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[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 54663 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT, PLANCK_CONSTANT
using Polymers.Physics.SingleChain: parameters
using Polymers.Physics.SingleChain.Ufjc.Morse.Thermodynamics: MORSEFJC
@testset "physics::single_chain::ufjc::morse::thermodynamics::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::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 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::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 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::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 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::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())
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,
link_stiffness,
parameters.link_energy_reference,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::morse::thermodynamics::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::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_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
@testset "physics::single_chain::ufjc::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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 | 1712 | """
The Morse potential freely-jointed chain (Morse-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 Morse-FJC model in the isometric ensemble.
$(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 approximated using an asymptotic approach.
"""
asymptotic::Any
end
"""
Initializes and returns an instance of the thermodynamics of the Morse-FJC model in the isometric ensemble.
$(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,
Asymptotic.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 | 5583 | module Test
using Test
using Polymers.Physics.SingleChain: parameters
using Polymers.Physics.SingleChain.Ufjc.Morse.Thermodynamics.Isometric: MORSEFJC
@testset "physics::single_chain::ufjc::morse::thermodynamics::isometric::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::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 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::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 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::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 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::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())
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,
link_stiffness,
parameters.link_energy_reference,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::morse::thermodynamics::isometric::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::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_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 | 2224 | """
The Morse potential freely-jointed chain (Morse-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 Morse-FJC model in the isometric ensemble approximated using an asymptotic approach.
$(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 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 Morse-FJC model in the isometric ensemble approximated using an asymptotic approach.
$(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,
Reduced.MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
),
Legendre.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 | 5678 | module Test
using Test
using Polymers.Physics.SingleChain: parameters
using Polymers.Physics.SingleChain.Ufjc.Morse.Thermodynamics.Isometric.Asymptotic: MORSEFJC
@testset "physics::single_chain::ufjc::morse::thermodynamics::isometric::asymptotic::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::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 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::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 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::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 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::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())
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,
link_stiffness,
parameters.link_energy_reference,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::morse::thermodynamics::isometric::asymptotic::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::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_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 | 24224 | """
The Morse potential freely-jointed chain (Morse-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 Morse-FJC model in the isometric ensemble approximated using an asymptotic approach and a Legendre transformation.
$(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 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},
link_energy::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,
link_energy_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isometric_asymptotic_legendre_force,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
link_energy_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
link_energy,
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_link_energy::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_link_energy_i,
nondimensional_end_to_end_length_per_link_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isometric_asymptotic_legendre_nondimensional_force,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_end_to_end_length_per_link_i,
),
nondimensional_link_stiffness,
nondimensional_link_energy,
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},
link_energy::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,
link_energy_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isometric_asymptotic_legendre_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
link_energy_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
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},
link_energy::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,
link_energy_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isometric_asymptotic_legendre_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
link_energy_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
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},
link_energy::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,
link_energy_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isometric_asymptotic_legendre_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
link_energy_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
link_energy,
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},
link_energy::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,
link_energy_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isometric_asymptotic_legendre_relative_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,
link_stiffness_i,
link_energy_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
link_energy,
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_link_energy::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_link_energy_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isometric_asymptotic_legendre_nondimensional_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_link_energy,
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_link_energy::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_link_energy_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isometric_asymptotic_legendre_nondimensional_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_link_energy,
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_link_energy::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_link_energy_i,
nondimensional_end_to_end_length_per_link_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isometric_asymptotic_legendre_nondimensional_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_link_energy,
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_link_energy::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_link_energy_i,
nondimensional_end_to_end_length_per_link_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isometric_asymptotic_legendre_nondimensional_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_end_to_end_length_per_link_i,
),
nondimensional_link_stiffness,
nondimensional_link_energy,
nondimensional_end_to_end_length_per_link,
)
end
"""
Initializes and returns an instance of the thermodynamics of the Morse-FJC model in the isometric ensemble approximated using an asymptotic approach and a Legendre transformation.
$(TYPEDSIGNATURES)
"""
function MORSEFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
link_energy::Float64,
)
BOLTZMANN_CONSTANT::Float64 = 8.314462618
return MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
(end_to_end_length, temperature) -> force(
number_of_links,
link_length,
link_stiffness,
link_energy,
end_to_end_length,
temperature,
),
(nondimensional_end_to_end_length_per_link, temperature) -> nondimensional_force(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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,
link_energy,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> helmholtz_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> relative_helmholtz_free_energy(
number_of_links,
link_length,
link_stiffness,
link_energy,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> relative_helmholtz_free_energy_per_link(
number_of_links,
link_length,
link_stiffness,
link_energy,
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,
link_energy / 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,
link_energy / 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,
link_energy / 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,
link_energy / 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 | 50275 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ZERO, parameters
using Polymers.Physics.SingleChain.Ufjc.Morse.Thermodynamics.Isometric.Asymptotic.Legendre:
MORSEFJC
using Polymers.Physics.SingleChain.Ufjc.Morse.Thermodynamics.Isotensional.Asymptotic:
nondimensional_end_to_end_length_per_link as isotensional_nondimensional_end_to_end_length_per_link
@testset "physics::single_chain::ufjc::morse::thermodynamics::isometric::asymptotic::legendre::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::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 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::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 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::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 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::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())
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,
link_stiffness,
parameters.link_energy_reference,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::morse::thermodynamics::isometric::asymptotic::legendre::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::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_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
@testset "physics::single_chain::ufjc::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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 | 1864 | """
The Morse potential freely-jointed chain (Morse-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 Morse-FJC model in the isometric ensemble approximated using an reduced asymptotic approach.
$(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 approximated using an reduced asymptotic approach.
"""
legendre::Any
end
"""
Initializes and returns an instance of the thermodynamics of the Morse-FJC model in the isometric ensemble approximated using an reduced asymptotic approach.
$(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,
Legendre.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 | 5754 | module Test
using Test
using Polymers.Physics.SingleChain: parameters
using Polymers.Physics.SingleChain.Ufjc.Morse.Thermodynamics.Isometric.Asymptotic.Reduced:
MORSEFJC
@testset "physics::single_chain::ufjc::morse::thermodynamics::isometric::asymptotic::reduced::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::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 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::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 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::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 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::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())
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,
link_stiffness,
parameters.link_energy_reference,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::morse::thermodynamics::isometric::asymptotic::reduced::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::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_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 | 24327 | """
The Morse potential freely-jointed chain (Morse-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 Morse-FJC model in the isometric ensemble approximated using a reduced asymptotic approach and a Legendre transformation.
$(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 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},
link_energy::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,
link_energy_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isometric_asymptotic_reduced_legendre_force,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
link_energy_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
link_energy,
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_link_energy::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_link_energy_i,
nondimensional_end_to_end_length_per_link_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isometric_asymptotic_reduced_legendre_nondimensional_force,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_end_to_end_length_per_link_i,
),
nondimensional_link_stiffness,
nondimensional_link_energy,
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},
link_energy::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,
link_energy_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isometric_asymptotic_reduced_legendre_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
link_energy_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
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},
link_energy::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,
link_energy_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isometric_asymptotic_reduced_legendre_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
link_energy_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
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},
link_energy::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,
link_energy_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isometric_asymptotic_reduced_legendre_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
link_energy_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
link_energy,
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},
link_energy::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,
link_energy_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isometric_asymptotic_reduced_legendre_relative_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,
link_stiffness_i,
link_energy_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
link_energy,
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_link_energy::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_link_energy_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isometric_asymptotic_reduced_legendre_nondimensional_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_link_energy,
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_link_energy::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_link_energy_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isometric_asymptotic_reduced_legendre_nondimensional_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_link_energy,
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_link_energy::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_link_energy_i,
nondimensional_end_to_end_length_per_link_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isometric_asymptotic_reduced_legendre_nondimensional_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_link_energy,
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_link_energy::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_link_energy_i,
nondimensional_end_to_end_length_per_link_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isometric_asymptotic_reduced_legendre_nondimensional_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_end_to_end_length_per_link_i,
),
nondimensional_link_stiffness,
nondimensional_link_energy,
nondimensional_end_to_end_length_per_link,
)
end
"""
Initializes and returns an instance of the thermodynamics of the Morse-FJC model in the isometric ensemble approximated using a reduced asymptotic approach and a Legendre transformation.
$(TYPEDSIGNATURES)
"""
function MORSEFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
link_energy::Float64,
)
BOLTZMANN_CONSTANT::Float64 = 8.314462618
return MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
(end_to_end_length, temperature) -> force(
number_of_links,
link_length,
link_stiffness,
link_energy,
end_to_end_length,
temperature,
),
(nondimensional_end_to_end_length_per_link, temperature) -> nondimensional_force(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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,
link_energy,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> helmholtz_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> relative_helmholtz_free_energy(
number_of_links,
link_length,
link_stiffness,
link_energy,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> relative_helmholtz_free_energy_per_link(
number_of_links,
link_length,
link_stiffness,
link_energy,
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,
link_energy / 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,
link_energy / 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,
link_energy / 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,
link_energy / 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 | 50777 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ZERO, parameters
using Polymers.Physics.SingleChain.Ufjc.Morse.Thermodynamics.Isometric.Asymptotic.Reduced.Legendre:
MORSEFJC
using Polymers.Physics.SingleChain.Ufjc.Morse.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::morse::thermodynamics::isometric::asymptotic::reduced::legendre::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::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 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::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 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::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 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::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
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,
link_stiffness,
parameters.link_energy_reference,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::morse::thermodynamics::isometric::asymptotic::reduced::legendre::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::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
link_energy =
parameters.link_energy_reference + parameters.link_energy_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
@testset "physics::single_chain::ufjc::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
nondimensional_end_to_end_length_per_link_max =
isotensional_nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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 | 26975 | """
The Morse potential freely-jointed chain (Morse-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 Morse-FJC model in the isotensional ensemble.
$(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 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},
link_energy::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,
link_energy_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
link_energy_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
link_energy,
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},
link_energy::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, link_energy_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
link_stiffness_i,
link_energy_i,
force_i,
temperature_i,
),
link_length,
link_stiffness,
link_energy,
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_link_energy::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_link_energy_i,
nondimensional_force_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_nondimensional_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_link_energy,
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_link_energy::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_nondimensional_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
),
nondimensional_link_stiffness,
nondimensional_link_energy,
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},
link_energy::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,
link_energy_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
link_energy_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
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},
link_energy::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,
link_energy_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
link_stiffness_i,
link_energy_i,
force_i,
temperature_i,
),
link_length,
hinge_mass,
link_stiffness,
link_energy,
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},
link_energy::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,
link_energy_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
link_energy_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
link_energy,
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},
link_energy::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, link_energy_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
link_stiffness_i,
link_energy_i,
force_i,
temperature_i,
),
link_length,
link_stiffness,
link_energy,
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_link_energy::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_link_energy_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_nondimensional_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_link_energy,
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_link_energy::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_link_energy_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_nondimensional_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
temperature_i,
),
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_link_energy,
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_link_energy::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_link_energy_i,
nondimensional_force_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_nondimensional_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_link_energy,
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 [Morse](https://doi.org/10.1103/PhysRev.34.57) as
```math
\\beta u(\\lambda) = \\varepsilon\\left[1 - e^{\\alpha(\\lambda - 1)}\\right]^2,
```
where ``\\varepsilon\\equiv\\beta u_b=\\kappa/72`` is the nondimensional potential energy scale, ``\\alpha\\equiv a\\ell_b=\\sqrt{\\kappa/2\\varepsilon}`` is the nondimensional Morse parameter, ``\\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_link_energy::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_nondimensional_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
),
nondimensional_link_stiffness,
nondimensional_link_energy,
nondimensional_force,
)
end
"""
Initializes and returns an instance of the thermodynamics of the Morse-FJC model in the isotensional ensemble.
$(TYPEDSIGNATURES)
"""
function MORSEFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
link_energy::Float64,
)
BOLTZMANN_CONSTANT::Float64 = 8.314462618
return MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
Asymptotic.MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
),
Legendre.MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
),
(force, temperature) -> end_to_end_length(
number_of_links,
link_length,
link_stiffness,
link_energy,
force,
temperature,
),
(force, temperature) -> end_to_end_length_per_link(
link_length,
link_stiffness,
link_energy,
force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_end_to_end_length(
number_of_links,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(nondimensional_force, temperature) -> nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(force, temperature) -> gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
force,
temperature,
),
(force, temperature) -> gibbs_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness,
link_energy,
force,
temperature,
),
(force, temperature) -> relative_gibbs_free_energy(
number_of_links,
link_length,
link_stiffness,
link_energy,
force,
temperature,
),
(force, temperature) -> relative_gibbs_free_energy_per_link(
link_length,
link_stiffness,
link_energy,
force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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,
link_energy / 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,
link_energy / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(nondimensional_force, temperature) ->
nondimensional_relative_gibbs_free_energy_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 94272 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ONE, ZERO, POINTS, integrate, parameters
using Polymers.Physics.SingleChain.Ufjc.Morse.Thermodynamics.Isotensional: MORSEFJC
@testset "physics::single_chain::ufjc::morse::thermodynamics::isotensional::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::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 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::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 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::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 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::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())
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,
link_stiffness,
parameters.link_energy_reference,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::morse::thermodynamics::isotensional::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::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_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
@testset "physics::single_chain::ufjc::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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
link_energy = 0.5 * link_stiffness * link_length^2
model = MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
)
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_morse_parameter =
sqrt(link_stiffness * link_length^2 / link_energy / 2.0)
nondimensional_link_stretch_max =
1.0 + log(2.0) / nondimensional_morse_parameter
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::morse::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
link_energy = 0.5 * link_stiffness * link_length^2
model = MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
)
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_morse_parameter =
sqrt(link_stiffness * link_length^2 / link_energy / 2.0)
nondimensional_link_stretch_max =
1.0 + log(2.0) / nondimensional_morse_parameter
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::morse::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
link_energy = 0.5 * link_stiffness * link_length^2
model = MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
)
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_morse_parameter =
sqrt(link_stiffness * link_length^2 / link_energy / 2.0)
nondimensional_link_stretch_max =
1.0 + log(2.0) / nondimensional_morse_parameter
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::morse::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
link_energy = 0.5 * link_stiffness * link_length^2
model = MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
)
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_morse_parameter =
sqrt(link_stiffness * link_length^2 / link_energy / 2.0)
nondimensional_link_stretch_max =
1.0 + log(2.0) / nondimensional_morse_parameter
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::morse::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
link_energy = 0.5 * link_stiffness * link_length^2
model = MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
)
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_morse_parameter =
sqrt(link_stiffness * link_length^2 / link_energy / 2.0)
nondimensional_link_stretch_max =
1.0 + log(2.0) / nondimensional_morse_parameter
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::morse::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
link_energy = 0.5 * link_stiffness * link_length^2
model = MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
)
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_morse_parameter =
sqrt(link_stiffness * link_length^2 / link_energy / 2.0)
nondimensional_link_stretch_max =
1.0 + log(2.0) / nondimensional_morse_parameter
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::morse::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
link_energy = 0.5 * link_stiffness * link_length^2
model = MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
)
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_morse_parameter =
sqrt(link_stiffness * link_length^2 / link_energy / 2.0)
nondimensional_link_stretch_max =
1.0 + log(2.0) / nondimensional_morse_parameter
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::morse::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
link_energy = 0.5 * link_stiffness * link_length^2
model = MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
)
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_morse_parameter =
sqrt(link_stiffness * link_length^2 / link_energy / 2.0)
nondimensional_link_stretch_max =
1.0 + log(2.0) / nondimensional_morse_parameter
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 | 27983 | """
The Morse potential freely-jointed chain (Morse-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 Morse-FJC model in the isotensional ensemble approximated using an asymptotic approach.
$(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 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},
link_energy::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,
link_energy_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
link_energy_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
link_energy,
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},
link_energy::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, link_energy_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
link_stiffness_i,
link_energy_i,
force_i,
temperature_i,
),
link_length,
link_stiffness,
link_energy,
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_link_energy::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_link_energy_i,
nondimensional_force_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_nondimensional_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_link_energy,
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 [Buche et al.](10.1016/j.jmps.2021.104593) as
```math
\\eta(\\lambda) = \\sqrt{\\frac{2\\varepsilon}{\\kappa}}\\,\\ln\\left[\\frac{2}{1+\\sqrt{1-\\eta/\\eta_\\mathrm{max}}}\\right],
```
where ``\\eta_\\mathrm{max}=\\sqrt{\\kappa\\varepsilon/8}`` is the maximum nondimensional force the link can support.
```
$(TYPEDSIGNATURES)
"""
function nondimensional_end_to_end_length_per_link(
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_link_energy::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_nondimensional_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
),
nondimensional_link_stiffness,
nondimensional_link_energy,
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},
link_energy::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,
link_energy_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
link_energy_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
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},
link_energy::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,
link_energy_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
link_stiffness_i,
link_energy_i,
force_i,
temperature_i,
),
link_length,
hinge_mass,
link_stiffness,
link_energy,
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},
link_energy::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,
link_energy_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
link_energy_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
link_energy,
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},
link_energy::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, link_energy_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
link_stiffness_i,
link_energy_i,
force_i,
temperature_i,
),
link_length,
link_stiffness,
link_energy,
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_link_energy::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_link_energy_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_nondimensional_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_link_energy,
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_link_energy::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_link_energy_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_nondimensional_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
temperature_i,
),
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_link_energy,
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_link_energy::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_link_energy_i,
nondimensional_force_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_nondimensional_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_link_energy,
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 [Morse](https://doi.org/10.1103/PhysRev.34.57) as
```math
\\beta u(\\lambda) = \\varepsilon\\left[1 - e^{\\alpha(\\lambda - 1)}\\right]^2,
```
where ``\\varepsilon\\equiv\\beta u_b=\\kappa/72`` is the nondimensional potential energy scale, ``\\alpha\\equiv a\\ell_b=\\sqrt{\\kappa/2\\varepsilon}`` is the nondimensional Morse parameter, ``1/c\\equiv 1-u'''(1)/2u''(1)=1 + 3\\alpha/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_link_energy::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_nondimensional_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
),
nondimensional_link_stiffness,
nondimensional_link_energy,
nondimensional_force,
)
end
"""
Initializes and returns an instance of the thermodynamics of the Morse-FJC model in the isotensional ensemble approximated using an asymptotic approach.
$(TYPEDSIGNATURES)
"""
function MORSEFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
link_energy::Float64,
)
BOLTZMANN_CONSTANT::Float64 = 8.314462618
return MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
Reduced.MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
),
Legendre.MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
),
(force, temperature) -> end_to_end_length(
number_of_links,
link_length,
link_stiffness,
link_energy,
force,
temperature,
),
(force, temperature) -> end_to_end_length_per_link(
link_length,
link_stiffness,
link_energy,
force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_end_to_end_length(
number_of_links,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(nondimensional_force, temperature) -> nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(force, temperature) -> gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
force,
temperature,
),
(force, temperature) -> gibbs_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness,
link_energy,
force,
temperature,
),
(force, temperature) -> relative_gibbs_free_energy(
number_of_links,
link_length,
link_stiffness,
link_energy,
force,
temperature,
),
(force, temperature) -> relative_gibbs_free_energy_per_link(
link_length,
link_stiffness,
link_energy,
force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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,
link_energy / 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,
link_energy / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(nondimensional_force, temperature) ->
nondimensional_relative_gibbs_free_energy_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 83992 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ONE, ZERO, POINTS, integrate, parameters
using Polymers.Physics.SingleChain.Ufjc.Morse.Thermodynamics.Isotensional.Asymptotic:
MORSEFJC
@testset "physics::single_chain::ufjc::morse::thermodynamics::isotensional::asymptotic::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::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 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::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 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::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 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::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())
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,
link_stiffness,
parameters.link_energy_reference,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::morse::thermodynamics::isotensional::asymptotic::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::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_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
@testset "physics::single_chain::ufjc::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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
link_energy = 0.5 * link_stiffness * link_length^2
model = MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
)
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 =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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
link_energy = 0.5 * link_stiffness * link_length^2
model = MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
)
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 =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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
link_energy = 0.5 * link_stiffness * link_length^2
model = MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
)
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 =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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
link_energy = 0.5 * link_stiffness * link_length^2
model = MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
)
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 =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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 | 18514 | """
The Morse potential freely-jointed chain (Morse-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 Morse-FJC model in the isotensional ensemble approximated using an asymptotic approach and a Legendre transformation.
$(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 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},
link_energy::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,
link_energy_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_legendre_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
link_energy_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
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},
link_energy::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,
link_energy_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_legendre_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
link_stiffness_i,
link_energy_i,
force_i,
temperature_i,
),
link_length,
hinge_mass,
link_stiffness,
link_energy,
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},
link_energy::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,
link_energy_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_legendre_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
link_energy_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
link_energy,
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},
link_energy::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, link_energy_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_legendre_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
link_stiffness_i,
link_energy_i,
force_i,
temperature_i,
),
link_length,
link_stiffness,
link_energy,
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_link_energy::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_link_energy_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_legendre_nondimensional_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_link_energy,
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_link_energy::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_link_energy_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_legendre_nondimensional_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
temperature_i,
),
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_link_energy,
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_link_energy::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_link_energy_i,
nondimensional_force_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_legendre_nondimensional_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_link_energy,
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_link_energy::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_legendre_nondimensional_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
),
nondimensional_link_stiffness,
nondimensional_link_energy,
nondimensional_force,
)
end
"""
Initializes and returns an instance of the thermodynamics of the Morse-FJC model in the isotensional ensemble approximated using an asymptotic approach and a Legendre transformation.
$(TYPEDSIGNATURES)
"""
function MORSEFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
link_energy::Float64,
)
BOLTZMANN_CONSTANT::Float64 = 8.314462618
return MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
(force, temperature) -> helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
force,
temperature,
),
(force, temperature) -> helmholtz_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness,
link_energy,
force,
temperature,
),
(force, temperature) -> relative_helmholtz_free_energy(
number_of_links,
link_length,
link_stiffness,
link_energy,
force,
temperature,
),
(force, temperature) -> relative_helmholtz_free_energy_per_link(
link_length,
link_stiffness,
link_energy,
force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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,
link_energy / 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,
link_energy / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(nondimensional_force, temperature) ->
nondimensional_relative_helmholtz_free_energy_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 35406 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ONE, ZERO, POINTS, integrate, parameters
using Polymers.Physics.SingleChain.Ufjc.Morse.Thermodynamics.Isotensional.Asymptotic.Legendre:
MORSEFJC
@testset "physics::single_chain::ufjc::morse::thermodynamics::isotensional::asymptotic::legendre::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::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 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::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 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::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 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::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 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::thermodynamics::isotensional::asymptotic::legendre::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::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())
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
@testset "physics::single_chain::ufjc::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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 | 27529 | """
The Morse potential freely-jointed chain (Morse-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 Morse-FJC model in the isotensional ensemble approximated using an reduced asymptotic approach.
$(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 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},
link_energy::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,
link_energy_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_reduced_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
link_energy_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
link_energy,
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},
link_energy::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, link_energy_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_reduced_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
link_stiffness_i,
link_energy_i,
force_i,
temperature_i,
),
link_length,
link_stiffness,
link_energy,
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_link_energy::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_link_energy_i,
nondimensional_force_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_reduced_nondimensional_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_link_energy,
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 [Buche et al.](10.1016/j.jmps.2021.104593) as
```math
\\eta(\\lambda) = \\sqrt{\\frac{2\\varepsilon}{\\kappa}}\\,\\ln\\left[\\frac{2}{1+\\sqrt{1-\\eta/\\eta_\\mathrm{max}}}\\right],
```
where ``\\eta_\\mathrm{max}=\\sqrt{\\kappa\\varepsilon/8}`` is the maximum nondimensional force the link can support.
$(TYPEDSIGNATURES)
"""
function nondimensional_end_to_end_length_per_link(
nondimensional_link_stiffness::Union{Float64,Vector,Matrix,Array},
nondimensional_link_energy::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_reduced_nondimensional_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
),
nondimensional_link_stiffness,
nondimensional_link_energy,
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},
link_energy::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,
link_energy_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_reduced_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
link_energy_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
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},
link_energy::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,
link_energy_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_reduced_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
link_stiffness_i,
link_energy_i,
force_i,
temperature_i,
),
link_length,
hinge_mass,
link_stiffness,
link_energy,
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},
link_energy::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,
link_energy_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_reduced_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
link_energy_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
link_energy,
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},
link_energy::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, link_energy_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_reduced_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
link_stiffness_i,
link_energy_i,
force_i,
temperature_i,
),
link_length,
link_stiffness,
link_energy,
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_link_energy::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_link_energy_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_reduced_nondimensional_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_link_energy,
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_link_energy::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_link_energy_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_reduced_nondimensional_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
temperature_i,
),
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_link_energy,
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_link_energy::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_link_energy_i,
nondimensional_force_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_reduced_nondimensional_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_link_energy,
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 [Morse](https://doi.org/10.1103/PhysRev.34.57) as
```math
\\beta u(\\lambda) = \\varepsilon\\left[1 - e^{\\alpha(\\lambda - 1)}\\right]^2,
```
where ``\\varepsilon\\equiv\\beta u_b=\\kappa/72`` is the nondimensional potential energy scale, ``\\alpha\\equiv a\\ell_b=\\sqrt{\\kappa/2\\varepsilon}`` is the nondimensional Morse parameter, ``1/c\\equiv 1-u'''(1)/2u''(1)=1 + 3\\alpha/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_link_energy::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_reduced_nondimensional_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
),
nondimensional_link_stiffness,
nondimensional_link_energy,
nondimensional_force,
)
end
"""
Initializes and returns an instance of the thermodynamics of the Morse-FJC model in the isotensional ensemble approximated using an reduced asymptotic approach.
$(TYPEDSIGNATURES)
"""
function MORSEFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
link_energy::Float64,
)
BOLTZMANN_CONSTANT::Float64 = 8.314462618
return MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
Legendre.MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
),
(force, temperature) -> end_to_end_length(
number_of_links,
link_length,
link_stiffness,
link_energy,
force,
temperature,
),
(force, temperature) -> end_to_end_length_per_link(
link_length,
link_stiffness,
link_energy,
force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_end_to_end_length(
number_of_links,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(nondimensional_force, temperature) -> nondimensional_end_to_end_length_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(force, temperature) -> gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
force,
temperature,
),
(force, temperature) -> gibbs_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness,
link_energy,
force,
temperature,
),
(force, temperature) -> relative_gibbs_free_energy(
number_of_links,
link_length,
link_stiffness,
link_energy,
force,
temperature,
),
(force, temperature) -> relative_gibbs_free_energy_per_link(
link_length,
link_stiffness,
link_energy,
force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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,
link_energy / 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,
link_energy / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(nondimensional_force, temperature) ->
nondimensional_relative_gibbs_free_energy_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 72677 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ONE, ZERO, POINTS, integrate, parameters
using Polymers.Physics.SingleChain.Ufjc.Morse.Thermodynamics.Isotensional.Asymptotic.Reduced:
MORSEFJC
@testset "physics::single_chain::ufjc::morse::thermodynamics::isotensional::asymptotic::reduced::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::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 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::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 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::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 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::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())
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,
link_stiffness,
parameters.link_energy_reference,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::morse::thermodynamics::isotensional::asymptotic::reduced::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::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_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
@testset "physics::single_chain::ufjc::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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 | 18601 | """
The Morse potential freely-jointed chain (Morse-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 Morse-FJC model in the isotensional ensemble approximated using a reduced asymptotic approach and a Legendre transformation.
$(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 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},
link_energy::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,
link_energy_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_reduced_legendre_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
link_energy_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
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},
link_energy::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,
link_energy_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_reduced_legendre_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
link_stiffness_i,
link_energy_i,
force_i,
temperature_i,
),
link_length,
hinge_mass,
link_stiffness,
link_energy,
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},
link_energy::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,
link_energy_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_reduced_legendre_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
link_energy_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
link_energy,
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},
link_energy::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, link_energy_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_reduced_legendre_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
link_stiffness_i,
link_energy_i,
force_i,
temperature_i,
),
link_length,
link_stiffness,
link_energy,
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_link_energy::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_link_energy_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_reduced_legendre_nondimensional_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_link_energy,
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_link_energy::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_link_energy_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_reduced_legendre_nondimensional_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
temperature_i,
),
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_link_energy,
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_link_energy::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_link_energy_i,
nondimensional_force_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_reduced_legendre_nondimensional_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_link_energy,
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_link_energy::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_asymptotic_reduced_legendre_nondimensional_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
),
nondimensional_link_stiffness,
nondimensional_link_energy,
nondimensional_force,
)
end
"""
Initializes and returns an instance of the thermodynamics of the Morse-FJC model in the isotensional ensemble approximated using a reduced asymptotic approach and a Legendre transformation.
$(TYPEDSIGNATURES)
"""
function MORSEFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
link_energy::Float64,
)
BOLTZMANN_CONSTANT::Float64 = 8.314462618
return MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
(force, temperature) -> helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
force,
temperature,
),
(force, temperature) -> helmholtz_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness,
link_energy,
force,
temperature,
),
(force, temperature) -> relative_helmholtz_free_energy(
number_of_links,
link_length,
link_stiffness,
link_energy,
force,
temperature,
),
(force, temperature) -> relative_helmholtz_free_energy_per_link(
link_length,
link_stiffness,
link_energy,
force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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,
link_energy / 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,
link_energy / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(nondimensional_force, temperature) ->
nondimensional_relative_helmholtz_free_energy_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 35621 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ONE, ZERO, POINTS, integrate, parameters
using Polymers.Physics.SingleChain.Ufjc.Morse.Thermodynamics.Isotensional.Asymptotic.Reduced.Legendre:
MORSEFJC
@testset "physics::single_chain::ufjc::morse::thermodynamics::isotensional::asymptotic::reduced::legendre::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::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 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::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 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::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 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::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 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::thermodynamics::isotensional::asymptotic::reduced::legendre::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::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())
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
@testset "physics::single_chain::ufjc::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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 | 18343 | """
The Morse potential freely-jointed chain (Morse-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 Morse-FJC model in the isotensional ensemble approximated using a Legendre transformation.
$(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 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},
link_energy::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,
link_energy_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_legendre_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
link_stiffness_i,
link_energy_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
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},
link_energy::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,
link_energy_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_legendre_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
link_stiffness_i,
link_energy_i,
force_i,
temperature_i,
),
link_length,
hinge_mass,
link_stiffness,
link_energy,
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},
link_energy::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,
link_energy_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_legendre_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
link_stiffness_i,
link_energy_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
link_stiffness,
link_energy,
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},
link_energy::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, link_energy_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_legendre_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64),
link_length_i,
link_stiffness_i,
link_energy_i,
force_i,
temperature_i,
),
link_length,
link_stiffness,
link_energy,
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_link_energy::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_link_energy_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_legendre_nondimensional_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_link_energy,
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_link_energy::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_link_energy_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_legendre_nondimensional_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
temperature_i,
),
link_length,
hinge_mass,
nondimensional_link_stiffness,
nondimensional_link_energy,
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_link_energy::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_link_energy_i,
nondimensional_force_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_legendre_nondimensional_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_link_stiffness,
nondimensional_link_energy,
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_link_energy::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
) -> ccall(
(
:physics_single_chain_ufjc_morse_thermodynamics_isotensional_legendre_nondimensional_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64),
nondimensional_link_stiffness_i,
nondimensional_link_energy_i,
nondimensional_force_i,
),
nondimensional_link_stiffness,
nondimensional_link_energy,
nondimensional_force,
)
end
"""
Initializes and returns an instance of the thermodynamics of the Morse-FJC model in the isotensional ensemble approximated using a Legendre transformation.
$(TYPEDSIGNATURES)
"""
function MORSEFJC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
link_stiffness::Float64,
link_energy::Float64,
)
BOLTZMANN_CONSTANT::Float64 = 8.314462618
return MORSEFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
(force, temperature) -> helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
link_energy,
force,
temperature,
),
(force, temperature) -> helmholtz_free_energy_per_link(
link_length,
hinge_mass,
link_stiffness,
link_energy,
force,
temperature,
),
(force, temperature) -> relative_helmholtz_free_energy(
number_of_links,
link_length,
link_stiffness,
link_energy,
force,
temperature,
),
(force, temperature) -> relative_helmholtz_free_energy_per_link(
link_length,
link_stiffness,
link_energy,
force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / 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,
link_energy / 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,
link_energy / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
(nondimensional_force, temperature) ->
nondimensional_relative_helmholtz_free_energy_per_link(
link_stiffness * link_length^2 / BOLTZMANN_CONSTANT / temperature,
link_energy / BOLTZMANN_CONSTANT / temperature,
nondimensional_force,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 35114 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ONE, ZERO, POINTS, integrate, parameters
using Polymers.Physics.SingleChain.Ufjc.Morse.Thermodynamics.Isotensional.Legendre: MORSEFJC
@testset "physics::single_chain::ufjc::morse::thermodynamics::isotensional::legendre::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::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 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::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 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::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 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::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 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::thermodynamics::isotensional::legendre::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::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())
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
@testset "physics::single_chain::ufjc::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
sqrt(link_stiffness * link_energy / 8) / BOLTZMANN_CONSTANT / temperature *
link_length
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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::morse::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())
link_energy =
parameters.link_energy_reference + parameters.link_energy_scale * (0.5 - rand())
model =
MORSEFJC(number_of_links, link_length, hinge_mass, link_stiffness, link_energy)
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 | 1172 | """
The worm-like chain (WLC) single-chain model.
"""
module Wlc
using DocStringExtensions
include("thermodynamics/mod.jl")
"""
The structure of the WLC model.
$(FIELDS)
"""
struct WLC
"""
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 persistance length of the chain in units of nm.
"""
persistance_length::Float64
"""
The thermodynamic functions of the model.
"""
thermodynamics::Any
end
"""
Initializes and returns an instance of the WLC model.
$(TYPEDSIGNATURES)
"""
function WLC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
persistance_length::Float64,
)
return WLC(
number_of_links,
link_length,
hinge_mass,
persistance_length,
Thermodynamics.WLC(number_of_links, link_length, hinge_mass, persistance_length),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 3738 | module Test
using Test
using Polymers.Physics.SingleChain: parameters
using Polymers.Physics.SingleChain.Wlc: WLC
@testset "physics::single_chain::wlc::test::base::init" begin
@test isa(
WLC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.persistance_length_reference,
),
Any,
)
end
@testset "physics::single_chain::wlc::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 WLC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.persistance_length_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::wlc::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 WLC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.persistance_length_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::wlc::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 WLC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.persistance_length_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::wlc::test::base::persistance_length" begin
for _ = 1:parameters.number_of_loops
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
@test WLC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
persistance_length,
).persistance_length == persistance_length
end
end
@testset "physics::single_chain::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
@test all(
WLC(
number_of_links,
link_length,
hinge_mass,
persistance_length,
).number_of_links == number_of_links &&
WLC(number_of_links, link_length, hinge_mass, persistance_length).link_length ==
link_length &&
WLC(number_of_links, link_length, hinge_mass, persistance_length).hinge_mass ==
hinge_mass &&
WLC(
number_of_links,
link_length,
hinge_mass,
persistance_length,
).persistance_length == persistance_length,
)
end
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 1478 | """
The worm-like chain (WLC) model thermodynamics.
"""
module Thermodynamics
using DocStringExtensions
include("isometric/mod.jl")
include("isotensional/mod.jl")
"""
The structure of the thermodynamics of the WLC model.
$(FIELDS)
"""
struct WLC
"""
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 persistance length of the chain in units of nm.
"""
persistance_length::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 WLC model.
$(TYPEDSIGNATURES)
"""
function WLC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
persistance_length::Float64,
)
return WLC(
number_of_links,
link_length,
hinge_mass,
persistance_length,
Isometric.WLC(number_of_links, link_length, hinge_mass, persistance_length),
Isotensional.WLC(number_of_links, link_length, hinge_mass, persistance_length),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 42845 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT, PLANCK_CONSTANT
using Polymers.Physics.SingleChain: parameters
using Polymers.Physics.SingleChain.Wlc.Thermodynamics: WLC
@testset "physics::single_chain::wlc::thermodynamics::test::base::init" begin
@test isa(
WLC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.persistance_length_reference,
),
Any,
)
end
@testset "physics::single_chain::wlc::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 WLC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.persistance_length_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::wlc::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 WLC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.persistance_length_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::wlc::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 WLC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.persistance_length_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::wlc::thermodynamics::test::base::persistance_length" begin
for _ = 1:parameters.number_of_loops
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
@test WLC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
persistance_length,
).persistance_length == persistance_length
end
end
@testset "physics::single_chain::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
@test all(
WLC(
number_of_links,
link_length,
hinge_mass,
persistance_length,
).number_of_links == number_of_links &&
WLC(number_of_links, link_length, hinge_mass, persistance_length).link_length ==
link_length &&
WLC(number_of_links, link_length, hinge_mass, persistance_length).hinge_mass ==
hinge_mass &&
WLC(
number_of_links,
link_length,
hinge_mass,
persistance_length,
).persistance_length == persistance_length,
)
end
end
@testset "physics::single_chain::wlc::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())
persistance_length =
parameters.nondimensional_persistance_length_small *
number_of_links *
link_length
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.nondimensional_persistance_length_small *
number_of_links *
link_length
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.nondimensional_persistance_length_small *
number_of_links *
link_length
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.nondimensional_persistance_length_small *
number_of_links *
link_length
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.nondimensional_persistance_length_small *
number_of_links *
link_length
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.nondimensional_persistance_length_small *
number_of_links *
link_length
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.nondimensional_persistance_length_small *
number_of_links *
link_length
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.nondimensional_persistance_length_small *
number_of_links *
link_length
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.nondimensional_persistance_length_small *
number_of_links *
link_length
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.nondimensional_persistance_length_small *
number_of_links *
link_length
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.nondimensional_persistance_length_small *
number_of_links *
link_length
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.nondimensional_persistance_length_small *
number_of_links *
link_length
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.nondimensional_persistance_length_small *
number_of_links *
link_length
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.nondimensional_persistance_length_small *
number_of_links *
link_length
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.nondimensional_persistance_length_small *
number_of_links *
link_length
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.nondimensional_persistance_length_small *
number_of_links *
link_length
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.nondimensional_persistance_length_small *
number_of_links *
link_length
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.nondimensional_persistance_length_small *
number_of_links *
link_length
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.nondimensional_persistance_length_small *
number_of_links *
link_length
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.nondimensional_persistance_length_small *
number_of_links *
link_length
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.nondimensional_persistance_length_small *
number_of_links *
link_length
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.nondimensional_persistance_length_small *
number_of_links *
link_length
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 31325 | """
The worm-like chain (WLC) model thermodynamics in the isometric ensemble.
"""
module Isometric
using DocStringExtensions
using ......Polymers: PROJECT_ROOT
using ....SingleChain: ONE, ZERO, POINTS, integrate
include("legendre/mod.jl")
"""
The structure of the thermodynamics of the WLC model in the isometric ensemble.
$(FIELDS)
"""
struct WLC
"""
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 persistance length of the chain in units of nm.
"""
persistance_length::Float64
nondimensional_persistance_length::Float64
normalization_nondimensional_equilibrium_distribution::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``, link length ``\\ell_b``, and persistance length ``\\ell_p``,
```math
f(\\xi, T) = \\frac{\\partial \\psi}{\\partial\\xi}.
```
$(TYPEDSIGNATURES)
"""
function force(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
persistance_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,
persistance_length_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isometric_force,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
persistance_length_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
persistance_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`` and nondimensional persistance length ``\\zeta``,
```math
\\eta(\\gamma) = \\frac{\\partial\\vartheta}{\\partial\\gamma}.
```
$(TYPEDSIGNATURES)
"""
function nondimensional_force(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_persistance_length::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_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isometric_nondimensional_force,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
nondimensional_persistance_length,
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``, hinge mass ``m``, and persistance length ``\\ell_p``,
```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},
persistance_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,
hinge_mass_i,
persistance_length_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isometric_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,
persistance_length_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
persistance_length,
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``, hinge mass ``m``, and persistance length ``\\ell_p``.
$(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},
persistance_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,
hinge_mass_i,
persistance_length_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isometric_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,
persistance_length_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
persistance_length,
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 persistance length ``\\ell_p``,
```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},
persistance_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,
persistance_length_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isometric_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
persistance_length_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
persistance_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`` link length ``\\ell_b``, and persistance length ``\\ell_p``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
persistance_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,
persistance_length_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isometric_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,
persistance_length_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
persistance_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``, hinge mass ``m``, and nondimensional persistance length ``\\zeta``.
$(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_persistance_length::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_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isometric_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_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_persistance_length,
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``, hinge mass ``m``, and nondimensional persistance length ``\\zeta``.
$(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_persistance_length::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_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isometric_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_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_persistance_length,
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 nondimensional persistance length ``\\zeta``,
```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(
nondimensional_persistance_length::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_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isometric_nondimensional_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64),
nondimensional_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
),
nondimensional_persistance_length,
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`` and nondimensional persistance length ``\\zeta``,
```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_persistance_length::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_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isometric_nondimensional_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
nondimensional_persistance_length,
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 persistance length ``\\ell_p``,
```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},
persistance_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, persistance_length_i, end_to_end_length_i) ->
ccall(
(
:physics_single_chain_wlc_thermodynamics_isometric_equilibrium_distribution,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
persistance_length_i,
normalization_nondimensional_equilibrium_distribution,
end_to_end_length_i,
),
number_of_links,
link_length,
persistance_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`` and nondimensional persistance length ``\\zeta``,
```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},
nondimensional_persistance_length::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,
nondimensional_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isometric_nondimensional_equilibrium_distribution,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
nondimensional_persistance_length_i,
normalization_nondimensional_equilibrium_distribution,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
nondimensional_persistance_length,
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 persistance length ``\\ell_p``,
```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},
persistance_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, persistance_length_i, end_to_end_length_i) ->
ccall(
(
:physics_single_chain_wlc_thermodynamics_isometric_equilibrium_radial_distribution,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
persistance_length_i,
normalization_nondimensional_equilibrium_distribution,
end_to_end_length_i,
),
number_of_links,
link_length,
persistance_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`` and nondimensional persistance length ``\\zeta``,
```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_persistance_length::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,
nondimensional_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isometric_nondimensional_equilibrium_radial_distribution,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
nondimensional_persistance_length_i,
normalization_nondimensional_equilibrium_distribution,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
nondimensional_persistance_length,
nondimensional_end_to_end_length_per_link,
)
end
"""
Initializes and returns an instance of the thermodynamics of the WLC model in the isometric ensemble.
$(TYPEDSIGNATURES)
"""
function WLC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
persistance_length::Float64,
)
nondimensional_persistance_length = persistance_length / number_of_links / link_length
normalization_nondimensional_equilibrium_distribution = integrate(
nondimensional_end_to_end_length_per_link ->
nondimensional_equilibrium_radial_distribution(
number_of_links,
nondimensional_persistance_length,
1.0,
nondimensional_end_to_end_length_per_link,
),
ZERO,
ONE,
POINTS,
)
return WLC(
number_of_links,
link_length,
hinge_mass,
persistance_length,
nondimensional_persistance_length,
normalization_nondimensional_equilibrium_distribution,
Legendre.WLC(number_of_links, link_length, hinge_mass, persistance_length),
(end_to_end_length, temperature) -> force(
number_of_links,
link_length,
persistance_length,
end_to_end_length,
temperature,
),
(nondimensional_end_to_end_length_per_link) -> nondimensional_force(
number_of_links,
nondimensional_persistance_length,
nondimensional_end_to_end_length_per_link,
),
(end_to_end_length, temperature) -> helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
persistance_length,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> helmholtz_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
persistance_length,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> relative_helmholtz_free_energy(
number_of_links,
link_length,
persistance_length,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> relative_helmholtz_free_energy_per_link(
number_of_links,
link_length,
persistance_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_persistance_length,
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_persistance_length,
nondimensional_end_to_end_length_per_link,
temperature,
),
(nondimensional_end_to_end_length_per_link) ->
nondimensional_relative_helmholtz_free_energy(
nondimensional_persistance_length,
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_persistance_length,
nondimensional_end_to_end_length_per_link,
),
(end_to_end_length) -> equilibrium_distribution(
number_of_links,
link_length,
persistance_length,
normalization_nondimensional_equilibrium_distribution,
end_to_end_length,
),
(nondimensional_end_to_end_length_per_link) ->
nondimensional_equilibrium_distribution(
number_of_links,
nondimensional_persistance_length,
normalization_nondimensional_equilibrium_distribution,
nondimensional_end_to_end_length_per_link,
),
(end_to_end_length) -> equilibrium_radial_distribution(
number_of_links,
link_length,
persistance_length,
normalization_nondimensional_equilibrium_distribution,
end_to_end_length,
),
(nondimensional_end_to_end_length_per_link) ->
nondimensional_equilibrium_radial_distribution(
number_of_links,
nondimensional_persistance_length,
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 | 71308 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ONE, ZERO, POINTS, integrate, parameters
using Polymers.Physics.SingleChain.Wlc.Thermodynamics.Isometric: WLC
@testset "physics::single_chain::wlc::thermodynamics::isometric::test::base::init" begin
@test isa(
WLC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.persistance_length_reference,
),
Any,
)
end
@testset "physics::single_chain::wlc::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 WLC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.persistance_length_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::wlc::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 WLC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.persistance_length_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::wlc::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 WLC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.persistance_length_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::wlc::thermodynamics::isometric::test::base::persistance_length" begin
for _ = 1:parameters.number_of_loops
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
@test WLC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
persistance_length,
).persistance_length == persistance_length
end
end
@testset "physics::single_chain::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
@test all(
WLC(
number_of_links,
link_length,
hinge_mass,
persistance_length,
).number_of_links == number_of_links &&
WLC(number_of_links, link_length, hinge_mass, persistance_length).link_length ==
link_length &&
WLC(number_of_links, link_length, hinge_mass, persistance_length).hinge_mass ==
hinge_mass &&
WLC(
number_of_links,
link_length,
hinge_mass,
persistance_length,
).persistance_length == persistance_length,
)
end
end
@testset "physics::single_chain::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
nondimensional_equilibrium_radial_distribution_0 =
model.equilibrium_radial_distribution(ZERO)
@test abs(nondimensional_equilibrium_radial_distribution_0) <= ZERO
end
end
@testset "physics::single_chain::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 18346 | """
The worm-like chain (WLC) model thermodynamics in the isometric ensemble approximated using a Legendre transformation.
"""
module Legendre
using DocStringExtensions
using .......Polymers: PROJECT_ROOT
"""
The structure of the thermodynamics of the WLC model in the isometric ensemble approximated using a Legendre transformation.
$(FIELDS)
"""
struct WLC
"""
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 persistance length of the chain in units of nm.
"""
persistance_length::Float64
nondimensional_persistance_length::Float64
"""
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 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``, hinge mass ``m``, and persistance length ``\\ell_p``,
```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},
persistance_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,
hinge_mass_i,
persistance_length_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isometric_legendre_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,
persistance_length_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
persistance_length,
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``, hinge mass ``m``, and persistance length ``\\ell_p``.
$(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},
persistance_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,
hinge_mass_i,
persistance_length_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isometric_legendre_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,
persistance_length_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
persistance_length,
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``, link length ``\\ell_b``, and persistance length ``\\ell_p``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
persistance_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,
persistance_length_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isometric_legendre_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
persistance_length_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
persistance_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``, link length ``\\ell_b``, and persistance length ``\\ell_p``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
persistance_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,
persistance_length_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isometric_legendre_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,
persistance_length_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
persistance_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``, hinge mass ``m``, and nondimensional persistance length ``\\zeta``.
$(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_persistance_length::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_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isometric_legendre_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_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_persistance_length,
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``, hinge mass ``m``, and nondimensional persistance length ``\\zeta``.
$(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_persistance_length::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_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isometric_legendre_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_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_persistance_length,
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`` and nondimensional persistance length ``\\zeta``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_persistance_length::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_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isometric_legendre_nondimensional_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
nondimensional_persistance_length,
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`` and nondimensional persistance length ``\\zeta``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_persistance_length::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_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isometric_legendre_nondimensional_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
nondimensional_persistance_length,
nondimensional_end_to_end_length_per_link,
)
end
"""
Initializes and returns an instance of the thermodynamics of the WLC model in the isometric ensemble approximated using a Legendre transformation.
$(TYPEDSIGNATURES)
"""
function WLC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
persistance_length::Float64,
)
nondimensional_persistance_length = persistance_length / number_of_links / link_length
return WLC(
number_of_links,
link_length,
hinge_mass,
persistance_length,
nondimensional_persistance_length,
(end_to_end_length, temperature) -> gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
persistance_length,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> gibbs_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
persistance_length,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> relative_gibbs_free_energy(
number_of_links,
link_length,
persistance_length,
end_to_end_length,
temperature,
),
(end_to_end_length, temperature) -> relative_gibbs_free_energy_per_link(
number_of_links,
link_length,
persistance_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_persistance_length,
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_persistance_length,
nondimensional_end_to_end_length_per_link,
temperature,
),
(nondimensional_end_to_end_length_per_link) ->
nondimensional_relative_gibbs_free_energy(
number_of_links,
nondimensional_persistance_length,
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_persistance_length,
nondimensional_end_to_end_length_per_link,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 30690 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ZERO, parameters
using Polymers.Physics.SingleChain.Wlc.Thermodynamics.Isometric.Legendre: WLC
@testset "physics::single_chain::wlc::thermodynamics::isometric::legendre::test::base::init" begin
@test isa(
WLC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.persistance_length_reference,
),
Any,
)
end
@testset "physics::single_chain::wlc::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 WLC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.persistance_length_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::wlc::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 WLC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.persistance_length_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::wlc::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 WLC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.persistance_length_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::wlc::thermodynamics::isometric::legendre::test::base::persistance_length" begin
for _ = 1:parameters.number_of_loops
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
@test WLC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
persistance_length,
).persistance_length == persistance_length
end
end
@testset "physics::single_chain::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
@test all(
WLC(
number_of_links,
link_length,
hinge_mass,
persistance_length,
).number_of_links == number_of_links &&
WLC(number_of_links, link_length, hinge_mass, persistance_length).link_length ==
link_length &&
WLC(number_of_links, link_length, hinge_mass, persistance_length).hinge_mass ==
hinge_mass &&
WLC(
number_of_links,
link_length,
hinge_mass,
persistance_length,
).persistance_length == persistance_length,
)
end
end
@testset "physics::single_chain::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 24273 | """
The worm-like chain (WLC) 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 WLC model in the isotensional ensemble.
$(FIELDS)
"""
struct WLC
"""
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 persistance length of the chain in units of nm.
"""
persistance_length::Float64
nondimensional_persistance_length::Float64
"""
The thermodynamic functions of the model in the isotensional ensemble approximated using a Legendre transformation.
"""
legendre::Any
"""
The expected force ``f`` 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 force ``f`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and persistance length ``\\ell_p``.
$(TYPEDSIGNATURES)
"""
function end_to_end_length(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
persistance_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, persistance_length_i, force_i, temperature_i) ->
ccall(
(
:physics_single_chain_wlc_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,
persistance_length_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
persistance_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 number of links ``N_b``, link length ``\\ell_b``, and persistance length ``\\ell_p``.
$(TYPEDSIGNATURES)
"""
function end_to_end_length_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
persistance_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, persistance_length_i, force_i, temperature_i) ->
ccall(
(
:physics_single_chain_wlc_thermodynamics_isotensional_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,
persistance_length_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
persistance_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`` and nondimensional persistance length ``\\zeta``.
$(TYPEDSIGNATURES)
"""
function nondimensional_end_to_end_length(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_persistance_length::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_persistance_length_i, nondimensional_force_i) ->
ccall(
(
:physics_single_chain_wlc_thermodynamics_isotensional_nondimensional_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_persistance_length_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_persistance_length,
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 number of links ``N_b`` and nondimensional persistance length ``\\zeta``.
$(TYPEDSIGNATURES)
"""
function nondimensional_end_to_end_length_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_persistance_length::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_persistance_length_i, nondimensional_force_i) ->
ccall(
(
:physics_single_chain_wlc_thermodynamics_isotensional_nondimensional_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_persistance_length_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_persistance_length,
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 persistance length ``\\ell_p``.
$(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},
persistance_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,
hinge_mass_i,
persistance_length_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_wlc_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,
persistance_length_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
persistance_length,
end_to_end_length,
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 number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and persistance length ``\\ell_p``.
$(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},
persistance_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,
hinge_mass_i,
persistance_length_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isotensional_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,
persistance_length_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
persistance_length,
end_to_end_length,
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 persistance length ``\\ell_p``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
persistance_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,
persistance_length_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_wlc_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,
persistance_length_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
persistance_length,
end_to_end_length,
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 number of links ``N_b`` link length ``\\ell_b``, and persistance length ``\\ell_p``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
persistance_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,
persistance_length_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isotensional_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,
persistance_length_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
persistance_length,
end_to_end_length,
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 persistance length ``\\zeta``.
$(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_persistance_length::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_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_wlc_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_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_persistance_length,
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 force ``\\eta`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and nondimensional persistance length ``\\zeta``.
$(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_persistance_length::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_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isotensional_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_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_persistance_length,
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 force ``\\eta``,
parameterized by the nondimensional persistance length ``\\zeta``.
```
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_persistance_length::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_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isotensional_nondimensional_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
nondimensional_persistance_length,
nondimensional_end_to_end_length_per_link,
)
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 number of links ``N_b`` and nondimensional persistance length ``\\zeta``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_persistance_length::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_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isotensional_nondimensional_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
nondimensional_persistance_length,
nondimensional_end_to_end_length_per_link,
)
end
"""
Initializes and returns an instance of the thermodynamics of the WLC model in the isotensional ensemble.
$(TYPEDSIGNATURES)
"""
function WLC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
persistance_length::Float64,
)
nondimensional_persistance_length = persistance_length / number_of_links / link_length
return WLC(
number_of_links,
link_length,
hinge_mass,
persistance_length,
nondimensional_persistance_length,
Legendre.WLC(number_of_links, link_length, hinge_mass, persistance_length),
(force, temperature) -> end_to_end_length(
number_of_links,
link_length,
persistance_length,
force,
temperature,
),
(force, temperature) -> end_to_end_length_per_link(
number_of_links,
link_length,
persistance_length,
force,
temperature,
),
(nondimensional_force) -> nondimensional_end_to_end_length(
number_of_links,
nondimensional_persistance_length,
nondimensional_force,
),
(nondimensional_force) -> nondimensional_end_to_end_length_per_link(
number_of_links,
nondimensional_persistance_length,
nondimensional_force,
),
(force, temperature) -> gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
persistance_length,
force,
temperature,
),
(force, temperature) -> gibbs_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
persistance_length,
force,
temperature,
),
(force, temperature) -> relative_gibbs_free_energy(
number_of_links,
link_length,
persistance_length,
force,
temperature,
),
(force, temperature) -> relative_gibbs_free_energy_per_link(
number_of_links,
link_length,
persistance_length,
force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
nondimensional_persistance_length,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_gibbs_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
nondimensional_persistance_length,
nondimensional_force,
temperature,
),
(nondimensional_force) -> nondimensional_relative_gibbs_free_energy(
number_of_links,
nondimensional_persistance_length,
nondimensional_force,
),
(nondimensional_force) -> nondimensional_relative_gibbs_free_energy_per_link(
number_of_links,
nondimensional_persistance_length,
nondimensional_force,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 61243 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ZERO, parameters
using Polymers.Physics.SingleChain.Wlc.Thermodynamics.Isotensional: WLC
@testset "physics::single_chain::wlc::thermodynamics::isotensional::test::base::init" begin
@test isa(
WLC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.persistance_length_reference,
),
Any,
)
end
@testset "physics::single_chain::wlc::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 WLC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.persistance_length_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::wlc::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 WLC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.persistance_length_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::wlc::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 WLC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.persistance_length_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::wlc::thermodynamics::isotensional::test::base::persistance_length" begin
for _ = 1:parameters.number_of_loops
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
@test WLC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
persistance_length,
).persistance_length == persistance_length
end
end
@testset "physics::single_chain::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
@test all(
WLC(
number_of_links,
link_length,
hinge_mass,
persistance_length,
).number_of_links == number_of_links &&
WLC(number_of_links, link_length, hinge_mass, persistance_length).link_length ==
link_length &&
WLC(number_of_links, link_length, hinge_mass, persistance_length).hinge_mass ==
hinge_mass &&
WLC(
number_of_links,
link_length,
hinge_mass,
persistance_length,
).persistance_length == persistance_length,
)
end
end
@testset "physics::single_chain::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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 | 17190 | """
The worm-like chain (WLC) 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 WLC model in the isotensional ensemble approximated using a Legendre transformation.
$(FIELDS)
"""
struct WLC
"""
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 persistance length of the chain in units of nm.
"""
persistance_length::Float64
nondimensional_persistance_length::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 persistance length ``\\ell_p``.
```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},
persistance_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,
hinge_mass_i,
persistance_length_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_wlc_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,
persistance_length_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
persistance_length,
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 number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and persistance length ``\\ell_p``.
$(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},
persistance_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,
hinge_mass_i,
persistance_length_i,
force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isotensional_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,
persistance_length_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
persistance_length,
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 persistance length ``\\ell_p``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
persistance_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, persistance_length_i, force_i, temperature_i) ->
ccall(
(
:physics_single_chain_wlc_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,
persistance_length_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
persistance_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 number of links ``N_b``, link length ``\\ell_b``, and persistance length ``\\ell_p``.
$(TYPEDSIGNATURES)
"""
function relative_helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
persistance_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, persistance_length_i, force_i, temperature_i) ->
ccall(
(
:physics_single_chain_wlc_thermodynamics_isotensional_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,
persistance_length_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
persistance_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``, hinge mass ``m``, and nondimensional persistance length ``\\zeta``.
$(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_persistance_length::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_persistance_length_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_wlc_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_persistance_length_i,
nondimensional_force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_persistance_length,
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 number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and nondimensional persistance length ``\\zeta``.
$(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_persistance_length::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_persistance_length_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isotensional_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_persistance_length_i,
nondimensional_force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_persistance_length,
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 persistance length ``\\zeta``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_persistance_length::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_persistance_length_i, nondimensional_force_i) ->
ccall(
(
:physics_single_chain_wlc_thermodynamics_isotensional_legendre_nondimensional_relative_helmholtz_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_persistance_length_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_persistance_length,
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 number of links ``N_b`` and nondimensional persistance length ``\\zeta``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_helmholtz_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_persistance_length::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_persistance_length_i, nondimensional_force_i) ->
ccall(
(
:physics_single_chain_wlc_thermodynamics_isotensional_legendre_nondimensional_relative_helmholtz_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_persistance_length_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_persistance_length,
nondimensional_force,
)
end
"""
Initializes and returns an instance of the thermodynamics of the WLC model in the isotensional ensemble approximated using a Legendre transformation.
$(TYPEDSIGNATURES)
"""
function WLC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
persistance_length::Float64,
)
nondimensional_persistance_length = persistance_length / number_of_links / link_length
return WLC(
number_of_links,
link_length,
hinge_mass,
persistance_length,
nondimensional_persistance_length,
(force, temperature) -> helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
persistance_length,
force,
temperature,
),
(force, temperature) -> helmholtz_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
persistance_length,
force,
temperature,
),
(force, temperature) -> relative_helmholtz_free_energy(
number_of_links,
link_length,
persistance_length,
force,
temperature,
),
(force, temperature) -> relative_helmholtz_free_energy_per_link(
number_of_links,
link_length,
persistance_length,
force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_helmholtz_free_energy(
number_of_links,
link_length,
hinge_mass,
nondimensional_persistance_length,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) ->
nondimensional_helmholtz_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
nondimensional_persistance_length,
nondimensional_force,
temperature,
),
(nondimensional_force) -> nondimensional_relative_helmholtz_free_energy(
number_of_links,
nondimensional_persistance_length,
nondimensional_force,
),
(nondimensional_force) -> nondimensional_relative_helmholtz_free_energy_per_link(
number_of_links,
nondimensional_persistance_length,
nondimensional_force,
),
)
end
end
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | code | 30049 | module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ZERO, parameters
using Polymers.Physics.SingleChain.Wlc.Thermodynamics.Isotensional.Legendre: WLC
@testset "physics::single_chain::wlc::thermodynamics::isotensional::legendre::test::base::init" begin
@test isa(
WLC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.persistance_length_reference,
),
Any,
)
end
@testset "physics::single_chain::wlc::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 WLC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.persistance_length_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::wlc::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 WLC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.persistance_length_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::wlc::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 WLC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.persistance_length_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::wlc::thermodynamics::isotensional::legendre::test::base::persistance_length" begin
for _ = 1:parameters.number_of_loops
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
@test WLC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
persistance_length,
).persistance_length == persistance_length
end
end
@testset "physics::single_chain::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
@test all(
WLC(
number_of_links,
link_length,
hinge_mass,
persistance_length,
).number_of_links == number_of_links &&
WLC(number_of_links, link_length, hinge_mass, persistance_length).link_length ==
link_length &&
WLC(number_of_links, link_length, hinge_mass, persistance_length).hinge_mass ==
hinge_mass &&
WLC(
number_of_links,
link_length,
hinge_mass,
persistance_length,
).persistance_length == persistance_length,
)
end
end
@testset "physics::single_chain::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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::wlc::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())
persistance_length =
parameters.persistance_length_reference +
parameters.persistance_length_scale * (0.5 - rand())
model = WLC(number_of_links, link_length, hinge_mass, persistance_length)
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 | 7881 | using Test
using Polymers
include("../src/physics/single_chain/test.jl")
include("../src/physics/single_chain/ideal/test.jl")
include("../src/physics/single_chain/ideal/thermodynamics/test.jl")
include("../src/physics/single_chain/ideal/thermodynamics/isometric/test.jl")
include("../src/physics/single_chain/ideal/thermodynamics/isotensional/test.jl")
include("../src/physics/single_chain/fjc/test.jl")
include("../src/physics/single_chain/fjc/thermodynamics/test.jl")
include("../src/physics/single_chain/fjc/thermodynamics/isometric/test.jl")
include("../src/physics/single_chain/fjc/thermodynamics/isometric/legendre/test.jl")
include("../src/physics/single_chain/fjc/thermodynamics/isotensional/test.jl")
include("../src/physics/single_chain/fjc/thermodynamics/isotensional/legendre/test.jl")
include("../src/physics/single_chain/fjc/thermodynamics/modified_canonical/test.jl")
include(
"../src/physics/single_chain/fjc/thermodynamics/modified_canonical/asymptotic/test.jl",
)
include(
"../src/physics/single_chain/fjc/thermodynamics/modified_canonical/asymptotic/strong_potential/test.jl",
)
include(
"../src/physics/single_chain/fjc/thermodynamics/modified_canonical/asymptotic/weak_potential/test.jl",
)
include("../src/physics/single_chain/efjc/test.jl")
include("../src/physics/single_chain/efjc/thermodynamics/test.jl")
include("../src/physics/single_chain/efjc/thermodynamics/isometric/test.jl")
include("../src/physics/single_chain/efjc/thermodynamics/isometric/asymptotic/test.jl")
include(
"../src/physics/single_chain/efjc/thermodynamics/isometric/asymptotic/legendre/test.jl",
)
include(
"../src/physics/single_chain/efjc/thermodynamics/isometric/asymptotic/alternative/test.jl",
)
include(
"../src/physics/single_chain/efjc/thermodynamics/isometric/asymptotic/alternative/legendre/test.jl",
)
include(
"../src/physics/single_chain/efjc/thermodynamics/isometric/asymptotic/reduced/test.jl",
)
include(
"../src/physics/single_chain/efjc/thermodynamics/isometric/asymptotic/reduced/legendre/test.jl",
)
include("../src/physics/single_chain/efjc/thermodynamics/isotensional/test.jl")
include("../src/physics/single_chain/efjc/thermodynamics/isotensional/legendre/test.jl")
include("../src/physics/single_chain/efjc/thermodynamics/isotensional/asymptotic/test.jl")
include(
"../src/physics/single_chain/efjc/thermodynamics/isotensional/asymptotic/legendre/test.jl",
)
include(
"../src/physics/single_chain/efjc/thermodynamics/isotensional/asymptotic/alternative/test.jl",
)
include(
"../src/physics/single_chain/efjc/thermodynamics/isotensional/asymptotic/alternative/legendre/test.jl",
)
include(
"../src/physics/single_chain/efjc/thermodynamics/isotensional/asymptotic/reduced/test.jl",
)
include(
"../src/physics/single_chain/efjc/thermodynamics/isotensional/asymptotic/reduced/legendre/test.jl",
)
include("../src/physics/single_chain/swfjc/test.jl")
include("../src/physics/single_chain/swfjc/thermodynamics/test.jl")
include("../src/physics/single_chain/swfjc/thermodynamics/isometric/test.jl")
include("../src/physics/single_chain/swfjc/thermodynamics/isometric/legendre/test.jl")
include("../src/physics/single_chain/swfjc/thermodynamics/isotensional/test.jl")
include("../src/physics/single_chain/swfjc/thermodynamics/isotensional/legendre/test.jl")
include("../src/physics/single_chain/ufjc/test.jl")
include("../src/physics/single_chain/ufjc/lennard_jones/test.jl")
include("../src/physics/single_chain/ufjc/lennard_jones/thermodynamics/test.jl")
include("../src/physics/single_chain/ufjc/lennard_jones/thermodynamics/isometric/test.jl")
include(
"../src/physics/single_chain/ufjc/lennard_jones/thermodynamics/isometric/asymptotic/test.jl",
)
include(
"../src/physics/single_chain/ufjc/lennard_jones/thermodynamics/isometric/asymptotic/legendre/test.jl",
)
include(
"../src/physics/single_chain/ufjc/lennard_jones/thermodynamics/isometric/asymptotic/reduced/test.jl",
)
include(
"../src/physics/single_chain/ufjc/lennard_jones/thermodynamics/isometric/asymptotic/reduced/legendre/test.jl",
)
include(
"../src/physics/single_chain/ufjc/lennard_jones/thermodynamics/isotensional/test.jl",
)
include(
"../src/physics/single_chain/ufjc/lennard_jones/thermodynamics/isotensional/legendre/test.jl",
)
include(
"../src/physics/single_chain/ufjc/lennard_jones/thermodynamics/isotensional/asymptotic/test.jl",
)
include(
"../src/physics/single_chain/ufjc/lennard_jones/thermodynamics/isotensional/asymptotic/legendre/test.jl",
)
include(
"../src/physics/single_chain/ufjc/lennard_jones/thermodynamics/isotensional/asymptotic/reduced/test.jl",
)
include(
"../src/physics/single_chain/ufjc/lennard_jones/thermodynamics/isotensional/asymptotic/reduced/legendre/test.jl",
)
include("../src/physics/single_chain/ufjc/log_squared/test.jl")
include("../src/physics/single_chain/ufjc/log_squared/thermodynamics/test.jl")
include("../src/physics/single_chain/ufjc/log_squared/thermodynamics/isometric/test.jl")
include(
"../src/physics/single_chain/ufjc/log_squared/thermodynamics/isometric/asymptotic/test.jl",
)
include(
"../src/physics/single_chain/ufjc/log_squared/thermodynamics/isometric/asymptotic/legendre/test.jl",
)
include(
"../src/physics/single_chain/ufjc/log_squared/thermodynamics/isometric/asymptotic/reduced/test.jl",
)
include(
"../src/physics/single_chain/ufjc/log_squared/thermodynamics/isometric/asymptotic/reduced/legendre/test.jl",
)
include("../src/physics/single_chain/ufjc/log_squared/thermodynamics/isotensional/test.jl")
include(
"../src/physics/single_chain/ufjc/log_squared/thermodynamics/isotensional/legendre/test.jl",
)
include(
"../src/physics/single_chain/ufjc/log_squared/thermodynamics/isotensional/asymptotic/test.jl",
)
include(
"../src/physics/single_chain/ufjc/log_squared/thermodynamics/isotensional/asymptotic/legendre/test.jl",
)
include(
"../src/physics/single_chain/ufjc/log_squared/thermodynamics/isotensional/asymptotic/reduced/test.jl",
)
include(
"../src/physics/single_chain/ufjc/log_squared/thermodynamics/isotensional/asymptotic/reduced/legendre/test.jl",
)
include("../src/physics/single_chain/ufjc/morse/test.jl")
include("../src/physics/single_chain/ufjc/morse/thermodynamics/test.jl")
include("../src/physics/single_chain/ufjc/morse/thermodynamics/isometric/test.jl")
include(
"../src/physics/single_chain/ufjc/morse/thermodynamics/isometric/asymptotic/test.jl",
)
include(
"../src/physics/single_chain/ufjc/morse/thermodynamics/isometric/asymptotic/legendre/test.jl",
)
include(
"../src/physics/single_chain/ufjc/morse/thermodynamics/isometric/asymptotic/reduced/test.jl",
)
include(
"../src/physics/single_chain/ufjc/morse/thermodynamics/isometric/asymptotic/reduced/legendre/test.jl",
)
include("../src/physics/single_chain/ufjc/morse/thermodynamics/isotensional/test.jl")
include(
"../src/physics/single_chain/ufjc/morse/thermodynamics/isotensional/legendre/test.jl",
)
include(
"../src/physics/single_chain/ufjc/morse/thermodynamics/isotensional/asymptotic/test.jl",
)
include(
"../src/physics/single_chain/ufjc/morse/thermodynamics/isotensional/asymptotic/legendre/test.jl",
)
include(
"../src/physics/single_chain/ufjc/morse/thermodynamics/isotensional/asymptotic/reduced/test.jl",
)
include(
"../src/physics/single_chain/ufjc/morse/thermodynamics/isotensional/asymptotic/reduced/legendre/test.jl",
)
include("../src/physics/single_chain/wlc/test.jl")
include("../src/physics/single_chain/wlc/thermodynamics/test.jl")
include("../src/physics/single_chain/wlc/thermodynamics/isometric/test.jl")
include("../src/physics/single_chain/wlc/thermodynamics/isometric/legendre/test.jl")
include("../src/physics/single_chain/wlc/thermodynamics/isotensional/test.jl")
include("../src/physics/single_chain/wlc/thermodynamics/isotensional/legendre/test.jl")
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 545 | # Code of Conduct
Inspired by [the Sandia values](https://hr.sandia.gov/career/performance-management/sandia-values/), contributors are required to do the following:
- **Act with integrity.** Trust is a fragile thing, so be honest and responsible.
- **Deliver with excellence.** Standards are high for code performance, style, and testing.
- **Respect each other.** Criticize ideas, not people, and treat everyone with innate dignity.
- **Team up for great results.** Combine knowledge and skillsets for the best outcome, and help each other.
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 1881 | # Contributing
These are guidelines for contributing to the Polymers Modeling Library. Contributors can open issues or create pull requests.
## Issues
Contributors can open new issues on the GitHub repository [here](https://github.com/sandialabs/polymers/issues).
An issue can either report an existing bug, or request a new feature.
Contributors should ensure that their candidate issue does not match an existing open issue before opening it.
If a closely-related but incomplete open issue exists, contributors should comment on the existing open issue.
### Bug Reports
A new bug report can be opened [here](https://github.com/sandialabs/polymers/issues/new?template=bug_report.md).
### Feature Requests
A new feature request can be opened [here](https://github.com/sandialabs/polymers/issues/new?template=feature_request.md).
Feature requests that are deemed feasible will be considered by the developers, and could even be addressed by a contributor through a pull request.
Feature requests that are deemed infeasible will likely be denied.
## Pull Requests
Contributors can propose changes to the code in the repository by creating a pull request as follows:
- Fork the base repository [here](https://github.com/sandialabs/Polymers/fork).
- Clone the forked repository, make changes, and push them back to the fork.
- Create a pull request between the base and forked repositories [here](https://github.com/sandialabs/polymers/pulls).
- Wait for the pull request to be either approved or dismissed. Approval and subsequent merging of pull requests is contingent upon:
- The tests are all passing, resulting in a high (desirably, complete) code coverage, and any changes are properly tested.
- The documentation is successfully built, and any changes are properly documented.
- The changes provide an appropriate and substantial improvement to the repository.
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 2614 | # Polymers Modeling Library
[](https://sandialabs.github.io/Polymers)
[](https://mybinder.org/v2/gh/sandialabs/Polymers/main)
The library is implemented entirely in Rust, including the Python API. The Julia API calls the Rust library.
## Python
[](https://polymers.readthedocs.io/en/stable)
[](https://polymers.readthedocs.io/en/latest)
[](https://pypi.org/project/polymers)
The library can be installed as a Python package:
```shell
pip install polymers
```
## Julia
[](https://sandialabs.github.io/Polymers/julia/docs/stable)
[](https://sandialabs.github.io/Polymers/julia/docs/latest)
[](#)
The library can be installed as a Julia package:
```julia
using Pkg
Pkg.add("Polymers")
```
## Rust
[](https://docs.rs/crate/polymers)
[](https://sandialabs.github.io/Polymers/rust/docs/latest)
[](https://crates.io/crates/polymers)
The library can be added to an existing Rust project:
```shell
cargo add polymers
```
## Citation
[](https://doi.org/10.5281/zenodo.7041983)
Michael R. Buche. Polymers Modeling Library. [Zenodo (2023)](https://doi.org/10.5281/zenodo.7041983).
## Copyright
[](https://github.com/sandialabs/polymers/blob/main/LICENSE)
Copyright 2022 National Technology & Engineering Solutions of Sandia, LLC (NTESS). Under the terms of Contract DE-NA0003525 with NTESS, the U.S. Government retains certain rights in this software.
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 152 | # Security Policy
## Reporting a Vulnerability
If there are any vulnerabilities, do not hesitate to report them, but please report them privately. | Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 778 | # Pull Request Template
This template should be used for making any pull requests.
## Goal
Here, describe the goal of the pull request, i.e. what does it seek to address?
Does this pull request fix an existing bug, or create a new feature?
Why are the changes proposed by this pull request necessary?
## Specifics
Here, describe the specific changes to the repository suggested by this pull request.
Which modules/methods/etc. were added or edited, and why?
Have any new dependencies been introduced, and why?
## Verification
Here, describe steps taken to verify that the pull request is up to the standards of the repository.
Were the suggested changes fully documented and tested, and do they match the existing code style?
How exactly was this verification completed?
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 834 | ---
name: Bug report
about: Create a report to help us improve
title: ''
labels: ''
assignees: ''
---
**Describe the bug**
A clear and concise description of what the bug is.
**To Reproduce**
Steps to reproduce the behavior:
1. Go to '...'
2. Click on '....'
3. Scroll down to '....'
4. See error
**Expected behavior**
A clear and concise description of what you expected to happen.
**Screenshots**
If applicable, add screenshots to help explain your problem.
**Desktop (please complete the following information):**
- OS: [e.g. iOS]
- Browser [e.g. chrome, safari]
- Version [e.g. 22]
**Smartphone (please complete the following information):**
- Device: [e.g. iPhone6]
- OS: [e.g. iOS8.1]
- Browser [e.g. stock browser, safari]
- Version [e.g. 22]
**Additional context**
Add any other context about the problem here.
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 595 | ---
name: Feature request
about: Suggest an idea for this project
title: ''
labels: ''
assignees: ''
---
**Is your feature request related to a problem? Please describe.**
A clear and concise description of what the problem is. Ex. I'm always frustrated when [...]
**Describe the solution you'd like**
A clear and concise description of what you want to happen.
**Describe alternatives you've considered**
A clear and concise description of any alternative solutions or features you've considered.
**Additional context**
Add any other context or screenshots about the feature request here.
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 27 | # Index
```@index
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 1329 | # Polymers Modeling Library
[](https://sandialabs.github.io/Polymers/julia/docs/stable)
[](https://sandialabs.github.io/Polymers/julia/docs/latest)
This is the documentation for Julia API, which calls the Rust library.
## Installation
[](#)
The library can be installed as a Julia package:
```julia
using Pkg
Pkg.add("Polymers")
```
## Citation
[](https://doi.org/10.5281/zenodo.7041983)
Michael R. Buche. Polymers Modeling Library. [Zenodo (2023)](https://doi.org/10.5281/zenodo.7041983).
## Copyright
[](https://github.com/sandialabs/polymers/blob/main/LICENSE)
Copyright 2022 National Technology & Engineering Solutions of Sandia, LLC (NTESS). Under the terms of Contract DE-NA0003525 with NTESS, the U.S. Government retains certain rights in this software.
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 140 | # Polymer physics models
* [Single-chain models for polymer physics](single_chain)
```@autodocs
Modules = [Polymers.Physics]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 434 | # Single-chain models for polymer physics
* [Ideal chain model](../ideal)
* [Freely-jointed chain (FJC) model](../fjc)
* [Extensible freely-jointed chain (EFJC) model](../efjc)
* [Square-well freely-jointed chain (SWFJC) model](../swfjc)
* [Arbitrary link potential freely-jointed chain (uFJC) model](../ufjc)
* [Worm-like chain (WLC) model](../wlc)
```@autodocs
Modules = [Polymers.Physics.SingleChain]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 166 | # Extensible freely-jointed chain (EFJC) model
* [EFJC model thermodynamics](../../thermodynamics)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Efjc]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 159 | # Freely-jointed chain (FJC) model
* [FJC model thermodynamics](../../thermodynamics)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Fjc]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 154 | # Ideal chain model
* [Ideal chain model thermodynamics](../../thermodynamics)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Ideal]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 170 | # Square-well freely-jointed chain (SWFJC) model
* [SWFJC model thermodynamics](../../thermodynamics)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Swfjc]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 390 | # Arbitrary link potential freely-jointed chain (uFJC) model
* [Lennard-Jones potential freely-jointed chain (Lennard-Jones-FJC) model](../../lennard_jones)
* [Log-squared potential freely-jointed chain (log-squared-FJC) model](../../log_squared)
* [Morse potential freely-jointed chain (Morse-FJC) model](../../morse)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Ufjc]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 154 | # Worm-like chain (WLC) model
* [WLC model thermodynamics](../../thermodynamics)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Wlc]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 250 | # EFJC model thermodynamics
* [EFJC model thermodynamics (isometric)](../../../isometric)
* [EFJC model thermodynamics (isotensional)](../../../isotensional)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Efjc.Thermodynamics]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 212 | # EFJC model thermodynamics (isometric)
* [EFJC model thermodynamics (isometric/legendre)](../../../../legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Efjc.Thermodynamics.Isometric]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 304 | # EFJC model thermodynamics (isotensional)
* [EFJC model thermodynamics (isotensional/asymptotic)](../../../../asymptotic)
* [EFJC model thermodynamics (isotensional/legendre)](../../../../legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Efjc.Thermodynamics.Isotensional]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 432 | # EFJC model thermodynamics (isometric/asymptotic)
* [EFJC model thermodynamics (isometric/asymptotic/alternative)](../../../../../alternative)
* [EFJC model thermodynamics (isometric/asymptotic/reduced)](../../../../../reduced)
* [EFJC model thermodynamics (isometric/asymptotic/legendre)](../../../../../legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Efjc.Thermodynamics.Isometric.Asymptotic]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 287 | # EFJC model thermodynamics (isometric/asymptotic/alternative)
* [EFJC model thermodynamics (isometric/asymptotic/alternative/legendre)](../../../../../../legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Efjc.Thermodynamics.Isometric.Asymptotic.Alternative]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 169 | # EFJC model thermodynamics (isometric/asymptotic/legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Efjc.Thermodynamics.Isometric.Asymptotic.Legendre]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 275 | # EFJC model thermodynamics (isometric/asymptotic/reduced)
* [EFJC model thermodynamics (isometric/asymptotic/reduced/legendre)](../../../../../../legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Efjc.Thermodynamics.Isometric.Asymptotic.Reduced]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 193 | # EFJC model thermodynamics (isometric/asymptotic/alternative/legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Efjc.Thermodynamics.Isometric.Asymptotic.Alternative.Legendre]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 185 | # EFJC model thermodynamics (isometric/asymptotic/reduced/legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Efjc.Thermodynamics.Isometric.Asymptotic.Reduced.Legendre]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 447 | # EFJC model thermodynamics (isotensional/asymptotic)
* [EFJC model thermodynamics (isotensional/asymptotic/alternative)](../../../../../alternative)
* [EFJC model thermodynamics (isotensional/asymptotic/reduced)](../../../../../reduced)
* [EFJC model thermodynamics (isotensional/asymptotic/legendre)](../../../../../legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Efjc.Thermodynamics.Isotensional.Asymptotic]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 153 | # EFJC model thermodynamics (isotensional/legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Efjc.Thermodynamics.Isotensional.Legendre]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 296 | # EFJC model thermodynamics (isotensional/asymptotic/alternative)
* [EFJC model thermodynamics (isotensional/asymptotic/alternative/legendre)](../../../../../../legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Efjc.Thermodynamics.Isotensional.Asymptotic.Alternative]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 175 | # EFJC model thermodynamics (isotensional/asymptotic/legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Efjc.Thermodynamics.Isotensional.Asymptotic.Legendre]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 284 | # EFJC model thermodynamics (isotensional/asymptotic/reduced)
* [EFJC model thermodynamics (isotensional/asymptotic/reduced/legendre)](../../../../../../legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Efjc.Thermodynamics.Isotensional.Asymptotic.Reduced]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 199 | # EFJC model thermodynamics (isotensional/asymptotic/alternative/legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Efjc.Thermodynamics.Isotensional.Asymptotic.Alternative.Legendre]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 191 | # EFJC model thermodynamics (isotensional/asymptotic/reduced/legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Efjc.Thermodynamics.Isotensional.Asymptotic.Reduced.Legendre]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 328 | # FJC model thermodynamics
* [FJC model thermodynamics (isometric)](../../../isometric)
* [FJC model thermodynamics (isotensional)](../../../isotensional)
* [FJC model thermodynamics (modified canonical)](../../../modified_canonical)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Fjc.Thermodynamics]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 209 | # FJC model thermodynamics (isometric)
* [FJC model thermodynamics (isometric/legendre)](../../../../legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Fjc.Thermodynamics.Isometric]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 218 | # FJC model thermodynamics (isotensional)
* [FJC model thermodynamics (isotensional/legendre)](../../../../legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Fjc.Thermodynamics.Isotensional]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 239 | # FJC model thermodynamics (modified canonical)
* [FJC model thermodynamics (modified canonical/asymptotic)](../../../../asymptotic)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Fjc.Thermodynamics.ModifiedCanonical]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 150 | # FJC model thermodynamics (isometric/legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Fjc.Thermodynamics.Isometric.Legendre]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 156 | # FJC model thermodynamics (isotensional/legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Fjc.Thermodynamics.Isotensional.Legendre]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 397 | # FJC model thermodynamics (modified canonical/asymptotic)
* [FJC model thermodynamics (modified canonical/asymptotic/strong potential)](../../../../../strong_potential)
* [FJC model thermodynamics (modified canonical/asymptotic/weak potential)](../../../../../weak_potential)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Fjc.Thermodynamics.ModifiedCanonical.Asymptotic]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 204 | # FJC model thermodynamics (modified canonical/asymptotic/strong potential)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Fjc.Thermodynamics.ModifiedCanonical.Asymptotic.StrongPotential]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 200 | # FJC model thermodynamics (modified canonical/asymptotic/weak potential)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Fjc.Thermodynamics.ModifiedCanonical.Asymptotic.WeakPotential]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 272 | # Ideal chain model thermodynamics
* [Ideal chain model thermodynamics (isometric)](../../../isometric)
* [Ideal chain model thermodynamics (isotensional)](../../../isotensional)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Ideal.Thermodynamics]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 142 | # Ideal chain model thermodynamics (isometric)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Ideal.Thermodynamics.Isometric]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 148 | # Ideal chain model thermodynamics (isotensional)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Ideal.Thermodynamics.Isotensional]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 254 | # SWFJC model thermodynamics
* [SWFJC model thermodynamics (isometric)](../../../isometric)
* [SWFJC model thermodynamics (isotensional)](../../../isotensional)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Swfjc.Thermodynamics]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 215 | # SWFJC model thermodynamics (isometric)
* [SWFJC model thermodynamics (isometric/legendre)](../../../../legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Swfjc.Thermodynamics.Isometric]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 224 | # SWFJC model thermodynamics (isotensional)
* [SWFJC model thermodynamics (isotensional/legendre)](../../../../legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Swfjc.Thermodynamics.Isotensional]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 154 | # SWFJC model thermodynamics (isometric/legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Swfjc.Thermodynamics.Isometric.Legendre]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 160 | # SWFJC model thermodynamics (isotensional/legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Swfjc.Thermodynamics.Isotensional.Legendre]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 228 | # Lennard-Jones potential freely-jointed chain (Lennard-Jones-FJC) model
* [Lennard-Jones-FJC model thermodynamics](../../../thermodynamics)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Ufjc.LennardJones]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 220 | # Log-squared potential freely-jointed chain (log-squared-FJC) model
* [Log-squared-FJC model thermodynamics](../../../thermodynamics)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Ufjc.LogSquared]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 197 | # Morse potential freely-jointed chain (Morse-FJC) model
* [Morse-FJC model thermodynamics](../../../thermodynamics)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Ufjc.Morse]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 308 | # Lennard-Jones-FJC model thermodynamics
* [Lennard-Jones-FJC model thermodynamics (isometric)](../../../../isometric)
* [Lennard-Jones-FJC model thermodynamics (isotensional)](../../../../isotensional)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Ufjc.LennardJones.Thermodynamics]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 258 | # Lennard-Jones-FJC model thermodynamics (isometric)
* [Lennard-Jones-FJC model thermodynamics (isometric/asymptotic)](../../../../../asymptotic)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Ufjc.LennardJones.Thermodynamics.Isometric]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 362 | # Lennard-Jones-FJC model thermodynamics (isotensional)
* [Lennard-Jones-FJC model thermodynamics (isotensional/asymptotic)](../../../../../asymptotic)
* [Lennard-Jones-FJC model thermodynamics (isotensional/legendre)](../../../../../legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Ufjc.LennardJones.Thermodynamics.Isotensional]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 394 | # Lennard-Jones-FJC model thermodynamics (isometric/asymptotic)
* [Lennard-Jones-FJC model thermodynamics (isometric/asymptotic/reduced)](../../../../../../reduced)
* [Lennard-Jones-FJC model thermodynamics (isometric/asymptotic/legendre)](../../../../../../legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Ufjc.LennardJones.Thermodynamics.Isometric.Asymptotic]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 195 | # Lennard-Jones-FJC model thermodynamics (isometric/asymptotic/legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Ufjc.LennardJones.Thermodynamics.Isometric.Asymptotic.Legendre]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 317 | # Lennard-Jones-FJC model thermodynamics (isometric/asymptotic/reduced)
* [Lennard-Jones-FJC model thermodynamics (isometric/asymptotic/reduced/legendre)](../../../../../../../legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Ufjc.LennardJones.Thermodynamics.Isometric.Asymptotic.Reduced]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 211 | # Lennard-Jones-FJC model thermodynamics (isometric/asymptotic/reduced/legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Ufjc.LennardJones.Thermodynamics.Isometric.Asymptotic.Reduced.Legendre]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 406 | # Lennard-Jones-FJC model thermodynamics (isotensional/asymptotic)
* [Lennard-Jones-FJC model thermodynamics (isotensional/asymptotic/reduced)](../../../../../../reduced)
* [Lennard-Jones-FJC model thermodynamics (isotensional/asymptotic/legendre)](../../../../../../legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Ufjc.LennardJones.Thermodynamics.Isotensional.Asymptotic]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 179 | # Lennard-Jones-FJC model thermodynamics (isotensional/legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Ufjc.LennardJones.Thermodynamics.Isotensional.Legendre]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 201 | # Lennard-Jones-FJC model thermodynamics (isotensional/asymptotic/legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Ufjc.LennardJones.Thermodynamics.Isotensional.Asymptotic.Legendre]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
|
[
"BSD-3-Clause"
] | 0.3.7 | 5c9185bac8d9a5f2d96a37387c88fa5cf535e1be | docs | 326 | # Lennard-Jones-FJC model thermodynamics (isotensional/asymptotic/reduced)
* [Lennard-Jones-FJC model thermodynamics (isotensional/asymptotic/reduced/legendre)](../../../../../../../legendre)
```@autodocs
Modules = [Polymers.Physics.SingleChain.Ufjc.LennardJones.Thermodynamics.Isotensional.Asymptotic.Reduced]
```
| Polymers | https://github.com/sandialabs/Polymers.git |
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