-squared-FJC model in the isometric ensemble approximated using an asymptotic approach.
$(TYPEDSIGNATURES)
"""
function LOGSQUAREDFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
)
return LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
Reduced.LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness),
Legendre.LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 4271 | module Test
using Test
using Polymers.Physics.SingleChain: parameters
using Polymers.Physics.SingleChain.Ufjc.LogSquared.Thermodynamics.Isometric.Asymptotic:
LOGSQUAREDFJC
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::test::base::init" begin
@test isa(
LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
),
Any,
)
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test LOGSQUAREDFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.link_stiffness_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::test::base::link_stiffness" begin
for _ = 1:parameters.number_of_loops
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
link_stiffness,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test all(
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).number_of_links == number_of_links &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_length == link_length &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).hinge_mass == hinge_mass &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_stiffness == link_stiffness,
)
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 22022 | """
The log-squared potential freely-jointed chain (log-squared-FJC) model thermodynamics in the isometric ensemble approximated using an asymptotic approach and a Legendre transformation.
"""
module Legendre
using DocStringExtensions
using .........Polymers: PROJECT_ROOT
import ........Physics: BOLTZMANN_CONSTANT
"""
The structure of the thermodynamics of the log-squared-FJC model in the isometric ensemble approximated using an asymptotic approach and a Legendre transformation.
$(FIELDS)
"""
struct LOGSQUAREDFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The stiffness of each link in the chain ``k_0`` in units of J/(mol⋅nm^2).
"""
link_stiffness::Float64
"""
The expected force ``f`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
force::Function
"""
The expected nondimensional force ``\\eta`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``.
"""
nondimensional_force::Function
"""
The Helmholtz free energy ``\\psi`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
helmholtz_free_energy::Function
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
helmholtz_free_energy_per_link::Function
"""
The relative Helmholtz free energy ``\\Delta\\psi\\equiv\\psi(\\xi,T)-\\psi(0,T)`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
relative_helmholtz_free_energy::Function
"""
The relative Helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
relative_helmholtz_free_energy_per_link::Function
"""
The nondimensional Helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy::Function
"""
The nondimensional Helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy_per_link::Function
"""
The nondimensional relative Helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``.
"""
nondimensional_relative_helmholtz_free_energy::Function
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``
"""
nondimensional_relative_helmholtz_free_energy_per_link::Function
end
"""
The expected force as a function ``f`` of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function force(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isometric_asymptotic_legendre_force,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
end_to_end_length,
temperature,
)
end
"""
The expected nondimensional force as a function ``\\eta`` of the applied nondimensional end-to-end length per link ``\\gamma``,
parameterized by the link length ``\\ell_b`` and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_force(
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(nondimensional_link_stiffness_i, nondimensional_end_to_end_length_per_link_i) ->
ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isometric_asymptotic_legendre_nondimensional_force,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
),
nondimensional_link_stiffness,
nondimensional_end_to_end_length_per_link,
)
end
"""
The Helmholtz free energy ``\\psi`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, link stiffness ``k_0``, and hinge mass ``m``,
```math
\\psi(\\xi, T) \\sim \\varphi\\left[f(\\xi, T)\\right] + \\xi f(\\xi, T) \\quad \\text{for } N_b\\gg 1,
```
where ``f(\\xi, T)`` is given by the Legendre transformation approximation above.
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isometric_asymptotic_legendre_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
end_to_end_length,
temperature,
)
end
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, link stiffness ``k_0``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isometric_asymptotic_legendre_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
end_to_end_length,
temperature,
)
end
"""
The relative Helmholtz free energy ``\\Delta\\psi\\equiv\\psi(\\xi,T)-\\psi(0,T)`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isometric_asymptotic_legendre_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
end_to_end_length,
temperature,
)
end
"""
The relative Helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isometric_asymptotic_legendre_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
end_to_end_length,
temperature,
)
end
"""
The nondimensional Helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isometric_asymptotic_legendre_nondimensional_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_end_to_end_length_per_link,
temperature,
)
end
"""
The nondimensional Helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isometric_asymptotic_legendre_nondimensional_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_end_to_end_length_per_link,
temperature,
)
end
"""
The nondimensional relative Helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the number of links ``N_b`` and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isometric_asymptotic_legendre_nondimensional_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_end_to_end_length_per_link,
)
end
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(nondimensional_link_stiffness_i, nondimensional_end_to_end_length_per_link_i) ->
ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isometric_asymptotic_legendre_nondimensional_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
),
nondimensional_link_stiffness,
nondimensional_end_to_end_length_per_link,
)
end
"""
Initializes and returns an instance of the thermodynamics of the log-squared-FJC model in the isometric ensemble approximated using an asymptotic approach and a Legendre transformation.
$(TYPEDSIGNATURES)
"""
function LOGSQUAREDFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
)
BOLTZMANN_CONSTANT::Float64 = 8.314462618
return LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
(end_to_end_length, temperature) -> force(
number_of_links,
link_length,
link_stiffness,
end_to_end_length,
temperature,
),
(nondimensional_end_to_end_length_per_link, temperature) -> nondimensional_force(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_end_to_end_length_per_link,
),
(end_to_end_length, temperature) -> helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> helmholtz_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> relative_helmholtz_free_energy(
number_of_links,
link_length,
link_stiffness,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> relative_helmholtz_free_energy_per_link(
number_of_links,
link_length,
link_stiffness,
end_to_end_length,
temperature,
),
(nondimensional_end_to_end_length_per_link, temperature) ->
nondimensional_helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_end_to_end_length_per_link,
temperature,
),
(nondimensional_end_to_end_length_per_link, temperature) ->
nondimensional_helmholtz_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_end_to_end_length_per_link,
temperature,
),
(nondimensional_end_to_end_length_per_link, temperature) ->
nondimensional_relative_helmholtz_free_energy(
number_of_links,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_end_to_end_length_per_link,
),
(nondimensional_end_to_end_length_per_link, temperature) ->
nondimensional_relative_helmholtz_free_energy_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_end_to_end_length_per_link,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 44751 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ZERO, parameters
using Polymers.Physics.SingleChain.Ufjc.LogSquared.Thermodynamics.Isometric.Asymptotic.Legendre:
LOGSQUAREDFJC
using Polymers.Physics.SingleChain.Ufjc.LogSquared.Thermodynamics.Isotensional.Asymptotic:
nondimensional_end_to_end_length_per_link as isotensional_nondimensional_end_to_end_length_per_link
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::legendre::test::base::init" begin
@test isa(
LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
),
Any,
)
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::legendre::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test LOGSQUAREDFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::legendre::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::legendre::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.link_stiffness_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::legendre::test::base::link_stiffness" begin
for _ = 1:parameters.number_of_loops
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
link_stiffness,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::legendre::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test all(
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).number_of_links == number_of_links &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_length == link_length &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).hinge_mass == hinge_mass &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_stiffness == link_stiffness,
)
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::legendre::test::nondimensional::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1.0)
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_force = model.nondimensional_force(
nondimensional_end_to_end_length_per_link,
temperature,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
force = model.force(end_to_end_length, temperature)
residual_abs =
force / BOLTZMANN_CONSTANT / temperature * link_length - nondimensional_force
residual_rel = residual_abs / nondimensional_force
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::legendre::test::nondimensional::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1.0)
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy = model.helmholtz_free_energy(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::legendre::test::nondimensional::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1.0)
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::legendre::test::nondimensional::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1.0)
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(end_to_end_length, temperature)
residual_abs =
relative_helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::legendre::test::nondimensional::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1.0)
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
relative_helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::legendre::test::per_link::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1.0)
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy = model.helmholtz_free_energy(end_to_end_length, temperature)
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy / number_of_links - helmholtz_free_energy_per_link
residual_rel = residual_abs / helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::legendre::test::per_link::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1.0)
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(end_to_end_length, temperature)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
relative_helmholtz_free_energy / number_of_links -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::legendre::test::per_link::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1.0)
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy / number_of_links -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::legendre::test::per_link::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1.0)
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy / number_of_links -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::legendre::test::relative::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1.0)
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy = model.helmholtz_free_energy(end_to_end_length, temperature)
helmholtz_free_energy_0 =
model.helmholtz_free_energy(ZERO * number_of_links * link_length, temperature)
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy - helmholtz_free_energy_0 - relative_helmholtz_free_energy
residual_rel = residual_abs / relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::legendre::test::relative::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1.0)
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(end_to_end_length, temperature)
helmholtz_free_energy_per_link_0 = model.helmholtz_free_energy_per_link(
ZERO * number_of_links * link_length,
temperature,
)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy_per_link - helmholtz_free_energy_per_link_0 -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::legendre::test::relative::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1.0)
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_0 =
model.nondimensional_helmholtz_free_energy(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy - nondimensional_helmholtz_free_energy_0 -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::legendre::test::relative::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1.0)
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_per_link_0 =
model.nondimensional_helmholtz_free_energy_per_link(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy_per_link -
nondimensional_helmholtz_free_energy_per_link_0 -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::legendre::test::zero::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force_0 = model.force(ZERO * number_of_links * link_length, temperature)
@test abs(force_0) <=
3.1 * ZERO * number_of_links * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::legendre::test::zero::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_0 = model.nondimensional_force(ZERO, temperature)
@test abs(nondimensional_force_0) <= 3.1 * ZERO
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::legendre::test::zero::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_0 = model.relative_helmholtz_free_energy(
ZERO * number_of_links * link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_0) <=
ZERO * number_of_links * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::legendre::test::zero::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_per_link_0 =
model.relative_helmholtz_free_energy_per_link(
ZERO * number_of_links * link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::legendre::test::zero::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_0 =
model.nondimensional_relative_helmholtz_free_energy(ZERO, temperature)
@test abs(nondimensional_relative_helmholtz_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::legendre::test::zero::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_per_link_0 =
model.nondimensional_relative_helmholtz_free_energy_per_link(ZERO, temperature)
@test abs(nondimensional_relative_helmholtz_free_energy_per_link_0) <= ZERO
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::legendre::test::connection::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1.0)
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
force = model.force(end_to_end_length, temperature)
h = parameters.rel_tol * number_of_links * link_length
force_from_derivative =
(
model.relative_helmholtz_free_energy(
end_to_end_length + 0.5 * h,
temperature,
) - model.relative_helmholtz_free_energy(
end_to_end_length - 0.5 * h,
temperature,
)
) / h
residual_abs = force - force_from_derivative
residual_rel = residual_abs / force
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::legendre::test::connection::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1.0)
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_force = model.nondimensional_force(
nondimensional_end_to_end_length_per_link,
temperature,
)
h = parameters.rel_tol
nondimensional_force_from_derivative =
(
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link + 0.5 * h,
temperature,
) - model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link - 0.5 * h,
temperature,
)
) / h
residual_abs = nondimensional_force - nondimensional_force_from_derivative
residual_rel = residual_abs / nondimensional_force
@test abs(residual_rel) <= h
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 1656 | """
The log-squared potential freely-jointed chain (log-squared-FJC) model thermodynamics in the isometric ensemble approximated using an reduced asymptotic approach.
"""
module Reduced
using DocStringExtensions
using .........Polymers: PROJECT_ROOT
include("legendre/mod.jl")
"""
The structure of the thermodynamics of the log-squared-FJC model in the isometric ensemble approximated using an reduced asymptotic approach.
$(FIELDS)
"""
struct LOGSQUAREDFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The stiffness of each link in the chain ``k_0`` in units of J/(mol⋅nm^2).
"""
link_stiffness::Float64
"""
The thermodynamic functions of the model in the isometric ensemble approximated using an reduced asymptotic approach.
"""
legendre::Any
end
"""
Initializes and returns an instance of the thermodynamics of the log-squared-FJC model in the isometric ensemble approximated using an reduced asymptotic approach.
$(TYPEDSIGNATURES)
"""
function LOGSQUAREDFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
)
return LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
Legendre.LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 4325 | module Test
using Test
using Polymers.Physics.SingleChain: parameters
using Polymers.Physics.SingleChain.Ufjc.LogSquared.Thermodynamics.Isometric.Asymptotic:
LOGSQUAREDFJC
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::test::base::init" begin
@test isa(
LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
),
Any,
)
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test LOGSQUAREDFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.link_stiffness_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::test::base::link_stiffness" begin
for _ = 1:parameters.number_of_loops
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
link_stiffness,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test all(
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).number_of_links == number_of_links &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_length == link_length &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).hinge_mass == hinge_mass &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_stiffness == link_stiffness,
)
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 22125 | """
The log-squared potential freely-jointed chain (log-squared-FJC) model thermodynamics in the isometric ensemble approximated using a reduced asymptotic approach and a Legendre transformation.
"""
module Legendre
using DocStringExtensions
using ..........Polymers: PROJECT_ROOT
import .........Physics: BOLTZMANN_CONSTANT
"""
The structure of the thermodynamics of the log-squared-FJC model in the isometric ensemble approximated using a reduced asymptotic approach and a Legendre transformation.
$(FIELDS)
"""
struct LOGSQUAREDFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The stiffness of each link in the chain ``k_0`` in units of J/(mol⋅nm^2).
"""
link_stiffness::Float64
"""
The expected force ``f`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
force::Function
"""
The expected nondimensional force ``\\eta`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``.
"""
nondimensional_force::Function
"""
The Helmholtz free energy ``\\psi`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
helmholtz_free_energy::Function
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
helmholtz_free_energy_per_link::Function
"""
The relative Helmholtz free energy ``\\Delta\\psi\\equiv\\psi(\\xi,T)-\\psi(0,T)`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
relative_helmholtz_free_energy::Function
"""
The relative Helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``.
"""
relative_helmholtz_free_energy_per_link::Function
"""
The nondimensional Helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy::Function
"""
The nondimensional Helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy_per_link::Function
"""
The nondimensional relative Helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``.
"""
nondimensional_relative_helmholtz_free_energy::Function
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma``
"""
nondimensional_relative_helmholtz_free_energy_per_link::Function
end
"""
The expected force as a function ``f`` of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function force(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isometric_asymptotic_reduced_legendre_force,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
end_to_end_length,
temperature,
)
end
"""
The expected nondimensional force as a function ``\\eta`` of the applied nondimensional end-to-end length per link ``\\gamma``,
parameterized by the link length ``\\ell_b`` and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_force(
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(nondimensional_link_stiffness_i, nondimensional_end_to_end_length_per_link_i) ->
ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isometric_asymptotic_reduced_legendre_nondimensional_force,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
),
nondimensional_link_stiffness,
nondimensional_end_to_end_length_per_link,
)
end
"""
The Helmholtz free energy ``\\psi`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, link stiffness ``k_0``, and hinge mass ``m``,
```math
\\psi(\\xi, T) \\sim \\varphi\\left[f(\\xi, T)\\right] + \\xi f(\\xi, T) \\quad \\text{for } N_b\\gg 1,
```
where ``f(\\xi, T)`` is given by the Legendre transformation approximation above.
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isometric_asymptotic_reduced_legendre_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
end_to_end_length,
temperature,
)
end
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, link stiffness ``k_0``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isometric_asymptotic_reduced_legendre_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
end_to_end_length,
temperature,
)
end
"""
The relative Helmholtz free energy ``\\Delta\\psi\\equiv\\psi(\\xi,T)-\\psi(0,T)`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isometric_asymptotic_reduced_legendre_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
end_to_end_length,
temperature,
)
end
"""
The relative Helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied end-to-end length ``\\xi`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isometric_asymptotic_reduced_legendre_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
end_to_end_length,
temperature,
)
end
"""
The nondimensional Helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isometric_asymptotic_reduced_legendre_nondimensional_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_end_to_end_length_per_link,
temperature,
)
end
"""
The nondimensional Helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isometric_asymptotic_reduced_legendre_nondimensional_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_end_to_end_length_per_link,
temperature,
)
end
"""
The nondimensional relative Helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the number of links ``N_b`` and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isometric_asymptotic_reduced_legendre_nondimensional_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_end_to_end_length_per_link,
)
end
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional end-to-end length per link ``\\gamma`` and temperature ``T``,
parameterized by the nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(nondimensional_link_stiffness_i, nondimensional_end_to_end_length_per_link_i) ->
ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isometric_asymptotic_reduced_legendre_nondimensional_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_end_to_end_length_per_link_i,
),
nondimensional_link_stiffness,
nondimensional_end_to_end_length_per_link,
)
end
"""
Initializes and returns an instance of the thermodynamics of the log-squared-FJC model in the isometric ensemble approximated using a reduced asymptotic approach and a Legendre transformation.
$(TYPEDSIGNATURES)
"""
function LOGSQUAREDFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
)
BOLTZMANN_CONSTANT::Float64 = 8.314462618
return LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
(end_to_end_length, temperature) -> force(
number_of_links,
link_length,
link_stiffness,
end_to_end_length,
temperature,
),
(nondimensional_end_to_end_length_per_link, temperature) -> nondimensional_force(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_end_to_end_length_per_link,
),
(end_to_end_length, temperature) -> helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> helmholtz_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> relative_helmholtz_free_energy(
number_of_links,
link_length,
link_stiffness,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> relative_helmholtz_free_energy_per_link(
number_of_links,
link_length,
link_stiffness,
end_to_end_length,
temperature,
),
(nondimensional_end_to_end_length_per_link, temperature) ->
nondimensional_helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_end_to_end_length_per_link,
temperature,
),
(nondimensional_end_to_end_length_per_link, temperature) ->
nondimensional_helmholtz_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_end_to_end_length_per_link,
temperature,
),
(nondimensional_end_to_end_length_per_link, temperature) ->
nondimensional_relative_helmholtz_free_energy(
number_of_links,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_end_to_end_length_per_link,
),
(nondimensional_end_to_end_length_per_link, temperature) ->
nondimensional_relative_helmholtz_free_energy_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_end_to_end_length_per_link,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 45010 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ZERO, parameters
using Polymers.Physics.SingleChain.Ufjc.LogSquared.Thermodynamics.Isometric.Asymptotic.Reduced.Legendre:
LOGSQUAREDFJC
using Polymers.Physics.SingleChain.Ufjc.LogSquared.Thermodynamics.Isotensional.Asymptotic.Reduced:
nondimensional_end_to_end_length_per_link as isotensional_nondimensional_end_to_end_length_per_link
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::legendre::test::base::init" begin
@test isa(
LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
),
Any,
)
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::legendre::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test LOGSQUAREDFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::legendre::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::legendre::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.link_stiffness_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::legendre::test::base::link_stiffness" begin
for _ = 1:parameters.number_of_loops
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
link_stiffness,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::legendre::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test all(
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).number_of_links == number_of_links &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_length == link_length &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).hinge_mass == hinge_mass &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_stiffness == link_stiffness,
)
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::legendre::test::nondimensional::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1.0)
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_force = model.nondimensional_force(
nondimensional_end_to_end_length_per_link,
temperature,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
force = model.force(end_to_end_length, temperature)
residual_abs =
force / BOLTZMANN_CONSTANT / temperature * link_length - nondimensional_force
residual_rel = residual_abs / nondimensional_force
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::legendre::test::nondimensional::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1.0)
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy = model.helmholtz_free_energy(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::legendre::test::nondimensional::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1.0)
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::legendre::test::nondimensional::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1.0)
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(end_to_end_length, temperature)
residual_abs =
relative_helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::legendre::test::nondimensional::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1.0)
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
relative_helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::legendre::test::per_link::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1.0)
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy = model.helmholtz_free_energy(end_to_end_length, temperature)
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy / number_of_links - helmholtz_free_energy_per_link
residual_rel = residual_abs / helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::legendre::test::per_link::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1.0)
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(end_to_end_length, temperature)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
relative_helmholtz_free_energy / number_of_links -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::legendre::test::per_link::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1.0)
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy / number_of_links -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::legendre::test::per_link::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1.0)
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy / number_of_links -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::legendre::test::relative::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1.0)
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy = model.helmholtz_free_energy(end_to_end_length, temperature)
helmholtz_free_energy_0 =
model.helmholtz_free_energy(ZERO * number_of_links * link_length, temperature)
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy - helmholtz_free_energy_0 - relative_helmholtz_free_energy
residual_rel = residual_abs / relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::legendre::test::relative::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1.0)
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(end_to_end_length, temperature)
helmholtz_free_energy_per_link_0 = model.helmholtz_free_energy_per_link(
ZERO * number_of_links * link_length,
temperature,
)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy_per_link - helmholtz_free_energy_per_link_0 -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::legendre::test::relative::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1.0)
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_helmholtz_free_energy = model.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_0 =
model.nondimensional_helmholtz_free_energy(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy - nondimensional_helmholtz_free_energy_0 -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::legendre::test::relative::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1.0)
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_per_link_0 =
model.nondimensional_helmholtz_free_energy_per_link(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy_per_link -
nondimensional_helmholtz_free_energy_per_link_0 -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::legendre::test::zero::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force_0 = model.force(ZERO * number_of_links * link_length, temperature)
@test abs(force_0) <=
3.1 * ZERO * number_of_links * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::legendre::test::zero::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_0 = model.nondimensional_force(ZERO, temperature)
@test abs(nondimensional_force_0) <= 3.1 * ZERO
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::legendre::test::zero::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_0 = model.relative_helmholtz_free_energy(
ZERO * number_of_links * link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_0) <=
ZERO * number_of_links * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::legendre::test::zero::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_per_link_0 =
model.relative_helmholtz_free_energy_per_link(
ZERO * number_of_links * link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::legendre::test::zero::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_0 =
model.nondimensional_relative_helmholtz_free_energy(ZERO, temperature)
@test abs(nondimensional_relative_helmholtz_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::legendre::test::zero::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_per_link_0 =
model.nondimensional_relative_helmholtz_free_energy_per_link(ZERO, temperature)
@test abs(nondimensional_relative_helmholtz_free_energy_per_link_0) <= ZERO
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::legendre::test::connection::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1.0)
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
force = model.force(end_to_end_length, temperature)
h = parameters.rel_tol * number_of_links * link_length
force_from_derivative =
(
model.relative_helmholtz_free_energy(
end_to_end_length + 0.5 * h,
temperature,
) - model.relative_helmholtz_free_energy(
end_to_end_length - 0.5 * h,
temperature,
)
) / h
residual_abs = force - force_from_derivative
residual_rel = residual_abs / force
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isometric::asymptotic::reduced::legendre::test::connection::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1.0)
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
0.999 * nondimensional_force_max,
)
nondimensional_end_to_end_length_per_link =
nondimensional_end_to_end_length_per_link_max * rand()
nondimensional_force = model.nondimensional_force(
nondimensional_end_to_end_length_per_link,
temperature,
)
h = parameters.rel_tol
nondimensional_force_from_derivative =
(
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link + 0.5 * h,
temperature,
) - model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link - 0.5 * h,
temperature,
)
) / h
residual_abs = nondimensional_force - nondimensional_force_from_derivative
residual_rel = residual_abs / nondimensional_force
@test abs(residual_rel) <= h
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 23816 | """
The log-squared potential freely-jointed chain (log-squared-FJC) model thermodynamics in the isotensional ensemble.
"""
module Isotensional
using DocStringExtensions
using .......Polymers: PROJECT_ROOT
import ......Physics: BOLTZMANN_CONSTANT
include("asymptotic/mod.jl")
include("legendre/mod.jl")
"""
The structure of the thermodynamics of the log-squared-FJC model in the isotensional ensemble.
$(FIELDS)
"""
struct LOGSQUAREDFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The stiffness of each link in the chain ``k_0`` in units of J/(mol⋅nm^2).
"""
link_stiffness::Float64
"""
The thermodynamic functions of the model in the isotensional ensemble approximated using an asymptotic approach.
"""
asymptotic::Any
"""
The thermodynamic functions of the model in the isotensional ensemble approximated using a Legendre transformation.
"""
legendre::Any
"""
The expected end-to-end length ``\\xi`` as a function of the applied force ``f`` and temperature ``T``.
"""
end_to_end_length::Function
"""
The expected end-to-end length per link ``\\xi/N_b=\\ell_b\\gamma`` as a function of the applied force ``f`` and temperature ``T``.
"""
end_to_end_length_per_link::Function
"""
The expected nondimensional end-to-end length ``N_b\\gamma=\\xi/\\ell_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_end_to_end_length::Function
"""
The expected nondimensional end-to-end length per link ``\\gamma\\equiv\\xi/N_b\\ell_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_end_to_end_length_per_link::Function
"""
The Gibbs free energy ``\\varphi`` as a function of the applied force ``f`` and temperature ``T``.
"""
gibbs_free_energy::Function
"""
The Gibbs free energy per link ``\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
gibbs_free_energy_per_link::Function
"""
The relative Gibbs free energy ``\\Delta\\varphi\\equiv\\varphi(f,T)-\\varphi(0,T)`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_gibbs_free_energy::Function
"""
The relative Gibbs free energy per link ``\\Delta\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_gibbs_free_energy_per_link::Function
"""
The nondimensional Gibbs free energy ``N_b\\varrho=\\beta\\varphi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_gibbs_free_energy::Function
"""
The nondimensional Gibbs free energy per link ``\\varrho\\equiv\\beta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_gibbs_free_energy_per_link::Function
"""
The nondimensional relative Gibbs free energy ``N_b\\Delta\\varrho=\\beta\\Delta\\varphi`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_gibbs_free_energy::Function
"""
The nondimensional relative Gibbs free energy per link ``\\Delta\\varrho\\equiv\\beta\\Delta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_gibbs_free_energy_per_link::Function
end
"""
The expected end-to-end length ``N_b\\gamma=\\xi/\\ell_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``,
```math
\\xi(f, T) = -\\frac{\\partial\\varphi}{\\partial f}.
```
$(TYPEDSIGNATURES)
"""
function end_to_end_length(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, link_stiffness_i, force_i, temperature_i) ->
ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The expected end-to-end length per link ``\\xi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function end_to_end_length_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The expected nondimensional end-to-end length ``N_b\\gamma=\\xi/\\ell_b`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b`` and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_end_to_end_length(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_link_stiffness_i, nondimensional_force_i) ->
ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_nondimensional_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
The expected nondimensional end-to-end length per link ``\\gamma\\equiv \\xi/N_b\\ell_b`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``,
given by [Buche et al.](https://doi.org/10.1103/PhysRevE.106.024502) as
```math
\\gamma(\\eta) = -\\frac{\\partial}{\\partial\\eta}\\,\\ln\\left[\\int \\frac{\\sinh(s\\eta)}{s\\eta}\\,e^{-\\beta u(s)}s^2\\,ds\\right].
```
$(TYPEDSIGNATURES)
"""
function nondimensional_end_to_end_length_per_link(
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(nondimensional_link_stiffness_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_nondimensional_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
The Gibbs free energy ``\\varphi`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and link stiffness ``k_0``.
```math
\\varphi(f, T) = -kT\\ln Z(f, T).
```
$(TYPEDSIGNATURES)
"""
function gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
)
end
"""
The Gibbs free energy per link ``\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, hinge_mass_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
)
end
"""
The relative Gibbs free energy ``\\Delta\\varphi\\equiv\\varphi(f,T)-\\varphi(0,T)`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, link_stiffness_i, force_i, temperature_i) ->
ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The relative Gibbs free energy per link ``\\Delta\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The nondimensional Gibbs free energy ``N_b\\varrho=\\beta\\varphi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_nondimensional_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_force,
temperature,
)
end
"""
The nondimensional Gibbs free energy per link ``\\varrho\\equiv\\beta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_nondimensional_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
),
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_force,
temperature,
)
end
"""
The nondimensional relative Gibbs free energy ``N_b\\Delta\\varrho=\\beta\\Delta\\varphi`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b`` and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_link_stiffness_i, nondimensional_force_i) ->
ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_nondimensional_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
The nondimensional relative Gibbs free energy per link ``\\Delta\\varrho\\equiv\\beta\\Delta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``,
given by [Buche et al.](https://doi.org/10.1103/PhysRevE.106.024502) as
```math
\\Delta\\varrho(\\eta) = \\ln\\left[\\int \\frac{\\sinh(s\\eta)}{s\\eta}\\,e^{-\\beta u(s)}s^2\\,ds\\right] - \\ln\\left[\\int e^{-\\beta u(s)}s^2\\,ds\\right],
```
where the nondimensional link potential ``\\beta u`` is given by
```math
\\beta u(\\lambda) = \\frac{\\varepsilon}{2}\\left[\\ln(\\lambda)\\right]^2,
```
where ``\\varepsilon\\equiv\\beta u_b=\\kappa`` is the nondimensional potential energy scale, ``\\kappa\\equiv\\beta k_b\\ell_b^2`` is the nondimensional link stiffness, and ``\\lambda\\equiv\\ell/\\ell_b`` is the nondimensional link stretch.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(nondimensional_link_stiffness_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_nondimensional_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
Initializes and returns an instance of the thermodynamics of the log-squared-FJC model in the isotensional ensemble.
$(TYPEDSIGNATURES)
"""
function LOGSQUAREDFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
)
BOLTZMANN_CONSTANT::Float64 = 8.314462618
return LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
Asymptotic.LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness),
Legendre.LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness),
(force, temperature) -> end_to_end_length(
number_of_links,
link_length,
link_stiffness,
force,
temperature,
),
(force, temperature) ->
end_to_end_length_per_link(link_length, link_stiffness, force, temperature),
(nondimensional_force, temperature) -> nondimensional_end_to_end_length(
number_of_links,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(nondimensional_force, temperature) -> nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(force, temperature) -> gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
),
(force, temperature) -> gibbs_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
),
(force, temperature) -> relative_gibbs_free_energy(
number_of_links,
link_length,
link_stiffness,
force,
temperature,
),
(force, temperature) -> relative_gibbs_free_energy_per_link(
link_length,
link_stiffness,
force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_gibbs_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_relative_gibbs_free_energy(
number_of_links,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(nondimensional_force, temperature) ->
nondimensional_relative_gibbs_free_energy_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 84846 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ONE, ZERO, POINTS, integrate, parameters
using Polymers.Physics.SingleChain.Ufjc.LogSquared.Thermodynamics.Isotensional:
LOGSQUAREDFJC
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::base::init" begin
@test isa(
LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
),
Any,
)
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test LOGSQUAREDFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.link_stiffness_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::base::link_stiffness" begin
for _ = 1:parameters.number_of_loops
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
link_stiffness,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test all(
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).number_of_links == number_of_links &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_length == link_length &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).hinge_mass == hinge_mass &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_stiffness == link_stiffness,
)
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::nondimensional::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
residual_abs = end_to_end_length / link_length - nondimensional_end_to_end_length
residual_rel = residual_abs / nondimensional_end_to_end_length
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::nondimensional::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
residual_abs =
end_to_end_length_per_link / link_length -
nondimensional_end_to_end_length_per_link
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::nondimensional::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
residual_abs =
gibbs_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_gibbs_free_energy
residual_rel = residual_abs / nondimensional_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::nondimensional::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
residual_abs =
gibbs_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::nondimensional::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
residual_abs =
relative_gibbs_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_gibbs_free_energy
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::nondimensional::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
residual_abs =
relative_gibbs_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::per_link::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
residual_abs = end_to_end_length / number_of_links - end_to_end_length_per_link
residual_rel = residual_abs / end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::per_link::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_end_to_end_length / number_of_links -
nondimensional_end_to_end_length_per_link
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::per_link::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
residual_abs = gibbs_free_energy / number_of_links - gibbs_free_energy_per_link
residual_rel = residual_abs / gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::per_link::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
residual_abs =
relative_gibbs_free_energy / number_of_links -
relative_gibbs_free_energy_per_link
residual_rel = residual_abs / relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::per_link::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_gibbs_free_energy / number_of_links -
nondimensional_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::per_link::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_relative_gibbs_free_energy / number_of_links -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::relative::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
gibbs_free_energy_0 = model.gibbs_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
residual_abs = gibbs_free_energy - gibbs_free_energy_0 - relative_gibbs_free_energy
residual_rel = residual_abs / gibbs_free_energy_0
@test abs(residual_abs) <=
BOLTZMANN_CONSTANT * temperature * number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::relative::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
gibbs_free_energy_per_link_0 = model.gibbs_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
residual_abs =
gibbs_free_energy_per_link - gibbs_free_energy_per_link_0 -
relative_gibbs_free_energy_per_link
residual_rel = residual_abs / gibbs_free_energy_per_link_0
@test abs(residual_abs) <= BOLTZMANN_CONSTANT * temperature * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::relative::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
nondimensional_gibbs_free_energy_0 =
model.nondimensional_gibbs_free_energy(ZERO, temperature)
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_gibbs_free_energy - nondimensional_gibbs_free_energy_0 -
nondimensional_relative_gibbs_free_energy
residual_rel = residual_abs / nondimensional_gibbs_free_energy_0
@test abs(residual_abs) <= number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::relative::nondimensional_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_gibbs_free_energy_per_link_0 =
model.nondimensional_gibbs_free_energy_per_link(ZERO, temperature)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_gibbs_free_energy_per_link -
nondimensional_gibbs_free_energy_per_link_0 -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link_0
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::zero::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_gibbs_free_energy_0 = model.relative_gibbs_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_gibbs_free_energy_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature * number_of_links
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::zero::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_gibbs_free_energy_per_link_0 = model.relative_gibbs_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_gibbs_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::zero::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy_0 =
model.nondimensional_relative_gibbs_free_energy(ZERO, temperature)
@test abs(nondimensional_relative_gibbs_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::zero::nondimensional_relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy_per_link_0 =
model.nondimensional_relative_gibbs_free_energy_per_link(ZERO, temperature)
@test abs(nondimensional_relative_gibbs_free_energy_per_link_0) <= ZERO
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::connection::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
h = parameters.rel_tol * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_from_derivative =
-(
model.relative_gibbs_free_energy(force + 0.5 * h, temperature) -
model.relative_gibbs_free_energy(force - 0.5 * h, temperature)
) / h
residual_abs = end_to_end_length - end_to_end_length_from_derivative
residual_rel = residual_abs / end_to_end_length
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::connection::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
h = parameters.rel_tol * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link_from_derivative =
-(
model.relative_gibbs_free_energy_per_link(force + 0.5 * h, temperature) -
model.relative_gibbs_free_energy_per_link(force - 0.5 * h, temperature)
) / h
residual_abs =
end_to_end_length_per_link - end_to_end_length_per_link_from_derivative
residual_rel = residual_abs / end_to_end_length_per_link
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::connection::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
h = parameters.rel_tol
nondimensional_end_to_end_length_from_derivative =
-(
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force + 0.5 * h,
temperature,
) - model.nondimensional_relative_gibbs_free_energy(
nondimensional_force - 0.5 * h,
temperature,
)
) / h
residual_abs =
nondimensional_end_to_end_length -
nondimensional_end_to_end_length_from_derivative
residual_rel = residual_abs / nondimensional_end_to_end_length
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::connection::nondimensional_end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
h = parameters.rel_tol
nondimensional_end_to_end_length_per_link_from_derivative =
-(
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force + 0.5 * h,
temperature,
) - model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force - 0.5 * h,
temperature,
)
) / h
residual_abs =
nondimensional_end_to_end_length_per_link -
nondimensional_end_to_end_length_per_link_from_derivative
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::legendre::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
gibbs_free_energy_legendre =
model.legendre.helmholtz_free_energy(force, temperature) -
force * end_to_end_length
residual_abs = gibbs_free_energy - gibbs_free_energy_legendre
residual_rel = residual_abs / gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::legendre::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
gibbs_free_energy_per_link_legendre =
model.legendre.helmholtz_free_energy_per_link(force, temperature) -
force * end_to_end_length_per_link
residual_abs = gibbs_free_energy_per_link - gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::legendre::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
end_to_end_length_0 = model.end_to_end_length(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
relative_gibbs_free_energy_legendre =
model.legendre.relative_helmholtz_free_energy(force, temperature) -
force * end_to_end_length +
ZERO * BOLTZMANN_CONSTANT * temperature / link_length * end_to_end_length_0
residual_abs = relative_gibbs_free_energy - relative_gibbs_free_energy_legendre
residual_rel = residual_abs / relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::legendre::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
end_to_end_length_per_link_0 = model.end_to_end_length_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
relative_gibbs_free_energy_per_link_legendre =
model.legendre.relative_helmholtz_free_energy_per_link(force, temperature) -
force * end_to_end_length_per_link +
ZERO * BOLTZMANN_CONSTANT * temperature / link_length *
end_to_end_length_per_link_0
residual_abs =
relative_gibbs_free_energy_per_link -
relative_gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::legendre::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
nondimensional_gibbs_free_energy_legendre =
model.legendre.nondimensional_helmholtz_free_energy(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length
residual_abs =
nondimensional_gibbs_free_energy - nondimensional_gibbs_free_energy_legendre
residual_rel = residual_abs / nondimensional_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::legendre::nondimensional_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_gibbs_free_energy_per_link_legendre =
model.legendre.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length_per_link
residual_abs =
nondimensional_gibbs_free_energy_per_link -
nondimensional_gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::legendre::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
nondimensional_end_to_end_length_0 =
model.nondimensional_end_to_end_length(ZERO, temperature)
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
)
nondimensional_relative_gibbs_free_energy_legendre =
model.legendre.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length +
ZERO * nondimensional_end_to_end_length_0
residual_abs =
nondimensional_relative_gibbs_free_energy -
nondimensional_relative_gibbs_free_energy_legendre
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::legendre::nondimensional_relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_end_to_end_length_per_link_0 =
model.nondimensional_end_to_end_length_per_link(ZERO, temperature)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_relative_gibbs_free_energy_per_link_legendre =
model.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length_per_link +
ZERO * nondimensional_end_to_end_length_per_link_0
residual_abs =
nondimensional_relative_gibbs_free_energy_per_link -
nondimensional_relative_gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::legendre_connection::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
h = parameters.rel_tol * BOLTZMANN_CONSTANT * temperature / link_length
force_from_derivative =
(
model.legendre.relative_helmholtz_free_energy(
force + 0.5 * h,
temperature,
) -
model.legendre.relative_helmholtz_free_energy(force - 0.5 * h, temperature)
) / (
model.end_to_end_length(force + 0.5 * h, temperature) -
model.end_to_end_length(force - 0.5 * h, temperature)
)
residual_abs = force - force_from_derivative
residual_rel = residual_abs / force
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::legendre_connection::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
h = parameters.rel_tol
nondimensional_force_from_derivative =
(
model.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force + 0.5 * h,
temperature,
) - model.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force - 0.5 * h,
temperature,
)
) / (
model.nondimensional_end_to_end_length_per_link(
nondimensional_force + 0.5 * h,
temperature,
) - model.nondimensional_end_to_end_length_per_link(
nondimensional_force - 0.5 * h,
temperature,
)
)
residual_abs = nondimensional_force - nondimensional_force_from_derivative
residual_rel = residual_abs / nondimensional_force
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::asymptotic::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return (
model.end_to_end_length(force, temperature) -
model.asymptotic.end_to_end_length(force, temperature)
)^2
end
function integrand_denominator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return model.end_to_end_length(force, temperature)^2
end
nondimensional_link_stretch_max = exp(1)
nondimensional_force_max = nondimensional_link_stretch_max
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_link_stiffness_big)
residual_rel_2 = residual_rel(
parameters.nondimensional_link_stiffness_big * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(0.5 * log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::asymptotic::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return (
model.end_to_end_length_per_link(force, temperature) -
model.asymptotic.end_to_end_length_per_link(force, temperature)
)^2
end
function integrand_denominator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return model.end_to_end_length_per_link(force, temperature)^2
end
nondimensional_link_stretch_max = exp(1)
nondimensional_force_max = nondimensional_link_stretch_max
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_link_stiffness_big)
residual_rel_2 = residual_rel(
parameters.nondimensional_link_stiffness_big * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(0.5 * log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::asymptotic::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
return (
model.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
) - model.asymptotic.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_force)
return model.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
)^2
end
nondimensional_link_stretch_max = exp(1)
nondimensional_force_max = nondimensional_link_stretch_max
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_link_stiffness_big)
residual_rel_2 = residual_rel(
parameters.nondimensional_link_stiffness_big * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(0.5 * log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::asymptotic::nondimensional_end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
return (
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
) - model.asymptotic.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_force)
return model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)^2
end
nondimensional_link_stretch_max = exp(1)
nondimensional_force_max = nondimensional_link_stretch_max
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_link_stiffness_big)
residual_rel_2 = residual_rel(
parameters.nondimensional_link_stiffness_big * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(0.5 * log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::asymptotic_reduced::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return (
model.end_to_end_length(force, temperature) -
model.asymptotic.reduced.end_to_end_length(force, temperature)
)^2
end
function integrand_denominator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return model.end_to_end_length(force, temperature)^2
end
nondimensional_link_stretch_max = exp(1)
nondimensional_force_max = nondimensional_link_stretch_max
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_link_stiffness_big)
residual_rel_2 = residual_rel(
parameters.nondimensional_link_stiffness_big * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::asymptotic_reduced::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return (
model.end_to_end_length_per_link(force, temperature) -
model.asymptotic.reduced.end_to_end_length_per_link(force, temperature)
)^2
end
function integrand_denominator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return model.end_to_end_length_per_link(force, temperature)^2
end
nondimensional_link_stretch_max = exp(1)
nondimensional_force_max = nondimensional_link_stretch_max
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_link_stiffness_big)
residual_rel_2 = residual_rel(
parameters.nondimensional_link_stiffness_big * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::asymptotic_reduced::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
return (
model.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
) - model.asymptotic.reduced.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_force)
return model.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
)^2
end
nondimensional_link_stretch_max = exp(1)
nondimensional_force_max = nondimensional_link_stretch_max
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_link_stiffness_big)
residual_rel_2 = residual_rel(
parameters.nondimensional_link_stiffness_big * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::asymptotic_reduced::nondimensional_end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
return (
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
) - model.asymptotic.reduced.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_force)
return model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)^2
end
nondimensional_link_stretch_max = exp(1)
nondimensional_force_max = nondimensional_link_stretch_max
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_link_stiffness_big)
residual_rel_2 = residual_rel(
parameters.nondimensional_link_stiffness_big * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 24600 | """
The log-squared potential freely-jointed chain (log-squared-FJC) model thermodynamics in the isotensional ensemble approximated using an asymptotic approach.
"""
module Asymptotic
using DocStringExtensions
using ........Polymers: PROJECT_ROOT
import .......Physics: BOLTZMANN_CONSTANT
include("reduced/mod.jl")
include("legendre/mod.jl")
"""
The structure of the thermodynamics of the log-squared-FJC model in the isotensional ensemble approximated using an asymptotic approach.
$(FIELDS)
"""
struct LOGSQUAREDFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The stiffness of each link in the chain ``k_0`` in units of J/(mol⋅nm^2).
"""
link_stiffness::Float64
"""
The thermodynamic functions of the model in the isotensional ensemble approximated using a reduced asymptotic approach.
"""
reduced::Any
"""
The thermodynamic functions of the model in the isotensional ensemble approximated using an asymptotic approach and a Legendre transformation.
"""
legendre::Any
"""
The expected end-to-end length ``\\xi`` as a function of the applied force ``f`` and temperature ``T``.
"""
end_to_end_length::Function
"""
The expected end-to-end length per link ``\\xi/N_b=\\ell_b\\gamma`` as a function of the applied force ``f`` and temperature ``T``.
"""
end_to_end_length_per_link::Function
"""
The expected nondimensional end-to-end length ``N_b\\gamma=\\xi/\\ell_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_end_to_end_length::Function
"""
The expected nondimensional end-to-end length per link ``\\gamma\\equiv\\xi/N_b\\ell_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_end_to_end_length_per_link::Function
"""
The Gibbs free energy ``\\varphi`` as a function of the applied force ``f`` and temperature ``T``.
"""
gibbs_free_energy::Function
"""
The Gibbs free energy per link ``\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
gibbs_free_energy_per_link::Function
"""
The relative Gibbs free energy ``\\Delta\\varphi\\equiv\\varphi(f,T)-\\varphi(0,T)`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_gibbs_free_energy::Function
"""
The relative Gibbs free energy per link ``\\Delta\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_gibbs_free_energy_per_link::Function
"""
The nondimensional Gibbs free energy ``N_b\\varrho=\\beta\\varphi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_gibbs_free_energy::Function
"""
The nondimensional Gibbs free energy per link ``\\varrho\\equiv\\beta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_gibbs_free_energy_per_link::Function
"""
The nondimensional relative Gibbs free energy ``N_b\\Delta\\varrho=\\beta\\Delta\\varphi`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_gibbs_free_energy::Function
"""
The nondimensional relative Gibbs free energy per link ``\\Delta\\varrho\\equiv\\beta\\Delta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_gibbs_free_energy_per_link::Function
end
"""
The expected end-to-end length ``N_b\\gamma=\\xi/\\ell_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``,
```math
\\xi(f, T) = -\\frac{\\partial\\varphi}{\\partial f}.
```
$(TYPEDSIGNATURES)
"""
function end_to_end_length(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, link_stiffness_i, force_i, temperature_i) ->
ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The expected end-to-end length per link ``\\xi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function end_to_end_length_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The expected nondimensional end-to-end length ``N_b\\gamma=\\xi/\\ell_b`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b`` and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_end_to_end_length(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_link_stiffness_i, nondimensional_force_i) ->
ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_nondimensional_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
The expected nondimensional end-to-end length per link ``\\gamma\\equiv \\xi/N_b\\ell_b`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``,
given by [Buche et al.](https://doi.org/10.1103/PhysRevE.106.024502) as
```math
\\Delta\\varrho(\\eta) \\sim \\mathcal{L}(\\eta) + \\frac{\\eta}{\\kappa}\\left[\\frac{1 - \\mathcal{L}(\\eta)\\coth(\\eta)}{c + (\\eta/\\kappa)\\coth(\\eta)}\\right] + \\Delta\\lambda(\\eta) \\quad \\text{for } \\varepsilon,\\kappa\\gg 1,
```
where ``\\mathcal{L}(x)=\\coth(x)-1/x`` is the Langevin function, and ``\\Delta\\lambda(\\eta)`` is the incremental link stretch,
```math
\\Delta\\lambda(\\eta) = W_0(\\eta),
```
where ``W_0(\\eta)`` is the Lambert ``W`` function.
$(TYPEDSIGNATURES)
"""
function nondimensional_end_to_end_length_per_link(
nondimensional_link_stiffness_i::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(nondimensional_link_stiffness_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_nondimensional_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
nondimensional_link_stiffness_i,
nondimensional_force,
)
end
"""
The Gibbs free energy ``\\varphi`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and link stiffness ``k_0``.
```math
\\varphi(f, T) = -kT\\ln Z(f, T).
```
$(TYPEDSIGNATURES)
"""
function gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
)
end
"""
The Gibbs free energy per link ``\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, hinge_mass_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
)
end
"""
The relative Gibbs free energy ``\\Delta\\varphi\\equiv\\varphi(f,T)-\\varphi(0,T)`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, link_stiffness_i, force_i, temperature_i) ->
ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The relative Gibbs free energy per link ``\\Delta\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The nondimensional Gibbs free energy ``N_b\\varrho=\\beta\\varphi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_nondimensional_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_force,
temperature,
)
end
"""
The nondimensional Gibbs free energy per link ``\\varrho\\equiv\\beta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_nondimensional_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
),
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_force,
temperature,
)
end
"""
The nondimensional relative Gibbs free energy ``N_b\\Delta\\varrho=\\beta\\Delta\\varphi`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b`` and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_link_stiffness_i, nondimensional_force_i) ->
ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_nondimensional_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
The nondimensional relative Gibbs free energy per link ``\\Delta\\varrho\\equiv\\beta\\Delta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``,
given by [Buche et al.](https://doi.org/10.1103/PhysRevE.106.024502) as
```math
\\Delta\\varrho(\\eta) \\sim \\ln\\left[\\frac{\\eta}{\\sinh(\\eta)}\\right] - \\ln\\left[1 + \\frac{\\eta}{c\\kappa}\\,\\coth(\\eta)\\right] + \\beta u[\\lambda(\\eta)] - \\eta\\Delta\\lambda(\\eta) \\quad \\text{for } \\varepsilon,\\kappa\\gg 1,
```
where the nondimensional link potential ``\\beta u`` is given by
```math
\\beta u(\\lambda) = \\frac{\\varepsilon}{2}\\left[\\ln(\\lambda)\\right]^2,
```
where ``\\varepsilon\\equiv\\beta u_b=\\kappa`` is the nondimensional potential energy scale, ``1/c\\equiv 1-u'''(1)/2u''(1)=5/2`` is related to anharmonicity, ``\\kappa\\equiv\\beta k_b\\ell_b^2`` is the nondimensional link stiffness, and ``\\lambda\\equiv\\ell/\\ell_b`` is the nondimensional link stretch.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(nondimensional_link_stiffness_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_nondimensional_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
Initializes and returns an instance of the thermodynamics of the log-squared-FJC model in the isotensional ensemble approximated using an asymptotic approach.
$(TYPEDSIGNATURES)
"""
function LOGSQUAREDFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
)
BOLTZMANN_CONSTANT::Float64 = 8.314462618
return LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
Reduced.LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness),
Legendre.LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness),
(force, temperature) -> end_to_end_length(
number_of_links,
link_length,
link_stiffness,
force,
temperature,
),
(force, temperature) ->
end_to_end_length_per_link(link_length, link_stiffness, force, temperature),
(nondimensional_force, temperature) -> nondimensional_end_to_end_length(
number_of_links,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(nondimensional_force, temperature) -> nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(force, temperature) -> gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
),
(force, temperature) -> gibbs_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
),
(force, temperature) -> relative_gibbs_free_energy(
number_of_links,
link_length,
link_stiffness,
force,
temperature,
),
(force, temperature) -> relative_gibbs_free_energy_per_link(
link_length,
link_stiffness,
force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_gibbs_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_relative_gibbs_free_energy(
number_of_links,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(nondimensional_force, temperature) ->
nondimensional_relative_gibbs_free_energy_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 76521 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ONE, ZERO, POINTS, integrate, parameters
using Polymers.Physics.SingleChain.Ufjc.LogSquared.Thermodynamics.Isotensional.Asymptotic:
LOGSQUAREDFJC
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::base::init" begin
@test isa(
LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
),
Any,
)
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test LOGSQUAREDFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.link_stiffness_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::base::link_stiffness" begin
for _ = 1:parameters.number_of_loops
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
link_stiffness,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test all(
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).number_of_links == number_of_links &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_length == link_length &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).hinge_mass == hinge_mass &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_stiffness == link_stiffness,
)
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::nondimensional::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
residual_abs = end_to_end_length / link_length - nondimensional_end_to_end_length
residual_rel = residual_abs / nondimensional_end_to_end_length
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::nondimensional::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
residual_abs =
end_to_end_length_per_link / link_length -
nondimensional_end_to_end_length_per_link
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::nondimensional::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
residual_abs =
gibbs_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_gibbs_free_energy
residual_rel = residual_abs / nondimensional_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::nondimensional::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
residual_abs =
gibbs_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::nondimensional::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
residual_abs =
relative_gibbs_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_gibbs_free_energy
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::nondimensional::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
residual_abs =
relative_gibbs_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::per_link::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
residual_abs = end_to_end_length / number_of_links - end_to_end_length_per_link
residual_rel = residual_abs / end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::per_link::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_end_to_end_length / number_of_links -
nondimensional_end_to_end_length_per_link
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::per_link::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
residual_abs = gibbs_free_energy / number_of_links - gibbs_free_energy_per_link
residual_rel = residual_abs / gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::per_link::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
residual_abs =
relative_gibbs_free_energy / number_of_links -
relative_gibbs_free_energy_per_link
residual_rel = residual_abs / relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::per_link::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_gibbs_free_energy / number_of_links -
nondimensional_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::per_link::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_relative_gibbs_free_energy / number_of_links -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::relative::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
gibbs_free_energy_0 = model.gibbs_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
residual_abs = gibbs_free_energy - gibbs_free_energy_0 - relative_gibbs_free_energy
residual_rel = residual_abs / gibbs_free_energy_0
@test abs(residual_abs) <=
BOLTZMANN_CONSTANT * temperature * number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::relative::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
gibbs_free_energy_per_link_0 = model.gibbs_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
residual_abs =
gibbs_free_energy_per_link - gibbs_free_energy_per_link_0 -
relative_gibbs_free_energy_per_link
residual_rel = residual_abs / gibbs_free_energy_per_link_0
@test abs(residual_abs) <= BOLTZMANN_CONSTANT * temperature * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::relative::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
nondimensional_gibbs_free_energy_0 =
model.nondimensional_gibbs_free_energy(ZERO, temperature)
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_gibbs_free_energy - nondimensional_gibbs_free_energy_0 -
nondimensional_relative_gibbs_free_energy
residual_rel = residual_abs / nondimensional_gibbs_free_energy_0
@test abs(residual_abs) <= number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::relative::nondimensional_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_gibbs_free_energy_per_link_0 =
model.nondimensional_gibbs_free_energy_per_link(ZERO, temperature)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_gibbs_free_energy_per_link -
nondimensional_gibbs_free_energy_per_link_0 -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link_0
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::zero::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_gibbs_free_energy_0 = model.relative_gibbs_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_gibbs_free_energy_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature * number_of_links
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::zero::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_gibbs_free_energy_per_link_0 = model.relative_gibbs_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_gibbs_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::zero::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy_0 =
model.nondimensional_relative_gibbs_free_energy(ZERO, temperature)
@test abs(nondimensional_relative_gibbs_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::zero::nondimensional_relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy_per_link_0 =
model.nondimensional_relative_gibbs_free_energy_per_link(ZERO, temperature)
@test abs(nondimensional_relative_gibbs_free_energy_per_link_0) <= ZERO
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::connection::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
h = parameters.rel_tol * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_from_derivative =
-(
model.relative_gibbs_free_energy(force + 0.5 * h, temperature) -
model.relative_gibbs_free_energy(force - 0.5 * h, temperature)
) / h
residual_abs = end_to_end_length - end_to_end_length_from_derivative
residual_rel = residual_abs / end_to_end_length
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::connection::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
h = parameters.rel_tol * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link_from_derivative =
-(
model.relative_gibbs_free_energy_per_link(force + 0.5 * h, temperature) -
model.relative_gibbs_free_energy_per_link(force - 0.5 * h, temperature)
) / h
residual_abs =
end_to_end_length_per_link - end_to_end_length_per_link_from_derivative
residual_rel = residual_abs / end_to_end_length_per_link
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::connection::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
h = parameters.rel_tol
nondimensional_end_to_end_length_from_derivative =
-(
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force + 0.5 * h,
temperature,
) - model.nondimensional_relative_gibbs_free_energy(
nondimensional_force - 0.5 * h,
temperature,
)
) / h
residual_abs =
nondimensional_end_to_end_length -
nondimensional_end_to_end_length_from_derivative
residual_rel = residual_abs / nondimensional_end_to_end_length
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::connection::nondimensional_end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
h = parameters.rel_tol
nondimensional_end_to_end_length_per_link_from_derivative =
-(
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force + 0.5 * h,
temperature,
) - model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force - 0.5 * h,
temperature,
)
) / h
residual_abs =
nondimensional_end_to_end_length_per_link -
nondimensional_end_to_end_length_per_link_from_derivative
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::legendre::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
gibbs_free_energy_legendre =
model.legendre.helmholtz_free_energy(force, temperature) -
force * end_to_end_length
residual_abs = gibbs_free_energy - gibbs_free_energy_legendre
residual_rel = residual_abs / gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::legendre::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
gibbs_free_energy_per_link_legendre =
model.legendre.helmholtz_free_energy_per_link(force, temperature) -
force * end_to_end_length_per_link
residual_abs = gibbs_free_energy_per_link - gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::legendre::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
end_to_end_length_0 = model.end_to_end_length(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
relative_gibbs_free_energy_legendre =
model.legendre.relative_helmholtz_free_energy(force, temperature) -
force * end_to_end_length +
ZERO * BOLTZMANN_CONSTANT * temperature / link_length * end_to_end_length_0
residual_abs = relative_gibbs_free_energy - relative_gibbs_free_energy_legendre
residual_rel = residual_abs / relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::legendre::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
end_to_end_length_per_link_0 = model.end_to_end_length_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
relative_gibbs_free_energy_per_link_legendre =
model.legendre.relative_helmholtz_free_energy_per_link(force, temperature) -
force * end_to_end_length_per_link +
ZERO * BOLTZMANN_CONSTANT * temperature / link_length *
end_to_end_length_per_link_0
residual_abs =
relative_gibbs_free_energy_per_link -
relative_gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::legendre::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
nondimensional_gibbs_free_energy_legendre =
model.legendre.nondimensional_helmholtz_free_energy(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length
residual_abs =
nondimensional_gibbs_free_energy - nondimensional_gibbs_free_energy_legendre
residual_rel = residual_abs / nondimensional_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::legendre::nondimensional_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_gibbs_free_energy_per_link_legendre =
model.legendre.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length_per_link
residual_abs =
nondimensional_gibbs_free_energy_per_link -
nondimensional_gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::legendre::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
nondimensional_end_to_end_length_0 =
model.nondimensional_end_to_end_length(ZERO, temperature)
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
)
nondimensional_relative_gibbs_free_energy_legendre =
model.legendre.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length +
ZERO * nondimensional_end_to_end_length_0
residual_abs =
nondimensional_relative_gibbs_free_energy -
nondimensional_relative_gibbs_free_energy_legendre
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::legendre::nondimensional_relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_end_to_end_length_per_link_0 =
model.nondimensional_end_to_end_length_per_link(ZERO, temperature)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_relative_gibbs_free_energy_per_link_legendre =
model.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length_per_link +
ZERO * nondimensional_end_to_end_length_per_link_0
residual_abs =
nondimensional_relative_gibbs_free_energy_per_link -
nondimensional_relative_gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::legendre_connection::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
h = parameters.rel_tol * BOLTZMANN_CONSTANT * temperature / link_length
force_from_derivative =
(
model.legendre.relative_helmholtz_free_energy(
force + 0.5 * h,
temperature,
) -
model.legendre.relative_helmholtz_free_energy(force - 0.5 * h, temperature)
) / (
model.end_to_end_length(force + 0.5 * h, temperature) -
model.end_to_end_length(force - 0.5 * h, temperature)
)
residual_abs = force - force_from_derivative
residual_rel = residual_abs / force
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::legendre_connection::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
h = parameters.rel_tol
nondimensional_force_from_derivative =
(
model.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force + 0.5 * h,
temperature,
) - model.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force - 0.5 * h,
temperature,
)
) / (
model.nondimensional_end_to_end_length_per_link(
nondimensional_force + 0.5 * h,
temperature,
) - model.nondimensional_end_to_end_length_per_link(
nondimensional_force - 0.5 * h,
temperature,
)
)
residual_abs = nondimensional_force - nondimensional_force_from_derivative
residual_rel = residual_abs / nondimensional_force
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::asymptotic_reduced::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return (
model.end_to_end_length(force, temperature) -
model.reduced.end_to_end_length(force, temperature)
)^2
end
function integrand_denominator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return model.end_to_end_length(force, temperature)^2
end
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_link_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_link_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(residual_rel_1) <= 2.0 / parameters.nondimensional_link_stiffness_large &&
abs(residual_rel_2) <=
2.0 / parameters.nondimensional_link_stiffness_large /
parameters.log_log_scale &&
abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::asymptotic_reduced::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return (
model.end_to_end_length_per_link(force, temperature) -
model.reduced.end_to_end_length_per_link(force, temperature)
)^2
end
function integrand_denominator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return model.end_to_end_length_per_link(force, temperature)^2
end
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_link_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_link_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(residual_rel_1) <= 2.0 / parameters.nondimensional_link_stiffness_large &&
abs(residual_rel_2) <=
2.0 / parameters.nondimensional_link_stiffness_large /
parameters.log_log_scale &&
abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::asymptotic_reduced::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
return (
model.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
) - model.reduced.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_force)
return model.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
)^2
end
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_link_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_link_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(residual_rel_1) <= 2.0 / parameters.nondimensional_link_stiffness_large &&
abs(residual_rel_2) <=
2.0 / parameters.nondimensional_link_stiffness_large /
parameters.log_log_scale &&
abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::test::asymptotic_reduced::nondimensional_end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
return (
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
) - model.reduced.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_force)
return model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)^2
end
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_link_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_link_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(residual_rel_1) <= 2.0 / parameters.nondimensional_link_stiffness_large &&
abs(residual_rel_2) <=
2.0 / parameters.nondimensional_link_stiffness_large /
parameters.log_log_scale &&
abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 16565 | """
The log-squared potential freely-jointed chain (log-squared-FJC) model thermodynamics in the isotensional ensemble approximated using an asymptotic approach and a Legendre transformation.
"""
module Legendre
using DocStringExtensions
using .........Polymers: PROJECT_ROOT
import ........Physics: BOLTZMANN_CONSTANT
"""
The structure of the thermodynamics of the log-squared-FJC model in the isotensional ensemble approximated using an asymptotic approach and a Legendre transformation.
$(FIELDS)
"""
struct LOGSQUAREDFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The stiffness of each link in the chain ``k_0`` in units of J/(mol⋅nm^2).
"""
link_stiffness::Float64
"""
The Helmholtz free energy ``\\psi`` as a function of the applied force ``f`` and temperature ``T``.
"""
helmholtz_free_energy::Function
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
helmholtz_free_energy_per_link::Function
"""
The relative helmholtz free energy ``\\Delta\\psi\\equiv\\psi(f,T)-\\psi(0,T)`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_helmholtz_free_energy::Function
"""
The relative helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_helmholtz_free_energy_per_link::Function
"""
The nondimensional helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy::Function
"""
The nondimensional helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy_per_link::Function
"""
The nondimensional relative helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_helmholtz_free_energy::Function
"""
The nondimensional relative helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_helmholtz_free_energy_per_link::Function
end
"""
The Helmholtz free energy ``\\psi`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and link stiffness ``k_0``.
```math
\\psi(f, T) \\sim \\varphi(f, T) + f \\xi(f, T) \\quad \\text{for } N_b\\gg 1.
```
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_legendre_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
)
end
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, hinge_mass_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_legendre_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
)
end
"""
The relative Helmholtz free energy ``\\Delta\\psi\\equiv\\psi(f,T)-\\psi(0,T)`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, link_stiffness_i, force_i, temperature_i) ->
ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_legendre_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The relative Helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_legendre_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The nondimensional Helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_legendre_nondimensional_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_force,
temperature,
)
end
"""
The nondimensional Helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
link_length_i,
hinge_mass_i,
link_stiffness_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_legendre_nondimensional_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
link_stiffness_i,
nondimensional_force_i,
temperature_i,
),
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_force,
temperature,
)
end
"""
The nondimensional relative Helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b`` and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_link_stiffness_i, nondimensional_force_i) ->
ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_legendre_nondimensional_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta``
parameterized by the nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(nondimensional_link_stiffness_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_legendre_nondimensional_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
Initializes and returns an instance of the thermodynamics of the log-squared-FJC model in the isotensional ensemble approximated using an asymptotic approach and a Legendre transformation.
$(TYPEDSIGNATURES)
"""
function LOGSQUAREDFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
)
BOLTZMANN_CONSTANT::Float64 = 8.314462618
return LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
(force, temperature) -> helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
),
(force, temperature) -> helmholtz_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
),
(force, temperature) -> relative_helmholtz_free_energy(
number_of_links,
link_length,
link_stiffness,
force,
temperature,
),
(force, temperature) -> relative_helmholtz_free_energy_per_link(
link_length,
link_stiffness,
force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) ->
nondimensional_helmholtz_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) ->
nondimensional_relative_helmholtz_free_energy(
number_of_links,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(nondimensional_force, temperature) ->
nondimensional_relative_helmholtz_free_energy_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 31767 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ZERO, parameters
using Polymers.Physics.SingleChain.Ufjc.LogSquared.Thermodynamics.Isotensional.Asymptotic.Legendre:
LOGSQUAREDFJC
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::legendre::test::base::init" begin
@test isa(
LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
),
Any,
)
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::legendre::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test LOGSQUAREDFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::legendre::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::legendre::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.link_stiffness_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::legendre::test::base::link_stiffness" begin
for _ = 1:parameters.number_of_loops
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
link_stiffness,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::legendre::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test all(
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).number_of_links == number_of_links &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_length == link_length &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).hinge_mass == hinge_mass &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_stiffness == link_stiffness,
)
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::legendre::test::nondimensional::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_helmholtz_free_energy =
model.nondimensional_helmholtz_free_energy(nondimensional_force, temperature)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy = model.helmholtz_free_energy(force, temperature)
residual_abs =
helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::legendre::test::nondimensional::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(force, temperature)
residual_abs =
helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::legendre::test::nondimensional::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(force, temperature)
residual_abs =
relative_helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::legendre::test::nondimensional::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(force, temperature)
residual_abs =
relative_helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::legendre::test::per_link::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy = model.helmholtz_free_energy(force, temperature)
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(force, temperature)
residual_abs =
helmholtz_free_energy / number_of_links - helmholtz_free_energy_per_link
residual_rel = residual_abs / helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::legendre::test::per_link::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(force, temperature)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(force, temperature)
residual_abs =
relative_helmholtz_free_energy / number_of_links -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::legendre::test::per_link::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_helmholtz_free_energy =
model.nondimensional_helmholtz_free_energy(nondimensional_force, temperature)
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy / number_of_links -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::legendre::test::per_link::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy / number_of_links -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::legendre::test::relative::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy = model.helmholtz_free_energy(force, temperature)
helmholtz_free_energy_0 = model.helmholtz_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(force, temperature)
residual_abs =
helmholtz_free_energy - helmholtz_free_energy_0 - relative_helmholtz_free_energy
residual_rel = residual_abs / helmholtz_free_energy_0
@test abs(residual_abs) <=
BOLTZMANN_CONSTANT * temperature * number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::legendre::test::relative::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(force, temperature)
helmholtz_free_energy_per_link_0 = model.helmholtz_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(force, temperature)
residual_abs =
helmholtz_free_energy_per_link - helmholtz_free_energy_per_link_0 -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / helmholtz_free_energy_per_link_0
@test abs(residual_abs) <= BOLTZMANN_CONSTANT * temperature * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::legendre::test::relative::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_helmholtz_free_energy =
model.nondimensional_helmholtz_free_energy(nondimensional_force, temperature)
nondimensional_helmholtz_free_energy_0 =
model.nondimensional_helmholtz_free_energy(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy - nondimensional_helmholtz_free_energy_0 -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_0
@test abs(residual_abs) <= number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::legendre::test::relative::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_helmholtz_free_energy_per_link_0 =
model.nondimensional_helmholtz_free_energy_per_link(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy_per_link -
nondimensional_helmholtz_free_energy_per_link_0 -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link_0
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::legendre::test::zero::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_0 = model.relative_helmholtz_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature * number_of_links
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::legendre::test::zero::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_per_link_0 =
model.relative_helmholtz_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::legendre::test::zero::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_0 =
model.nondimensional_relative_helmholtz_free_energy(ZERO, temperature)
@test abs(nondimensional_relative_helmholtz_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::legendre::test::zero::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_per_link_0 =
model.nondimensional_relative_helmholtz_free_energy_per_link(ZERO, temperature)
@test abs(nondimensional_relative_helmholtz_free_energy_per_link_0) <= ZERO
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 24166 | """
The log-squared potential freely-jointed chain (log-squared-FJC) model thermodynamics in the isotensional ensemble approximated using an reduced asymptotic approach.
"""
module Reduced
using DocStringExtensions
using .........Polymers: PROJECT_ROOT
import ........Physics: BOLTZMANN_CONSTANT
include("legendre/mod.jl")
"""
The structure of the thermodynamics of the log-squared-FJC model in the isotensional ensemble approximated using an reduced asymptotic approach.
$(FIELDS)
"""
struct LOGSQUAREDFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The stiffness of each link in the chain ``k_0`` in units of J/(mol⋅nm^2).
"""
link_stiffness::Float64
"""
The thermodynamic functions of the model in the isotensional ensemble approximated using an reduced asymptotic approach.
"""
legendre::Any
"""
The expected end-to-end length ``\\xi`` as a function of the applied force ``f`` and temperature ``T``.
"""
end_to_end_length::Function
"""
The expected end-to-end length per link ``\\xi/N_b=\\ell_b\\gamma`` as a function of the applied force ``f`` and temperature ``T``.
"""
end_to_end_length_per_link::Function
"""
The expected nondimensional end-to-end length ``N_b\\gamma=\\xi/\\ell_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_end_to_end_length::Function
"""
The expected nondimensional end-to-end length per link ``\\gamma\\equiv\\xi/N_b\\ell_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_end_to_end_length_per_link::Function
"""
The Gibbs free energy ``\\varphi`` as a function of the applied force ``f`` and temperature ``T``.
"""
gibbs_free_energy::Function
"""
The Gibbs free energy per link ``\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
gibbs_free_energy_per_link::Function
"""
The relative Gibbs free energy ``\\Delta\\varphi\\equiv\\varphi(f,T)-\\varphi(0,T)`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_gibbs_free_energy::Function
"""
The relative Gibbs free energy per link ``\\Delta\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_gibbs_free_energy_per_link::Function
"""
The nondimensional Gibbs free energy ``N_b\\varrho=\\beta\\varphi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_gibbs_free_energy::Function
"""
The nondimensional Gibbs free energy per link ``\\varrho\\equiv\\beta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_gibbs_free_energy_per_link::Function
"""
The nondimensional relative Gibbs free energy ``N_b\\Delta\\varrho=\\beta\\Delta\\varphi`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_gibbs_free_energy::Function
"""
The nondimensional relative Gibbs free energy per link ``\\Delta\\varrho\\equiv\\beta\\Delta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_gibbs_free_energy_per_link::Function
end
"""
The expected end-to-end length ``N_b\\gamma=\\xi/\\ell_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``,
```math
\\xi(f, T) = -\\frac{\\partial\\varphi}{\\partial f}.
```
$(TYPEDSIGNATURES)
"""
function end_to_end_length(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, link_stiffness_i, force_i, temperature_i) ->
ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_reduced_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The expected end-to-end length per link ``\\xi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function end_to_end_length_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_reduced_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The expected nondimensional end-to-end length ``N_b\\gamma=\\xi/\\ell_b`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b`` and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_end_to_end_length(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_link_stiffness_i, nondimensional_force_i) ->
ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_reduced_nondimensional_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
The expected nondimensional end-to-end length per link ``\\gamma\\equiv \\xi/N_b\\ell_b`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``,
given by [Buche et al.](https://doi.org/10.1103/PhysRevE.106.024502) as
```math
\\Delta\\varrho(\\eta) \\sim \\mathcal{L}(\\eta) + \\Delta\\lambda(\\eta) \\quad \\text{for } \\varepsilon,\\kappa\\gg 1,
```
where ``\\mathcal{L}(x)=\\coth(x)-1/x`` is the Langevin function, and ``\\Delta\\lambda(\\eta)`` is the incremental link stretch,
```math
\\Delta\\lambda(\\eta) = W_0(\\eta),
```
where ``W_0(\\eta)`` is the Lambert ``W`` function.
$(TYPEDSIGNATURES)
"""
function nondimensional_end_to_end_length_per_link(
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(nondimensional_link_stiffness_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_reduced_nondimensional_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
The Gibbs free energy ``\\varphi`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and link stiffness ``k_0``.
```math
\\varphi(f, T) = -kT\\ln Z(f, T).
```
$(TYPEDSIGNATURES)
"""
function gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_reduced_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
)
end
"""
The Gibbs free energy per link ``\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, hinge_mass_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_reduced_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
)
end
"""
The relative Gibbs free energy ``\\Delta\\varphi\\equiv\\varphi(f,T)-\\varphi(0,T)`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, link_stiffness_i, force_i, temperature_i) ->
ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_reduced_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The relative Gibbs free energy per link ``\\Delta\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_reduced_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The nondimensional Gibbs free energy ``N_b\\varrho=\\beta\\varphi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_reduced_nondimensional_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_force,
temperature,
)
end
"""
The nondimensional Gibbs free energy per link ``\\varrho\\equiv\\beta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_reduced_nondimensional_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
),
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_force,
temperature,
)
end
"""
The nondimensional relative Gibbs free energy ``N_b\\Delta\\varrho=\\beta\\Delta\\varphi`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b`` and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_link_stiffness_i, nondimensional_force_i) ->
ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_reduced_nondimensional_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
The nondimensional relative Gibbs free energy per link ``\\Delta\\varrho\\equiv\\beta\\Delta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``,
given by [Buche et al.](https://doi.org/10.1103/PhysRevE.106.024502) as
```math
\\Delta\\varrho(\\eta) \\sim \\ln\\left[\\frac{\\eta}{\\sinh(\\eta)}\\right] + \\beta u[\\lambda(\\eta)] - \\eta\\Delta\\lambda(\\eta) \\quad \\text{for } \\varepsilon,\\kappa\\gg 1,
```
where the nondimensional link potential ``\\beta u`` is given by
```math
\\beta u(\\lambda) = \\frac{\\varepsilon}{2}\\left[\\ln(\\lambda)\\right]^2,
```
where ``\\varepsilon\\equiv\\beta u_b=\\kappa`` is the nondimensional potential energy scale, ``\\kappa\\equiv\\beta k_b\\ell_b^2`` is the nondimensional link stiffness, and ``\\lambda\\equiv\\ell/\\ell_b`` is the nondimensional link stretch.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(nondimensional_link_stiffness_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_reduced_nondimensional_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
Initializes and returns an instance of the thermodynamics of the log-squared-FJC model in the isotensional ensemble approximated using an reduced asymptotic approach.
$(TYPEDSIGNATURES)
"""
function LOGSQUAREDFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
)
BOLTZMANN_CONSTANT::Float64 = 8.314462618
return LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
Legendre.LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness),
(force, temperature) -> end_to_end_length(
number_of_links,
link_length,
link_stiffness,
force,
temperature,
),
(force, temperature) ->
end_to_end_length_per_link(link_length, link_stiffness, force, temperature),
(nondimensional_force, temperature) -> nondimensional_end_to_end_length(
number_of_links,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(nondimensional_force, temperature) -> nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(force, temperature) -> gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
),
(force, temperature) -> gibbs_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
),
(force, temperature) -> relative_gibbs_free_energy(
number_of_links,
link_length,
link_stiffness,
force,
temperature,
),
(force, temperature) -> relative_gibbs_free_energy_per_link(
link_length,
link_stiffness,
force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_gibbs_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_relative_gibbs_free_energy(
number_of_links,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(nondimensional_force, temperature) ->
nondimensional_relative_gibbs_free_energy_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 65961 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ZERO, parameters
using Polymers.Physics.SingleChain.Ufjc.LogSquared.Thermodynamics.Isotensional.Asymptotic.Reduced:
LOGSQUAREDFJC
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::base::init" begin
@test isa(
LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
),
Any,
)
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test LOGSQUAREDFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.link_stiffness_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::base::link_stiffness" begin
for _ = 1:parameters.number_of_loops
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
link_stiffness,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test all(
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).number_of_links == number_of_links &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_length == link_length &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).hinge_mass == hinge_mass &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_stiffness == link_stiffness,
)
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::nondimensional::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
residual_abs = end_to_end_length / link_length - nondimensional_end_to_end_length
residual_rel = residual_abs / nondimensional_end_to_end_length
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::nondimensional::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
residual_abs =
end_to_end_length_per_link / link_length -
nondimensional_end_to_end_length_per_link
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::nondimensional::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
residual_abs =
gibbs_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_gibbs_free_energy
residual_rel = residual_abs / nondimensional_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::nondimensional::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
residual_abs =
gibbs_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::nondimensional::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
residual_abs =
relative_gibbs_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_gibbs_free_energy
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::nondimensional::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
residual_abs =
relative_gibbs_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::per_link::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
residual_abs = end_to_end_length / number_of_links - end_to_end_length_per_link
residual_rel = residual_abs / end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::per_link::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_end_to_end_length / number_of_links -
nondimensional_end_to_end_length_per_link
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::per_link::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
residual_abs = gibbs_free_energy / number_of_links - gibbs_free_energy_per_link
residual_rel = residual_abs / gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::per_link::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
residual_abs =
relative_gibbs_free_energy / number_of_links -
relative_gibbs_free_energy_per_link
residual_rel = residual_abs / relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::per_link::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_gibbs_free_energy / number_of_links -
nondimensional_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::per_link::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_relative_gibbs_free_energy / number_of_links -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::relative::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
gibbs_free_energy_0 = model.gibbs_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
residual_abs = gibbs_free_energy - gibbs_free_energy_0 - relative_gibbs_free_energy
residual_rel = residual_abs / gibbs_free_energy_0
@test abs(residual_abs) <=
BOLTZMANN_CONSTANT * temperature * number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::relative::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
gibbs_free_energy_per_link_0 = model.gibbs_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
residual_abs =
gibbs_free_energy_per_link - gibbs_free_energy_per_link_0 -
relative_gibbs_free_energy_per_link
residual_rel = residual_abs / gibbs_free_energy_per_link_0
@test abs(residual_abs) <= BOLTZMANN_CONSTANT * temperature * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::relative::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
nondimensional_gibbs_free_energy_0 =
model.nondimensional_gibbs_free_energy(ZERO, temperature)
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_gibbs_free_energy - nondimensional_gibbs_free_energy_0 -
nondimensional_relative_gibbs_free_energy
residual_rel = residual_abs / nondimensional_gibbs_free_energy_0
@test abs(residual_abs) <= number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::relative::nondimensional_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_gibbs_free_energy_per_link_0 =
model.nondimensional_gibbs_free_energy_per_link(ZERO, temperature)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_gibbs_free_energy_per_link -
nondimensional_gibbs_free_energy_per_link_0 -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link_0
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::zero::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_gibbs_free_energy_0 = model.relative_gibbs_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_gibbs_free_energy_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature * number_of_links
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::zero::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_gibbs_free_energy_per_link_0 = model.relative_gibbs_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_gibbs_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::zero::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy_0 =
model.nondimensional_relative_gibbs_free_energy(ZERO, temperature)
@test abs(nondimensional_relative_gibbs_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::zero::nondimensional_relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy_per_link_0 =
model.nondimensional_relative_gibbs_free_energy_per_link(ZERO, temperature)
@test abs(nondimensional_relative_gibbs_free_energy_per_link_0) <= ZERO
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::connection::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
h = parameters.rel_tol * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_from_derivative =
-(
model.relative_gibbs_free_energy(force + 0.5 * h, temperature) -
model.relative_gibbs_free_energy(force - 0.5 * h, temperature)
) / h
residual_abs = end_to_end_length - end_to_end_length_from_derivative
residual_rel = residual_abs / end_to_end_length
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::connection::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
h = parameters.rel_tol * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link_from_derivative =
-(
model.relative_gibbs_free_energy_per_link(force + 0.5 * h, temperature) -
model.relative_gibbs_free_energy_per_link(force - 0.5 * h, temperature)
) / h
residual_abs =
end_to_end_length_per_link - end_to_end_length_per_link_from_derivative
residual_rel = residual_abs / end_to_end_length_per_link
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::connection::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
h = parameters.rel_tol
nondimensional_end_to_end_length_from_derivative =
-(
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force + 0.5 * h,
temperature,
) - model.nondimensional_relative_gibbs_free_energy(
nondimensional_force - 0.5 * h,
temperature,
)
) / h
residual_abs =
nondimensional_end_to_end_length -
nondimensional_end_to_end_length_from_derivative
residual_rel = residual_abs / nondimensional_end_to_end_length
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::connection::nondimensional_end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
h = parameters.rel_tol
nondimensional_end_to_end_length_per_link_from_derivative =
-(
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force + 0.5 * h,
temperature,
) - model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force - 0.5 * h,
temperature,
)
) / h
residual_abs =
nondimensional_end_to_end_length_per_link -
nondimensional_end_to_end_length_per_link_from_derivative
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::legendre::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
gibbs_free_energy_legendre =
model.legendre.helmholtz_free_energy(force, temperature) -
force * end_to_end_length
residual_abs = gibbs_free_energy - gibbs_free_energy_legendre
residual_rel = residual_abs / gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::legendre::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
gibbs_free_energy_per_link_legendre =
model.legendre.helmholtz_free_energy_per_link(force, temperature) -
force * end_to_end_length_per_link
residual_abs = gibbs_free_energy_per_link - gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::legendre::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
end_to_end_length_0 = model.end_to_end_length(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
relative_gibbs_free_energy_legendre =
model.legendre.relative_helmholtz_free_energy(force, temperature) -
force * end_to_end_length +
ZERO * BOLTZMANN_CONSTANT * temperature / link_length * end_to_end_length_0
residual_abs = relative_gibbs_free_energy - relative_gibbs_free_energy_legendre
residual_rel = residual_abs / relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::legendre::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
end_to_end_length_per_link_0 = model.end_to_end_length_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
relative_gibbs_free_energy_per_link_legendre =
model.legendre.relative_helmholtz_free_energy_per_link(force, temperature) -
force * end_to_end_length_per_link +
ZERO * BOLTZMANN_CONSTANT * temperature / link_length *
end_to_end_length_per_link_0
residual_abs =
relative_gibbs_free_energy_per_link -
relative_gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::legendre::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
nondimensional_gibbs_free_energy_legendre =
model.legendre.nondimensional_helmholtz_free_energy(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length
residual_abs =
nondimensional_gibbs_free_energy - nondimensional_gibbs_free_energy_legendre
residual_rel = residual_abs / nondimensional_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::legendre::nondimensional_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_gibbs_free_energy_per_link_legendre =
model.legendre.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length_per_link
residual_abs =
nondimensional_gibbs_free_energy_per_link -
nondimensional_gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::legendre::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
nondimensional_end_to_end_length_0 =
model.nondimensional_end_to_end_length(ZERO, temperature)
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
)
nondimensional_relative_gibbs_free_energy_legendre =
model.legendre.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length +
ZERO * nondimensional_end_to_end_length_0
residual_abs =
nondimensional_relative_gibbs_free_energy -
nondimensional_relative_gibbs_free_energy_legendre
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::legendre::nondimensional_relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_end_to_end_length_per_link_0 =
model.nondimensional_end_to_end_length_per_link(ZERO, temperature)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_relative_gibbs_free_energy_per_link_legendre =
model.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length_per_link +
ZERO * nondimensional_end_to_end_length_per_link_0
residual_abs =
nondimensional_relative_gibbs_free_energy_per_link -
nondimensional_relative_gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::legendre_connection::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
h = parameters.rel_tol * BOLTZMANN_CONSTANT * temperature / link_length
force_from_derivative =
(
model.legendre.relative_helmholtz_free_energy(
force + 0.5 * h,
temperature,
) -
model.legendre.relative_helmholtz_free_energy(force - 0.5 * h, temperature)
) / (
model.end_to_end_length(force + 0.5 * h, temperature) -
model.end_to_end_length(force - 0.5 * h, temperature)
)
residual_abs = force - force_from_derivative
residual_rel = residual_abs / force
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::test::legendre_connection::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
h = parameters.rel_tol
nondimensional_force_from_derivative =
(
model.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force + 0.5 * h,
temperature,
) - model.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force - 0.5 * h,
temperature,
)
) / (
model.nondimensional_end_to_end_length_per_link(
nondimensional_force + 0.5 * h,
temperature,
) - model.nondimensional_end_to_end_length_per_link(
nondimensional_force - 0.5 * h,
temperature,
)
)
residual_abs = nondimensional_force - nondimensional_force_from_derivative
residual_rel = residual_abs / nondimensional_force
@test abs(residual_rel) <= h
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 16652 | """
The log-squared potential freely-jointed chain (log-squared-FJC) model thermodynamics in the isotensional ensemble approximated using a reduced asymptotic approach and a Legendre transformation.
"""
module Legendre
using DocStringExtensions
using ..........Polymers: PROJECT_ROOT
import .........Physics: BOLTZMANN_CONSTANT
"""
The structure of the thermodynamics of the log-squared-FJC model in the isotensional ensemble approximated using a reduced asymptotic approach and a Legendre transformation.
$(FIELDS)
"""
struct LOGSQUAREDFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The stiffness of each link in the chain ``k_0`` in units of J/(mol⋅nm^2).
"""
link_stiffness::Float64
"""
The Helmholtz free energy ``\\psi`` as a function of the applied force ``f`` and temperature ``T``.
"""
helmholtz_free_energy::Function
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
helmholtz_free_energy_per_link::Function
"""
The relative helmholtz free energy ``\\Delta\\psi\\equiv\\psi(f,T)-\\psi(0,T)`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_helmholtz_free_energy::Function
"""
The relative helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_helmholtz_free_energy_per_link::Function
"""
The nondimensional helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy::Function
"""
The nondimensional helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy_per_link::Function
"""
The nondimensional relative helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_helmholtz_free_energy::Function
"""
The nondimensional relative helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_helmholtz_free_energy_per_link::Function
end
"""
The Helmholtz free energy ``\\psi`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and link stiffness ``k_0``.
```math
\\psi(f, T) \\sim \\varphi(f, T) + f \\xi(f, T) \\quad \\text{for } N_b\\gg 1.
```
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_reduced_legendre_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
)
end
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, hinge_mass_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_reduced_legendre_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
)
end
"""
The relative Helmholtz free energy ``\\Delta\\psi\\equiv\\psi(f,T)-\\psi(0,T)`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, link_stiffness_i, force_i, temperature_i) ->
ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_reduced_legendre_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The relative Helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_reduced_legendre_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The nondimensional Helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_reduced_legendre_nondimensional_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_force,
temperature,
)
end
"""
The nondimensional Helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
link_length_i,
hinge_mass_i,
link_stiffness_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_reduced_legendre_nondimensional_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
link_stiffness_i,
nondimensional_force_i,
temperature_i,
),
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_force,
temperature,
)
end
"""
The nondimensional relative Helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b`` and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_link_stiffness_i, nondimensional_force_i) ->
ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_reduced_legendre_nondimensional_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta``
parameterized by the nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(nondimensional_link_stiffness_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_asymptotic_reduced_legendre_nondimensional_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
Initializes and returns an instance of the thermodynamics of the log-squared-FJC model in the isotensional ensemble approximated using a reduced asymptotic approach and a Legendre transformation.
$(TYPEDSIGNATURES)
"""
function LOGSQUAREDFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
)
BOLTZMANN_CONSTANT::Float64 = 8.314462618
return LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
(force, temperature) -> helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
),
(force, temperature) -> helmholtz_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
),
(force, temperature) -> relative_helmholtz_free_energy(
number_of_links,
link_length,
link_stiffness,
force,
temperature,
),
(force, temperature) -> relative_helmholtz_free_energy_per_link(
link_length,
link_stiffness,
force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) ->
nondimensional_helmholtz_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) ->
nondimensional_relative_helmholtz_free_energy(
number_of_links,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(nondimensional_force, temperature) ->
nondimensional_relative_helmholtz_free_energy_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 31973 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ZERO, parameters
using Polymers.Physics.SingleChain.Ufjc.LogSquared.Thermodynamics.Isotensional.Asymptotic.Reduced.Legendre:
LOGSQUAREDFJC
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::legendre::test::base::init" begin
@test isa(
LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
),
Any,
)
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::legendre::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test LOGSQUAREDFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::legendre::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::legendre::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.link_stiffness_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::legendre::test::base::link_stiffness" begin
for _ = 1:parameters.number_of_loops
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
link_stiffness,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::legendre::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test all(
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).number_of_links == number_of_links &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_length == link_length &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).hinge_mass == hinge_mass &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_stiffness == link_stiffness,
)
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::legendre::test::nondimensional::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_helmholtz_free_energy =
model.nondimensional_helmholtz_free_energy(nondimensional_force, temperature)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy = model.helmholtz_free_energy(force, temperature)
residual_abs =
helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::legendre::test::nondimensional::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(force, temperature)
residual_abs =
helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::legendre::test::nondimensional::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(force, temperature)
residual_abs =
relative_helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::legendre::test::nondimensional::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(force, temperature)
residual_abs =
relative_helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::legendre::test::per_link::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy = model.helmholtz_free_energy(force, temperature)
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(force, temperature)
residual_abs =
helmholtz_free_energy / number_of_links - helmholtz_free_energy_per_link
residual_rel = residual_abs / helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::legendre::test::per_link::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(force, temperature)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(force, temperature)
residual_abs =
relative_helmholtz_free_energy / number_of_links -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::legendre::test::per_link::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_helmholtz_free_energy =
model.nondimensional_helmholtz_free_energy(nondimensional_force, temperature)
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy / number_of_links -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::legendre::test::per_link::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy / number_of_links -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::legendre::test::relative::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy = model.helmholtz_free_energy(force, temperature)
helmholtz_free_energy_0 = model.helmholtz_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(force, temperature)
residual_abs =
helmholtz_free_energy - helmholtz_free_energy_0 - relative_helmholtz_free_energy
residual_rel = residual_abs / helmholtz_free_energy_0
@test abs(residual_abs) <=
BOLTZMANN_CONSTANT * temperature * number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::legendre::test::relative::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(force, temperature)
helmholtz_free_energy_per_link_0 = model.helmholtz_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(force, temperature)
residual_abs =
helmholtz_free_energy_per_link - helmholtz_free_energy_per_link_0 -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / helmholtz_free_energy_per_link_0
@test abs(residual_abs) <= BOLTZMANN_CONSTANT * temperature * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::legendre::test::relative::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_helmholtz_free_energy =
model.nondimensional_helmholtz_free_energy(nondimensional_force, temperature)
nondimensional_helmholtz_free_energy_0 =
model.nondimensional_helmholtz_free_energy(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy - nondimensional_helmholtz_free_energy_0 -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_0
@test abs(residual_abs) <= number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::legendre::test::relative::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_helmholtz_free_energy_per_link_0 =
model.nondimensional_helmholtz_free_energy_per_link(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy_per_link -
nondimensional_helmholtz_free_energy_per_link_0 -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link_0
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::legendre::test::zero::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_0 = model.relative_helmholtz_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature * number_of_links
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::legendre::test::zero::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_per_link_0 =
model.relative_helmholtz_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::legendre::test::zero::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_0 =
model.nondimensional_relative_helmholtz_free_energy(ZERO, temperature)
@test abs(nondimensional_relative_helmholtz_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::asymptotic::reduced::legendre::test::zero::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_per_link_0 =
model.nondimensional_relative_helmholtz_free_energy_per_link(ZERO, temperature)
@test abs(nondimensional_relative_helmholtz_free_energy_per_link_0) <= ZERO
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 16394 | """
The log-squared potential freely-jointed chain (log-squared-FJC) model thermodynamics in the isotensional ensemble approximated using a Legendre transformation.
"""
module Legendre
using DocStringExtensions
using ........Polymers: PROJECT_ROOT
import .......Physics: BOLTZMANN_CONSTANT
"""
The structure of the thermodynamics of the log-squared-FJC model in the isotensional ensemble approximated using a Legendre transformation.
$(FIELDS)
"""
struct LOGSQUAREDFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The stiffness of each link in the chain ``k_0`` in units of J/(mol⋅nm^2).
"""
link_stiffness::Float64
"""
The Helmholtz free energy ``\\psi`` as a function of the applied force ``f`` and temperature ``T``.
"""
helmholtz_free_energy::Function
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
helmholtz_free_energy_per_link::Function
"""
The relative helmholtz free energy ``\\Delta\\psi\\equiv\\psi(f,T)-\\psi(0,T)`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_helmholtz_free_energy::Function
"""
The relative helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_helmholtz_free_energy_per_link::Function
"""
The nondimensional helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy::Function
"""
The nondimensional helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_helmholtz_free_energy_per_link::Function
"""
The nondimensional relative helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_helmholtz_free_energy::Function
"""
The nondimensional relative helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_helmholtz_free_energy_per_link::Function
end
"""
The Helmholtz free energy ``\\psi`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and link stiffness ``k_0``.
```math
\\psi(f, T) \\sim \\varphi(f, T) + f \\xi(f, T) \\quad \\text{for } N_b\\gg 1.
```
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_legendre_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
)
end
"""
The Helmholtz free energy per link ``\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, hinge_mass_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_legendre_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
)
end
"""
The relative Helmholtz free energy ``\\Delta\\psi\\equiv\\psi(f,T)-\\psi(0,T)`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, link_stiffness_i, force_i, temperature_i) ->
ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_legendre_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The relative Helmholtz free energy per link ``\\Delta\\psi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and link stiffness ``k_0``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
link_stiffness::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, link_stiffness_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_legendre_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
link_stiffness_i,
force_i,
temperature_i,
),
link_length,
link_stiffness,
force,
temperature,
)
end
"""
The nondimensional Helmholtz free energy ``N_b\\vartheta=\\beta\\psi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_legendre_nondimensional_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_force,
temperature,
)
end
"""
The nondimensional Helmholtz free energy per link ``\\vartheta\\equiv\\beta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the link length ``\\ell_b``, hinge mass ``m``, and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_helmholtz_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
link_length_i,
hinge_mass_i,
link_stiffness_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_legendre_nondimensional_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
link_stiffness_i,
nondimensional_force_i,
temperature_i,
),
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_force,
temperature,
)
end
"""
The nondimensional relative Helmholtz free energy ``N_b\\Delta\\vartheta=\\beta\\Delta\\psi`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b`` and nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_link_stiffness_i, nondimensional_force_i) ->
ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_legendre_nondimensional_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
The nondimensional relative Helmholtz free energy per link ``\\Delta\\vartheta\\equiv\\beta\\Delta\\psi/N_b`` as a function of the applied nondimensional force ``\\eta``
parameterized by the nondimensional link stiffness ``\\kappa\\equiv\\beta k_0\\ell_b^2``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(nondimensional_link_stiffness_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_ufjc_log_squared_thermodynamics_isotensional_legendre_nondimensional_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_force_i,
),
nondimensional_link_stiffness,
nondimensional_force,
)
end
"""
Initializes and returns an instance of the thermodynamics of the log-squared-FJC model in the isotensional ensemble approximated using a Legendre transformation.
$(TYPEDSIGNATURES)
"""
function LOGSQUAREDFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
)
BOLTZMANN_CONSTANT::Float64 = 8.314462618
return LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
(force, temperature) -> helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
),
(force, temperature) -> helmholtz_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness,
force,
temperature,
),
(force, temperature) -> relative_helmholtz_free_energy(
number_of_links,
link_length,
link_stiffness,
force,
temperature,
),
(force, temperature) -> relative_helmholtz_free_energy_per_link(
link_length,
link_stiffness,
force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) ->
nondimensional_helmholtz_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) ->
nondimensional_relative_helmholtz_free_energy(
number_of_links,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(nondimensional_force, temperature) ->
nondimensional_relative_helmholtz_free_energy_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 31492 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ZERO, parameters
using Polymers.Physics.SingleChain.Ufjc.LogSquared.Thermodynamics.Isotensional.Legendre:
LOGSQUAREDFJC
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::legendre::test::base::init" begin
@test isa(
LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
),
Any,
)
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::legendre::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test LOGSQUAREDFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::legendre::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::legendre::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.link_stiffness_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::legendre::test::base::link_stiffness" begin
for _ = 1:parameters.number_of_loops
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
link_stiffness,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::legendre::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test all(
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).number_of_links == number_of_links &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_length == link_length &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).hinge_mass == hinge_mass &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_stiffness == link_stiffness,
)
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::legendre::test::nondimensional::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_helmholtz_free_energy =
model.nondimensional_helmholtz_free_energy(nondimensional_force, temperature)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy = model.helmholtz_free_energy(force, temperature)
residual_abs =
helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::legendre::test::nondimensional::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(force, temperature)
residual_abs =
helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::legendre::test::nondimensional::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(force, temperature)
residual_abs =
relative_helmholtz_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::legendre::test::nondimensional::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(force, temperature)
residual_abs =
relative_helmholtz_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::legendre::test::per_link::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy = model.helmholtz_free_energy(force, temperature)
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(force, temperature)
residual_abs =
helmholtz_free_energy / number_of_links - helmholtz_free_energy_per_link
residual_rel = residual_abs / helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::legendre::test::per_link::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(force, temperature)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(force, temperature)
residual_abs =
relative_helmholtz_free_energy / number_of_links -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::legendre::test::per_link::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_helmholtz_free_energy =
model.nondimensional_helmholtz_free_energy(nondimensional_force, temperature)
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy / number_of_links -
nondimensional_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::legendre::test::per_link::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy / number_of_links -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::legendre::test::relative::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy = model.helmholtz_free_energy(force, temperature)
helmholtz_free_energy_0 = model.helmholtz_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_helmholtz_free_energy =
model.relative_helmholtz_free_energy(force, temperature)
residual_abs =
helmholtz_free_energy - helmholtz_free_energy_0 - relative_helmholtz_free_energy
residual_rel = residual_abs / helmholtz_free_energy_0
@test abs(residual_abs) <=
BOLTZMANN_CONSTANT * temperature * number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::legendre::test::relative::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
helmholtz_free_energy_per_link =
model.helmholtz_free_energy_per_link(force, temperature)
helmholtz_free_energy_per_link_0 = model.helmholtz_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_helmholtz_free_energy_per_link =
model.relative_helmholtz_free_energy_per_link(force, temperature)
residual_abs =
helmholtz_free_energy_per_link - helmholtz_free_energy_per_link_0 -
relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / helmholtz_free_energy_per_link_0
@test abs(residual_abs) <= BOLTZMANN_CONSTANT * temperature * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::legendre::test::relative::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_helmholtz_free_energy =
model.nondimensional_helmholtz_free_energy(nondimensional_force, temperature)
nondimensional_helmholtz_free_energy_0 =
model.nondimensional_helmholtz_free_energy(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy =
model.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy - nondimensional_helmholtz_free_energy_0 -
nondimensional_relative_helmholtz_free_energy
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_0
@test abs(residual_abs) <= number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::legendre::test::relative::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_helmholtz_free_energy_per_link =
model.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_helmholtz_free_energy_per_link_0 =
model.nondimensional_helmholtz_free_energy_per_link(ZERO, temperature)
nondimensional_relative_helmholtz_free_energy_per_link =
model.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy_per_link -
nondimensional_helmholtz_free_energy_per_link_0 -
nondimensional_relative_helmholtz_free_energy_per_link
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link_0
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::legendre::test::zero::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_0 = model.relative_helmholtz_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature * number_of_links
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::legendre::test::zero::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_helmholtz_free_energy_per_link_0 =
model.relative_helmholtz_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_helmholtz_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::legendre::test::zero::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_0 =
model.nondimensional_relative_helmholtz_free_energy(ZERO, temperature)
@test abs(nondimensional_relative_helmholtz_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::legendre::test::zero::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_helmholtz_free_energy_per_link_0 =
model.nondimensional_relative_helmholtz_free_energy_per_link(ZERO, temperature)
@test abs(nondimensional_relative_helmholtz_free_energy_per_link_0) <= ZERO
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 1491 | """
The Morse potential freely-jointed chain (Morse-FJC) single-chain model.
"""
module Morse
using DocStringExtensions
include("thermodynamics/mod.jl")
"""
The structure of the Morse-FJC model.
$(FIELDS)
"""
struct MORSEFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The stiffness of each link in the chain ``k_0`` in units of J/(mol⋅nm^2).
"""
link_stiffness::Float64
"""
The energy of each link in the chain ``u_0`` in units of J/mol.
"""
link_energy::Float64
"""
The thermodynamic functions of the model.
"""
thermodynamics::Any
end
"""
Initializes and returns an instance of the Morse-FJC model.
$(TYPEDSIGNATURES)
"""
function MORSEFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
link_energy::Float64,
)
return MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
Thermodynamics.MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 5135 | module Test
using Test
using Polymers.Physics.SingleChain: parameters
using Polymers.Physics.SingleChain.Ufjc.Morse: MORSEFJC
@testset "physics::single_chain::ufjc::morse::test::base::init" begin
@test isa(
MORSEFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
parameters.link_energy_reference,
),
Any,
)
end
@testset "physics::single_chain::ufjc::morse::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test MORSEFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
parameters.link_energy_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ufjc::morse::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test MORSEFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
parameters.link_energy_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ufjc::morse::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test MORSEFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.link_stiffness_reference,
parameters.link_energy_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ufjc::morse::test::base::link_stiffness" begin
for _ = 1:parameters.number_of_loops
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test MORSEFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
link_stiffness,
parameters.link_energy_reference,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::morse::test::base::link_energy" begin
for _ = 1:parameters.number_of_loops
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
@test MORSEFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
link_energy,
).link_energy == link_energy
end
end
@testset "physics::single_chain::ufjc::morse::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
@test all(
MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
).number_of_links == number_of_links &&
MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
).link_length == link_length &&
MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
).hinge_mass == hinge_mass &&
MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
).link_stiffness == link_stiffness &&
MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
).link_energy == link_energy,
)
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 1899 | """
The Morse potential freely-jointed chain (Morse-FJC) single-chain model thermodynamics.
"""
module Thermodynamics
using DocStringExtensions
include("isometric/mod.jl")
include("isotensional/mod.jl")
"""
The structure of the thermodynamics of the Morse-FJC model.
$(FIELDS)
"""
struct MORSEFJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The stiffness of each link in the chain ``k_0`` in units of J/(mol⋅nm^2).
"""
link_stiffness::Float64
"""
The energy of each link in the chain ``u_0`` in units of J/mol.
"""
link_energy::Float64
"""
The thermodynamic functions of the model in the isometric ensemble.
"""
isometric::Any
"""
The thermodynamic functions of the model in the isotensional ensemble.
"""
isotensional::Any
end
"""
Initializes and returns an instance of the thermodynamics of the Morse-FJC model.
$(TYPEDSIGNATURES)
"""
function MORSEFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
link_energy::Float64,
)
return MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
Isometric.MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
),
Isotensional.MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.