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https://par.nsf.gov/biblio/10362447-black-holegalaxy-scaling-relations-fire-importance-black-hole-location-mergers
|
Black hole–galaxy scaling relations in FIRE: the importance of black hole location and mergers
ABSTRACT
The concurrent growth of supermassive black holes (SMBHs) and their host galaxies remains to be fully explored, especially at high redshift. While often understood as a consequence of self-regulation via AGN feedback, it can also be explained by alternative SMBH accretion models. Here, we expand on previous work by studying the growth of SMBHs with the help of a large suite of cosmological zoom-in simulations (MassiveFIRE) that are part of the Feedback in Realistic Environments (FIRE) project. The growth of SMBHs is modelled in post-processing with different black hole accretion models, placements, and merger treatments, and validated by comparing to on-the-fly calculations. Scaling relations predicted by the gravitational torque-driven accretion (GTDA) model agree with observations at low redshift without the need for AGN feedback, in contrast to models in which the accretion rate depends strongly on SMBH mass. At high redshift, we find deviations from the local scaling relations in line with previous theoretical results. In particular, SMBHs are undermassive, presumably due to stellar feedback, but start to grow efficiently once their host galaxies reach M* ∼ 1010M⊙. We analyse and explain these findings in the context of a simple analytic model. Finally, we show that the predicted scaling more »
Authors:
; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10362447
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
511
Issue:
1
Page Range or eLocation-ID:
p. 506-535
ISSN:
0035-8711
Publisher:
Oxford University Press
1. ABSTRACT Observations of massive galaxies at low redshift have revealed approximately linear scaling relations between the mass of a supermassive black hole (SMBH) and properties of its host galaxy. How these scaling relations evolve with redshift and whether they extend to lower-mass galaxies, however, remain open questions. Recent galaxy formation simulations predict a delayed, or ‘two-phase,’ growth of SMBHs: slow, highly intermittent BH growth due to repeated gas ejection by stellar feedback in low-mass galaxies, followed by more sustained gas accretion that eventually brings BHs on to the local scaling relations. The predicted two-phase growth implies a steep increase, or ‘kink,’ in BH-galaxy scaling relations at a stellar mass $\rm {M}_{*}\sim 5\times 10^{10}$ M⊙. We develop a parametric, semi-analytic model to compare different SMBH growth models against observations of the quasar luminosity function (QLF) at z ∼ 0.5−4. We compare models in which the relation between SMBH mass and galaxy mass is purely linear versus two-phase models. The models are anchored to the observed galaxy stellar mass function, and the BH mass functions at different redshifts are consistently connected by the accretion rates contributing to the QLF. The best fits suggest that two-phase evolution is significantly preferred by the QLFmore »
Several recent simulations of galaxy formation predict two main phases of supermassive black hole (BH) accretion: an early, highly intermittent phase (during which BHs are undermassive relative to local scaling relations), followed by a phase of accelerated growth. We investigate physical factors that drive the transition in BH accretion in cosmological zoom-in simulations from the FIRE project, ranging from dwarf galaxies to galaxies sufficiently massive to host luminous quasars. The simulations model multichannel stellar feedback, but neglect AGN feedback. We show that multiple physical properties, including halo mass, galaxy stellar mass, and depth of the central gravitational potential correlate with accelerated BH fuelling: constant thresholds in these properties are typically crossed within ∼0.1 Hubble time of accelerated BH fuelling. Black hole masses increase sharply when the stellar surface density in the inner 1 kpc crosses a threshold $\Sigma^\star _{1\,\rm kpc}\approx 10^{9.5} \, {\rm M_{\odot }}\,{\rm kpc}^{-2}$, a characteristic value above which gravity prevents stellar feedback from ejecting gas, and similar to the value above which galaxies are observed to quench. We further show that accelerated BH growth correlates with the emergence of long-lived thin gas discs, as well as with virialization of the inner circumgalactic medium. The halo mass Mhalomore »
5. ABSTRACT Supermassive black holes (SMBHs) that reside at the centres of galaxies can inject vast amounts of energy into the surrounding gas and are thought to be a viable mechanism to quench star formation in massive galaxies. Here, we study the $10^{9-12.5}\, \mathrm{M_\odot }$ stellar mass central galaxy population of the IllustrisTNG simulation, specifically the TNG100 and TNG300 volumes at z = 0, and show how the three components – SMBH, galaxy, and circumgalactic medium (CGM) – are interconnected in their evolution. We find that gas entropy is a sensitive diagnostic of feedback injection. In particular, we demonstrate how the onset of the low-accretion black hole (BH) feedback mode, realized in the IllustrisTNG model as a kinetic, BH-driven wind, leads not only to star formation quenching at stellar masses $\gtrsim 10^{10.5}\, \mathrm{M_\odot }$ but also to a change in thermodynamic properties of the (non-star-forming) gas, both within the galaxy and beyond. The IllustrisTNG kinetic feedback from SMBHs increases the average gas entropy, within the galaxy and in the CGM, lengthening typical gas cooling times from $10\!-\!100\, \mathrm{Myr}$ to $1\!-\!10\, \mathrm{Gyr}$, effectively ceasing ongoing star formation and inhibiting radiative cooling and future gas accretion. In practice, the same active galactic nucleusmore »
| 2023-02-03T05:11:28 |
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|
https://lammps.sandia.gov/doc/angle_table.html
|
# angle_style table/omp command
## Syntax
angle_style table style N
• style = linear or spline = method of interpolation
• N = use N values in table
## Examples
angle_style table linear 1000
angle_coeff 3 file.table ENTRY1
## Description
Style table creates interpolation tables of length N from angle potential and derivative values listed in a file(s) as a function of angle The files are read by the angle_coeff command.
The interpolation tables are created by fitting cubic splines to the file values and interpolating energy and derivative values at each of N angles. During a simulation, these tables are used to interpolate energy and force values on individual atoms as needed. The interpolation is done in one of 2 styles: linear or spline.
For the linear style, the angle is used to find 2 surrounding table values from which an energy or its derivative is computed by linear interpolation.
For the spline style, a cubic spline coefficients are computed and stored at each of the N values in the table. The angle is used to find the appropriate set of coefficients which are used to evaluate a cubic polynomial which computes the energy or derivative.
The following coefficients must be defined for each angle type via the angle_coeff command as in the example above.
• filename
• keyword
The filename specifies a file containing tabulated energy and derivative values. The keyword specifies a section of the file. The format of this file is described below.
The format of a tabulated file is as follows (without the parenthesized comments):
# Angle potential for harmonic (one or more comment or blank lines)
HAM (keyword is the first text on line)
N 181 FP 0 0 EQ 90.0 (N, FP, EQ parameters)
(blank line)
N 181 FP 0 0 (N, FP parameters)
1 0.0 200.5 2.5 (index, angle, energy, derivative)
2 1.0 198.0 2.5
...
181 180.0 0.0 0.0
A section begins with a non-blank line whose 1st character is not a “#”; blank lines or lines starting with “#” can be used as comments between sections. The first line begins with a keyword which identifies the section. The line can contain additional text, but the initial text must match the argument specified in the angle_coeff command. The next line lists (in any order) one or more parameters for the table. Each parameter is a keyword followed by one or more numeric values.
The parameter “N” is required and its value is the number of table entries that follow. Note that this may be different than the N specified in the angle_style table command. Let Ntable = N in the angle_style command, and Nfile = “N” in the tabulated file. What LAMMPS does is a preliminary interpolation by creating splines using the Nfile tabulated values as nodal points. It uses these to interpolate as needed to generate energy and derivative values at Ntable different points. The resulting tables of length Ntable are then used as described above, when computing energy and force for individual angles and their atoms. This means that if you want the interpolation tables of length Ntable to match exactly what is in the tabulated file (with effectively no preliminary interpolation), you should set Ntable = Nfile.
The “FP” parameter is optional. If used, it is followed by two values fplo and fphi, which are the 2nd derivatives at the innermost and outermost angle settings. These values are needed by the spline construction routines. If not specified by the “FP” parameter, they are estimated (less accurately) by the first two and last two derivative values in the table.
The “EQ” parameter is also optional. If used, it is followed by a the equilibrium angle value, which is used, for example, by the fix shake command. If not used, the equilibrium angle is set to 180.0.
Following a blank line, the next N lines list the tabulated values. On each line, the 1st value is the index from 1 to N, the 2nd value is the angle value (in degrees), the 3rd value is the energy (in energy units), and the 4th is -dE/d(theta) (also in energy units). The 3rd term is the energy of the 3-atom configuration for the specified angle. The last term is the derivative of the energy with respect to the angle (in degrees, not radians). Thus the units of the last term are still energy, not force. The angle values must increase from one line to the next. The angle values must also begin with 0.0 and end with 180.0, i.e. span the full range of possible angles.
Note that one file can contain many sections, each with a tabulated potential. LAMMPS reads the file section by section until it finds one that matches the specified keyword.
Styles with a gpu, intel, kk, omp, or opt suffix are functionally the same as the corresponding style without the suffix. They have been optimized to run faster, depending on your available hardware, as discussed on the Speed packages doc page. The accelerated styles take the same arguments and should produce the same results, except for round-off and precision issues.
These accelerated styles are part of the GPU, USER-INTEL, KOKKOS, USER-OMP and OPT packages, respectively. They are only enabled if LAMMPS was built with those packages. See the Build package doc page for more info.
You can specify the accelerated styles explicitly in your input script by including their suffix, or you can use the -suffix command-line switch when you invoke LAMMPS, or you can use the suffix command in your input script.
See the Speed packages doc page for more instructions on how to use the accelerated styles effectively.
Restart info:
This angle style writes the settings for the “angle_style table” command to binary restart files, so a angle_style command does not need to specified in an input script that reads a restart file. However, the coefficient information is not stored in the restart file, since it is tabulated in the potential files. Thus, angle_coeff commands do need to be specified in the restart input script.
## Restrictions
This angle style can only be used if LAMMPS was built with the MOLECULE package. See the Build package doc page for more info.
| 2020-06-01T16:38:37 |
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|
http://theory.fnal.gov/events/event/theory-seminar-title-tbd/
|
## The half-life of a free neutron from Lattice QCD
• Nov. 28, 2017, 2:30 pm
• Wilson Hall, Curia II
• Jason Chang, LBNL
• Ciaran
• Inspires
The axial coupling of the nucleon, $g_A$, is a fundamental property of neutrons and protons. The long-range nuclear force between nucleons and the $\beta$-decay rate of a free neutron both depend on $g_A^2$. This coupling therefore underpins all of low-energy nuclear physics, controlling, for example, the primordial composition of the universe. While the value of $g_A$ is, in principle, determined by the fundamental theory of nuclear strong interactions, Quantum Chromodynamics (QCD), it is daunting to compute, as QCD is non-perturbative and has evaded an analytic solution. Lattice QCD provides a rigorous, non-perturbative definition of the theory through a discretised formulation which can be numerically implemented.
Using an innovative computational method, we resolve the two outstanding challenges identified by the lattice QCD community for determining $g_A$: we demonstrably control excited state lattice artifacts and are able to utilise exponentially more precise numerical data resulting in the determination $g_A^{QCD} = 1.275 \pm 0.012$, compatible with the experimentally measured value and with unprecedented precision of $0.95\%$. This milestone calculation signals a new era of precision lattice QCD applications to high-impact experimental searches for physics beyond the Standard Model in nuclear environments.
| 2018-07-16T10:57:42 |
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|
https://www.nist.gov/publications/compressed-liquid-densities-three-reference-fuels-combustion-testing
|
# Compressed-Liquid Densities of Three Reference Fuels for Combustion Testing
Published: September 19, 2016
### Author(s)
Stephanie L. Outcalt
### Abstract
Compressed-liquid densities of three aviation fuels have been measured with a vibrating-tube densimeter. The measurements were made from 270 K to 470 K, and 0.5 MPa to 45 MPa and have an overall combined uncertainty of 0.81 kg.m-3. The data from each of the samples have been correlated with a modified Tait equation and the parameters are given for each. Compressed- liquid densities of the fuels reported herein are compared with previously measured densities of a Jet-A and correlations for JP-5 and JP-8.
Citation: Energy and Fuels
Pub Type: Journals
| 2019-11-15T05:21:49 |
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|
https://pos.sissa.it/314/316
|
Volume 314 - The European Physical Society Conference on High Energy Physics (EPS-HEP2017) - Higgs and New Physics (Parallel Session). Conveners: Andre David; Marie-Helene Genest; Giuliano Panico. Scientific Secretary: Roberto Rossin.
Probing Chirality of Top-Higgs FCNC Couplings at Linear Colliders
B. Melic,* M. Patra
*corresponding author
Full text: pdf
Pre-published on: 2017 November 07
Published on: 2018 March 20
Abstract
We study the nature of the top-Higgs flavor changing neutral current (FCNC) couplings in the
$t\bar t$ production at polarized linear colliders. We show how the polarized linear colliders can be
used to determine the chirality of the FCNC coupling by using the angular distributions of the top
decay products and by examining relevant asymmetries along with the top spin polarizations and
correlations. We obtain a limit on the couplings and find the 3σ upper bound on BR(t → qH) <
8.84×10−4 a%t √s = 500 GeV and L = 500 fb−1.
DOI: https://doi.org/10.22323/1.314.0316
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
| 2020-01-20T11:55:47 |
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|
https://control.com/textbook/electric-power-measurement-and-control/instantaneous-and-time-overcurrent-5051-protection/
|
# Instantaneous and Time-overcurrent (50/51) Protection
## Chapter 25 - Electric Power Measurement and Control Systems
Perhaps the most basic and necessary protective relay function is overcurrent: commanding a circuit breaker to trip when the line current becomes excessive. The purpose of overcurrent protection is to guard against power distribution equipment damage, due to the fact that excessive current in a power system dissipates excessive heat in the metal conductors comprising that system. Overcurrent protection is also applied to machines such as motors and generators for the exact same reason: electric current dissipates heat in the windings’ resistance ($$P = I^2 R$$), and excessive heat will damage those winding conductors.
Instantaneous overcurrent protection is where a protective relay initiates a breaker trip based on current exceeding a pre-programmed “pickup” value for any length of time. This is the simplest form of overcurrent protection, both in concept and in implementation (relay design). In small, self-tripping circuit breakers, this type of protection is best modeled by “magnetic” breakers where the tripping mechanism is actuated by the magnetic field strength of the line conductors: any amount of current greater than the tripping threshold will cause the mechanism to unlatch and open the breaker. In protective relay-based systems, the instantaneous overcurrent protection function is designated by the ANSI/IEEE number code 50.
Time overcurrent protection is where a protective relay initiates a breaker trip based on the combination of overcurrent magnitude and overcurrent duration, the relay tripping sooner with greater current magnitude. This is a more sophisticated form of overcurrent protection than instantaneous, expressed as a “time curve” relating overcurrent magnitude to trip time. In small, self-tripping circuit breakers, this type of protection is best modeled by “thermal” breakers where the tripping mechanism is actuated by the force of a bimetallic strip heated by line current: excessive current heats the metal strip, which then forces the mechanism to unlatch and open the breaker. In protective relay-based systems, the time overcurrent protection function is designated by the ANSI/IEEE number code 51. Time overcurrent protection allows for significant overcurrent magnitudes, so long as these overcurrent events are brief enough that the power equipment avoids heat damage.
Electromechanical 50 (instantaneous overcurrent) relays are models of simplicity, consisting of nothing more than a coil817, armature, and contact assembly (a “relay” in the general electrical/electronic sense of the word). Spring tension holds the trip contacts open, but if the magnetic field developed by the CT secondary current becomes strong enough to overcome the spring’s tension, the contacts close, commanding the circuit breaker to trip:
The protective relay circuit in the above diagram is for one phase of the three-phase power system only. In practice, three different protective relay circuits (three CTs, and three 50 relays with their trip contacts wired in parallel) would be connected together to the circuit breaker’s trip coil, so that the breaker will trip if any of the 50 relays detect an instantaneous overcurrent condition. The monitoring of all three line currents is necessary because power line faults are usually unbalanced: one line will see a much greater share of the fault current than the other lines. A single 50 relay sensing current on a single line would not provide adequate instantaneous overcurrent protection for all three lines.
The amount of CT secondary current necessary to activate the 50 relay is called the pickup current. Its value may be varied by adjusting a movable magnetic pole inside the core of the relay. Calibration of an instantaneous overcurrent (50) relay consists simply of verifying that the unit “picks up” within a reasonably short amount of time if ever the current magnitude exceeds the prescribed pickup value.
Electromechanical 51 (time overcurrent) relays are more complicated in design, using a rotating metal “induction disk” to physically time the overcurrent event, and trip the circuit breaker only if the overcurrent condition persists long enough. A photograph of a General Electric time-overcurrent induction-disk relay appears here:
The round disk you see in the photograph receives a torque from an electromagnet coil assembly acting like the stator coils of an induction motor: alternating current passing through these coils cause alternating magnetic fields to develop through the rear section of the disk, inducing currents in the aluminum disk, generating a “motor” torque on the disk to rotate it clockwise (as seen from the vantage point of the camera in the above photo). A spiral spring applies a counter-clockwise restraining torque to the disk’s shaft. The pickup value for the induction disk (i.e. the minimum amount of CT current necessary to overcome the spring’s torque and begin to rotate the disk) is established by the spring tension and the stator coil field strength. If the CT current exceeds the pickup value for a long enough time, the disk rotates until it closes a normally-open contact to send 125 VDC power to the circuit breaker’s trip coil.
A silver-colored permanent magnet assembly at the front of the disk provides a consistent “drag” force opposing disk rotation. As the aluminum disk rotates through the permanent magnet’s field, eddy currents induced in the disk set up their own magnetic poles to oppose the disk’s motion (Lenz’s Law). The effect is akin to having the disk rotate through a viscous liquid, and it is this dynamic retarding force that provides a repeatable, inverse time delay.
A set of three photographs show the motion of a peg mounted on the induction disk as it approaches the stationary trip contact. From left to right we see the disk in the resting position, partially rotated, and fully rotated:
The mechanical force actuating the time-overcurrent contact is not nearly as strong as the force actuating the instantaneous overcurrent contact. The peg may only lightly touch the stationary contact when it reaches its final position, failing to provide a secure and lasting electrical contact when needed. For this reason, a seal-in relay actuated by current in the 125 VDC trip circuit is provided to maintain firm electrical contact closure in parallel with the rotating peg contact. This “seal-in” contact ensures a reliable circuit breaker trip even if the peg momentarily brushes or bounces against the stationary contact. The parallel seal-in contact also helps reduce arcing at the peg’s contact by carrying most of the trip coil current.
A simplified diagram of an induction disk time-overcurrent relay is shown in the following diagram, for one phase of the three-phase power system only. In practice, three different protective relay circuits (three CTs, and three 51 relays with their trip contacts wired in parallel) would be connected together to the circuit breaker’s trip coil, so that the breaker will trip if any of the 51 relays detect a timed overcurrent condition:
The seal-in unit is shown as an electromechanical relay connected with its contact in parallel with the induction disk contact, but with its actuating coil connected in series to sense the current in the 125 VDC trip circuit. Once the induction disk contact closes to initiate current in the DC trip circuit, even momentarily, the seal-in coil will energize which closes the seal-in contact and ensures the continuation of DC trip current to the circuit breaker’s trip coil. The relay’s seal-in function will subsequently maintain the trip command until some external contact opens to break the trip circuit, usually an auxiliary contact within the circuit breaker itself.
Calibration of a time overcurrent (51) relay consists first of verifying that the unit “picks up” (begins to time) if ever the current magnitude exceeds the prescribed pickup value. In electromagnetic relays such as the General Electric model showcased here, this setting may be coarsely adjusted by connecting a movable wire to one of several taps on a transformer coil inside the relay, varying the ratio of CT current sent to the induction disk stator coils. Each tap is labeled with the number of whole amperes (AC) delivered by the secondary winding of the CT required for relay pick-up (e.g. a tap value of “5” means that approximately 5 amps of CT secondary current is required for induction disk pickup). A fine adjustment is provided in the form of a variable resistor in series with the stator coils.
A photograph of the tap wire setting (coarse pickup adjustment) and resistor (fine pickup adjustment) are shown here. The tap in this first photograph happens to be set at the 4 amp position:
Proper setting of the pickup tap value is determined by the maximum continuous current rating of the system being protected and the ratio of the current transformer (CT) used to sense that current.
After the proper pickup value has been set, the time value is established by rotating a small wheel called the time dial located above the induction disk. This wheel functions as an adjustable stop for the induction disk’s motion, positioning the disk closer to or farther away from the trip contact in its resting condition:
The amount of disk rotation necessary to close the trip contact may be set by adjusting the position of this time dial: a low number on the time dial (e.g. 1) means the disk need only rotate a small amount to close the contact; a high number on the time dial (e.g. 10) sets the resting position farther away from contact, so that the disk must rotate farther to trip. These time dial values are linear multipliers: a time dial setting of 10, for example, exhibits twice the time to trip than a setting of 5, for any given overload condition.
Calibration of the time-overcurrent protective function must be performed at multiple values of current exceeding the pickup value, in order to ensure the relay trips within the right amount of time for those current values. Like process instruments which are often calibrated at five points along their measurement range, time-overcurrent relays must also be checked at multiple points along their prescribed “curve” in order to ensure the relay is performing the way it should.
Time overcurrent relays exhibit different “curves” relating trip time to multiples of pickup current. All 51 relays are inverse in that the amount of time to trip varies inversely with overcurrent magnitude: the greater the sensed current, the less time to trip. However, the function of trip time versus overcurrent magnitude is a curve, and several different curve shapes are available for United States applications:
• Moderately inverse
• Inverse
• Very inverse
• Extremely inverse
• Short-time inverse
Time curves standardized by the Swiss standards agency IEC (International Electrotechnical Commission) include:
• Standard inverse
• Very inverse
• Extremely inverse
• Long-time inverse
• Short-time inverse
The purpose for having different curves in time-overcurrent relays is related to a concept called coordination, where the 51 relay is just one of multiple overcurrent protection devices in a power system. Other overcurrent protection devices include fuses and additional 51 relays at different locations along the same line. Ideally, only the device closest to the fault will trip, allowing power to be maintained at all “upstream” locations. This means we want overcurrent protection devices at the remote end(s) of a power system to be more sensitive and to trip faster than devices closer to the source, where a trip would mean an interruption of power to a greater number of loads.
Legacy electromechanical time-overcurrent (51) relays implemented these different inverse curve functions by using induction disks with different “cam” shapes. Modern microprocessor-based 51 relays contain multiple curve functions as mathematical formulae stored within read-only memory (ROM), and as such may be programmed to implement any curve desired. It is an amusing anachronism that even in digital 51 relays containing no electromagnets or induction disks, you will find parameters labeled “pickup” and “time dial” in honor of legacy electromechanical relay behavior.
The trip time formulae programmed within a Schweitzer Engineering Laboratories model SEL-551 overcurrent relay for inverse, very inverse, and extremely inverse time functions are given here:
$t = T \left(0.18 + {5.95 \over {M^2 - 1}} \right) \hskip 30pt \hbox{Inverse curve}$
$t = T \left(0.0963 + {3.88 \over {M^2 - 1}} \right) \hskip 30pt \hbox{Very inverse curve}$
$t = T \left(0.0352 + {5.67 \over {M^2 - 1}} \right) \hskip 30pt \hbox{Extremely inverse curve}$
Where,
$$t$$ = Trip time (seconds)
$$T$$ = Time Dial setting (typically 0.5 to 15)
$$M$$ = Multiples of pickup current (e.g. if $$I_{pickup}$$ = 4.5 amps, a 9.0 amp signal would be $$M = 2$$)
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| 2021-04-23T11:57:31 |
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https://gea.esac.esa.int/archive/documentation/GDR3/Gaia_archive/chap_datamodel/sec_dm_astrophysical_parameter_tables/ssec_dm_astrophysical_parameters.html
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# 20.2.1 astrophysical_parameters
This is the main table containing the 1D astrophysical parameters produced by the Apsis processing chain developed in Gaia DPAC CU8 (see Chapter 11). Additional parameters can be found in table astrophysical_parameters_supp.
Columns description:
solution_id : Solution Identifier (long)
All Gaia data processed by the Data Processing and Analysis Consortium comes tagged with a solution identifier. This is a numeric field attached to each table row that can be used to unequivocally identify the version of all the subsystems that were used in the generation of the data as well as the input data used. It is mainly for internal DPAC use but is included in the published data releases to enable end users to examine the provenance of processed data products. To decode a given solution ID visit https://gaia.esac.esa.int/decoder/solnDecoder.jsp
source_id : Source Identifier (long)
A unique single numerical identifier of the source obtained from gaia_source (for a detailed description see gaia_source.source_id).
classprob_dsc_combmod_quasar : Probability from DSC-Combmod of being a quasar (data used: BP/RP spectrum, photometry, astrometry) (float)
Probability that the object is of the named class. This is the overall probability for this class, computed by combining the class probabilities from DSC-Specmod (which classifies objects using BP/RP spectra) and DSC-Allosmod (which classifies objects using several astrometric and photometric features). It is important to realise that the DSC classes are defined by the training data used, and that this may produce a narrower definition of the class than may be expected given the class name. This is a posterior probability that includes the global class prior, given in the documentation.
classprob_dsc_combmod_galaxy : Probability from DSC-Combmod of being a galaxy (data used: BP/RP spectrum, photometry, astrometry) (float)
Probability that the object is of the named class. This is the overall probability for this class, computed by combining the class probabilities from DSC-Specmod (which classifies objects using BP/RP spectra) and DSC-Allosmod (which classifies objects using several astrometric and photometric features). It is important to realise that the DSC classes are defined by the training data used, and that this may produce a narrower definition of the class than may be expected given the class name. This is a posterior probability that includes the global class prior, given in the documentation.
classprob_dsc_combmod_star : Probability from DSC-Combmod of being a single star (but not a white dwarf) (data used: BP/RP spectrum, photometry, astrometry) (float)
Probability that the object is of the named class. This is the overall probability for this class, computed by combining the class probabilities from DSC-Specmod (which classifies objects using BP/RP spectra) and DSC-Allosmod (which classifies objects using several astrometric and photometric features). It is important to realise that the DSC classes are defined by the training data used, and that this may produce a narrower definition of the class than may be expected given the class name. This is a posterior probability that includes the global class prior, given in the documentation.
classprob_dsc_combmod_whitedwarf : Probability from DSC-Combmod of being a white dwarf (data used: BP/RP spectrum, photometry, astrometry) (float)
Probability that the object is of the named class. This is the overall probability for this class, computed by combining the class probabilities from DSC-Specmod (which classifies objects using BP/RP spectra) and DSC-Allosmod (which classifies objects using several astrometric and photometric features). It is important to realise that the DSC classes are defined by the training data used, and that this may produce a narrower definition of the class than may be expected given the class name. This is a posterior probability that includes the global class prior, given in the documentation.
classprob_dsc_combmod_binarystar : Probability from DSC-Combmod of being a binary star (data used: BP/RP spectrum, photometry, astrometry) (float)
Probability that the object is of the named class. This is the overall probability for this class, computed by combining the class probabilities from DSC-Specmod (which classifies objects using BP/RP spectra) and DSC-Allosmod (which classifies objects using several astrometric and photometric features). It is important to realise that the DSC classes are defined by the training data used, and that this may produce a narrower definition of the class than may be expected given the class name. This is a posterior probability that includes the global class prior, given in the documentation.
classprob_dsc_specmod_quasar : Probability from DSC-Specmod of being a quasar (data used: BP/RP spectrum) (float)
Probability that the object is of the named class. This is the probability from a classifier that uses the BP/RP spectrum (module DSC-Specmod). It is important to realise that the DSC classes are defined by the training data used, and that this may produce a narrower definition of the class than may be expected given the class name. This is a posterior probability that includes the global class prior, given in the documentation.
classprob_dsc_specmod_galaxy : Probability from DSC-Specmod of being a galaxy (data used: BP/RP spectrum) (float)
Probability that the object is of the named class. This is the probability from a classifier that uses the BP/RP spectrum (module DSC-Specmod). It is important to realise that the DSC classes are defined by the training data used, and that this may produce a narrower definition of the class than may be expected given the class name. This is a posterior probability that includes the global class prior, given in the documentation.
classprob_dsc_specmod_star : Probability from DSC-Specmod of being a single star (but not a white dwarf) (data used: BP/RP spectrum) (float)
Probability that the object is of the named class. This is the probability from a classifier that uses the BP/RP spectrum (module DSC-Specmod). It is important to realise that the DSC classes are defined by the training data used, and that this may produce a narrower definition of the class than may be expected given the class name. This is a posterior probability that includes the global class prior, given in the documentation.
classprob_dsc_specmod_whitedwarf : Probability from DSC-Specmod of being a white dwarf (data used: BP/RP spectrum) (float)
Probability that the object is of the named class. This is the probability from a classifier that uses the BP/RP spectrum (module DSC-Specmod). It is important to realise that the DSC classes are defined by the training data used, and that this may produce a narrower definition of the class than may be expected given the class name. This is a posterior probability that includes the global class prior, given in the documentation.
classprob_dsc_specmod_binarystar : Probability from DSC-Specmod of being a binary star (data used: BP/RP spectrum) (float)
Probability that the object is of the named class. This is the probability from a classifier that uses the BP/RP spectrum (module DSC-Specmod). It is important to realise that the DSC classes are defined by the training data used, and that this may produce a narrower definition of the class than may be expected given the class name. This is a posterior probability that includes the global class prior, given in the documentation.
classprob_dsc_allosmod_quasar : Probability from DSC-Allosmod of being a quasar (data used: photometry, astrometry) (float)
Probability that the object is of the named class. This is the probability from a classifier that uses various astrometric and photometric features (module DSC-Allosmod). It is important to realise that the DSC classes are defined by the training data used, and that this may produce a narrower definition of the class than may be expected given the class name. This is a posterior probability that includes the global class prior, given in the documentation.
classprob_dsc_allosmod_galaxy : Probability from DSC-Allosmod of being a galaxy (data used: photometry, astrometry) (float)
Probability that the object is of the named class. This is the probability from a classifier that uses various astrometric and photometric features (module DSC-Allosmod). It is important to realise that the DSC classes are defined by the training data used, and that this may produce a narrower definition of the class than may be expected given the class name. This is a posterior probability that includes the global class prior, given in the documentation.
classprob_dsc_allosmod_star : Probability from DSC-Allosmod of being a star (data used: photometry, astrometry) (float)
Probability that the object is of the named class. This is the probability from a classifier that uses various astrometric and photometric features (module DSC-Allosmod). It is important to realise that the DSC classes are defined by the training data used, and that this may produce a narrower definition of the class than may be expected given the class name. This is a posterior probability that includes the global class prior, given in the documentation.
teff_gspphot : Effective temperature from GSP-Phot Aeneas best library using BP/RP spectra (float, Temperature[K])
Effective temperature (assuming source is a single star) inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax (see Section 11.3.3 of the online documentation). This is the median of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value.
teff_gspphot_lower : Lower confidence level (16%) of effective temperature from GSP-Phot Aeneas best library using BP/RP spectra (float, Temperature[K])
Lower confidence level (16%) of effective temperature (assuming source is a single star) inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax. This is the 16th percentile of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value. Lower and upper levels include 68% confidence interval.
teff_gspphot_upper : Upper confidence level (84%) of effective temperature from GSP-Phot Aeneas best library using BP/RP spectra (float, Temperature[K])
Upper confidence level (84%) of effective temperature (assuming source is a single star) inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax. This is the 84th percentile of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value. Lower and upper levels include 68% confidence interval.
logg_gspphot : Surface gravity from GSP-Phot Aeneas best library using BP/RP spectra (float, GravitySurface[log cgs])
Surface gravity (assuming source is a single star) inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax (see Section 11.3.3 of the online documentation). This is the median of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value.
logg_gspphot_lower : Lower confidence level (16%) of surface gravity from GSP-Phot Aeneas best library using BP/RP spectra (float, GravitySurface[log cgs])
Lower confidence level (16%) of surface gravity (assuming source is a single star) inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax. This is the 16th percentile of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value. Lower and upper levels include 68% confidence interval.
logg_gspphot_upper : Upper confidence level (84%) of surface gravity from GSP-Phot Aeneas best library using BP/RP spectra (float, GravitySurface[log cgs])
Upper confidence level (84%) of surface gravity (assuming source is a single star) inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax. This is the 84th percentile of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value. Lower and upper levels include 68% confidence interval.
mh_gspphot : Iron abundance from GSP-Phot Aeneas best library using BP/RP spectra (float, Abundances[dex])
Decimal logarithm of the ratio of the number abundance of iron to the number abundance of hydrogen relative to the same ratio of solar abundances inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax, assuming source is a single star (see Section 11.3.3 of the online documentation). This is the median of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value.
mh_gspphot_lower : Lower confidence level (16%) of iron abundance from GSP-Phot Aeneas best library using BP/RP spectra (float, Abundances[dex])
Decimal logarithm of the ratio of the number abundance of iron to the number abundance of hydrogen relative to the same ratio of solar abundances inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax, assuming source is a single star (see Section 11.3.3 of the online documentation). This is the 16th percentile of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value. Lower and upper levels include 68% confidence interval.
mh_gspphot_upper : Upper confidence level (84%) of iron abundance from GSP-Phot Aeneas best library using BP/RP spectra (float, Abundances[dex])
Decimal logarithm of the ratio of the number abundance of iron to the number abundance of hydrogen relative to the same ratio of solar abundances inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax, assuming source is a single star (see Section 11.3.3 of the online documentation). This is the 84th percentile of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value. Lower and upper levels include 68% confidence interval.
distance_gspphot : Distance from GSP-Phot Aeneas best library using BP/RP spectra (float, Length & Distance[pc])
Distance (assuming source is a single star) inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax(see Section 11.3.3 of the online documentation). This is the median of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value. NB: The actual fit parameter is $\log_{10}d$ and a prior is imposed to ensure a value between [0,5], thus the minimum possible distance is 1 pc and the maximum is 100 kpc.
distance_gspphot_lower : Lower confidence level (16%) of distance from GSP-Phot Aeneas best library using BP/RP spectra (float, Length & Distance[pc])
Lower confidence level (16%) of distance (assuming source is a single star) inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax. This is the 16th percentile of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value. Lower and upper levels include 68% confidence interval. NB: The actual fit parameter is $\log_{10}d$ and a prior is imposed to ensure a value between [0,5], thus the minimum possible distance is 1 pc and the maximum is 100 kpc.
distance_gspphot_upper : Upper confidence level (84%) of distance from GSP-Phot Aeneas best library using BP/RP spectra (float, Length & Distance[pc])
Upper confidence level (84%) of distance (assuming source is a single star) inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax. This is the 84th percentile of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value. Lower and upper levels include 68% confidence interval. NB: The actual fit parameter is $\log_{10}d$ and a prior is imposed to ensure a value between [0,5], thus the minimum possible distance is 1 pc and the maximum is 100 kpc.
azero_gspphot : Monochromatic extinction $A_{0}$ at 541.4 nm from GSP-Phot Aeneas best library using BP/RP spectra (float, Magnitude[mag])
Monochromatic extinction $A_{0}$ at 541.4 nm (assuming source is a single star) inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax. This is the median of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value. NB: This is the extinction parameter in the adopted Fitzpatrick extinction law (Fitzpatrick 1999, see Section 11.2.3 of the online documentation).
azero_gspphot_lower : Lower confidence level (16%) of monochromatic extinction $A_{0}$ at 541.4 nm from GSP-Phot Aeneas best library using BP/RP spectra (float, Magnitude[mag])
Lower confidence level (16%) of monochromatic extinction $A_{0}$ at 541.4 nm (assuming source is a single star) inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax. This is the 16th percentile of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value. Lower and upper levels include 68% confidence interval. NB: This is the extinction parameter in the adopted Fitzpatrick extinction law (Fitzpatrick 1999, see Section 11.2.3 of the online documentation).
azero_gspphot_upper : Upper confidence level (84%) of monochromatic extinction $A_{0}$ at 541.4 nm from GSP-Phot Aeneas best library using BP/RP spectra (float, Magnitude[mag])
Upper confidence level (84%) of monochromatic extinction $A_{0}$ at 541.4 nm (assuming source is a single star) inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax. This is the 84th percentile of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value. Lower and upper levels include 68% confidence interval. NB: This is the extinction parameter in the adopted Fitzpatrick extinction law (Fitzpatrick 1999, see Section 11.2.3 of the online documentation).
ag_gspphot : Extinction in G band from GSP-Phot Aeneas best library using BP/RP spectra (float, Magnitude[mag])
Broadband extinction in G band (assuming source is a single star) inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax. This is the median of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value.
ag_gspphot_lower : Lower confidence level (16%) of extinction in G band from GSP-Phot Aeneas best library using BP/RP spectra (float, Magnitude[mag])
Lower confidence level (16%) of broadband extinction in G band (assuming source is a single star) inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax. This is the 16th percentile of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value. Lower and upper levels include 68% confidence interval.
ag_gspphot_upper : Upper confidence level (84%) of extinction in G band from GSP-Phot Aeneas best library using BP/RP spectra (float, Magnitude[mag])
Upper confidence level (84%) of broadband extinction in G band (assuming source is a single star) inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax. This is the 84th percentile of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value. Lower and upper levels include 68% confidence interval.
abp_gspphot : Extinction in $G_{\rm BP}$ band from GSP-Phot Aeneas best library using BP/RP spectra (float, Magnitude[mag])
Broadband extinction in $G_{\rm BP}$ band (assuming source is a single star) inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax. This is the median of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value.
abp_gspphot_lower : Lower confidence level (16%) of extinction in $G_{\rm BP}$ band from GSP-Phot Aeneas best library using BP/RP spectra (float, Magnitude[mag])
Lower confidence level (16%) of broadband extinction in $G_{\rm BP}$ band (assuming source is a single star) inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax. This is the 16th percentile of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value. Lower and upper levels include 68% confidence interval.
abp_gspphot_upper : Upper confidence level (84%) of extinction in $G_{\rm BP}$ band from GSP-Phot Aeneas best library using BP/RP spectra (float, Magnitude[mag])
Upper confidence level (84%) of broadband extinction in $G_{\rm BP}$ band (assuming source is a single star) inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax. This is the 84th percentile of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value. Lower and upper levels include 68% confidence interval.
arp_gspphot : Extinction in $G_{\rm RP}$ band from GSP-Phot Aeneas best library using BP/RP spectra (float, Magnitude[mag])
Broadband extinction in $G_{\rm RP}$ band (assuming source is a single star) inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax. This is the median of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value.
arp_gspphot_lower : Lower confidence level (16%) of extinction in $G_{\rm RP}$ band from GSP-Phot Aeneas best library using BP/RP spectra (float, Magnitude[mag])
Lower confidence level (16%) of broadband extinction in $G_{\rm RP}$ band (assuming source is a single star) inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax. This is the 16th percentile of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value. Lower and upper levels include 68% confidence interval.
arp_gspphot_upper : Upper confidence level (84%) of extinction in $G_{\rm RP}$ band from GSP-Phot Aeneas best library using BP/RP spectra (float, Magnitude[mag])
Upper confidence level (84%) of broadband extinction in $G_{\rm RP}$ band (assuming source is a single star) inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax. This is the 84th percentile of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value. Lower and upper levels include 68% confidence interval.
ebpminrp_gspphot : Reddening $E(G_{\rm BP}-G_{\rm RP})$ from GSP-Phot Aeneas best library using BP/RP spectra (float, Magnitude[mag])
Reddening $E(G_{\rm BP}-G_{\rm RP})$ (assuming source is a single star) inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax. This is the median of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value. Note that while $E(G_{\rm BP}-G_{\rm RP})=A_{\rm BP}-A_{\rm RP}$, this was computed at the level of MCMC samples. Hence, this relation is not exactly true for the median values.
ebpminrp_gspphot_lower : Lower confidence level (16%) of reddening $E(G_{\rm BP}-G_{\rm RP})$ from GSP-Phot Aeneas best library using BP/RP spectra (float, Magnitude[mag])
Lower confidence level (16%) of reddening $E(G_{\rm BP}-G_{\rm RP})$ (assuming source is a single star) inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax. This is the 16th percentile of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value. Lower and upper levels include 68% confidence interval. Note that while $E(G_{\rm BP}-G_{\rm RP})=A_{\rm BP}-A_{\rm RP}$, this was computed at the level of MCMC samples. Hence, this relation is not exactly true for the lower confidence levels.
ebpminrp_gspphot_upper : Upper confidence level (84%) of reddening $E(G_{\rm BP}-G_{\rm RP})$ from GSP-Phot Aeneas best library using BP/RP spectra (float, Magnitude[mag])
Upper confidence level (84%) of reddening $E(G_{\rm BP}-G_{\rm RP})$ (assuming source is a single star) inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax. This is the 84th percentile of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value. Lower and upper levels include 68% confidence interval. Note that while $E(G_{\rm BP}-G_{\rm RP})=A_{\rm BP}-A_{\rm RP}$, this was computed at the level of MCMC samples. Hence, this relation is not exactly true for the upper confidence levels.
mg_gspphot : Absolute magnitude $M_{\rm G}$ from GSP-Phot Aeneas best library using BP/RP spectra (float, Magnitude[mag])
Absolute magnitude $M_{\rm G}$ (assuming source is a single star) inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax. This is the median of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value.
mg_gspphot_lower : Lower confidence level (16%) of absolute magnitude $M_{\rm G}$ from GSP-Phot Aeneas best library using BP/RP spectra (float, Magnitude[mag])
Lower confidence level (16%) of absolute magnitude $M_{\rm G}$ (assuming source is a single star) inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax. This is the 16th percentile of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value. Lower and upper levels include 68% confidence interval.
mg_gspphot_upper : Upper confidence level (84%) of absolute magnitude $M_{\rm G}$ from GSP-Phot Aeneas best library using BP/RP spectra (float, Magnitude[mag])
Upper confidence level (84%) of absolute magnitude $M_{\rm G}$ (assuming source is a single star) inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax. This is the 84th percentile of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value. Lower and upper levels include 68% confidence interval.
Stellar radius (assuming source is a single star) inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax. This is the median of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value.
radius_gspphot_lower : Lower confidence level (16%) of radius from GSP-Phot Aeneas best library using BP/RP spectra (float, Length & Distance[Solar Radius])
Lower confidence level (16%) of stellar radius (assuming source is a single star) inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax. This is the 16th percentile of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value. Lower and upper levels include 68% confidence interval.
radius_gspphot_upper : Upper confidence level (84%) of radius from GSP-Phot Aeneas best library using BP/RP spectra (float, Length & Distance[Solar Radius])
Upper confidence level (84%) of stellar radius (assuming source is a single star) inferred by GSP-Phot Aeneas from BP/RP spectra, apparent G magnitude and parallax. This is the 84th percentile of the MCMC samples. Taken from best library that achieves the highest goodness-of-fit value. Lower and upper levels include 68% confidence interval.
logposterior_gspphot : Goodness-of-fit score (mean log-posterior of MCMC) of GSP-Phot Aeneas MCMC best library (float)
Goodness-of-fit score defined as the mean log-posterior of all MCMC samples of GSP-Phot Aeneas MCMC for best library. The higher the goodness-of-fit score, the better the fit. Values are usually negative. NB: This is not a Bayesian evidence!
mcmcaccept_gspphot : MCMC acceptance rate of GSP-Phot Aeneas MCMC best library (float)
MCMC acceptance rate of GSP-Phot Aeneas MCMC best library. This is computed from all MCMC samples (before thinning the chain to 2000 or 100 samples).
libname_gspphot : Name of library that achieves the highest mean log-posterior in MCMC samples and was used to derive GSP-Phot parameters in this table (string)
Name of library of synthetic stellar spectra (one of A, MARCS, OB, PHOENIX) for which GSP-Phot achieves the highest goodness-of-fit score (i.e. the highest mean log-posterior in its MCMC samples), referred to as “best library”. This is the library used to derive GSP-Phot parameters in this table (astrophysical_parameters). For more information on the synthetic libraries see Section 11.2.3.
teff_gspspec : Effective temperature from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Temperature[K])
Median value of the effective temperature (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) from RVS spectra and Monte Carlo realisations.
teff_gspspec_lower : 16th percentile of effective temperature from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Temperature[K])
Lower confidence level (16%) of the median effective temperature (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) from RVS spectra. Lower and upper levels include 68% confidence interval.
teff_gspspec_upper : 84th percentile of effective temperature from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Temperature[K])
Upper confidence level (84%) of the median effective temperature (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) from RVS spectra. Lower and upper levels include 68% confidence interval.
logg_gspspec : Logarithm of the stellar surface gravity from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, GravitySurface[log cgs])
Median value of logarithm of the stellar surface gravity (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) from RVS spectra.
logg_gspspec_lower : 16th percentile of the logarithm of the stellar surface gravity from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, GravitySurface[log cgs])
Lower confidence level (16%) of the median value of logarithm of the stellar surface gravity (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) from RVS spectra. Lower and upper levels include 68% confidence interval.
logg_gspspec_upper : 84th percentile of the logarithm of the stellar surface gravity from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, GravitySurface[log cgs])
Upper confidence level (84%) of the median value of logarithm of the stellar surface gravity (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) from RVS spectra. Lower and upper levels include 68% confidence interval.
mh_gspspec : Global metallicity [M/H] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Median global metallicity (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) from RVS spectra.
mh_gspspec_lower : 16th percentile of global metallicity [M/H] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Lower confidence level (16%) of the median global metallicity (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) from RVS spectra. Lower and upper levels include 68% confidence interval.
mh_gspspec_upper : 84th percentile of global metallicity [M/H] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Upper confidence level (84%) of the median global metallicity (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) from RVS spectra. Lower and upper levels include 68% confidence interval.
alphafe_gspspec : Abundance of alpha-elements [alpha/Fe] with respect to iron from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Median abundance of alpha-elements with respect to iron (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) from RVS spectra. The considered alpha elements are: O, Ne, Mg, Si, S, Ar, Ca, Ti.
alphafe_gspspec_lower : 16th percentile of the abundance of alpha-elements [alpha/Fe] with respect to iron from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Lower confidence level (16%) of the median abundance of alpha-elements with respect to iron (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) from RVS spectra. Lower and upper levels include 68% confidence interval.
alphafe_gspspec_upper : 84th percentile of the abundance of alpha-elements [alpha/Fe] with respect to iron from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Upper confidence level (84%) of the median abundance of alpha-elements with respect to iron (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) from RVS spectra. Lower and upper levels include 68% confidence interval.
fem_gspspec : Abundance of neutral iron [Fe/M] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations, applied to the individual N lines of the element, given in fem_gspspec_nlines (float, Abundances[dex])
Median abundance of neutral iron (assuming source is a single star) from RVS spectra and Monte Carlo realisations derived using MatisseGauguin (Recio-Blanco and et al. 2022) atmospheric parameters and the Gauguin algorithm, applied to the individual N lines of the element, where the number of lines is given in fem_gspspec_nlines. The neutral iron abundance [Fe/H] is obtained by [Fe/H]=[Fe/M]+[M/H].
fem_gspspec_lower : 16th percentile of the abundance of neutral iron [Fe/M] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Lower confidence level (16%) of the median abundance of neutral iron (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) using RVS spectra. Lower and upper levels include 68% confidence interval. The neutral iron abundance [Fe/H] is obtained by [Fe/H]=[Fe/M]+[M/H].
fem_gspspec_upper : 84th percentile of the abundance of neutral iron [Fe/M] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Upper confidence level (84%) of the median abundance of neutral iron (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) using RVS spectra. Lower and upper levels include 68% confidence interval. The neutral iron abundance [Fe/H] is obtained by [Fe/H]=[Fe/M]+[M/H].
fem_gspspec_nlines : Number of lines used for [Fe/M] abundance estimation (int)
Number of lines used to compute the [Fe/M] abundance. Lines with interquartile difference (84th quantile value - 16th quantile value) in the Monte Carlo line abundance distribution higher than 0.5 dex have been excluded.
fem_gspspec_linescatter : Uncertainty estimation of [Fe/M] abundance using N lines of the element, given in fem_gspspec_nlines (float, Abundances[dex])
Standard deviation of the individual N lines (fem_gspspec_nlines) abundance results.
sife_gspspec : Abundance of silicon [Si/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations, applied to the individual N lines of the element, given in sife_gspspec_nlines (float, Abundances[dex])
Median abundance of silicon (assuming source is a single star) from RVS spectra and Monte Carlo realisations derived using MatisseGauguin (Recio-Blanco and et al. 2022) atmospheric parameters and the Gauguin algorithm, applied to the individual N lines of the element, where the number of lines is given in sife_gspspec_nlines.
sife_gspspec_lower : 16th percentile of the abundance of silicon [Si/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Lower confidence level (16%) of the median abundance of silicon (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) using RVS spectra. Lower and upper levels include 68% confidence interval.
sife_gspspec_upper : 84th percentile of the abundance of silicon [Si/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Upper confidence level (84%) of the median abundance of silicon (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) using RVS spectra. Lower and upper levels include 68% confidence interval.
sife_gspspec_nlines : Number of lines used for [Si/Fe] abundance estimation (int)
Number of lines used to compute the [Si/Fe] abundance. Lines with interquartile difference (84th quantile value - 16th quantile value) in the Monte Carlo line abundance distribution higher than 0.5 dex have been excluded.
sife_gspspec_linescatter : Uncertainty estimation of [Si/Fe] abundance using N lines of the element, given in sife_gspspec_nlines (float, Abundances[dex])
Standard deviation of the individual N lines (sife_gspspec_nlines) abundance results.
cafe_gspspec : Abundance of calcium [Ca/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations, applied to the individual N lines of the element, given in cafe_gspspec_nlines (float, Abundances[dex])
Median abundance of calcium (assuming source is a single star) from RVS spectra and Monte Carlo realisations derived using MatisseGauguin (Recio-Blanco and et al. 2022) atmospheric parameters and the Gauguin algorithm, applied to the individual N lines of the element, where the number of lines is given in cafe_gspspec_nlines.
cafe_gspspec_lower : 16th percentile of the abundance of calcium [Ca/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Lower confidence level (16%) of the median abundance of calcium (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) using RVS spectra. Lower and upper levels include 68% confidence interval.
cafe_gspspec_upper : 84th percentile of the abundance of calcium [Ca/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Upper confidence level (84%) of the median abundance of calcium (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) using RVS spectra. Lower and upper levels include 68% confidence interval.
cafe_gspspec_nlines : Number of lines used for [Ca/Fe] abundance estimation (int)
Number of lines used to compute the [Ca/Fe] abundance. Lines with interquartile difference (84th quantile value - 16th quantile value) in the Monte Carlo line abundance distribution higher than 0.5 dex have been excluded.
cafe_gspspec_linescatter : Uncertainty estimation of [Ca/Fe] abundance using N lines of the element, given in cafe_gspspec_nlines (float, Abundances[dex])
Standard deviation of the individual N lines (cafe_gspspec_nlines) abundance results.
tife_gspspec : Abundance of titanium [Ti/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations, applied to the individual N lines of the element, given in tife_gspspec_nlines (float, Abundances[dex])
Median abundance of titanium (assuming source is a single star) from RVS spectra and Monte Carlo realisations derived using MatisseGauguin (Recio-Blanco and et al. 2022) atmospheric parameters and the Gauguin algorithm, applied to the individual N lines of the element, where the number of lines is given in tife_gspspec_nlines.
tife_gspspec_lower : 16th percentile of the abundance of titanium [Ti/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Lower confidence level (16%) of the median abundance of titanium (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) using RVS spectra. Lower and upper levels include 68% confidence interval.
tife_gspspec_upper : 84th percentile of the abundance of titanium [Ti/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Upper confidence level (84%) of the median abundance of titanium (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) using RVS spectra. Lower and upper levels include 68% confidence interval.
tife_gspspec_nlines : Number of lines used for [Ti/Fe] abundance estimation (int)
Number of lines used to compute the [Ti/Fe] abundance. Lines with interquartile difference (84th quantile value - 16th quantile value) in the Monte Carlo line abundance distribution higher than 0.5 dex have been excluded.
tife_gspspec_linescatter : Uncertainty estimation of [Ti/Fe] abundance using N lines of the element, given in tife_gspspec_nlines (float, Abundances[dex])
Standard deviation of the individual N lines (tife_gspspec_nlines) abundance results.
mgfe_gspspec : Abundance of magnesium [Mg/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations, applied to the individual N lines of the element, given in mgfe_gspspec_nlines (float, Abundances[dex])
Median abundance of magnesium (assuming source is a single star) from RVS spectra and Monte Carlo realisations derived using MatisseGauguin (Recio-Blanco and et al. 2022) atmospheric parameters and the Gauguin algorithm, applied to the individual N lines of the element, where the number of lines is given in mgfe_gspspec_nlines.
mgfe_gspspec_lower : 16th percentile of the abundance of magnesium [Mg/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Lower confidence level (16%) of the median abundance of magnesium (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) using RVS spectra. Lower and upper levels include 68% confidence interval.
mgfe_gspspec_upper : 84th percentile of the abundance of magnesium [Mg/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Upper confidence level (84%) of the median abundance of magnesium (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) using RVS spectra. Lower and upper levels include 68% confidence interval.
mgfe_gspspec_nlines : Number of lines used for [Mg/Fe] abundance estimation (int)
Number of lines used to compute the [Mg/Fe] abundance. Lines with interquartile difference (84th quantile value - 16th quantile value) in the Monte Carlo line abundance distribution higher than 0.5 dex have been excluded.
mgfe_gspspec_linescatter : Uncertainty estimation of [Mg/Fe] abundance using N lines of the element, given in mgfe_gspspec_nlines (float, Abundances[dex])
Standard deviation of the individual N lines (mgfe_gspspec_nlines) abundance results.
ndfe_gspspec : Abundance of neodymium [Nd/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations, applied to the individual N lines of the element, given in ndfe_gspspec_nlines (float, Abundances[dex])
Median abundance of neodymium (assuming source is a single star) from RVS spectra and Monte Carlo realisations derived using MatisseGauguin (Recio-Blanco and et al. 2022) atmospheric parameters and the Gauguin algorithm, applied to the individual N lines of the element, where the number of lines is given in ndfe_gspspec_nlines.
ndfe_gspspec_lower : 16th percentile of the abundance of neodymium [Nd/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Lower confidence level (16%) of the median abundance of neodymium (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) using RVS spectra. Lower and upper levels include 68% confidence interval.
ndfe_gspspec_upper : 84th percentile of the abundance of neodymium [Nd/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Upper confidence level (84%) of the median abundance of neodymium (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) using RVS spectra. Lower and upper levels include 68% confidence interval.
ndfe_gspspec_nlines : Number of lines used for [Nd/Fe] abundance estimation (int)
Number of lines used to compute the [Nd/Fe] abundance. Lines with interquartile difference (84th quantile value - 16th quantile value) in the Monte Carlo line abundance distribution higher than 0.5 dex have been excluded.
ndfe_gspspec_linescatter : Uncertainty estimation of [Nd/Fe] abundance using N lines of the element, given in ndfe_gspspec_nlines (float, Abundances[dex])
Standard deviation of the individual N lines (ndfe_gspspec_nlines) abundance results.
feiim_gspspec : Abundance of ionised iron [FeII/M] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations, applied to the individual N lines of the element, given in feiim_gspspec_nlines (float, Abundances[dex])
Median abundance of ionised iron (assuming source is a single star) from RVS spectra and Monte Carlo realisations derived using MatisseGauguin (Recio-Blanco and et al. 2022) atmospheric parameters and the Gauguin algorithm, applied to the individual N lines of the element, where the number of lines is given in feiim_gspspec_nlines. The ionised iron abundance [FeII/H] is obtained by [FeII/H]=[FeII/M]+[M/H].
feiim_gspspec_lower : 16th percentile of the abundance of ionised iron [FeII/M] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Lower confidence level (16%) of the median abundance of ionised iron (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) using RVS spectra. Lower and upper levels include 68% confidence interval. The ionised iron abundance [FeII/H] is obtained by [FeII/H]=[FeII/M]+[M/H].
feiim_gspspec_upper : 84th percentile of the abundance of ionised iron [FeII/M] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Upper confidence level (84%) of the median abundance of ionised iron (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) using RVS spectra. Lower and upper levels include 68% confidence interval. The ionised iron abundance [FeII/H] is obtained by [FeII/H]=[FeII/M]+[M/H].
feiim_gspspec_nlines : Number of lines used for [FeII/M] abundance estimation (int)
Number of lines used to compute the [FeII/M] abundance. Lines with interquartile difference (84th quantile value - 16th quantile value) in the Monte Carlo line abundance distribution higher than 0.5 dex have been excluded.
feiim_gspspec_linescatter : Uncertainty estimation of [FeII/M] abundance using N lines of the element, given in feiim_gspspec_nlines (float, Abundances[dex])
Standard deviation of the individual N lines (feiim_gspspec_nlines) abundance results.
sfe_gspspec : Abundance of sulphur [S/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations, applied to the individual N lines of the element, given in sfe_gspspec_nlines (float, Abundances[dex])
Median abundance of sulphur (assuming source is a single star) from RVS spectra and Monte Carlo realisations derived using MatisseGauguin (Recio-Blanco and et al. 2022) atmospheric parameters and the Gauguin algorithm, applied to the individual N lines of the element, where the number of lines is given in sfe_gspspec_nlines.
sfe_gspspec_lower : 16th percentile of the abundance of sulphur [S/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Lower confidence level (16%) of the median abundance of sulphur (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) using RVS spectra. Lower and upper levels include 68% confidence interval.
sfe_gspspec_upper : 84th percentile of the abundance of sulphur [S/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Upper confidence level (84%) of the median abundance of sulphur (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) using RVS spectra. Lower and upper levels include 68% confidence interval.
sfe_gspspec_nlines : Number of lines used for [S/Fe] abundance estimation (int)
Number of lines used to compute the [S/Fe] abundance. Lines with interquartile difference (84th quantile value - 16th quantile value) in the Monte Carlo line abundance distribution higher than 0.5 dex have been excluded.
sfe_gspspec_linescatter : Uncertainty estimation of [S/Fe] abundance using N lines of the element, given in sfe_gspspec_nlines (float, Abundances[dex])
Standard deviation of the individual N lines (sfe_gspspec_nlines) abundance results.
zrfe_gspspec : Abundance of zirconium [Zr/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations, applied to the individual N lines of the element, given in zrfe_gspspec_nlines (float, Abundances[dex])
Median abundance of zirconium (assuming source is a single star) from RVS spectra and Monte Carlo realisations derived using MatisseGauguin (Recio-Blanco and et al. 2022) atmospheric parameters and the Gauguin algorithm, applied to the individual N lines of the element, where the number of lines is given in zrfe_gspspec_nlines.
zrfe_gspspec_lower : 16th percentile of the abundance of zirconium [Zr/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Lower confidence level (16%) of the median abundance of zirconium (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) using RVS spectra. Lower and upper levels include 68% confidence interval.
zrfe_gspspec_upper : 84th percentile of the abundance of zirconium [Zr/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Upper confidence level (84%) of the median abundance of zirconium (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) using RVS spectra. Lower and upper levels include 68% confidence interval.
zrfe_gspspec_nlines : Number of lines used for [Zr/Fe] abundance estimation (int)
Number of lines used to compute the [Zr/Fe] abundance. Lines with interquartile difference (84th quantile value - 16th quantile value) in the Monte Carlo line abundance distribution higher than 0.5 dex have been excluded.
zrfe_gspspec_linescatter : Uncertainty estimation of [Zr/Fe] abundance using N lines of the element, given in zrfe_gspspec_nlines (float, Abundances[dex])
Standard deviation of the individual N lines (zrfe_gspspec_nlines) abundance results.
nfe_gspspec : Abundance of nitrogen [N/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations, applied to the individual N lines of the element, given in nfe_gspspec_nlines (float, Abundances[dex])
Median abundance of nitrogen (assuming source is a single star) from RVS spectra and Monte Carlo realisations derived using MatisseGauguin (Recio-Blanco and et al. 2022) atmospheric parameters and the Gauguin algorithm, applied to the individual N lines of the element, where the number of lines is given in nfe_gspspec_nlines.
nfe_gspspec_lower : 16th percentile of the abundance of nitrogen [N/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Lower confidence level (16%) of the median abundance of nitrogen (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) using RVS spectra. Lower and upper levels include 68% confidence interval.
nfe_gspspec_upper : 84th percentile of the abundance of nitrogen [N/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Upper confidence level (84%) of the median abundance of nitrogen (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) using RVS spectra. Lower and upper levels include 68% confidence interval.
nfe_gspspec_nlines : Number of lines used for [N/Fe] abundance estimation (int)
Number of lines used to compute the [N/Fe] abundance. Lines with interquartile difference (84th quantile value - 16th quantile value) in the Monte Carlo line abundance distribution higher than 0.5 dex have been excluded.
nfe_gspspec_linescatter : Uncertainty estimation of [N/Fe] abundance using N lines of the element, given in nfe_gspspec_nlines (float, Abundances[dex])
Standard deviation of the individual N lines (nfe_gspspec_nlines) abundance results.
crfe_gspspec : Abundance of chromium [Cr/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations, applied to the individual N lines of the element, given in crfe_gspspec_nlines (float, Abundances[dex])
Median abundance of chromium (assuming source is a single star) from RVS spectra and Monte Carlo realisations derived using MatisseGauguin (Recio-Blanco and et al. 2022) atmospheric parameters and the Gauguin algorithm, applied to the individual N lines of the element, where the number of lines is given in crfe_gspspec_nlines.
crfe_gspspec_lower : 16th percentile of the abundance of chromium [Cr/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Lower confidence level (16%) of the median abundance of chromium (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) using RVS spectra. Lower and upper levels include 68% confidence interval.
crfe_gspspec_upper : 84th percentile of the abundance of chromium [Cr/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Upper confidence level (84%) of the median abundance of chromium (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) using RVS spectra. Lower and upper levels include 68% confidence interval.
crfe_gspspec_nlines : Number of lines used for [Cr/Fe] abundance estimation (int)
Number of lines used to compute the [Cr/Fe] abundance. Lines with interquartile difference (84th quantile value - 16th quantile value) in the Monte Carlo line abundance distribution higher than 0.5 dex have been excluded.
crfe_gspspec_linescatter : Uncertainty estimation of [Cr/Fe] abundance using N lines of the element, given in crfe_gspspec_nlines (float, Abundances[dex])
Standard deviation of the individual N lines (crfe_gspspec_nlines) abundance results.
cefe_gspspec : Abundance of cerium [Ce/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations, applied to the individual N lines of the element, given in cefe_gspspec_nlines (float, Abundances[dex])
Median abundance of cerium (assuming source is a single star) from RVS spectra and Monte Carlo realisations derived using MatisseGauguin (Recio-Blanco and et al. 2022) atmospheric parameters and the Gauguin algorithm, applied to the individual N lines of the element, where the number of lines is given in cefe_gspspec_nlines.
cefe_gspspec_lower : 16th percentile of the abundance of cerium [Ce/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Lower confidence level (16%) of the median abundance of cerium (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) using RVS spectra. Lower and upper levels include 68% confidence interval.
cefe_gspspec_upper : 84th percentile of the abundance of cerium [Ce/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Upper confidence level (84%) of the median abundance of cerium (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) using RVS spectra. Lower and upper levels include 68% confidence interval.
cefe_gspspec_nlines : Number of lines used for [Ce/Fe] abundance estimation (int)
Number of lines used to compute the [Ce/Fe] abundance. Lines with interquartile difference (84th quantile value - 16th quantile value) in the Monte Carlo line abundance distribution higher than 0.5 dex have been excluded.
cefe_gspspec_linescatter : Uncertainty estimation of [Ce/Fe] abundance using N lines of the element, given in cefe_gspspec_nlines (float, Abundances[dex])
Standard deviation of the individual N lines (cefe_gspspec_nlines) abundance results.
nife_gspspec : Abundance of nickel [Ni/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations, applied to the individual N lines of the element, given in nife_gspspec_nlines (float, Abundances[dex])
Median abundance of nickel (assuming source is a single star) from RVS spectra and Monte Carlo realisations derived using MatisseGauguin (Recio-Blanco and et al. 2022) atmospheric parameters and the Gauguin algorithm, applied to the individual N lines of the element, where the number of lines is given in nife_gspspec_nlines.
nife_gspspec_lower : 16th percentile of the abundance of nickel [Ni/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Lower confidence level (16%) of the median abundance of nickel (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) using RVS spectra. Lower and upper levels include 68% confidence interval.
nife_gspspec_upper : 84th percentile of the abundance of nickel [Ni/Fe] from GSP-Spec MatisseGauguin using RVS spectra and Monte Carlo realisations (float, Abundances[dex])
Upper confidence level (84%) of the median abundance of nickel (assuming source is a single star) inferred by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) using RVS spectra. Lower and upper levels include 68% confidence interval.
nife_gspspec_nlines : Number of lines used for [Ni/Fe] abundance estimation (int)
Number of lines used to compute the [Ni/Fe] abundance. Lines with interquartile difference (84th quantile value - 16th quantile value) in the Monte Carlo line abundance distribution higher than 0.5 dex have been excluded.
nife_gspspec_linescatter : Uncertainty estimation of [Ni/Fe] abundance using N lines of the element, given in nife_gspspec_nlines (float, Abundances[dex])
Standard deviation of the individual N lines (nife_gspspec_nlines) abundance results.
cn0ew_gspspec : Equivalent witdh of cyanogen absorption line, derived from RVS spectra (float, Length & Distance[nm])
Equivalent width of the residual feature (computed as the observed RVS spectrum divided by a synthetic one with the MatisseGauguin parameters) around the cyanogen line at 862.9 nm.
cn0ew_gspspec_uncertainty : Uncertainty of equivalent witdh of cyanogen absorption line, derived from RVS spectra (float, Length & Distance[nm])
Interquartile difference (84th quantile value - 16th quantile value) in the Monte Carlo distribution of cn0ew_gspspec, derived from RVS spectra.
cn0_gspspec_centralline : Central wavelength of cyanogen line, derived from RVS spectra using DIB algorithm (float, Length & Distance[nm])
Central wavelength of the Gaussian fit applied to the residual feature (computed as the observed RVS spectrum divided by a synthetic one with the MatisseGauguin parameters) around the cyanogen line at 862.9 nm.
cn0_gspspec_width : Width of cyoanogen line, derived from RVS spectra using DIB algorithm (float, Length & Distance[nm])
Width of the Gaussian fit applied to the residual feature (computed as the observed RVS spectrum divided by a synthetic one with the MatisseGauguin parameters) around the cyanogen line at 862.9 nm.
dib_gspspec_lambda : DIB central wavelength from GSP-Spec MatisseGauguin using RVS spectra (float, Length & Distance[nm])
Central wavelength of the DIB feature in the RVS spectrum derived by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022).
dib_gspspec_lambda_uncertainty : Uncertainty on DIB central wavelength from GSP-Spec MatisseGauguin using RVS spectra (float, Length & Distance[nm])
Uncertainty on central wavelength of the DIB feature in the RVS spectrum derived by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022).
dibew_gspspec : Equivalent width of the DIB from GSP-Spec MatisseGauguin using RVS spectra (float, Length & Distance[Å])
Equivalent width of the DIB feature in the RVS spectrum derived by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022).
dibew_gspspec_uncertainty : Global uncertainty on DIB equivalent width value using DIB algorithm (float, Length & Distance[Å])
Global uncertainty on equivalent width of the DIB feature in the RVS spectrum derived by GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022).
dibewnoise_gspspec_uncertainty : Uncertainty on DIB equivalent width value occuring from noise part (float, Length & Distance[Å])
Uncertainty on DIB equivalent width value based on the noise level.
dibp0_gspspec : Depth ($p_{0}$ parameter) of the DIB derived from a Gaussian model fit (float)
Depth ($p_{0}$ parameter) of the DIB defined from a Gaussian model fit. The flux is modelled as $p_{0}\times\exp\left(-\frac{(x-p_{1})^{2}}{2p_{2}^{2}}\right),$ where $p_{0}$ and $p_{2}$ are the depth and width of the DIB profile, $p_{1}$ is the central wavelength and $x$ is the spectral wavelength, cf. Zhao et al. (2021).
dibp2_gspspec : Width ($p_{2}$ parameter) of the DIB derived from a Gaussian model fit (float, Length & Distance[Å])
Width ($p_{2}$ parameter) of the DIB defined from a Gaussian model fit. The flux is modelled as $p_{0}\times\exp\left(-\frac{(x-p_{1})^{2}}{2p_{2}^{2}}\right),$ where $p_{0}$ and $p_{2}$ are the depth and width of the DIB profile, $p_{1}$ is the central wavelength and $x$ is the spectral wavelength, cf. Zhao et al. (2021).
dibp2_gspspec_uncertainty : Uncertainty on the dibp2_gspspec parameter (float, Length & Distance[Å])
Uncertainty on the $p_{2}$ parameter from the Gaussian fitting, given in dibp2_gspspec.
dibqf_gspspec : Quality flag of the DIB computation (int)
Quality flag on DIB computation: QF=$-1$ means that there is not a preliminary detection where sources are only measured if the detection threshold is above the 3-sigma level, QF=$-2$ means outside the considered temperature range, i.e., $T_{\rm eff}<3500$ K, or flux values are NaN in the DIB wavelength range between 860.5 and 864.0 nm.
flags_gspspec : Catalogue flags for GSP-Spec MatisseGauguin (string)
Definitions of each character in the GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022) quality flag chain. In this chain, value ‘0’ is the best, and ‘9’ is the worst. Flag names are split in three categories: parameter flags (green), individual abundance flags (blue) and equivalent width flags (maroon): In the following, the term ’gof’ refers to the chi-square value beteween the input spectrum fluxes array and the solution spectrum fluxes array.
Chain character Considered Possible number - name quality aspect adopted values 1 vbroadT vbroad induced bias in $T_{\rm eff}$ 0,1,2,9 2 vbroadG vbroad induced bias in $\log g$ 0,1,2,9 3 vbroadM vbroad induced bias in [M/H] 0,1,2,9 4 vradT vrad induced bias in $T_{\rm eff}$ 0,1,2,9 5 vradG vrad induced bias in $\log g$ 0,1,2,9 6 vradM vrad induced bias in [M/H] 0,1,2,9 7 fluxNoise flux noise uncertainties 0,1,2,3,4,5,9 8 extrapol extrapolation 0,1,2,3,4,9 9 neg_flux negative flux pixels 0,1,9 10 nanFlux NaN flux pixels 0,9 11 emission emission line 0,9 12 nullFluxErr null uncertainties 0,9 13 KMgiantPar KM-type giant stars 0,1,2 14 NUpLim nitrogen abundance upper limit 0,1,2,9 15 NUncer nitrogen abundance uncertainty quality 0,1,2,9 16 MgUpLim magnesium abundance upper limit 0,1,2,9 17 MgUncer magnesium abundance uncertainty quality 0,1,2,9 18 SiUpLim silicon abundance upper limit 0,1,2,9 19 SiUncer silicon abundance uncertainty quality 0,1,2,9 20 SUpLim sulphur abundance upper limit 0,1,2,9 21 SUncer sulphur abundance uncertainty quality 0,1,2,9 22 CaUpLim calcium abundance upper limit 0,1,2,9 23 CaUncer calcium abundance uncertainty quality 0,1,2,9 24 TiUpLim titanium abundance upper limit 0,1,2,9 25 TiUncer titanium abundance uncertainty quality 0,1,2,9 26 CrUpLim chromium abundance upper limit 0,1,2,9 27 CrUncer chromium abundance uncertainty quality 0,1,2,9 28 FeUpLim neutral iron abundance upper limit 0,1,2,9 29 FeUncer neutral iron abundance uncertainty quality 0,1,2,9 30 FeIIUpLim ionised iron abundance upper limit 0,1,2,9 31 FeIIUncer ionised iron abundance uncertainty quality 0,1,2,9 32 NiUpLim nickel abundance upper limit 0,1,2,9 33 NiUncer nickel abundance uncertainty quality 0,1,2,9 34 ZrUpLim zirconium abundance upper limit 0,1,2,9 35 ZrUncer zirconium abundance uncertainty quality 0,1,2,9 36 CeUpLim cerium abundance upper limit 0,1,2,9 37 CeUncer cerium abundance uncertainty quality 0,1,2,9 38 NdUpLim neodymium abundance upper limit 0,1,2,9 39 NdUncer neodymium abundance uncertainty quality 0,1,2,9 40 DeltaCNq cyanogen differential equivalent width quality 0,9 41 DIBq DIB quality flag 0,1,2,3,4,5,9
Definition of parameter flags considering potential biases due to rotational velocity and macroturbulence:
Flag name Condition Flag value vbroadT $\Delta$$T_{\rm eff}$$>$2000 K Filter all Flag $=$ 9 500$<\Delta$$T_{\rm eff}$$\leq$2000 K Flag $=$ 2 250$<\Delta$$T_{\rm eff}$$\leq$500 K Flag $=$ 1 $\Delta$$T_{\rm eff}$$\leq$250 K Flag $=$ 0 vbroadG $\Delta$$\log g$$>$2 dex Filter all except $T_{\rm eff}$ and DIB if $T_{\rm eff}$$>$7000 K Flag $=$ 9 1$<\Delta$$\log g$$\leq$2 dex Flag $=$ 2 0.5$<\Delta$$\log g$$\leq$1 dex Flag $=$ 1 $\Delta$$\log g$$\leq$0.5 dex Flag $=$ 0 vbroadM $\Delta$[M/H]$>$2 dex Filter [M/H] and [X/Fe] Flag $=$ 9 0.5$<\Delta$[M/H]$\leq$2 dex Flag $=$ 2 0.25$<\Delta$[M/H]$\leq$0.5 dex Flag $=$ 1 $\Delta$[M/H]$\leq$0.25 dex Flag $=$ 0
Definition of parameter flags considering potential biases due to uncertainties in the radial velocity shift correction:
Flag name Condition Flag value vradT $\Delta$$T_{\rm eff}$$>$2000 K Filter all Flag $=$ 9 500$<\Delta$$T_{\rm eff}$$\leq$2000 K Flag $=$ 2 250$<\Delta$$T_{\rm eff}$$\leq$500 K Flag $=$ 1 $\Delta$$T_{\rm eff}$$\leq$250 K Flag $=$ 0 vradG $\Delta$$\log g$$>$2 dex Filter all except $T_{\rm eff}$ and DIB if $T_{\rm eff}$$>$7000 K Flag $=$ 9 1$<\Delta$$\log g$$\leq$2 dex Flag $=$ 2 0.5$<\Delta$$\log g$$\leq$1 dex Flag $=$ 1 $\Delta$$\log g$$\leq$0.5 dex Flag $=$ 0 vradM $\Delta$[M/H]$>$2 dex Filter [M/H] and [X/Fe] Flag $=$ 9 0.5$<\Delta$[M/H]$\leq$2 dex Flag $=$ 2 0.25$<\Delta$[M/H]$\leq$0.5 dex Flag $=$ 1 $\Delta$[M/H]$\leq$0.25 dex Flag $=$ 0
Definition of parameter flags considering potential biases due to uncertainties in the RVS flux:
Flag name Condition Flag value fluxNoise $\sigma$$T_{\rm eff}$$>$2000 K or Filter all $\sigma$$\log g$$>$2 dex Flag $=$ 9 $\sigma$$T_{\rm eff}$$\leq$2000 K and $\sigma$$\log g$$\leq$2 dex and Filter [M/H], [X/Fe] $\sigma$[M/H]$>$2 dex Flag $=$ 5 $\sigma$$T_{\rm eff}$$\leq$2000 K and $\sigma$$\log g$$\leq$2 dex and Filter [$\alpha$/Fe], [X/Fe] $\sigma$[M/H]$\leq$2 dex and Flag $=$ 4 $\sigma$[$\alpha$/Fe]$>$0.8 dex 500$<\sigma$$T_{\rm eff}$$\leq$2000 K and Flag $=$ 3 1$<\sigma$$\log g$$\leq$2 dex and 0.5$<\sigma$[M/H]$\leq$2 dex and 0.2$<\sigma$[$\alpha$/Fe]$\leq$0.8 dex 250$<\sigma$$T_{\rm eff}$$\leq$500 K and Flag $=$ 2 0.5$<\sigma$$\log g$$\leq$1 dex and 0.25$<\sigma$[M/H]$\leq$0.5 dex and 0.1$<\sigma$[$\alpha$/Fe]$\leq$0.2 dex 100$<\sigma$$T_{\rm eff}$$\leq$250 K and Flag $=$ 1 0.2$<\sigma$$\log g$$\leq$0.5 dex and 0.1$<\sigma$[M/H]$\leq$0.25 dex and 0.05$<\sigma$[$\alpha$/Fe]$\leq$0.1 dex $\sigma$$T_{\rm eff}$$\leq$100 K and Flag $=$ 0 $\sigma$$\log g$$\leq$0.2 dex and $\sigma$[M/H]$\leq$0.1 dex and $\sigma$[$\alpha$/Fe]$\leq$0.05 dex
Definition of parameter flags considering potential biases due to extrapolated parameters:
Flag name Condition Flag value extrapol gof$=$NaN and Filter all ($T_{\rm eff}$$>$9000 K or $T_{\rm eff}$$<$2500 K or except DIB if $T_{\rm eff}$$>$7000 K $\log g$$>$6 dex or $\log g$$<-1$ dex ) Flag $=$ 9 gof$=$NaN and 2500$\leq$$T_{\rm eff}$$\leq$9000 K and Filter [M/H],[X/Fe] $-1\leq$$\log g$$\leq$6 dex and Flag $=$ 4 ([M/H]$<-6$ dex or [M/H]$>$1.5 dex ) gof$=$NaN and 2500$\leq$$T_{\rm eff}$$<$9000 K and $-1\leq$$\log g$$\leq$6 dex and Filter [X/Fe] $-6\leq$[M/H]$\leq$1.5 dex and Flag $=$ 3 [$\alpha$/Fe] out from standard by $\pm$ 0.8 gof$=$NaN and Flag $=$ 2 2500$\leq$$T_{\rm eff}$$\leq$9000 K and $-1\leq$$\log g$$\leq$6 dex and $-6\leq$[M/H]$\leq$1.5 dex and [$\alpha$/Fe] within $\pm$ 0.8 from standard gof$\neq$NaN and Flag $=$ 1 ($T_{\rm eff}$$\geq$7625 or $T_{\rm eff}$$\leq$3500 K or $\log g$$\geq$4.75 or $\log g$$\leq$0.25 dex or [M/H]$\leq-3$ or [M/H]$\geq$0.75 dex or [$\alpha$/Fe] out from standard by $\pm$ 0.35) gof$\neq$NaN and Flag $=$ 0 3500$<$$T_{\rm eff}$$<$7625 K and 0.25$<$$\log g$$<$4.75 dex and $-3<$[M/H]$<$0.75 dex and [$\alpha$/Fe] within $\pm$ 0.35 from standard
Definition of parameter flags considering RVS flux problems or emission line probability:
Flag name Condition Flag value nanFlux Flux$=$NaN Filter all except DIB if $T_{\rm eff}$$>$7000 K Flag $=$ 9 no Nans in Flux Flag $=$ 0 emission CU6_is_emission$=$True Filter all except DIB if $T_{\rm eff}$$>$7000 K Flag $=$ 9 CU6_is_emission$=$False Flag $=$ 0 neg_flux $>$ 2 pixels with flux$<$0 Filter all except DIB if $T_{\rm eff}$$>$7000 K Flag $=$ 9 1 or 2 pixels with flux$<$0 Flag $=$ 1 flux$>$0 Flag $=$ 0 nullFluxErr $\sigma$$T_{\rm eff}$$=$0 K or $\sigma$$\log g$$=$0 dex or Filter all $\sigma$[M/H]$=$0 dex or Flag $=$ 9 $\sigma$[$\alpha$/Fe]$=$0 dex no null uncertainties for all pixel flux Flag $=$ 0
Definition of parameter flags considering problems in the parameterisation of KM-type giants. $F_{\rm min}$ is the minumum flux value in the corresponding RVS spectrum:
Flag name Condition Flag value KMgiantPar $T_{\rm eff}$$<$4000 K and $\log g$$<$3.5 and Filter [$\alpha$/Fe] (gof$>-3.0$ or $F_{\rm min}$$>$0.22) Flag $=$ 2 $T_{\rm eff}$$<$4000 K and $\log g$$<$3.5 and ($-3.4<$gof$<-3.0$ or Filter [$\alpha$/Fe] (gof$>-3.0$ and $F_{\rm min}$$<$0.22) or Flag $=$ 1 (gof$<-3.4$ and $F_{\rm min}$$>$0.22)) ($T_{\rm eff}$$<$4000 K and $\log g$$<$3.5 and Flag $=$ 0 (gof$<-3.4$ or $F_{\rm min}$$<$0.22)) or $T_{\rm eff}$$<$4000 or $\log g$$>$3.5
Definition of individual abundance upper limit flags. Xfe_gspspec_upper is the upper confidence value of the abundance, corresponding to the 84th quantile of the Monte Carlo distribution. $\sigma$[X/Fe] is the 84th$-$16th interquantile abundance uncertainty. XfeUpperLimit is the mean value of the abundance upper limit for the considered lines of element X in the spectrum, depending on the mean signal-to-noise ratio (SNR) in the line pixels and on the stellar parameters. X_MAD_UpperLimit is the median absolute deviation of the upper limit in the line pixels; the coefficients c1 to c8 are reported in a table further below:
Flag name Condition Flag value XUpLim vbroadT$\geq$2 or vbroadG$\geq$2 or vbroadM$\geq$2 or $\sigma$[X/Fe]$=$0 or (Xfe_gspspec_upper$-$Xfe_gspspec)$=$ 0 or $T_{\rm eff}$$\leq$c1 or $T_{\rm eff}$$\geq$c2 or $\log g$$\leq$c3 or $\log g$$\geq$c4 or Filter [X/Fe] ((2$-$ XfeUpperLimit)/$\sigma$[X/Fe])$\leq$c5 or Flag $=$ 9 (SNR$\leq$c6 and gof$\geq$c7) or (Xfe_gspspec+[M/H])$\leq$c8 vbroadT$<$2 and vbroadG$<$2 and vbroadM$<$2 and Flag $=$ 2 $\sigma$[X/Fe]$\neq$0 and (Xfe_gspspec_upper$-$ Xfe_gspspec)$\neq$ 0 and c1$<$$T_{\rm eff}$$<$c2 and c3$<$$\log g$$<$c4 and ((2$-$ XfeUpperLimit)/$\sigma$[X/Fe])$>$c5 and (SNR$>$c6 or (SNR$\leq$c6 and gof$<$c7)) and (Xfe_gspspec+[M/H])$<$c8 and ((Xfe_gspspec$-$ XfeUpperLimit)/(1.48$\cdot$X_MAD_UpperLimit))$<$1.5 vbroadT$<$2 and vbroadG$<$2 and vbroadM$<$2 and Flag $=$ 1 $\sigma$[X/Fe]$\neq$0 and (Xfe_gspspec_upper$-$ Xfe_gspspec)$\neq$ 0 and c1$<$$T_{\rm eff}$$<$c2 and c3$<$$\log g$$<$c4 and ((2$-$ XfeUpperLimit)/$\sigma$[X/Fe])$>$c5 and (SNR$>$c6 or (SNR$\leq$c6 and gof$<$c7)) and (Xfe_gspspec+[M/H])$<$c8 and 1.5$\leq$((Xfe_gspspec$-$ XfeUpperLimit)/(1.48$\cdot$X_MAD_UpperLimit))$<$2.5 vbroadT$<$2 and vbroadG$<$2 and vbroadM$<$2 and Flag $=$ 0 $\sigma$[X/Fe]$\neq$0 and (Xfe_gspspec_upper$-$ Xfe_gspspec)$\neq$ 0 and c1$<$$T_{\rm eff}$$<$c2 and c3$<$$\log g$$<$c4 and ((2$-$ XfeUpperLimit)/$\sigma$[X/Fe])$>$c5 and (SNR$>$c6 or (SNR$\leq$c6 and gof$<$c7)) and (Xfe_gspspec+[M/H])$<$c8 and ((Xfe_gspspec$-$ XfeUpperLimit)/(1.48$\cdot$X_MAD_UpperLimit))$\geq$2.5
Definition of individual abundance uncertainty flags. Xfe_gspspec_upper is the upper confidence value of the abundance, corresponding to the 84th quantile of the Monte Carlo distribution. $\sigma$[X/Fe] is the 84th$-$16th interquantile abundance uncertainty. XfeUpperLimit is the mean value of the abundance upper limit for the considered lines of element X in the spectrum, depending on the mean SNR in the line pixels and the stellar parameters. X_MAD_UpperLimit is the median absolute deviation of the upper limit in the line pixels; the coefficients c1 to c8 are reported in a table further below:
Flag name Condition Flag value XUncer vbroadT$\geq$2 or vbroadG$\geq$2 or vbroadM$\geq$2 or $\sigma$[X/Fe]$=$0 or (Xfe_gspspec_upper$-$Xfe_gspspec)$=$ 0 or $T_{\rm eff}$$\leq$c1 or $T_{\rm eff}$$\geq$c2 or $\log g$$\leq$c3 or $\log g$$\geq$c4 or Filter [X/Fe] ((2$-$XfeUpperLimit)/$\sigma$[X/Fe])$\leq$c5 or Flag $=$ 9 (SNR$\leq$c6 and gof$\geq$c7) or (Xfe_gspspec+[M/H])$\leq$c8 vbroadT$<$2 and vbroadG$<$2 and vbroadM$<$2 and Flag $=$ 2 $\sigma$[X/Fe]$\neq$0 and (Xfe_gspspec_upper$-$Xfe_gspspec)$\neq$ 0 and c1$<$$T_{\rm eff}$$<$c2 and c3$<$$\log g$$<$c4 and c5$<$((2$-$XfeUpperLimit)/$\sigma$[X/Fe])$<$7 and (SNR$>$c6 or (SNR$\leq$c6 and gof$<$c7)) and (Xfe_gspspec+[M/H])$<$c8 vbroadT$<$2 and vbroadG$<$2 and vbroadM$<$2 and Flag $=$ 1 $\sigma$[X/Fe]$\neq$0 and (Xfe_gspspec_upper$-$Xfe_gspspec)$\neq$ 0 and c1$<$$T_{\rm eff}$$<$c2 and c3$<$$\log g$$<$c4 and 7$\leq$((2$-$XfeUpperLimit)/$\sigma$[X/Fe])$<$10 and (SNR$>$c6 or (SNR$\leq$c6 and gof$<$c7)) and (Xfe_gspspec+[M/H])$<$c8 vbroadT$<$2 and vbroadG$<$2 and vbroadM$<$2 and Flag $=$ 0 $\sigma$[X/Fe]$\neq$0 and (Xfe_gspspec_upper$-$Xfe_gspspec)$\neq$ 0 and c1$<$$T_{\rm eff}$$<$c2 and c3$<$$\log g$$<$c4 and ((2$-$XfeUpperLimit)/$\sigma$[X/Fe])$\geq$10 and (SNR$>$c6 or (SNR$\leq$c6 and gof$<$c7)) and (Xfe_gspspec+[M/H])$<$c8
Coefficients for individual chemical abundance filtering used in the previous two tables:
Chemical abundance c1 c2 c3 c4 c5 c6 c7 c8 [N/Fe] 4200 8000 0.0 5.5 4.5 100 $-3.6$ 99 [Mg/Fe] 3500 8000 $-1.0$ 5.5 5.5 80 $-3.5$ 99 [Si/Fe] 4000 8000 $-1.0$ 5.5 6.0 110 $-3.8$ 99 [S/Fe] 5500 8000 3.0 5.5 5.0 120 $-3.7$ 99 [Ca/Fe] 3500 8000 $-1.0$ 5.5 10.0 60 $-3.2$ 99 [Ti/Fe] 4000 6500 $-1.0$ 5.5 6.0 110 $-3.65$ 99 [Cr/Fe] 3500 6000 $-1.0$ 5.5 6.0 1000 $-3.65$ 1.5 [Fe/M] 3500 8000 $-1.0$ 5.5 5.0 1000 $-3.4$ 1.5 [FeII/M] 5700 8000 3.5 5.5 5.0 70 $-3.5$ 1.5 [Ni/Fe] 4000 6500 $-1.0$ 5.5 6.0 100 $-3.6$ 1.5 [Zr/Fe] 3500 8000 $-1.0$ 5.5 1.0 100 $-3.4$ 99 [Ce/Fe] 3500 8000 $-1.0$ 5.5 5.0 100 $-3.5$ 99 [Nd/Fe] 3500 5500 $-1.0$ 5.5 2.0 100 $-3.5$ 99
Definition of the quality flag of the CN equivalent width difference with respect to the standard C and N abundances. CN_EW_err is the uncertainty of equivalent witdh of the cyanogen absorption line (cn0ew_gspspec_uncertainty); CN_p1 is the measured central wavelength of the cyanogen absorption line (cn0_gspspec_centralline); CN_p2 is the width of the cyoanogen line (cn0_gspspec_width):
Flag name Condition Flag value DeltaCNq vbroadT$\geq$1 or vbroadG$\geq$1 or vbroadM$\geq$1 or CN_EW_err $=$ 0 or SNR$\leq$80 or gof$\geq-3.5$ or Filter CN $T_{\rm eff}$$\geq$4800 K or $\log g$$\geq$3.8 or Flag $=$ 9 abs(CN_p1 $-$ 862.884)$\geq$0.05 or CN_p2$\geq$0.25 vbroadT$<$1 and vbroadG$<$1 and vbroadM$<$1 and Flag $=$ 0 CN_EW$\_$err$\neq$0 and SNR$>$80 and gof$<-3.5$ and $T_{\rm eff}$$<$4800 K and $\log g$$<$3.8 and abs(CN_p1 $-$ 862.884)$<$0.05 and CN_p2$<$0.25
Definition of the quality flag for the diffuse interstellar band parameterisation. $p_{0}$ is the depth of the DIB (dibp0_gspspec); $p_{1}$ is the measured central wavelength of the DIB (dib_gspspec_lambda); $p_{2}$ is the width of the DIB (dibp2_gspspec); $R_{\rm a}$ is the standard deviation of the data–model residuals between 860.5 and 864.0 nm; $R_{\rm b}$ is the local noise level within the DIB profile :
Flag name Condition Flag value DIBq SNR$\leq$50 or radial_velocity_error$>$5 km/s or $T_{\rm eff}$$<$3500 K or $T_{\rm eff}$$>$10${}^{6}$ K or Filter DIB $flux<$ 0 or Flag $=$ 9 $p_{0}$ $<$ 3/SNR $p_{1}<$ 861.66 nm or $p_{1}>$ 862.81 nm or Flag $=$ 5 $p_{0}>0.15$ 861.66 nm $ 862.81 nm and Flag $=$ 4 $p_{0} and $0.6 861.66 nm $ 862.81 nm and Flag $=$ 3 $p_{0}>R_{\rm b}$ and $0.6 861.66 nm $ 862.81 nm and Flag $=$ 2 $p_{0}>\max(R_{\rm a},R_{\rm b})$ and $0.6 861.66 nm $ 862.81 nm and Flag $=$ 1 $p_{0}>R_{\rm b}$ and $1.2 861.66 nm $ 862.81 nm and Flag $=$ 0 $p_{0}>\max(R_{\rm a},R_{\rm b})$ and $1.2
logchisq_gspspec : Logarithm of the goodness-of-fit for the GSP-Spec MatisseGauguin parameters (float)
Logarithm to the base 10 of the chi-squared between input spectrum rebinned to 800 pixels and solution synthetic spectrum computed from GSP-Spec MatisseGauguin (Recio-Blanco and et al. 2022).
ew_espels_halpha : Halpha pseudo-equivalent width from ESP-ELS (float, Length & Distance[nm])
Pseudo-equivalent width of the H$\alpha$ line measured on the RP spectra (Section 11.3.7). The value is expected to be negative when emission is present. To try to compensate for the existence of blends with species other than hydrogen in the cooler stars and assuming that no photospheric H$\alpha$ absorption is expected for K and M stars, we subtracted at $T_{\mathrm{eff}}<$ 5 000 K the pseudo-equivalent width measured on a synthetic spectrum with astrophysical parameters close to those derived by GSP-Phot for the target. The value that was subtracted (i.e. when $T_{\mathrm{eff}}<$ 5 000 K) is stored in ew_espels_halpha_model. ESP-ELS was only applied on targets brighter than magnitude G=17.65. More information on the module can be found in Section 11.3.7 and Section 11.4.4.
ew_espels_halpha_uncertainty : Uncertainty of the Halpha pseudo-equivalent width from ESP-ELS (float, Length & Distance[nm])
Uncertainty estimated on the pseudo-equivalent width of the H$\alpha$ line. It is computed by propagating the RP flux uncertainties through the integration over the considered H$\alpha$ window. Correlations between samples were ignored. ESP-ELS was only applied on targets brighter than magnitude G=17.65. More information on the module can be found in Section 11.3.7 and Section 11.4.4.
ew_espels_halpha_flag : Quality flag of the Halpha pseudo-equivalent width from ESP-ELS (string)
Quality flag of the H$\alpha$ pseudo-equivalent width. It takes the following values:
• 0: if the value stored in ew_espels_halpha_model was not subtracted ($T_{\mathrm{eff}}\geq$ 5 000 K).
• 1: if the value stored in ew_espels_halpha_model was subtracted ($T_{\mathrm{eff}}<$ 5 000 K).
ESP-ELS was only applied on targets brighter than magnitude G=17.65. More information on the module can be found in Section 11.3.7 and Section 11.4.4.
ew_espels_halpha_model : Halpha pseudo-equivalent width from ESP-ELS measured on the synthetic spectrum (float, Length & Distance[nm])
H$\alpha$ pseudo-equivalent width measured on the synthetic spectrum having the nearest astrophysical parameters to those derived by GSP-Phot (best library value, before post-processing). The value is available even when no ELS classification was provided and even when the value was not subtracted from the pseudo-equivalent width measured on the observed spectrum. ESP-ELS was only applied on targets brighter than magnitude G=17.65. More information on the module can be found in Section 11.3.7 and Section 11.4.4.
classlabel_espels : Adopted ELS class label from ESP-ELS (string)
The emission-line star class is based on the analysis of the BP/RP spectrum. Two random forest algorithms were used to classify the ELS targets. The first classifier is aimed to identify Wolf-Rayet stars and planetary nebulæ, and was trained on a subset of Gaia spectra chosen to be representative of each class. The second classifier is applied once significant H$\alpha$ emission was detected in order to identify Be, Herbig Ae/Be, T Tauri, and active M dwarf stars. It was trained on Gaia BP/RP spectra and on the astrophysical parameters. The astrophysical parameters adopted during the training and the processing are those obtained by GSP-Phot (best library value, taken before any post-processing filter or calibration was applied) for the target. The class label corresponds to the one having the highest probability and can take the following values:
• beStar (Be star)
• HerbigStar (Herbig Ae/Be star)
• PlanetaryNebula (Planetary Nebula)
• RedDwarfEmStar (active M dwarf star)
• TTauri (T Tauri star)
• wC (Wolf-Rayet star of type WC)
• wN (Wolf-Rayet star of type WN)
When no emission was found or when the spectrum could not be classified, the field is empty. ESP-ELS was only applied on targets brighter than magnitude G=17.65. More information on the module can be found in Section 11.3.7 and Section 11.4.4.
classlabel_espels_flag : Quality flag of the adopted ELS class label from ESP-ELS (string)
The quality flag provided with the ELS class label (classlabel_espels) indicates better quality for lower values of the flag. In a first instance, the quality assessment is based on the difference ($\Delta p$) between the 2 highest probabilities. The flag therefore takes the following values:
• $\Delta p\geq 0.8$: 0
• $\Delta p\geq 0.6$: 1
• $\Delta p\geq 0.4$: 2
• $\Delta p\geq 0.2$: 3
• $\Delta p<0.2$: 4
It is important to note that the identification of Be stars, Herbig Ae/Be stars, T Tauri stars, and active M dwarf stars also relies on the astrophysical parameters (APs) derived by GSP-Phot. After validation and during the post-processing, a significant fraction of APs that were suspected of being wrong or inaccurate have been removed or changed. On the other hand part of the APs that survived the post-processing disagree significantly with the spectal type tag provided by ESP-ELS and may point towards issues with the APs, the spectral type tag, or/and with the input data. To identify both cases, the quality flag was updated after processing as follows:
• classlabel_espels_flag+10: APs and spectral type tag are not consistent.
• classlabel_espels_flag+20: APs were removed during the post-processing.
ESP-ELS was only applied on targets brighter than magnitude G=17.65. More information on the module can be found in Section 11.3.7 and Section 11.4.4.
classprob_espels_wcstar : Probability from ESP-ELS of being a Wolf-Rayet star of type WC (float)
The probability of being a Wolf-Rayet star of type WC is derived on the BP/RP spectra by applying a random forest algorithm trained on a subset of Gaia spectra chosen to be representative of the WC stellar class. ESP-ELS was only applied on targets brighter than magnitude G=17.65. More information on the module can be found in Section 11.3.7 and Section 11.4.4.
classprob_espels_wnstar : Probability from ESP-ELS of being a Wolf-Rayet star of type WN (float)
The probability of being a Wolf-Rayet star of type WN is derived on the BP/RP spectra by applying a random forest algorithm trained on a subset of Gaia spectra chosen to be representative of the WN stellar class. ESP-ELS was only applied on targets brighter than magnitude G=17.65. More information on the module can be found in Section 11.3.7 and Section 11.4.4.
classprob_espels_bestar : Probability from ESP-ELS of being a Be Star (float)
The probability of being a Be star is derived on the BP/RP spectra by applying a random forest algorithm trained on a subset of Gaia spectra chosen to be representative of the Be stellar class, as well as on the corresponding astrophysical parameters provided by GSP-Phot (best library estimate before post-processing). ESP-ELS module was only applied on targets brighter than magnitude G=17.65. More information on the module can be found in Section 11.3.7 and Section 11.4.4.
classprob_espels_ttauristar : Probability from ESP-ELS of being a T Tauri Star (float)
The probability of being a T Tauri star is derived on the BP/RP spectra by applying a random forest algorithm trained on a subset of Gaia spectra chosen to be representative of the T Tauri stellar class, as well as on the corresponding astrophysical parameters provided by GSP-Phot (best library estimate before post-processing). ESP-ELS was only applied on targets brighter than magnitude G=17.65. More information on the module can be found in Section 11.3.7 and Section 11.4.4.
classprob_espels_herbigstar : Probability from ESP-ELS of being a Herbig Ae/Be Star (float)
The probability of being a Herbig Ae/Be star is derived on the BP/RP spectra by applying a random forest algorithm trained on a subset of Gaia spectra chosen to be representative of the Herbig Ae/Be stellar class, as well as on the corresponding astrophysical parameters provided by GSP-Phot (best library estimate before post-processing). ESP-ELS was only applied on targets brighter than magnitude G=17.65. More information on the module can be found in Section 11.3.7 and Section 11.4.4.
classprob_espels_dmestar : Probability from ESP-ELS of being an active M dwarf Star (float)
The probability of being an active M dwarf (dMe) star is derived on the BP/RP spectra by applying a random forest algorithm trained on a subset of Gaia spectra chosen to be representative of the dMe stellar class, as well as on the corresponding astrophysical parameters provided by GSP-Phot (best library estimate before post-processing). ESP-ELS was only applied on targets brighter than magnitude G=17.65. More information on the module can be found in Section 11.3.7 and Section 11.4.4.
classprob_espels_pne : Probability from ESP-ELS of being a planetary nebula (float)
The probability of being a planetary nebula (PN/PNe) is derived on the BP/RP spectra by applying a random forest algorithm trained on a subset of Gaia spectra chosen to be representative of PNe. ESP-ELS was only applied on targets brighter than magnitude G=17.65. More information on the module can be found in Section 11.3.7 and Section 11.4.4.
azero_esphs : Monochromatic interstellar extinction, A${}_{\mathrm{0}}$, from ESP-HS (float, Magnitude[mag])
Monochromatic interstellar extinction, A${}_{\mathrm{0}}$, derived at 541.4 nm by ESP-HS from the comparison of the observed BP/RP and, when available, RVS spectra to simulations. ESP-HS is processing targets brighter than magnitude G=17.65, and which are tagged O, B, or A in the spectraltype_esphs field. A more detailed description of the module is provided in Section 11.3.8 and Section 11.4.6.
azero_esphs_uncertainty : Uncertainty at a 68% confidence level on A${}_{\mathrm{0}}$ from ESP-HS (float, Magnitude[mag])
Uncertainty on A${}_{\mathrm{0}}$ derived by ESP-HS. The value is provided by the diagonal of the covariance matrix. At all steps, the correlation between flux samples is ignored. Uncertainties were found to be underestimated by a factor 5 to 10 in the BP/RP+RVS processing mode (i.e. first digit/character of flags_esphs has value 0). ESP-HS is processing targets brighter than magnitude G=17.65, and which are tagged O, B, or A in the spectraltype_esphs field. A more detailed description of the module is provided in Section 11.3.8 and Section 11.4.6.
ag_esphs : Intersterstellar extinction in G band from ESP-HS (float, Magnitude[mag])
Interstellar extinction in G band, $A_{\rm G}$, derived by ESP-HS from the comparison of the observed BP/RP and, when available, RVS spectra to simulations. ESP-HS is processing targets brighter than magnitude G=17.65, and which are tagged O, B, or A in the spectraltype_esphs field. A more detailed description of the module is provided in Section 11.3.8 and Section 11.4.6.
ag_esphs_uncertainty : Uncertainty on $A_{\rm G}$ from ESP-HS (float, Magnitude[mag])
Uncertainty on $A_{\rm G}$ derived by ESP-HS. The value is inferred from the uncertainty of A${}_{\mathrm{0}}$. Uncertainties were found to be underestimated by a factor 5 to 10 in the BP/RP+RVS processing mode (i.e. first digit/character of flags_esphs has value 0). ESP-HS is processing targets brighter than magnitude G=17.65, and which are tagged O, B, or A in the spectraltype_esphs field. A more detailed description of the module is provided in Section 11.3.8 and Section 11.4.6.
ebpminrp_esphs : Reddening $E(G_{\rm BP}-G_{\rm RP})$ from ESP-HS (float, Magnitude[mag])
Interstellar reddening, $E(G_{\rm BP}-G_{\rm RP})$, derived by ESP-HS from the comparison of the observed BP/RP and, when available, RVS spectra to simulations. ESP-HS is processing targets brighter than magnitude G=17.65, and which are tagged O, B, or A in the spectraltype_esphs field. A more detailed description of the module is provided in Section 11.3.8 and Section 11.4.6.
ebpminrp_esphs_uncertainty : Uncertainty on $E(G_{\rm BP}-G_{\rm RP})$ from ESP-HS (float, Magnitude[mag])
Uncertainty on $E(G_{\rm BP}-G_{\rm RP})$ derived by ESP-HS. The value is inferred from the uncertainty of A${}_{\mathrm{0}}$. Uncertainties were found to be underestimated by a factor 5 to 10 in the BP/RP+RVS processing mode (i.e. first digit/character of flags_esphs has value 0). ESP-HS is processing targets brighter than magnitude G=17.65, and which are tagged O, B, or A in the spectraltype_esphs field. A more detailed description of the module is provided in Section 11.3.8 and Section 11.4.6.
teff_esphs : Effective temperature from ESP-HS (float, Temperature[K])
Effective temperature derived by fitting the BP/RP and, when available, the RVS spectra with synthetic spectra. The module assumes a solar chemical composition. ESP-HS is processing targets brighter than magnitude G=17.65, and which are tagged O, B, or A in the spectraltype_esphs field. A more detailed description of the module is provided in Section 11.3.8 and Section 11.4.4.
teff_esphs_uncertainty : Uncertainty at a 68% confidence level on the effective temperature from ESP-HS (float, Temperature[K])
Uncertainty on the effective temperature derived by ESP-HS. The value is extracted from the diagonal of the covariance matrix. At all steps, the correlation between flux samples is ignored. Uncertainties were found to be underestimated by a factor 5 to 10 in the BP/RP+RVS processing mode (i.e. first digit/character of spectraltype_esphs has value 0). A more detailed description of ESP-HS is provided in Section 11.3.8 and Section 11.4.4.
logg_esphs : Surface gravity from ESP-HS (float, GravitySurface[log cgs])
Surface gravity derived by fitting the BP/RP and, when available, the RVS spectra with synthetic spectra. The module assumes a solar chemical composition. ESP-HS is processing targets brighter than magnitude G=17.65, and which are tagged O, B, or A in the spectraltype_esphs field. A more detailed description of the module is provided in Section 11.3.8 and Section 11.4.4.
logg_esphs_uncertainty : Uncertainty at a 68% confidence level on the surface gravity from ESP-HS (float, GravitySurface[log cgs])
Uncertainty on the surface gravity derived by ESP-HS. The value is extracted from the diagonal of the covariance matrix. At all steps, the correlation between flux samples is ignored. Uncertainties were found to be underestimated by a factor 5 to 10 in the BP/RP+RVS processing mode (i.e. first digit/character of flags_esphs has value 0). A more detailed description of ESP-HS is provided in Section 11.3.8 and Section 11.4.4.
vsini_esphs : Projected rotational velocity from ESP-HS (float, Velocity[km s${}^{-1}$])
The line broadening of the RVS spectrum is derived by assuming that it is due to stellar rotation and by adopting the same method as described in Frémat et al. (2022). Therefore, we named it $v\sin i$. A value is only provided in the BP/RP+RVS mode (i.e. first digit/character of flags_esphs has value 0). ESP-HS is processing targets brighter than magnitude G=17.65, and which are tagged O, B, or A in the spectraltype_esphs field. A more detailed description of the module is provided in Section 11.3.8 and Section 11.4.4.
vsini_esphs_uncertainty : Uncertainty on the projected rotational velocity from ESP-HS (float, Velocity[km s${}^{-1}$])
The uncertainty on $v\sin i$ was derived by adopting the approach described in Zucker (2003).
flags_esphs : Quality flag of the ESP-HS parametrisation (string)
The quality flag usually has 2 digits. The first digit tells what processing mode was used to derive the effective temperature, surface gravity, interstellar extinction and reddening, and $v\sin i$. It takes the following values:
• 0: when both BP/RP and RVS spectra were used.
• 1: when BP/RP only was used. In this mode no $v\sin i$ is available.
The second digit is relative to the spectral type (spectraltype_esphs) that is derived from the analysis of the BP/RP spectrum only. During the processing a probability was assigned, and used for the quality assessment of the spectral type tagging. Therefore, the second digit of flags_esphs ranges from 1 to 5, depending on the first (p1) and second (p2) highest probability as follows:
• p1 $>0.5$ and p2 $\leq 0.1$: second digit of flags_esphs = 1
• p1 $>0.5$ and p2 $\leq 0.2$: second digit of flags_esphs = 2
• p1 $>0.5$ and p2 $\leq 0.3$: second digit of flags_esphs = 3
• p1 $>0.5$ and p2 $\leq 0.4$: second digit of flags_esphs = 4
• p1 $\leq 0.5$: second digit of flags_esphs = 5
• target brighter than G=17.65, but no spectral type tag was derived: flags_esphs = 999
During the validation of the CSTAR spectral type tag used to identify candidate carbon stars (Gaia Collaboration et al. 2022c), it was noted that only a fraction of these had significantly stronger than normal C${}_{2}$ and CN molecular bands. We flagged these targets by setting the second digit of flags_esphs to 0.
When the algorithm was not able to properly set the quality flag (for 2.7 % of the targets with a spectral type tag) it received the value ’999’. In these cases, no parameters nor classification was derived but the corresponding spectral type tag was kept.
spectraltype_esphs : Spectral type from ESP-ELS (string)
The spectral type tag is obtained by ESP-ELS. At the origin it was obtained by ESP-HS (we kept the module name), but the corresponding algorithm was later moved to the upstream module ESP-ELS. It is derived from the analysis of the BP/RP spectrum only, and takes the following values: CSTAR,M,K,G,F,A,B,O. ESP-ELS is processing targets brighter than magnitude G=17.65. A more detailed description of the module is provided in Section 11.3.7 and Section 11.4.4.
activityindex_espcs : Chromospheric activity index from ESP-CS, measured on the calcium triplet using RVS spectra (float, Length & Distance[nm])
The activity index from the Apsis module ESP-CS is computed by comparing the observed RVS spectrum with a purely photospheric template spectrum obtained by interpolating in a grid of synthetic spectra. The atmospheric parameters (APs) adopted in the interpolation are taken from the output of either GSP-Spec or GSP-Phot. GSP-Spec APs are adopted when all three parameters teff_gspspec, logg_gspspec, and mh_gspspec are provided. Otherwise teff_gspphot, logGspphot, and mh_gspphot are adopted, if they are all provided. The activity index gives the excess equivalent width factor in the cores of the Ca II infrared triplet lines with respect to the template inactive spectrum. The excess equivalent width is computed for each of the Ca II infrared triplet lines and the three values obtained are averaged. When the projected rotational velocity vbroad in table gaia_source is provided, rotational broadening is taken into account. See Section 11.3.9 for details.
activityindex_espcs_uncertainty : Uncertainty in the chromospheric activity index from ESP-CS (float, Length & Distance[nm])
Uncertainty in the activity index from ESP-CS (activityindex_espcs). The uncertainty is computed by considering the standard deviation of the excess equivalent width factor in each of the Ca II infrared triplet lines, taking spectrum noise into account, and applying error propagation. See Section 11.3.9 for details.
activityindex_espcs_input : Source of input stellar parameters for the computation of the activity index by ESP-CS (string)
Flag indicating the source of the stellar atmospheric parameters used by ESP-CS in deriving the activity index. The flag has the value “M1” if the source is GSP-Spec, and “M2” if the source is GSP-Phot. See the description of activityindex_espcs.
teff_espucd : Effective temperature estimate from ESP-UCD based on the RP spectrum (float, Temperature[K])
Effective temperature estimate from ESP-UCD inferred from the RP spectrum. The prediction module is based on a Gaussian Process trained with empirical examples. See Section 11.3.10 for details.
teff_espucd_uncertainty : Uncertainty of the effective temperature estimate produced by ESP-UCD (float, Temperature[K])
Standard deviation of 10 effective temperature predictions obtained by the ESP-UCD module for 10 RP spectra generated using random sampling from Gaussian distributions centred at the observed fluxes and with standard deviations given by the flux uncertainties. The value thus obtained is rescaled (multiplied by 7) to match the root-mean-square error of the module predictions for a set of well-known ultracool dwarfs (see Section 11.3.10 for further details).
flags_espucd : Quality flags of the ESP-UCD parameter estimates (string)
Two-digits ESP-UCD parameters quality flag. The first digit (0, 1 or 2) is based on the goodness-of-fit estimate and the RP spectrum signal-to-noise ratio, 0 being the best quality. The second digit is 1 for sources with inconsistent $T_{\rm eff}$ predictions given the value of $G+5\cdot\log_{10}(\varpi)+5$. It is 0 for all other sources. See Section 11.3.10 for a quantitative definition of the three quality categories for the first digit and of the inconsistency criterion for the second digit.
radius_flame : Radius of the star from FLAME using teff_gspphot and lum_flame (float, Length & Distance[Solar Radius])
The radius of the star from FLAME, derived from teff_gspphot and lum_flame using the Stefan-Boltzmann law with a solar effective temperature of 5772 K, see Section 1.2.3, and associated uncertainties. It is defined as the median value (50${}^{th}$ percentile) of the distribution from sampling.
Lower confidence level (16%) of the radius of the star from FLAME, see description for radius_flame. It is derived from teff_gspphot, lum_flame and associated uncertainties. It is defined as the 16${}^{th}$ percentile value of the distribution from sampling. Upper and lower levels include 68% confidence interval.
Upper confidence level (84%) of the radius of the star from FLAME, see description for radius_flame. It is derived from teff_gspphot, lum_flame and associated uncertainties. It is defined as the 84${}^{th}$ percentile value of the distribution from sampling. Upper and lower levels include 68% confidence interval.
lum_flame : Luminosity of the star from FLAME using G band magnitude, extinction (ag_gspphot), parallax or distance, and a bolometric correction bc_flame (float, Luminosity[Solar Luminosity])
Luminosity of the star from FLAME using G band magnitude, extinction from GSP-Phot (ag_gspphot), parallax or distance_gspphot, and a bolometric correction bc_flame. It is defined as the median value (50${}^{th}$ percentile) of the distribution from sampling. The bolometric correction depends on the effective temperature, metallicity and surface gravity, and these are based on GSP-Phot values. The bolometric magnitude of the Sun = 4.74 mag, see Section 1.2.3 and the reference absolute G-band magnitude of the Sun is 4.66 mag, see Section 11.3.6.
lum_flame_lower : Lower confidence level (16%) of lum_flame (float, Luminosity[Solar Luminosity])
Lower confidence level (16%) of the luminosity of the star from FLAME, see description for lum_flame. It is defined as the 16${}^{th}$ percentile value of the distribution from sampling. Upper and lower levels contain the 68% confidence interval.
lum_flame_upper : Upper confidence level (84%) of lum_flame (float, Luminosity[Solar Luminosity])
The upper confidence level (84%) of the luminosity of the star from FLAME, see description for lum_flame. It is defined as the 84${}^{th}$ percentile value of the distribution from sampling. Upper and lower levels contain the 68% confidence interval.
mass_flame : Mass of the star from FLAME using stellar models, lum_flame, and teff_gspphot (float, Mass[Solar Mass])
Mass of the star from FLAME. It is defined as the median value (50${}^{th}$ percentile) of the 1D projected distribution from sampling in mass and age. It is derived by comparing teff_gspphot and lum_flame to the BASTI solar metallicity stellar evolution models (Hidalgo et al. 2018), see Section 11.3.6 for details.
mass_flame_lower : Lower confidence level (16%) of mass_flame (float, Mass[Solar Mass])
Lower confidence level (16%) of the mass of the star from FLAME, see description for mass_flame. It is defined as the 16${}^{th}$ percentile value of the 1D projected distribution from sampling in mass and age. Upper and lower levels contain the 68% confidence interval.
mass_flame_upper : Upper confidence level (84%) of mass_flame (float, Mass[Solar Mass])
Upper confidence level (84%) of the mass of the star from FLAME, see description for mass_flame. It is defined as the 84${}^{th}$ percentile value of the 1D projected distribution from sampling in mass and age. Upper and lower levels contain the 68% confidence interval.
age_flame : Age of the star from FLAME using stellar models, see mass_flame for details (float, Time[Gyr])
Age of the star from FLAME. It is defined as the median value (50${}^{th}$ percentile) of the 1D projected distribution from sampling in mass and age, see mass_flame for details.
age_flame_lower : Lower confidence level (16%) of age_flame (float, Time[Gyr])
Lower confidence level (16%) of the age of the star from FLAME, see description for age_flame. It is defined as the 16${}^{th}$ percentile value of the 1D projected distribution from sampling in mass and age. Upper and lower levels contain the 68% confidence interval.
age_flame_upper : Upper confidence level (84%) of age_flame (float, Time[Gyr])
Upper confidence level (84%) of the age of the star from FLAME, see description for age_flame. It is defined as the 84${}^{th}$ percentile value of the 1D projected distribution from sampling in mass and age. Upper and lower levels contain the 68% confidence interval.
flags_flame : Flags indicating quality and processing information from FLAME (string)
This field contains the quality and processing flags from FLAME and takes the form ‘AB’. The first digit refers to the quality of the mass and age determination (A = 0, 1, 2) and the second digit (B) informs the user if the parallax or distance_gspphot was used for deriving all FLAME stellar parameters (lum_flame, radius_flame,…). Concerning the quality of the mass and age (first digit, A), the following is adopted:
• A=0
nothing to report
• A=1
the star is a giant and the mass and age should be considered with an uncertainty on the order of 20% - 30%
• A=2
the mass and age are not available
We note that while the evolstage_flame parameter is related to mass and age, this flag is not applicable to this parameter.
For the second digit, B, the following is adopted:
• B=0
parallax is used
• B=1
distance_gspphot is used
• B=2
parallax is used due to convergence issues with distance_gspphot
See Section 11.3.6 of the online documentation for details.
evolstage_flame : Evolutionary stage of the star from FLAME using stellar models, see mass_flame for details (int)
Evolution stage of the star from FLAME. It is an integer value typically between 100 and 1300 and defined using the median value (50${}^{th}$ percentile) of the 1D projected distribution from sampling in mass and age, see mass_flame for details. The value is adapted from the BASTI model grid (Hidalgo et al. 2018) adopting the following convention:
• $100=$ zero age main sequence (ZAMS)
• $300=$ first minimum of $T_{\rm eff}$ for massive stars or central hydrogen mass fraction = 0.30 for low-mass stars
• $360=$ main sequence turn-off
• $420=$ central hydrogen mass fraction = 0.00
• $490=$ base of the red giant branch (RGB)
• $860=$ maximum $\cal{L}$ along the RGB bump
• 890 = minimum $\cal{L}$ along the RGB bump
• 1290 = tip of the RGB
gravredshift_flame : Gravitational redshift from FLAME using radius_flame and logg_gspphot (float, Velocity[km s${}^{-1}$])
Gravitational redshift, in velocity, from FLAME using radius_flame and logg_gspphot.
gravredshift_flame_lower : Lower confidence level (16%) of gravredshift_flame (float, Velocity[km s${}^{-1}$])
Lower confidence level (16%) of the gravitational redshift of the star from FLAME, see description for gravredshift_flame. It is defined as the 16${}^{th}$ percentile value of the distribution from sampling. Upper and lower levels contain the 68% confidence interval.
gravredshift_flame_upper : Upper confidence level (84%) of gravredshift_flame (float, Velocity[km s${}^{-1}$])
Upper confidence level (84%) of the gravitational redshift of the star from FLAME, see description for gravredshift_flame. It is defined as the 84${}^{th}$ percentile value of the distribution from sampling. Upper and lower levels contain the 68% confidence interval.
bc_flame : Bolometric correction used to derive lum_flame (float, Magnitude[mag])
Bolometric correction for the G-band magnitude (${\mathrm{BC}_{G}}$) used to derive lum_flame. It is defined as the median value (50${}^{th}$ percentile) of the distribution from sampling. It is a function of effective temperature, surface gravity, and metallicity, and has been derived from MARCS models, see Section 11.2.3 of the online documentation. The bolometric correction for the Sun is defined as +0.08 mag, see Section 11.3.6, where M${}_{\rm bol,\odot}=4.74$ mag, see Section 1.2.3, i.e. M${}_{G\odot}=4.66$ mag.
mh_msc : Metallicity of the source treated as a binary system from MSC using BP/RP spectra and parallax (float, Abundances[dex])
Decimal logarithm of the ratio of the average number abundance of elements heavier than helium compared to hydrogen relative to the same ratio of solar abundances ([M/H]) (assuming source is a binary system) from MSC using BP/RP spectra and parallax. Because MSC uses an empirical BPRP forward model trained on APOGEE astrophysical parameters the results are tied to the metallicity scale of the set of APOGEE targets used as the training set. The metallicity value is the median of the MCMC samples. It is assumed that both components of the binary system have the same metallicity. For details see Section 11.3.5.
mh_msc_upper : Upper confidence level (84%) of the metallicity from MSC using BP/RP spectra and parallax (float, Abundances[dex])
Upper confidence level of the metallicity inferred by MSC from BP/RP spectra and parallax. This is the 84th percentile. Lower and upper levels include 68% confidence (corresponding to a conventional 1-sigma interval).
mh_msc_lower : Lower confidence level (16%) of the metallicity from MSC using BP/RP spectra and parallax (float, Abundances[dex])
Lower confidence level of the metallicity inferred by MSC from BP/RP spectra and parallax. This is the 16th percentile. Lower and upper levels include 68% confidence (corresponding to a conventional 1-sigma interval).
azero_msc : Monochromatic extinction $A_{0}$ at 541.4 nm of the source treated as a binary system from MSC using BP/RP spectra and parallax (float, Magnitude[mag])
Monochromatic extinction $A_{0}$ at 541.4 nm of the source (assuming source is a binary system) inferred by MSC from BP/RP spectra and parallax. This is the median of the MCMC samples. NB: This is the extinction parameter in the adopted Fitzpatrick extinction law (Fitzpatrick 1999, see Section 11.2.3 of the online documentation).
azero_msc_upper : Upper confidence level (84%) of monochromatic extinction $A_{0}$ at 541.4 nm from MSC using BP/RP spectra and parallax (float, Magnitude[mag])
Upper confidence level of $A_{0}$ inferred by MSC from BP/RP spectra and parallax. This is the 84th percentile. Lower and upper levels include 68% confidence (corresponding to a conventional 1-sigma interval).
azero_msc_lower : Lower confidence level (16%) of monochromatic extinction $A_{0}$ at 541.4 nm from MSC using BP/RP spectra and parallax (float, Magnitude[mag])
Lower confidence level of $A_{0}$ inferred by MSC from BP/RP spectra and parallax. This is the 16th percentile. Lower and upper levels include 68% confidence (corresponding to a conventional 1-sigma interval).
distance_msc : Distance from MSC using BP/RP spectra and parallax (float, Length & Distance[pc])
Distance of the source (assuming source is a binary system) inferred by MSC from BP/RP spectra and parallax. This is the median of the MCMC samples. For details see Section 11.3.5.
distance_msc_upper : Upper confidence level (84%) of distance from MSC using BP/RP spectra and parallax (float, Length & Distance[pc])
Upper confidence level of distance inferred by MSC from BP/RP spectra and parallax. This is the 84th percentile. Lower and upper levels include 68% confidence (corresponding to a conventional 1-sigma interval).
distance_msc_lower : Lower confidence level (16%) of distance from MSC using BP/RP spectra and parallax (float, Length & Distance[pc])
Lower confidence level of distance inferred by MSC from BP/RP spectra and parallax. This is the 16th percentile. Lower and upper levels include 68% confidence (corresponding to a conventional 1-sigma interval).
teff_msc1 : Effective temperature of the primary from MSC using BP/RP spectra and parallax (float, Temperature[K])
Effective temperature of the primary (assuming source is a binary system and the primary is the component with more flux in the BP and RP spectra combined) inferred by MSC from BP/RP spectra and parallax. This is the median of the MCMC samples. For details see Section 11.3.5.
teff_msc1_upper : Upper confidence level (84%) of effective temperature of the primary from MSC using BP/RP spectra and parallax (float, Temperature[K])
Upper confidence level of effective temperature of the primary inferred by MSC from BP/RP spectra and parallax. This is the 84th percentile. Lower and upper levels include 68% confidence (corresponding to a conventional 1-sigma interval).
teff_msc1_lower : Lower confidence level (16%) of effective temperature of the primary from MSC using BP/RP spectra and parallax (float, Temperature[K])
Lower confidence level of effective temperature of the primary inferred by MSC from BP/RP spectra and parallax. This is the 16th percentile. Lower and upper levels include 68% confidence (corresponding to a conventional 1-sigma interval).
teff_msc2 : Effective temperature of the secondary from MSC using BP/RP spectra and parallax (float, Temperature[K])
Effective temperature of the secondary (assuming source is a binary system and the secondary is the component with less flux in the BP and RP spectra combined) inferred by MSC from BP/RP spectra and parallax. This is the median of the MCMC samples. For details see Section 11.3.5.
teff_msc2_upper : Upper confidence level (84%) of effective temperature of the secondary from MSC using BP/RP spectra and parallax (float, Temperature[K])
Upper confidence level of effective temperature of the secondary inferred by MSC from BP/RP spectra and parallax. This is the 84th percentile. Lower and upper levels include 68% confidence (corresponding to a conventional 1-sigma interval).
teff_msc2_lower : Lower confidence level (16%) of effective temperature of the secondary from MSC using BP/RP spectra and parallax (float, Temperature[K])
Lower confidence level of effective temperature of the secondary inferred by MSC from BP/RP spectra and parallax. This is the 16th percentile. Lower and upper levels include 68% confidence (corresponding to a conventional 1-sigma interval).
logg_msc1 : Surface gravity of the primary from MSC using BP/RP spectra and parallax (float, GravitySurface[log cgs])
Surface gravity of the primary (assuming source is a binary system and the primary is the component with more flux in the BP and RP spectra combined) inferred by MSC from BP/RP spectra and parallax. This is the median of the MCMC samples. For details see Section 11.3.5.
logg_msc1_upper : Upper confidence level (84%) of surface gravity of the primary from MSC using BP/RP spectra and parallax (float, GravitySurface[log cgs])
Upper confidence level of surface gravity of the primary inferred by MSC from BP/RP spectra and parallax. This is the 84th percentile. Lower and upper levels include 68% confidence (corresponding to a conventional 1-sigma interval).
logg_msc1_lower : Lower confidence level (16%) of surface gravity of the primary from MSC using BP/RP spectra and parallax (float, GravitySurface[log cgs])
Lower confidence level of surface gravity of the primary inferred by MSC from BP/RP spectra and parallax. This is the 16th percentile. Lower and upper levels include 68% confidence (corresponding to a conventional 1-sigma interval).
logg_msc2 : Surface gravity of the secondary from MSC using BP/RP spectra and parallax (float, GravitySurface[log cgs])
Surface gravity of the secondary (assuming source is a binary system and the secondary is the component with less flux in the BP and RP spectra combined) inferred by MSC from BP/RP spectra and parallax. This is the median of the MCMC samples. For details see Section 11.3.5.
logg_msc2_upper : Upper confidence level (84%) of surface gravity of the secondary from MSC using BP/RP spectra and parallax (float, GravitySurface[log cgs])
Upper confidence level of surface gravity of the secondary inferred by MSC from BP/RP spectra and parallax. This is the 84th percentile. Lower and upper levels include 68% confidence (corresponding to a conventional 1-sigma interval).
logg_msc2_lower : Lower confidence level (16%) of surface gravity of the secondary from MSC using BP/RP spectra and parallax (float, GravitySurface[log cgs])
Lower confidence level of surface gravity of the secondary inferred by MSC from BP/RP spectra and parallax. This is the 16th percentile. Lower and upper levels include 68% confidence (corresponding to a conventional 1-sigma interval).
ag_msc : Extinction in G band of the source treated as a binary system from MSC using BP/RP spectra and parallax (float, Magnitude[mag])
G band extinction of the source (assuming source is a binary system) inferred by MSC from BP/RP spectra and parallax. This is the median of the MCMC samples. For details see Section 11.3.5.
ag_msc_upper : Upper confidence level (84%) of extinction in G band from MSC using BP/RP spectra and parallax (float, Magnitude[mag])
Upper confidence level of G band extinction inferred by MSC from BP/RP spectra and parallax. This is the 84th percentile. Lower and upper levels include 68% confidence (corresponding to a conventional 1-sigma interval).
ag_msc_lower : Lower confidence level (16%) of extinction in G band from MSC using BP/RP spectra and parallax (float, Magnitude[mag])
Lower confidence level of G band extinction inferred by MSC from BP/RP spectra and parallax. This is the 16th percentile. Lower and upper levels include 68% confidence (corresponding to a conventional 1-sigma interval).
logposterior_msc : Goodness-of-fit score (normalised log-posterior) of MSC MCMC (float)
Goodness-of-fit score of MSC MCMC. This was calculated as the mean log-posterior of all MCMC samples normalised with the uncertainty of the data. A higher value corresponds to a better fit.
mcmcaccept_msc : Mean MCMC acceptance rate of MSC MCMC (float)
Mean acceptance rate of MSC MCMC chain for all walkers.
mcmcdrift_msc : Mean drift of the MSC MCMC chain in units of parameter standard deviation (float)
Drift of the MCMC chain in units of parameter standard deviation, averaged over all parameters. Computed as the mean value of each parameter in the first MCMC ensemble state minus the mean value in the last MCMC ensemble state divided by the standard deviation of values in the last MCMC ensemble state. This is then averaged over all MSC parameters to provide a single value. If the MCMC chain has not converged, the first and last ensemble states will have low or zero overlap. In such a case, their mean values will show a large difference, larger than the standard deviation in the final ensemble state. Therefore, large values of this quantity indicate poor MCMC convergence, whereas values close to zero indicate good MCMC convergence.
flags_msc : Flag indicating quality information from MSC (string)
Catalogue flag for MSC. This is set to ‘0’ if logposterior_msc $\geq-1000$ & mcmcdrift_msc $\leq$ 1. In all other cases it is set to ‘1’ indicating an unreliable inference result.
neuron_oa_id : Identifier of the OA SOM map neuron that represents the source (long)
A unique identifier for the neuron that represents the source in the SOM map produced by the OA module. If the source was not considered as an outlier according to DSC classification or if it was discarded by OA module, then this field will be null. See Section 11.3.12 for further details.
neuron_oa_dist : Distance between the source XP spectra and the OA neuron XP prototype that represents the source (float)
Squared Euclidean distance between the source XP spectra (preprocessed) and the neuron XP prototype (xp_spectrum_prototype_flux in table oa_neuron_xp_spectra) that represents such a source. If the source was not considered as an outlier according to DSC classification or if it was discarded by the OA module, then this field will be null. See Section 11.3.12 for further details.
neuron_oa_dist_percentile_rank : Percentile rank according to the distance distribution of the OA neuron that represents the source (int)
Percentile rank according to the squared Euclidean distance distribution of the OA neuron that represents the source. If the source was not considered an outlier according to DSC classification or if it was discarded by the OA module, then this field will be null. See Section 11.3.12 for further details.
flags_oa : Flags indicating quality and processing information from OA (string)
Processing flags related to the quality of the classification and source processing performed by the OA module, which is encoded as follows:
$ABCD$
where:
Code Description Value range $A$ Number of gaps with negative fluxes in BP spectrum $[0,2]$ * $B$ Number of gaps with negative fluxes in RP spectrum $[0,2]$ * $C$ Source classification quality category $[0,5]$ $D$ Neuron quality category $[0,6]$
(*) $A$ and $B$ flags taking value 2 means two or more gaps taking negative flux values.
| 2022-08-08T04:32:16 |
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|
https://www.usgs.gov/center-news/volcano-watch-monitoring-volcanoes-real-time-gps
|
# Volcano Watch — Monitoring volcanoes in real-time with GPS
Release Date:
Boaters, hikers, pilots, and other outdoor enthusiasts can use hand-held Global Positioning System (GPS) receivers to locate themselves or to navigate to a point of known position. Volcanologists routinely use hand-held GPS receivers to map lava flows and other volcanic features.
Boaters, hikers, pilots, and other outdoor enthusiasts can use hand-held Global Positioning System (GPS) receivers to locate themselves or to navigate to a point of known position. Volcanologists routinely use hand-held GPS receivers to map lava flows and other volcanic features. They can now use specialized GPS receivers and sophisticated analysis software to continuously track the subtle ground movements that precede an eruption.
First, some background on GPS. The constellation of 24 GPS satellites was launched by the U.S. Department of Defense to locate people, equipment, and targets during military operations. The GPS satellites broadcast accurate classified military signals on two frequencies and less accurate civilian signals on one of those frequencies. These signals along with information about the GPS satellite orbits are encoded as modulations on the GPS broadcast frequencies, in a manner similar to how music is sent on radio waves. The music from your radio is decoded from modulations of radio waves broadcast by radio stations. The GPS "music" broadcast by the satellites provides accurate position and time.
Quality hand-held GPS receivers may be purchased for as little as \$150, but their accuracy is limited to about 300 feet. The military GPS receivers are accurate to about 20 feet. These receivers can track your position as you walk, drive, cruise, or fly. To monitor volcanic movements, we use more capable and expensive GPS receivers that are fixed to the ground and send their data by two-way radio to our computer. With sophisticated data processing software, we can obtain positions accurate to 3 mm (1/8 inch). Unfortunately, these results take an hour or more to compute, and in a volcanic crisis an hour is a long time.
A volcanic crisis begins when magma starts cracking its way to the surface, in a manner similar to the splitting of a log with a wedge. The crack propagates upward at less than 30 cm (1 foot) per second, and the magma takes several hours to reach the surface. This splitting of the ground deep within the volcano causes earthquakes and diffuse ground deformation that become more concentrated and larger as the magma nears the surface. We can use this precursory ground deformation to forecast the place and, with luck, the size of an eruption.
Until recently, tiltmeters provided our only real-time monitor of ground deformation. Last week we began testing real-time GPS monitoring of Mauna Loa. At the same time our mainland counterpart, Cascades Volcano Observatory (CVO), began tests at Long Valley Caldera, California. We are "beta" test sites for software developed by Magellan Corporation's Ashtech GPS subsidiary and distributed by Condor Earth Technologies. The expected primary market for the software, besides volcanologists, is engineers who monitor the stability of dams and bridges.
GPS has an expanding number of applications. HVO and CVO are testing a new capability, real-time volcano monitoring, which we expect will improve our ability to forecast eruptions.
### Volcano Activity Update
Lava continues to erupt from Puu O`o and flow through a network of tubes from the vent to the sea near Kamokuna. A bench collapse on the evening of April 9 or morning of April 10 destroyed a bench nearly 800 m (2,600 ft) long, including one newly formed since March 31 (1.6 ha, 3.5 acres) and a one-year old section (3.5 ha, 8.6 acres). The recently trimmed cliff line is exceptionally unstable, owing to the numerous cracks that occurred as the buttressing bench subsided beneath the waves. The public is reminded that the ocean-entry area is extremely hazardous, with explosions accompanying these frequent collapses of new land. The steam clouds are highly acidic and laced with glass particles.
A magnitude 3.4 earthquake occurred 8 km (5 mi) south southeast of Kawaihae at a depth of 13 km (8 mi). It was felt in Waikoloa.
| 2021-09-18T02:50:22 |
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|
https://www.usgs.gov/center-news/volcano-watch-hual-lai-volcano-kailua-konas-intriguing-neighbor
|
Volcano Watch — Hualālai Volcano: Kailua-Kona's intriguing neighbor
Release Date:
Visitors and residents of the Big Island's "gold" or Kona coast enjoy beautiful beaches, great snorkeling and lovely sunsets. Early risers may also get a good view of the summit of Hualālai volcano before the inversion-layer clouds come and blanket the peak.
Located only 10 miles (15 km) from the coastal areas of the town of Kailua-Kona, the summit of Hualālai rises to 8,271 ft (2,521 m). Although its quiet presence has become a familiar site, the intriguing landscape and potential impact of the volcano may be under-appreciated. Hualālai places an undistinguished third in a number of comparisons of the five Big Island volcanoes. It is the third tallest, third oldest, and third most active volcano on the island. It is even the runner up in the category of smallest volcano, in area above sea-level. Kohala wins that title, making up only about 6 percent of the island, while Hualālai runs a close second at around 7 percent. Huge Mauna Loa makes up 51 percent, Mauna Kea nearly 25 percent, and Kīlauea 14 percent of the Big Island.
One interesting trait is that Hualālai has three rift zones, one more than its active volcanic relatives, Mauna Loa and Kīlauea. One of these rift zones (an area of weakness extending down the flank of a volcano) was the site of the most recent eruptions. Very fluid, fast-moving flows from the northwest rift zone erupted for undefined periods before 1801. The largest and best known of these flows are the Kaupulehu flow -- which erupted from the 5,500 to 6,000-ft elevation and entered the ocean between the Kona Village Resort and Kiholo Bay -- and the Huehue flow, upon which most of the Keahole airport is built. The Huehue flow erupted from around the 500-ft elevation and destroyed Kamehameha's large and valuable fish pond Paaiea, located between Keahole Point and Mahaiula. An estimated 50 million cubic meters of lava was produced during this eruption, an amount generated by five to six months of the current Kīlauea eruption.
Looking up at Hualālai, one observes a steeper and "bumpier" profile than the smooth, gradual shield-volcano profile of Mauna Loa. Hualālai is in the "post-shield stage" of its life cycle and is moving off the hotspot that feeds Hawaiian eruptions. During this stage, the rate of eruptions is reduced, and much more erosion and weathering of the volcano can occur between eruptions.
Although the temperatures of most recent flows from Hualālai were 1150-1220° C (2100-2230° F), at least as hot as Kīlauea's lava temperatures, volcanoes in the post-shield stage tend to erupt lava that is slightly cooler, stickier, and gas-rich than during the earlier shield-building stage. This results in thick flows that steepen the sides of the volcano. It also causes explosive eruptions and high fountains that form cinder cones along its profile. The combination of cinder cones and thicker, more viscous flows concentrated near the summit causes Hawaiian volcanoes in this post-shield stage to be noticeably steeper and bumpier than in earlier shield-building stages. Although volcanoes in the post-shield stage tend not to have a single summit caldera, multiple cones and craters dot the summit area of Hualālai.
Hualālai erupts every few hundred years. In 1929, a series of several thousand earthquakes came from beneath Hualālai's northern flank, shaking the Island of HAWAII. Some of the earthquakes were strong enough to do damage in central Kona and were felt as far away as Honolulu. They were likely associated with subsurface movements of magma or readjustment of the mountain as a result of such movement.
At some future date, Hualālai will erupt again, and favorite picturesque beaches of Kona could be replaced by sections of lava-covered coastline. Hualālai should not be taken for granted. We should enjoy the beauty of the mountain and its downslope areas while we can.
Volcano Activity Update
Eruptive activity at Puu Oo continues. The Banana flow, which breaks out of the Mother's Day lava tube a short distance above Pulama pali, is entering the ocean off the 2002 Wilipea lava delta. The national park has marked a trail to within a short distance of the active lava delta, and thousands have been enjoying the show. In addition, lava has been visible between Pulama pali and Paliuli for the past several weeks, and on occasion lava cascades down Paliuli to the coastal flat. Eruptive activity in Puu Oo's crater is weak, with sporadic minor spattering and small flows.
No earthquakes were reported felt on the island during the week ending July 7.
Mauna Loa is not erupting. The summit region continues to inflate slowly. Seismic activity remains low, with 6 earthquakes located in the summit area during the past week.
| 2020-08-07T16:25:59 |
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|
https://zeno.nist.gov/Input.html
|
# Input file¶
The input file, also known as a .bod file, contains the description of the object and some additional input parameters.
## Defining the object(s)¶
A single object of interest must be described by a collection of spheres and cuboids, which may or may not be overlapping. The code has also be extended for the case of running not just a single snapshot composed of a collection of spheres, but also a trajectory or series of snapshots each composed of a collection of spheres. In all cases the shape of the object is defined in the .bod file.
### Spheres¶
Spheres are defined by lines of the form
SPHERE x y z r
where x, y, and z are the coordinates of the center of the sphere and r is the radius.
For example, a .bod file that contains the following describes an object composed of two spheres: one of radius 2 at $$x=0$$, $$y=0$$, and $$z=1$$ and one of radius 3 at $$x=0$$, $$y=0$$, and $$z=-1$$.
SPHERE 0 0 1 2
SPHERE 0 0 -1 3
### Cuboids¶
Cuboids can be defined in several ways. The most basic is a line of the form
CUBOID x1 y1 z1 x2 y2 z2
where x1, y1, and z1 are the coordinates of one corner of the cuboid and x2, y2, and z2 are the coordinates of the opposite corner. The edges of the cuboid are aligned with the $$x, y, z$$ axes.
A cuboid with all edges the same length is a cube. Cubes can be defined with lines of the form
CUBE x y z L
where x, y, and z are the coordinates of one corner of the cube and L is the edge length. This is equivalent to
CUBOID x y z x+L y+L z+L
For example, a .bod file that contains the following describes an object composed of two cuboids: one with a corner at $$x=0, y=0, z=0$$ and opposite corner at $$x=1, y=2, z=3$$ and one with a corner at $$x=1, y=0, z=0$$ and opposite corner at $$x=5, y=4, z=4$$.
CUBOID 0 0 0 1 2 3
CUBE 1 0 0 4
Finally, sets of cuboids can be defined in a binary file in the .fits.gz format [1] using the voxels command. Voxels are specified with lines of the form
VOXELS <relative path to .fits.gz file>
Paths to the .fits.gz file are relative to the location of the .bod file. So, for example, if you had a voxels file voxels.fits.gz in the same directory as the .bod file, you could simply specify it as
VOXELS voxels.fits.gz
### Multiple snapshots or trajectories of spheres¶
In order to be compatible with a variety of existing software packages, the trajectories of spheres are defined using the xyz file format and referenced in the .bod file. The format of the xyz file is
<number of atoms>
comment line
<atom type> <x> <y> <z>
...
where atom type can be either a number or string, such as an element symbol. This structure can be repeated multiple times for multiple snapshots. For example,
2
snapshot 1
A -1 0 0
B 0.25 0 0
1
snapshot 2
A 0 0 0
would define two spheres of different types for the first snapshot and one sphere for the second snapshot where that sphere is the same type as the first sphere in the first snapshot. As the xyz file format does not contain radii information, a second conversion file that defines the radius of each atom type is needed. The conversion file format is
<atom type> <radius>
Each atom type in the xyz file must be defined. A corresponding conversion file for the xyz file example could be
A 1
B 0.25
In this case, together the two examples define a system of two touching spheres one of radius 1 and one of radius 1/4 for the first snapshot and a single sphere of radius 1 for the second snapshot.
The xyz file and the conversion file are specified in the .bod file as
TRAJECTORY <relative path to xyz file> <relative path to conversion file>
Note that if a trajectory is given, no other geomerty may be included in the .bod file.
## Optional inputs¶
Command: rlaunch double Explanation: Sets the radius, which is radius of the sphere from which random walks are launched. The radius must be large enough to enclose the entire object. Default value: The smallest radius that encloses the smallest axis-aligned bounding-box of the object. Example: rlaunch 20 means that the launch radius is 20.
### Skin thickness¶
Command: st double Explanation: Sets the skin thickness. A random walker is assumed to have hit the surface of the object if the distance between the surface and the walker is less than the skin thickness. Default value: 1e-6 times the launch radius Example: st 0.01 means that the skin thickness is 0.01.
### Units for length¶
Command: hunits double string Explanation: Specifies the units for the length for all objects. Options: The string can take the following values: m (meters) cm (centimeters) nm (nanometers) A (Angstroms) L (generic or unspecified length units) Default value: 1 L Example: hunits 10 cm means that a length of 1 for an object is equivalent to 10 cm.
### Temperature¶
Command: temp double string Explanation: Specifies the temperature, which is used for computing the diffusion coefficient. Options: The string can take the following values: C (Celsius) K (Kelvin) Default value: None Example: temp 20 C means that the temperature is 20$$^\circ$$C.
### Mass¶
Command: mass double string Explanation: Specify the mass of the object, which is used for computing the intrinsic viscosity in conventional units and the sedimentation coefficient. Options: The string can take the following values: Da (Daltons) kDa (kiloDaltons) g (grams) kg (kilograms) Default value: None Example: mass 2 g means that the mass of the object is 2 grams.
### Solvent viscosity¶
Command: viscosity double string Explanation: Specify the solvent viscosity, which is used for computing the diffusion coefficient, the friction coefficient, and the sedimentation coefficient. Options: The string can take the following values: p (poise) cp (centipoise) Default value: None Example: viscosity 2 cp means that the solvent has a viscosity of 2 centipoise.
### Buoyancy factor¶
Command: bf double Explanation: Specify the buoyancy factor, which is used for computing the sedimentation coefficient. Default value: None Example: bf 2 means that the buoyancy factor is 2.
| 2021-02-28T13:41:43 |
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|
https://www.physics.lbl.gov/qiscom/
|
# QIS and Computational Physics
The LBNL QuantISED Quest Program brings together research initiatives started with FY18 QuantISED funding. The program has three research components: QIS for HEP, HEP for QIS, and Quantum computation. While each of these components has a well defined scope, there is a strong connection between them, making for a unified program that benefits from having all three elements. The program aims to be a hub for technology development. To that effect, already strong partnerships with university groups have been expanded, to benefit from expertise across and outside HEP.
Six institutes are partnered with LBNL: UC Berkeley, Caltech, U. of Massachusetts Amherst, Princeton U., Texas A&M U., and Yale U.
The QIS for HEP work aims to reach single quantum sensing, exploiting QIS developments, to enable future world leading searches for particle dark matter (DM) at low mass (MeV range down to sub-eV). It includes both sensor and target material R&D to make future experiments possible. Sensor development will focus on: Transition Edge Sensors (TES) and Kinetic Inductance Detectors (KID) for measuring athermal phonon energy, and Superconducting Nanowire Single Photon Detectors (SNSPD) for infrared photons and single He atoms. Superfluid He work will develop quantum evaporation of atoms from the liquid He surface and ejection of electrons specially prepared on He films (originally developed as qubits). All these technologies aim at measuring quanta with energies of 1-10\,meV- two orders of magnitude better than present state-of-the-art. Additionally, development of opto-mechanical cavities in liquid He aims to reach the $\mu$eV range for discrete energies. Theoretical work on DM coupling to coherent excitations informs this development and also finds new quantum materials that can enhance DM detection, some of which will be produced and measured.
The HEP for QIS work applies the above experience, theory, and sensors to study and improve superconducting qubit devices. It also applies particle physics data acquisition methods to control and read out qubits and qutrits. The above DM techniques are fundamentally about the production, transport, and measurement of quasiparticles (coherent excitations) in DM target materials.
Such quasiparticles are a major concern for qubit performance, as their presence causes degradation. With the above tools, both experimental and theoretical, we can study this problem in a systematic way, leading to better qubit device modeling and fabrication. For superconducting qubit readout, present technology does not scale to large systems. Development will focus on room temperature FPGA-based control and readout electronics, and cold transmission and multiplexing techniques.
Complementary to the above device-oriented work, the program will develop quantum computing applications in three directions. It will use quantum computing to calculate and simulate particle physics processes that are intractable with classical computers: notably collisions with many final state particles, of great interest for Large Hadron Collider physics. The program will emulate on ternary logic quantum devices (qutrits) the process of information scrambling and recovery thought to take place in black holes, as well as investigating the ground state of such devices. And it will use quantum computing hardware and algorithms to study highly combinatorial pattern recognition tasks necessary to analyze data from particle physics experiments.
| 2021-11-27T11:09:46 |
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https://tjyj.stats.gov.cn/CN/Y2013/V30/I8/25
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• 论文 •
### 主成分分析综合评价应该注意的问题
• 出版日期:2013-08-15 发布日期:2013-08-05
### Some Problems in Comprehensive Evaluation in the Principal Component Analysis
Lin Haiming & Du Zifang
• Online:2013-08-15 Published:2013-08-05
Abstract: The principal component analysis is widely used in comprehensive evaluation, but sometimes, the results of the principal component analysis evaluation index is unreasonable and even wrong. Therefore, the construction conditions of the principal component analysis evaluation index needs to be further studied. Applying the simple structure of factor loading matrix in factor analysis method and the rationality of weighted arithmetic mean, we get the construction conditions for the principal component analysis evaluation index: the indicators are positive and standardized; the principle component loading matrix gets a better simple structure; the principle component is positive; the principle components and variables are significantly related. Also, we propose some suggestions through empirical study.
| 2022-06-30T23:08:35 |
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http://trove.nla.gov.au/work/143567?q&versionId=152898
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English, Article, Journal or magazine article edition: Adaptive Model Selection Using Empirical Complexities Gábor Lugosi; Andrew B. Nobel
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Bookmark: http://trove.nla.gov.au/version/152898
Physical Description
• preprint
Language
• English
Edition details
Title
• Adaptive Model Selection Using Empirical Complexities
Author
• Gábor Lugosi
• Andrew B. Nobel
Physical Description
• preprint
Notes
• Given $n$ independent replicates of a jointly distributed pair $(X,Y) \in {\cal R}^d \times {\cal R}$, we wish to select from a fixed sequence of model classes ${\cal F}_1, {\cal F}_2, \ldots$ a deterministic prediction rule $f: {\cal R}^d \to {\cal R}$ whose risk is small. We investigate the possibility of empirically assessing the {\em complexity} of each model class, that is, the actual difficulty of the estimation problem within each class. The estimated complexities are in turn used to define an adaptive model selection procedure, which is based on complexity penalized empirical risk. The available data are divided into two parts. The first is used to form an empirical cover of each model class, and the second is used to select a candidate rule from each cover based on empirical risk. The covering radii are determined empirically to optimize a tight upper bound on the estimation error. An estimate is chosen from the list of candidates in order to minimize the sum of class complexity and empirical risk. A distinguishing feature of the approach is that the complexity of each model class is assessed empirically, based on the size of its empirical cover. Finite sample performance bounds are established for the estimates, and these bounds are applied to several non-parametric estimation problems. The estimates are shown to achieve a favorable tradeoff between approximation and estimation error, and to perform as well as if the distribution-dependent complexities of the model classes were known beforehand. In addition, it is shown that the estimate can be consistent, and even possess near optimal rates of convergence, when each model class has an infinite VC or pseudo dimension. For regression estimation with squared loss we modify our estimate to achieve a faster rate of convergence.
• Complexity regularization, classification, pattern recognition, regression estimation, curve fitting, minimum description length
• RePEc:upf:upfgen:323
Language
• English
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| 2017-05-22T17:00:26 |
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http://water.usgs.gov/wrri/00grants/FLmodels.html
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WATER RESOURCES RESEARCH GRANT PROPOSAL
Title: Development of Multiple Process and Multiple Scale Hydrologic Models
Statement of critical regional water problems
The natural hydrology of south Florida has been extensively altered though channelization to provide adequate water for urban growth and agriculture, and to provide flood protection to the area. Currently, water resource management in south Florida is governed by a number of federal, state, and county agencies. These agencies have developed or adopted hydrologic models to address a diverse set of needs. These range from large-scale models used to estimate impacts of alternative water management practices across all of south Florida, to field-scale models used to predict local impacts such as flooding or agricultural production. At present, there is no feedback mechanism in place for dynamically conveying of information across the wide range of scales addressed by this spectrum of models. Instead, static methods are used, where results from larger-scale models are used as boundary conditions for smaller-scale models. This ignores both the problem of upscaling parameters such as hydraulic conductivity that may be highly variable over small scales, as well as the problem of aggregating a variety of coupled hydrologic processes occurring over a wide range of temporal and spatial scales into a coherent and accurate model of a hydrologic system.
One area of particular interest in south Florida is the C-111 basin in Dade County, which runs from near the city of Homestead south to Florida Bay. This area is located in southern Dade County, Florida. Within the C-111 basin are portions of Everglades National Park and agricultural lands, including those recently acquired by the state of Florida referred to as the Frog Pond,'' and urban areas including portions of Homestead and Florida City. This area is bounded on the west by the Everglades National Park and on the east by residential and agricultural lands. As such, it is at the center of competing demands between environmental protection and restoration in Everglades National Park and in flood protection for the agricultural and residential lands.
Statement of the results, benefits, and/or information expected to be gained
This research will result in a greater understanding of the interrelation of hydrologic processes across a range of spatial and temporal scales. A variety of deterministic and stochastic methods for upscaling hydrologic parameters will be investigated and tested. A hydrologic model incorporating a variety of coupled processes and interactions will be developed using domain decomposition and multigrid techniques. The end result of this investigation will be a sophisticated hydrologic model that will be able to predict the effects of changes in water management structures, water management polices, extreme weather events, or gradual changes in weather patterns on urban, agricultural, and natural systems.
Nature, Scope, and Objectives of Research
Goals
This project will investigate how hydrologic processes such as ground water flow, river/canal flow, overland flow, infiltration, evapotranspiration, etc., are manifested across a broad range of spatial and temporal scales. We will focus on the interaction of these processes between scales, as well as understanding how agricultural, urban, and/or natural ecosystems impact-and are impacted by- hydrologic processes at a variety of scales.
The major objectives of this research are to:
• Establish a framework for the efficient exchange and integration of hydrologic information across a wide range of spatial and temporal scales.
• Develop methods for upscaling input parameters and predictions from detailed local models for use in larger-scale sub-regional and regional models.
• Develop a hydrologic model that incorporates these methods and is capable of making predictions over a range of scales.
• Apply this method to areas in southern Florida where agricultural, urban, and environmental interests must share limited water resources.
Background
One of the most challenging aspects of water resource management is the accurate modeling of a wide range of interrelated processes such as ground water flow, infiltration, evapotranspiration, overland flow, river/canal flow, rainfall, etc. Interactions between these processes include the exchange of water between rivers, lakes, and ground water, the relation between the soil moisture content and soil type and the amount of runoff generated from a rainfall event, the partitioning of water in the unsaturated zone between flow into the water table and plant uptake, etc. Even more complexity is added by the large scale of the problem, which can cover hundreds or thousands of square miles, and the fact that the results must be provided to a wide variety of diverse interests. If the appropriate balances between agricultural and urban water use and environmental protection and restoration are to be maintained these processes and interactions must be modeled in a realistic manner. One of the primary difficulties in the development and application of a large-scale hydrologic model is that the relevant processes and interactions occur over a wide range of spatial and temporal scales. This leads to two related issues that must be addressed by the model developer [Famiglietti and Wood, 1994] namely, the related matters of scale-dependent spatial variability and aggregation of the various relevant processes over the range of scales.
The first issue arises since hydrologic parameters such as soil type or hydraulic conductivity can exhibit a tremendous amount of spatial variability, in many cases over a range of several different scales. Other driving processes such as rainfall, evapotranspiration, etc., can also be highly variable in time and space. The second issue of aggregation deals with the matter of how to incorporate a variety of hydrologic processes occurring over a wide range of temporal and spatial scales into a coherent and accurate large-scale model of a hydrologic system. We are thus faced with the question: What is the appropriate method to generate a realistic hydrologic model given this complex hierarchy of parameters and scales? Any model that attempts to answer this question must address the problem of how to convey the information produced at one scale and incorporate that information into the model at another scale. It is obvious that such a model will require a complex network of feedback between the relevant processes and interactions over many spatial and temporal scales. Given the amount of information required in a large-scale hydrologic model the solution to this problem is far from straightforward. Efficient communication of the information across the various scales and processes is necessary if a realistic solution is to be obtained at a reasonable cost.
Examples of Hydrologic Models
Traditionally, modeling of large-scale water resources has fallen into two categories: a single model that attempts to encompass a wide range of processes and interactions, or a series of smaller models, each focusing on a specific scale, process (or a limited number of processes), or interaction between processes. An effective use of these models requires linking them together in an appropriate fashion. Most modeling of large-scale hydrologic problems seems fall within the second category since model design and implementation tends to be broken down along the lines of the separate processes modeled. Furthermore, computational constraints (time and/or memory) favor the use of smaller, individual models.
As a gross generalization, hydrologic models can be divided into four scales. Listed from largest to smallest we have:
• Macroscale or General Circulation Models (GCMs).
• Mesoscale or regional models.
• Sub-regional models.
• Local or field-scale models.
The macroscale models/GCMs typically cover the entire earth, or large portions of it, with grid scales on the order of hundreds of kilometers. In addition to modeling of hydrologic processes, GCMs also are used for predicting crop and ecosystem response, climate simulation, modeling of weather processes, etc. Examples of GCMs include the Biosphere-Atmosphere Transfer Scheme (BATS) [Dickinson et al., 1993] and the Simple Biosphere Model (1 and 2) (SiB, SiB2) [Sellers et al., 1986, 1996a,b].
Regional hydrologic models generally cover portions of a state or several states, i.e., several hundreds to thousands of square kilometers. A primary use of these models is for long-term planning of water resources, which may involve examining the relative impacts of a variety of alternative water management plans, or to model the hydrology of an extended aquifer system. Grid scales are typically on the order of several square kilometers to tens of square kilometers. Examples of regional models include the South Florida Water Management Model (SFWMM), and regional studies of aquifer hydrology by the United States Geological Survey [Tibbals, 1990; Bush and Johnston, 1988].
Sub-regional models cover areas of catchment or basin size, with grid spacings typically in the hundreds of meters to one or two kilometers. A primary use of these models are for the design of water use and management structures such as canals, levees, pump stations, well fields, etc.
Local or field scale models cover individual farm to sub-catchment scales, with grid spacings ranging from a few tens of meters up to a few hundred meters. These models attempt to predict the impact of water management plans on flooding, runoff, etc at the local scale. Additionally, many models on this scale deal with impacts of land management practices on surface and ground water quality (i.e., fertilizers, pesticides, etc.) Examples include CREAMS [Knisel, 1980], GLEAMS [Leonard et al., 1986], (see also Beasley et al. 1989), FHANTM [Tremwel and Campbell, 1992; Fraisse and Campbell, 1997], and EAHM [Savabi, 1999].
A major weakness of regional and sub-regional models is the scale problem mentioned above. The parameter representations on the large scale are extremely simplified representations of what may be a highly complex and spatially and/or temporally variable parameter over the small scale. For example, hydraulic conductivity can vary greatly over relatively small scales (a few meters to tens of meters), while a large scale-problem may have grid spacings of several kilometers and must use a single averaged value for the parameter. Immediately the problem arises of how to best represent this highly variable parameter with a single averaged value. The success of regional and sub-regional scale models is critically dependent on how well spatially and/or temporally variable parameters are represented at the large scale. Failure to address these issues properly will result in a poor match between model results and reality.
Water Management Models used in South Florida
Currently, water resource management in south Florida is governed by a number of federal, state, and county agencies. The natural hydrology of south Florida has been extensively altered though channelization to provide adequate water for urban growth and agriculture, and to provide flood protection to the area [Tarboton et al., 1999]. In order to estimate the system-wide impacts of various alternative water management schemes for planning purposes the South Florida Water Management District uses a large scale (2x2 mile grid) model to simulate the hydrology throughout the region. On the sub-regional scale, the U.S. Army Corps of Engineers uses a model with a 500x500 foot grid spacing to design water control structures such as pump stations, gates, canals, and levees. Results from the large-scale model are used as boundary conditions for this sub-regional model. On the local field scale, models are being developed by the U.S. Department of Agriculture-Agricultural Research Service to predict the impact of water management practices on farm-scale flooding, as well as the impacts of agricultural management practices on surface and ground water quality. These local scale models require canal water levels and water table elevation as boundary information. These data are typically provided by the larger scale models.
At present, there is no feedback mechanism in place for conveying of information across these different scales in a dynamic manner. Rather, a simulation using the large scale model is run to conclusion, and outputs from this are used as boundary conditions for the smaller scale models. Furthermore, there is no way to incorporate information from the smaller scale models back to the larger scale. It is recognized, however, that a formal plan to integrate these models is needed [Forum of Modelers and Agricultural Technical Experts].
One area of particular interest in south Florida is the canal C-111 drainage basin, or simply the C-111 basin'' [Schaffranek, 1996; Genereux and Guardiario, 1998; Genereux and Slater, 1999] located in southern Dade County, Florida. The C-111 canal runs from near the city of Homestead to Florida Bay. Within the C-111 basin are agricultural lands recently acquired by the state of Florida and referred to as the Frog Pond.'' This area is bounded on the west by the Everglades National Park and on the east by residential and agricultural lands. As such, it is at the center of competing demands between environmental protection and restoration in Everglades National Park and in flood protection for the agricultural and residential lands immediately to the east (Figure 1).
Figure 1. Southern Portion of the C-111 basin and Frog Pond'' area. From Genereux and Guardiario [1998]
The hydrogeology of the area has been studied by Genereux and Guardiario [1998] and Genereux and Slater [1999], who have determined transmissivities and hydraulic conductivities through drawdown experiments and examined exchange of water between the canals, aquifer, and adjacent wetlands. Additionally, Schaffranek [1996] is working on developing a numerical model to simulate flow and transport in the C-111 basin, with special attention given to understanding the dynamics of water and solute exchange between canals and wetlands.
Work on quantifying vertical exchange of water between ground water and surface water has been done by Harvey [1996]. This research also included studies to relate seepage fluxes to subsurface hydrogeologic properties and management of surface-water levels in canals and water conservation areas. A farm-scale deterministic model specific to agricultural interests in south Florida (EAHM) is currently being developed by Savabi [1999]. This model will simulate evapotranspiration, percolation, plant growth, infiltration, soil erosion, and the movement of agricultural chemicals within a soil profile.
Domain Decomposition Methods
Over the past several decades, domain decomposition techniques have been developed as a means of solving systems arising from the discretization of linear or nonlinear partial differential equations (PDEs) [Smith et al., 1996; Chan and Mathew, 1994]. Basically, domain decomposition refers to the process of splitting a problem into several smaller subproblems. This is done for several reasons [Smith et al., 1996]: First, it can be used as a method for distributing data from the discretized model among many processors on a parallel computer to solve the large problem much faster than on a computer with a singe processor. This approach can also be used to solve a large problem on a single processor computer that does not have sufficient memory resources to solve a large problem. Second, it can be done to separate the problem into physical subdomains with different processes operating which are modeled with different equations. These two cases are not mutually exclusive, and both of these approaches can be used in a given model.
In both of these cases, the primary technique consists of solving the subproblems at the subdomain level while enforcing appropriate continuity requirements between adjacent subproblems. Although many direct methods have been developed for solving the problems, most recent research in the area has focused on iterative methods, which are also the most applicable to the problem at hand. One large class of domain decomposition algorithms are collectively referred to as non-overlapping algorithms, since the domain is partitioned into non-overlapping subregions. In addition to the usual problem formulation with standard types of boundary conditions, non-overlapping approaches also result in what is termed a {\em transmission boundary condition} on the continuity of the flux of a quantity (such as water, energy, etc.) across the inter-domain boundaries [Chan and Mathew, 1994]. The main task in this algorithm is to determine the data, and consequently the fluxes, on the interfaces. At the beginning of the iterative process there are mismatches in the transmitted quantities between the subdomains, but with subsequent iterations the mismatch is reduced until it is below a predefined tolerance.
This technique has great significance for hydrologic problems since one of the fundamental reasons for using a large scale hydrologic model is to determine a water flux into our out of a given region. This can be a flux of surface water, subsurface water, or chemicals across a geographic boundary (e.g., into or out of a canal, across a property boundary, etc.), fluxes of water/chemicals/energy into the subsurface from the surface or into the atmosphere from the surface and subsurface due to evapotranspiration, etc. Accurate determination of these fluxes is important if the model results are to be used to allocate water resources among diverse interests, to help control flooding, and/or to determine the transport of chemicals. Non-overlapping domain decomposition algorithms are ideally suited to modeling this kind of complex interplay of various processes in a large-scale hydrologic model since determination of the fluxes between the subdomains are a fundamental part of the solution process. Furthermore, feedback between domains is an integral part of the iterative solution process. To date, however, only a few workers have taken advantage of domain decomposition methods in solving hydrologic problems [Beckie et al., 1993; San Soucie 1996].
Multigrid Methods
Multigrid and multilevel techniques [Briggs, 1987] are a subclass of domain decomposition methods that have gained widespread acceptance as efficient methods for solving systems of PDEs such as the ground water flow equations [Beckie et al., 1993]. Briefly, this method uses a series of nested grids with sequentially larger spacing to solve the system of equations resulting from discretization of PDEs. The rationale behind the development of multigrid algorithms is that when using an iterative method such as Gauss-Seidel technique to solve a PDE, errors with short wavelengths relative to the grid spacing are damped out much quicker than those with longer wavelengths. Consequently, a few iterations are performed at the finest grid spacing, then the current iteration of the solution is transferred up to the next coarsest grid. On this grid, errors that had relatively long wavelengths on the fine grid have shorter wavelengths (again, relative to the coarser grid) and so are damped out relatively quickly. This process is repeated over several different grid scales until an adequate solution is found.
Methods and Procedures
Research Methods
As part of the proposed research we will develop a model that encompasses a variety of hydrologic processes and interactions at different spatial and temporal scales. This model will utilize the domain decomposition and multigrid techniques discussed in the previous section to solve the coupled systems of equations of unsaturated ground water flow, saturated ground water flow, canal flow, and overland flow, and will incorporate infiltration and evapotranspiration effects. We will begin our work by developing the method for the C-111 basin in south Florida, with emphasis on the “Frog Pond” area. This is an ideal test case since it incorporates most if not all of the hydrologic processes discussed above.
We have formulated the following hypothesis to address our research objectives:
Hypothesis: Domain decomposition and multigrid techniques provide efficient and natural methods for conveying information between different spatial and temporal scales, as well as between physical domains where different processes are operating.
As discussed previously, domain decomposition and multigrid techniques were developed as a means of efficiently solving a particular PDE governing a particular process, and much of the current research in this area focus on this topic. However, the methodology underlying these methods can be adapted to facilitating the exchange of information between different models at different scales or between subdomains in a single model.
Furthermore, this approach inherently provides dynamic feedback across the various scales since an iterative process is used. This is in contrast to the method currently used in south Florida, where the large grid solution is found first and propagated downward to the smaller scale. This latter method has no natural method of providing feedback back to the larger scale from the smaller scale solution.
To address the above hypothesis and meet the objectives outlined in the introduction, we have defined four tasks to be accomplished:
Task 1: Develop a detailed hydrologic model of saturated and unsaturated ground water flow, canal flow, overland flow and infiltration, that incorporates rainfall and evapotranspiration. The model will rely on the domain decomposition and multigrid techniques outlined above to ensure that hydrologic information is efficiently communicated across various scales. The model will utilize grid scales ranging from approximately 10 meters up to approximately 4 kilometers.
Task 2: Gather relevant data to parameterize the model for the C-111 basin with emphasis on the Frog Pond area. This will include gathering information on hydrologic parameters such as hydraulic conductivity/transmissivity, soil properties, climatic data, canal operating levels, agricultural land use, crop water use, etc. This will involve meeting and collaborating with researchers from the University of Florida Tropical Research and Education Center (UF-TREC), the U.S. Geological Survey, the South Florida Water Management District, the U.S. Department of Agriculture-Agricultural Research Service, as well as researchers from other universities in Florida.
Task 3: Demonstrate the model by applying it to predict localized (farm-scale) areas of high flood potential within and immediately adjacent to the Frog Pond area. We will utilize a regional scale grid over the entire C-111 basin and telescope down to a local scale grid within the Frog Pond area.
Task 4: Meet with agencies with responsibility for water resource modeling in south Florida (e.g., South Florida Water Management District, U.S. Geological Survey, U.S. Department of Agriculture, U.S. Army Corps of Engineers) to explore the feasibility of utilizing the multi-scale modeling approach developed in this study to integrate the models which currently exist or are being developed for this region.
References
Beasley, D., W.G. Knisel, and A.P. Rice, eds., Proceedings of the CREAMS/GLEAMS symposium, Athens, Georgia, Agricultural Engineering Department, University of Georgia - Coastal Plain Experiment Station, 1989.
Beckie, R., E.F. Wood, and A.A. Aldama, Mixed finite element simulation of saturated groundwater flow using a multigrid accelerated domain decomposition technique, Water Resources Research, 29(9), 3145-3157, 1993.
Briggs, W.L., A Multigrid Tutorial, Society of Industrial and Applied Mathematics, Philadelphia, 1987.
Bush, P. and R.H. Johnston, Ground-water Hydraulics, Regional Flow, and Ground-Water Development of the Floridan Aquifer System in Florida and in Parts of Georgia, South Carolina, and Alabama, U.S. Geological Survey Professional Paper 1403-C, Washington, 1988.
Chan, T.F. and T.P. Mathew, Domain decomposition algorithms, Acta Numerica, 61-143, 1994.
Dickinson, R.E., A.Henderson-Sellers, and P.J. Kennedy, Biosphere-atmosphere transfer scheme (BATS) version 1E as coupled to the NCAR Community Climate Model, Technical Note TN-387+STR, National Center for Atmospheric Research, 1993.
Famiglietti, J.S. and E.F. Wood, Multiscale modeling of spatially variable water and energy balance processes, Water Resources Research, 30(11), 3061-3078, 1994.
Fraisse, C.W. and K.L. Campbell, FHANTM (Field Hydrologic And Nutrient Transport Model) version 2.0 user's manual, Research report, Agricultural and Biological Engineering Department, University of Florida, Gainesville, FL, 1997.
Genereux, D. and J. Guardiario, A canal drawdown experiment for determination of aquifer parameters, Journal of Hydrologic Engineering, 3(4), 294-302, 1998.
Genereux, D. and E. Slater, Water exchange between canals and surrounding aquifer and wetlands in the southern everglades, USA, Journal of Hydrology, 219, 153-168, 1999.
Harvey, J.W., Vertical exchange of ground water and surface water in the Florida Everglades, Fact sheet FS-169-96, U.S Department of the Interior, U.S. Geological Survey, 1996.
Knisel, W.G., CREAMS: A field-scale model for chemicals, runoff, and erosion from agricultural management systems, Conservation Research Report No. 26, U.S. Department of Agriculture, Washington, 1980.
Leonard, R.A., W.G. Knisel, and D.A. Still, GLEAMS: Groundwater Loading Effects of Agricultural Management Systems, American Society of Agricultural Engineers, Winter Meeting, Dec. 16-19, Chicago, IL, 1986.
San Soucie, C., Mixed Finite Element Methods for Variably Saturated Subsurface Flow, Ph.D. thesis, Rice University, Houston, Texas, 1996.
Savabi, M.R., Determining soil water characteristics for application of a hydrologic model in south Florida. Paper No. 992060, Presented at the 1999 ASAE Annual International Meeting, 2950 Niles Road, St. Joseph, MI 49085 USA, {ASAE}, 1999.
Schaffranek, R.W., Coupling models for canal and wetland interactions in the south Florida ecosystem, Fact sheet FS-139-96, U.S Department of the Interior, U.S. Geological Survey, 1996.
Sellers, P., S.O. Los, C.J. Tucker, C.O. Justice, D.A. Dazlich, G.J. Collatz, and D.A. Randall, A revised land surface parameterization (SiB2) for atmospheric GCMs. Part II: The generation of global fields of terrestrial biophysical parameters from satellite data, Journal of Climate, 9(4), 706-737, 1996a.
Sellers, P., Y. Mintz, Y. Sud, and A. Dalcher, A simple biosphere model (SiB) for use within general circulation models, Journal of the Atmospheric Sciences, 43(6), 505-531, 1986.
Sellers, P., D.A. Randall, G.J. Collatz, J.A. Berry, C.B. Field, D.A. Dazlich, C.~Zhang, G.~D. Collelo, and B.L., A revised land surface parameterization (SiB2) for atmospheric GCMs. Part I: Model formulation, Journal of Climate, 9(4), 676-705, 1996.
Smith, B., P. Bjorstad, and W. Gropp, Domain Decomposition, Cambridge University Press, New York, N.Y., 1996.
Summary, Forum of Modelers and Agricultural Technical Experts, South Miami-Dade Topographic Interest Group, Homestead, FL, 1999.
Tarboton, K.C., C.J. Neidrauer, E.R. Santee, and J.C. Needle, Regional hydrologic modeling for planning the management of south Florida's water resources through 2050. Presented at the 1999 ASAE Annual International Meeting, Paper No. 992060, ASAE, 2950 Niles Road, St. Joseph, MI 49085 USA, 1999.
Tibbals, C.H., Hydrology of the Floridan Aquifer System in East-Central Florida, U.S. Geological Survey Professional Paper 1403-E, Washington, 1990.
Tremwel, T.K. and K.L. Campbell, FHANTM, a modified DRAINMOD: Sensitivity and verification results, ASAE Paper No. 922045, 1992.
U.S. Department of the Interior, U.S. Geological Survey
URL: http://water.usgs.gov/wrri/00grants/FLmodels.html
Maintained by: John Schefter
Last Updated: Wednesday October 26, 2005 1:08 PM
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| 2014-09-19T19:52:44 |
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https://phys.libretexts.org/Bookshelves/College_Physics/Book%3A_College_Physics_(OpenStax)/22%3A_Magnetism/22.06_Force_on_a_Moving_Charge_in_a_Magnetic_Field%3A_Examples_and_Applications
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$$\require{cancel}$$
# 22.5: Force on a Moving Charge in a Magnetic Field: Examples and Applications
Magnetic force can cause a charged particle to move in a circular or spiral path. Cosmic rays are energetic charged particles in outer space, some of which approach the Earth. They can be forced into spiral paths by the Earth’s magnetic field. Protons in giant accelerators are kept in a circular path by magnetic force. The bubble chamber photograph in Figure $$\PageIndex{1}$$ shows charged particles moving in such curved paths. The curved paths of charged particles in magnetic fields are the basis of a number of phenomena and can even be used analytically, such as in a mass spectrometer.
Figure $$\PageIndex{1}$$:Trails of bubbles are produced by high-energy charged particles moving through the superheated liquid hydrogen in this artist’s rendition of a bubble chamber. There is a strong magnetic field perpendicular to the page that causes the curved paths of the particles. The radius of the path can be used to find the mass, charge, and energy of the particle.
So does the magnetic force cause circular motion? Magnetic force is always perpendicular to velocity, so that it does no work on the charged particle. The particle’s kinetic energy and speed thus remain constant. The direction of motion is affected, but not the speed. This is typical of uniform circular motion. The simplest case occurs when a charged particle moves perpendicular to a uniform $$B$$-field, such as shown in Figure 2. (If this takes place in a vacuum, the magnetic field is the dominant factor determining the motion.) Here, the magnetic force supplies the centripetal force $$F_{c} = mv^{2}/r$$. Noting that $$sin \theta = 1$$, we see that $$F = qvB$$.
Figure $$\PageIndex{2}$$: A negatively charged particle moves in the plane of the page in a region where the magnetic field is perpendicular into the page (represented by the small circles with x’s—like the tails of arrows). The magnetic force is perpendicular to the velocity, and so velocity changes in direction but not magnitude. Uniform circular motion results.
Because the magnetic force $$F$$ supplies the centripetal force $$F_{c}$$, we have $qvB = \frac{mv^{2}}{r}.\label{22.6.1}$ Solving for $$r$$ yields $r = \frac{mv}{qB}.\label{22.6.2}$ Here, $$r$$ is the radius of curvature of the path of a charged particle with mass $$m$$ and charge $$q$$, moving at speed $$v$$ perpendicular to a magnetic field of strength $$B$$. If the velocity is not perpendicular to the magnetic field, then $$v$$ is the component of the velocity perpendicular to the field. The component of the velocity parallel to the field is unaffected, since the magnetic force is zero for motion parallel to the field. This produces a spiral motion rather than a circular one.
Example $$\PageIndex{1}$$: Calculating the Curvature of the Path of an Electron Moving in a Magnetic Field: A magnet on a TV Screen
A magnet brought near an old-fashioned TV screen such as in Figure 3 (TV sets with cathode ray tubes instead of LCD screens) severely distorts its picture by altering the path of the electrons that make its phosphors glow. (Don't try this at home, as it will permanently magnetize and ruin the TV.) To illustrate this, calculate the radius of curvature of the path of an electron having a velocity of $$6.00 \times 10^{7} m/s$$ (corresponding to the accelerating voltage of about 10.0 kV used in some TVs) perpendicular to a magnetic field of strength $$B = 0.500 T$$ (obtainable with permanent magnets).
Figure $$\PageIndex{3}$$: Side view showing what happens when a magnet comes in contact with a computer monitor or TV screen. Electrons moving toward the screen spiral about magnetic field lines, maintaining the component of their velocity parallel to the field lines. This distorts the image on the screen.
Strategy:
We can find the radius of curvature $$r$$ directly from the equation $$r = \frac{mv}{qB}$$, since all other quantities in it are given or known.
Solution:
Using known values for the mass and charge of an electron, along with the given values of $$v$$ and $$B$$ gives us $r = \frac{mv}{qB} = \frac{\left( 9.11 \times 10^{-31} kg \right) \left( 6.00 \times 10^{7} m/s \right) } { \left( 1.60 \times 10^{-19} C \right) \left( 0.500 T \right) }$ $= 6.83 \times 10^{-4} m$ or $r = 0.683 mm.$
Discussion:
The small radius indicates a large effect. The electrons in the TV picture tube are made to move in very tight circles, greatly altering their paths and distorting the image.
Figure $$\PageIndex{4}$$ shows how electrons not moving perpendicular to magnetic field lines follow the field lines. The component of velocity parallel to the lines is unaffected, and so the charges spiral along the field lines. If field strength increases in the direction of motion, the field will exert a force to slow the charges, forming a kind of magnetic mirror, as shown below.
Figure $$\PageIndex{4}$$: When a charged particle moves along a magnetic field line into a region where the field becomes stronger, the particle experiences a force that reduces the component of velocity parallel to the field. This force slows the motion along the field line and here reverses it, forming a “magnetic mirror.”
The properties of charged particles in magnetic fields are related to such different things as the Aurora Australis or Aurora Borealis and particle accelerators. Charged particles approaching magnetic field lines may get trapped in spiral orbits about the lines rather than crossing them, as seen above. Some cosmic rays, for example, follow the Earth’s magnetic field lines, entering the atmosphere near the magnetic poles and causing the southern or northern lights through their ionization of molecules in the atmosphere. Those particles that approach middle latitudes must cross magnetic field lines, and many are prevented from penetrating the atmosphere. Cosmic rays are a component of background radiation; consequently, they give a higher radiation dose at the poles than at the equator.
Figure $$\PageIndex{5}$$: Energetic electrons and protons, components of cosmic rays, from the Sun and deep outer space often follow the Earth’s magnetic field lines rather than cross them. (Recall that the Earth’s north magnetic pole is really a south pole in terms of a bar magnet.)
Some incoming charged particles become trapped in the Earth’s magnetic field, forming two belts above the atmosphere known as the Van Allen radiation belts after the discoverer James A. Van Allen, an American astrophysicist (Figure $$\PageIndex{6}$$). Particles trapped in these belts form radiation fields (similar to nuclear radiation) so intense that manned space flights avoid them and satellites with sensitive electronics are kept out of them. In the few minutes it took lunar missions to cross the Van Allen radiation belts, astronauts received radiation doses more than twice the allowed annual exposure for radiation workers. Other planets have similar belts, especially those having strong magnetic fields like Jupiter.
Figure $$\PageIndex{6}$$:The Van Allen radiation belts are two regions in which energetic charged particles are trapped in the Earth’s magnetic field. One belt lies about 300 km above the Earth’s surface, the other about 16,000 km. Charged particles in these belts migrate along magnetic field lines and are partially reflected away from the poles by the stronger fields there. The charged particles that enter the atmosphere are replenished by the Sun and sources in deep outer space.
Back on Earth, we have devices that employ magnetic fields to contain charged particles. Among them are the giant particle accelerators that have been used to explore the substructure of matter (Figure $$\PageIndex{7}$$). Magnetic fields not only control the direction of the charged particles, they also are used to focus particles into beams and overcome the repulsion of like charges in these beams.
Figure $$\PageIndex{7}$$:The Fermilab facility in Illinois has a large particle accelerator (the most powerful in the world until 2008) that employs magnetic fields (magnets seen here in orange) to contain and direct its beam. This and other accelerators have been in use for several decades and have allowed us to discover some of the laws underlying all matter. (credit: ammcrim, Flickr)
Thermonuclear fusion (like that occurring in the Sun) is a hope for a future clean energy source. One of the most promising devices is the tokamak, which uses magnetic fields to contain (or trap) and direct the reactive charged particles (Figure $$\PageIndex{8}$$). Less exotic, but more immediately practical, amplifiers in microwave ovens use a magnetic field to contain oscillating electrons. These oscillating electrons generate the microwaves sent into the oven.
Figure $$\PageIndex{8}$$: Tokamaks such as the one shown in the figure are being studied with the goal of economical production of energy by nuclear fusion. Magnetic fields in the doughnut-shaped device contain and direct the reactive charged particles. (credit: David Mellis, Flickr)
Mass spectrometers have a variety of designs, and many use magnetic fields to measure mass. The curvature of a charged particle’s path in the field is related to its mass and is measured to obtain mass information. Historically, such techniques were employed in the first direct observations of electron charge and mass. Today, mass spectrometers (sometimes coupled with gas chromatographs) are used to determine the make-up and sequencing of large biological molecules.
# Summary
• Magnetic force can supply centripetal force and cause a charged particle to move in a circular path of radius $r = \frac{mv}{qB},$ where $$v$$ is the component of the velocity perpendicular to $$B$$ for a charged particle with mass $$m$$ and charge $$q$$.
## Contributors
• Paul Peter Urone (Professor Emeritus at California State University, Sacramento) and Roger Hinrichs (State University of New York, College at Oswego) with Contributing Authors: Kim Dirks (University of Auckland) and Manjula Sharma (University of Sydney). This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).
| 2019-09-19T23:44:48 |
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https://www.itl.nist.gov/div898/handbook/pri/section5/pri5971.htm
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5. Process Improvement
5.5.9. An EDA approach to experimental design
5.5.9.7. |Effects| plot
## Statistical significance
Formal statistical methods Formal statistical methods to answer the question of statistical significance commonly involve the use of
• ANOVA (analysis of variance); and
• t-based confidence intervals for the effects.
ANOVA The virtue of ANOVA is that it is a powerful, flexible tool with many applications. The drawback of ANOVA is that
• it is heavily quantitative and non-intuitive;
• it must have an assumed underlying model; and
• its validity depends on assumptions of a constant error variance and normality of the errors.
t confidence intervals T confidence intervals for the effects, using the t-distribution, are also heavily used for determining factor significance. As part of the t approach, one first needs to determine sd(effect), the standard deviation of an effect. For 2-level full and fractional factorial designs, such a standard deviation is related to σ, the standard deviation of an observation under fixed conditions, via the formula:
$$\mbox{sd(effect)} = \frac{2 \sigma}{\sqrt{n}}$$
which in turn leads to forming 95% confidence intervals for an effect via
c * sd(effect)
for an appropriate multiple c (from the t distribution). Thus in the context of the |effects| plot, "drawing the line" at c * sd(effect) would serve to separate, as desired, the list of effects into 2 domains:
• significant (that is, important); and
• not significant (that is, unimportant).
Estimating sd(effect) The key in the above approach is to determine an estimate for sd(effect). Three statistical approaches are common:
If σ is known, we can compute sd(effect) from the above expression and make use of a conservative (normal-based) 95% confidence interval by drawing the line at
$$\mbox{2 sd(effect)} = 2 \left( \frac{2 \sigma}{\sqrt{n}} \right)$$
This method is rarely used in practice because σ is rarely known.
2. Replication in the experimental design:
Replication will allow &sigma& to be estimated from the data without depending on the correctness of a deterministic model. This is a real benefit. On the other hand, the downside of such replication is that it increases the number of runs, time, and expense of the experiment. If replication can be afforded, this method should be used. In such a case, the analyst separates important from unimportant terms by drawing the line at
$$t \mbox{*sd(effect)} = t \mbox{*} \left( \frac{2\hat{\sigma}}{\sqrt{n}} \right)$$
with t denoting the 97.5 percent point from the appropriate Student's-t distribution.
3. Assume 3-factor interactions and higher are zero:
This approach "assumes away" all 3-factor interactions and higher and uses the data pertaining to these interactions to estimate σ. Specifically,
$$\hat{\sigma} = \sqrt{\frac{\mbox{SSQ}}{h}}$$
with h denoting the number of 3-factor interactions and higher, and SSQ is the sum of squares for these higher-order effects. The analyst separates important from unimportant effects by drawing the line at
$$t \mbox{*sd(effect)} = t \mbox{*} \left( \frac{2 \hat{\sigma}}{\sqrt{n}} \right)$$
with t denoting the 97.5 percent point from the appropriate (with h degrees of freedom) Student's-t distribution.
This method warrants caution:
• it involves an untestable assumption (that such interactions = 0);
• it can result in an estimate for sd(effect) based on few terms (even a single term); and
• it is virtually unusable for highly-fractionated designs (since high-order interactions are not directly estimable).
Non-statistical considerations The above statistical methods can and should be used. Additionally, the non-statistical considerations discussed in the next few sections are frequently insightful in practice and have their place in the EDA approach as advocated here.
| 2018-05-27T16:03:08 |
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https://dlmf.nist.gov/5.16
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§5.16 Sums
5.16.1 $\displaystyle\sum_{k=1}^{\infty}(-1)^{k}\psi'\left(k\right)$ $\displaystyle=-\frac{\pi^{2}}{8},$ ⓘ Symbols: $\pi$: the ratio of the circumference of a circle to its diameter, $\psi\left(\NVar{z}\right)$: psi (or digamma) function and $k$: nonnegative integer Permalink: http://dlmf.nist.gov/5.16.E1 Encodings: TeX, pMML, png See also: Annotations for 5.16 and 5 5.16.2 $\displaystyle\sum_{k=1}^{\infty}\frac{1}{k}\psi'\left(k+1\right)$ $\displaystyle=\zeta\left(3\right)=-\frac{1}{2}\psi''\left(1\right).$ ⓘ Symbols: $\zeta\left(\NVar{s}\right)$: Riemann zeta function, $\psi\left(\NVar{z}\right)$: psi (or digamma) function and $k$: nonnegative integer Permalink: http://dlmf.nist.gov/5.16.E2 Encodings: TeX, pMML, png See also: Annotations for 5.16 and 5
For further sums involving the psi function see Hansen (1975, pp. 360–367). For sums of gamma functions see Andrews et al. (1999, Chapters 2 and 3) and §§15.2(i), 16.2.
For related sums involving finite field analogs of the gamma and beta functions (Gauss and Jacobi sums) see Andrews et al. (1999, Chapter 1) and Terras (1999, pp. 90, 149).
| 2018-02-21T21:06:27 |
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https://www.zbmath.org/authors/?q=ai%3Azhu.xinwen
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## Zhu, Xinwen
Compute Distance To:
Author ID: zhu.xinwen Published as: Zhu, Xinwen Further Spellings: 朱歆文 Homepage: https://pma.caltech.edu/people/xinwen-zhu External Links: MGP · Wikidata · Google Scholar · Math-Net.Ru Awards: New Horizons in Mathematics Prize (2020)
Documents Indexed: 25 Publications since 2009 Co-Authors: 19 Co-Authors with 17 Joint Publications 655 Co-Co-Authors
all top 5
### Co-Authors
8 single-authored 2 Chen, Tsao-Hsien 2 Frenkel, Edward V. 2 Huang, An 2 Lian, Bong H. 2 Liu, Yifeng 2 Osipov, Denis Vasil’evich 2 Pappas, Georgios 2 Xiao, Liang 2 Zhang, Wei 1 Beuzart-Plessis, Raphaël 1 Deng, Ping 1 Donkin, Stephen 1 Horng, Shi-Jinn 1 Li, Tianrui 1 Liu, Ruochuan 1 Tian, Yichao 1 Wang, Hongjun 1 Xu, Daxin 1 Yau, Shing-Tung 1 Yun, Zhiwei
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### Serials
5 Inventiones Mathematicae 3 Annals of Mathematics. Second Series 2 Mathematical Research Letters 1 Advances in Mathematics 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Compositio Mathematica 1 Information Sciences 1 Journal of Differential Geometry 1 IMRN. International Mathematics Research Notices 1 Geometric and Functional Analysis. GAFA 1 Journal of Algebraic Geometry 1 Selecta Mathematica. New Series 1 Representation Theory 1 Algebra & Number Theory
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### Fields
18 Algebraic geometry (14-XX) 10 Number theory (11-XX) 5 Group theory and generalizations (20-XX) 5 Topological groups, Lie groups (22-XX) 2 Nonassociative rings and algebras (17-XX) 2 $$K$$-theory (19-XX) 1 Field theory and polynomials (12-XX) 1 Category theory; homological algebra (18-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Special functions (33-XX) 1 Ordinary differential equations (34-XX) 1 Differential geometry (53-XX) 1 Manifolds and cell complexes (57-XX) 1 Statistics (62-XX) 1 Computer science (68-XX)
### Citations contained in zbMATH Open
23 Publications have been cited 222 times in 156 Documents Cited by Year
Local models of Shimura varieties and a conjecture of Kottwitz. Zbl 1294.14012
Pappas, Georgios; Zhu, Xinwen
2013
Affine Grassmannians and the geometric Satake in mixed characteristic. Zbl 1390.14072
Zhu, Xinwen
2017
An introduction to affine Grassmannians and the geometric Satake equivalence. Zbl 1453.14122
Zhu, Xinwen
2017
On the coherence conjecture of Pappas and Rapoport. Zbl 1300.14042
Zhu, Xinwen
2014
The geometric Satake correspondence for ramified groups. Zbl 1392.11036
Zhu, Xinwen
2015
Affine Demazure modules and $$T$$-fixed point subschemes in the affine Grassmannian. Zbl 1167.14033
Zhu, Xinwen
2009
Rigidity and a Riemann-Hilbert correspondence for $$p$$-adic local systems. Zbl 1375.14090
Liu, Ruochuan; Zhu, Xinwen
2017
A categorical proof of the Parshin reciprocity laws on algebraic surfaces. Zbl 1237.19007
Osipov, Denis; Zhu, Xinwen
2011
Gerbal representations of double loop groups. Zbl 1280.22024
Frenkel, Edward; Zhu, Xinwen
2012
The two-dimensional Contou-Carrère symbol and reciprocity laws. Zbl 1346.19003
Osipov, Denis; Zhu, Xinwen
2016
Integral homology of loop groups via Langlands dual groups. Zbl 1267.57041
Yun, Zhiwei; Zhu, Xinwen
2011
Any flat bundle on a punctured disc has an oper structure. Zbl 1220.14013
Frenkel, Edward; Zhu, Xinwen
2010
Geometric Satake, categorical traces, and arithmetic of Shimura varieties. Zbl 1470.11169
Zhu, Xinwen
2018
Geometric Langlands in prime characteristic. Zbl 1390.14044
Chen, Tsao-Hsien; Zhu, Xinwen
2017
Frenkel-Gross’ irregular connection and Heinloth-Ngô-Yun’s are the same. Zbl 1393.14011
Zhu, Xinwen
2017
Period integrals and the Riemann-Hilbert correspondence. Zbl 1387.14042
Huang, An; Lian, Bong H.; Zhu, Xinwen
2016
Isolation of cuspidal spectrum, with application to the Gan-Gross-Prasad conjecture. Zbl 07395719
Beuzart-Plessis, Raphaël; Liu, Yifeng; Zhang, Wei; Zhu, Xinwen
2021
Non-abelian Hodge theory for algebraic curves in characteristic $$p$$. Zbl 1330.14015
Chen, Tsao-Hsien; Zhu, Xinwen
2015
Chain integral solutions to tautological systems. Zbl 1364.14031
Huang, An; Lian, Bong H.; Yau, Shing-Tung; Zhu, Xinwen
2016
Linear discriminant analysis guided by unsupervised ensemble learning. Zbl 1443.68145
Deng, Ping; Wang, Hongjun; Li, Tianrui; Horng, Shi-Jinn; Zhu, Xinwen
2019
Erratum to: Local models of Shimura varieties and a conjecture of Kottwitz. Zbl 1275.14025
Pappas, Georgios; Zhu, Xinwen
2013
On vector-valued twisted conjugation invariant functions on a group; with an appendix by Stephen Donkin. Zbl 1469.20049
Xiao, Liang; Zhu, Xinwen
2019
On the Beilinson-Bloch-Kato conjecture for Rankin-Selberg motives. Zbl 07495375
Liu, Yifeng; Tian, Yichao; Xiao, Liang; Zhang, Wei; Zhu, Xinwen
2022
On the Beilinson-Bloch-Kato conjecture for Rankin-Selberg motives. Zbl 07495375
Liu, Yifeng; Tian, Yichao; Xiao, Liang; Zhang, Wei; Zhu, Xinwen
2022
Isolation of cuspidal spectrum, with application to the Gan-Gross-Prasad conjecture. Zbl 07395719
Beuzart-Plessis, Raphaël; Liu, Yifeng; Zhang, Wei; Zhu, Xinwen
2021
Linear discriminant analysis guided by unsupervised ensemble learning. Zbl 1443.68145
Deng, Ping; Wang, Hongjun; Li, Tianrui; Horng, Shi-Jinn; Zhu, Xinwen
2019
On vector-valued twisted conjugation invariant functions on a group; with an appendix by Stephen Donkin. Zbl 1469.20049
Xiao, Liang; Zhu, Xinwen
2019
Geometric Satake, categorical traces, and arithmetic of Shimura varieties. Zbl 1470.11169
Zhu, Xinwen
2018
Affine Grassmannians and the geometric Satake in mixed characteristic. Zbl 1390.14072
Zhu, Xinwen
2017
An introduction to affine Grassmannians and the geometric Satake equivalence. Zbl 1453.14122
Zhu, Xinwen
2017
Rigidity and a Riemann-Hilbert correspondence for $$p$$-adic local systems. Zbl 1375.14090
Liu, Ruochuan; Zhu, Xinwen
2017
Geometric Langlands in prime characteristic. Zbl 1390.14044
Chen, Tsao-Hsien; Zhu, Xinwen
2017
Frenkel-Gross’ irregular connection and Heinloth-Ngô-Yun’s are the same. Zbl 1393.14011
Zhu, Xinwen
2017
The two-dimensional Contou-Carrère symbol and reciprocity laws. Zbl 1346.19003
Osipov, Denis; Zhu, Xinwen
2016
Period integrals and the Riemann-Hilbert correspondence. Zbl 1387.14042
Huang, An; Lian, Bong H.; Zhu, Xinwen
2016
Chain integral solutions to tautological systems. Zbl 1364.14031
Huang, An; Lian, Bong H.; Yau, Shing-Tung; Zhu, Xinwen
2016
The geometric Satake correspondence for ramified groups. Zbl 1392.11036
Zhu, Xinwen
2015
Non-abelian Hodge theory for algebraic curves in characteristic $$p$$. Zbl 1330.14015
Chen, Tsao-Hsien; Zhu, Xinwen
2015
On the coherence conjecture of Pappas and Rapoport. Zbl 1300.14042
Zhu, Xinwen
2014
Local models of Shimura varieties and a conjecture of Kottwitz. Zbl 1294.14012
Pappas, Georgios; Zhu, Xinwen
2013
Erratum to: Local models of Shimura varieties and a conjecture of Kottwitz. Zbl 1275.14025
Pappas, Georgios; Zhu, Xinwen
2013
Gerbal representations of double loop groups. Zbl 1280.22024
Frenkel, Edward; Zhu, Xinwen
2012
A categorical proof of the Parshin reciprocity laws on algebraic surfaces. Zbl 1237.19007
Osipov, Denis; Zhu, Xinwen
2011
Integral homology of loop groups via Langlands dual groups. Zbl 1267.57041
Yun, Zhiwei; Zhu, Xinwen
2011
Any flat bundle on a punctured disc has an oper structure. Zbl 1220.14013
Frenkel, Edward; Zhu, Xinwen
2010
Affine Demazure modules and $$T$$-fixed point subschemes in the affine Grassmannian. Zbl 1167.14033
Zhu, Xinwen
2009
all top 5
### Cited by 176 Authors
9 He, Xuhua 7 Zhu, Xinwen 6 Osipov, Denis Vasil’evich 6 Richarz, Timo 5 Lan, Kai-Wen 5 Pappas, Georgios 4 Gorchinskiĭ, Sergeĭ Olegovich 4 Haines, Thomas J. 4 Hamacher, Paul 4 Levin, Brandon 4 Nie, Sian 4 Riche, Simon 4 Viehmann, Eva 4 Weekes, Alex 3 Chen, Tsao-Hsien 3 Ivanov, Alexander B. 3 Kamnitzer, Joel 3 Kim, Wansu 3 Muthiah, Dinakar 3 Rapoport, Michael 3 Scholbach, Jakob 3 Stroh, Benoît 3 Wang, Haining 3 Yacobi, Oded 2 Achar, Pramod N. 2 Chan, Charlotte 2 Chen, Ling 2 Finkelberg, Michael Vladlenovich 2 Frenkel, Edward V. 2 Gille, Philippe 2 Görtz, Ulrich 2 Gröchenig, Michael 2 Imai, Naoki 2 Kamgarpour, Masoud 2 Kato, Syu 2 Lam, Thomas F. 2 Le Hung, Bao V. 2 Le, Daniel 2 Liu, Dongwen 2 Rostami, Sean 2 Safronov, Pavel 2 Scholze, Peter 2 Shen, Xu 2 Tian, Yichao 2 Xiao, Liang 2 Yu, Chia-Fu 2 Yun, Zhiwei 2 Zhang, Wei 2 Zhou, Rong 1 Anschütz, Johannes 1 Ardakov, Konstantin 1 Baumann, Pierre 1 Beraldo, Dario 1 Beuzart-Plessis, Raphaël 1 Biswas, Indranil 1 Bode, Andreas 1 Bräunling, Oliver 1 Braverman, Alexander 1 Bültel, Oliver 1 Caraiani, Ana 1 Casbi, Elie 1 Cass, Robert 1 Casselman, William A. 1 Cautis, Sabin 1 Cely, Jorge E. 1 Česnavičius, Kęstutis 1 Chaudouard, Pierre-Henri 1 Chen, Jingyue 1 Chen, Miaofen 1 Chernousov, Vladimir I. 1 Chi, Jingren 1 Chinburg, Ted 1 Contou-Carrere, Carlos Enrique 1 de Jong, Aise Johan 1 de Shalit, Ehud 1 Deng, Ping 1 Deninger, Christopher 1 Derryberry, Richard 1 Dumanski, Ilya 1 Elliott, Chris 1 Faltings, Gerd 1 Feigin, Evgeny 1 Feng, Shizhe 1 Feng, Tony 1 Florence, Mathieu 1 Ginzburg, Victor 1 Goren, Eyal Z. 1 Gross, Benedict Hyman 1 Hahn, Jeremy 1 Hales, Thomas Callister 1 Hartwig, Philipp 1 He, Siqi 1 Heinloth, Jochen 1 Heleodoro, Aron 1 Helm, David 1 Hernandez, David 1 Horozov, Ivan Emilov 1 Howard, Benjamin 1 Huang, An 1 Huang, Shinnyih ...and 76 more Authors
all top 5
### Cited in 64 Serials
11 Compositio Mathematica 11 Mathematische Annalen 9 Selecta Mathematica. New Series 8 Duke Mathematical Journal 8 Journal of the American Mathematical Society 7 Forum of Mathematics, Sigma 6 Advances in Mathematics 5 Journal of Algebra 4 Annales de l’Institut Fourier 4 Inventiones Mathematicae 4 Mathematische Zeitschrift 4 Annals of Mathematics. Second Series 4 Forum of Mathematics, Pi 3 Journal für die Reine und Angewandte Mathematik 3 Transactions of the American Mathematical Society 3 Journal of Algebraic Geometry 3 Representation Theory 3 Journal of the Institute of Mathematics of Jussieu 3 Algebra & Number Theory 2 Communications in Mathematical Physics 2 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 2 Russian Mathematical Surveys 2 Publications Mathématiques 2 Manuscripta Mathematica 2 Geometric and Functional Analysis. GAFA 1 Israel Journal of Mathematics 1 Letters in Mathematical Physics 1 Nuclear Physics. B 1 Journal of Geometry and Physics 1 Acta Mathematica 1 Acta Mathematica Vietnamica 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Canadian Journal of Mathematics 1 Canadian Mathematical Bulletin 1 Commentarii Mathematici Helvetici 1 Functional Analysis and its Applications 1 Geometriae Dedicata 1 Information Sciences 1 Journal of the London Mathematical Society. Second Series 1 Journal of Pure and Applied Algebra 1 Proceedings of the American Mathematical Society 1 Rendiconti del Seminario Matematico della Università di Padova 1 Tohoku Mathematical Journal. Second Series 1 International Journal of Mathematics 1 Applied Mathematical Modelling 1 St. Petersburg Mathematical Journal 1 Documenta Mathematica 1 Transformation Groups 1 Journal of the Australian Mathematical Society 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Oberwolfach Reports 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Proceedings of the Steklov Institute of Mathematics 1 Frontiers of Mathematics in China 1 Journal of $$K$$-Theory 1 Annales Mathématiques du Québec 1 EMS Surveys in Mathematical Sciences 1 Research in the Mathematical Sciences 1 Journal de l’École Polytechnique – Mathématiques 1 Transactions of the American Mathematical Society. Series B 1 Journal of Combinatorial Algebra 1 Higher Structures 1 Tunisian Journal of Mathematics 1 Peking Mathematical Journal
all top 5
### Cited in 30 Fields
122 Algebraic geometry (14-XX) 69 Number theory (11-XX) 42 Group theory and generalizations (20-XX) 29 Topological groups, Lie groups (22-XX) 13 $$K$$-theory (19-XX) 12 Nonassociative rings and algebras (17-XX) 5 Commutative algebra (13-XX) 5 Category theory; homological algebra (18-XX) 4 Several complex variables and analytic spaces (32-XX) 4 Quantum theory (81-XX) 3 Ordinary differential equations (34-XX) 2 Combinatorics (05-XX) 2 Associative rings and algebras (16-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Differential geometry (53-XX) 2 Algebraic topology (55-XX) 2 Manifolds and cell complexes (57-XX) 1 General and overarching topics; collections (00-XX) 1 Field theory and polynomials (12-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Functions of a complex variable (30-XX) 1 Special functions (33-XX) 1 Partial differential equations (35-XX) 1 Abstract harmonic analysis (43-XX) 1 General topology (54-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Statistics (62-XX) 1 Numerical analysis (65-XX) 1 Computer science (68-XX) 1 Mechanics of deformable solids (74-XX)
### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2022-07-02T19:51:03 |
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|
https://par.nsf.gov/biblio/10275623-mapping-tilt-milky-way-bulge-velocity-ellipsoids-argos-gaia-dr2
|
Mapping the tilt of the Milky Way bulge velocity ellipsoids with ARGOS and Gaia DR2
ABSTRACT Until the recent advent of Gaia Data Release 2 (DR2) and deep multi-object spectroscopy, it has been difficult to obtain 6D phase space information for large numbers of stars beyond 4 kpc, in particular towards the Galactic Centre, where dust and crowding are significant. We combine line-of-sight velocities from the Abundances and Radial velocity Galactic Origins Survey (ARGOS) with proper motions from Gaia DR2 to obtain a sample of ∼7000 red clump stars with 3D velocities. We perform a large-scale stellar kinematics study of the Milky Way bulge to characterize the bulge velocity ellipsoids in 20 fields. The tilt of the major-axis of the velocity ellipsoid in the radial-longitudinal velocity plane, or vertex deviation, is characteristic of non-axisymmetric systems and a significant tilt is a robust indicator of non-axisymmetry or bar presence. We compare the observations to the predicted kinematics of an N-body boxy-bulge model formed from dynamical instabilities. In the model, the lv values are strongly correlated with the angle (α) between the bulge major-axis and the Sun-Galactic centre line of sight. We use a maximum likelihood method to obtain an independent measurement of α, from bulge stellar kinematics alone, performing a robust error analysis. The most likely value more »
Authors:
; ; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10275623
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
502
Issue:
2
Page Range or eLocation-ID:
1740 to 1752
ISSN:
0035-8711
We investigate the structure of our Galaxy’s young stellar disc by fitting the distribution functions (DFs) of a new family to 5D Gaia data for a sample of $47\, 000$ OB stars. Tests of the fitting procedure show that the young disc’s DF would be strongly constrained by Gaia data if the distribution of Galactic dust were accurately known. The DF that best fits the real data accurately predicts the kinematics of stars at their observed locations, but it predicts the spatial distribution of stars poorly, almost certainly on account of errors in the best-available dust map. We argue that dust models could be greatly improved by modifying the dust model until the spatial distribution of stars predicted by a DF agreed with the data. The surface density of OB stars is predicted to peak at $R\simeq 5.5\, \mathrm{kpc}$, slightly outside the reported peak in the surface density of molecular gas; we suggest that the latter radius may have been underestimated through the use of poor kinematic distances. The velocity distributions predicted by the best-fitting DF for stars with measured line-of-sight velocities v∥ reveal that the outer disc is disturbed at the level of $10\, \mathrm{km\, s}^{-1}$ in agreementmore »
| 2022-12-08T17:25:55 |
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|
https://pdglive.lbl.gov/DataBlock.action?node=M300J6
|
#### $\mathbf {{{\mathit a}_{{0}}{(2020)}} }$ $\mathit I{}^{G}(\mathit J{}^{PC}) = 1{}^{-}(0{}^{++})$
MASS ${\mathrm {(MeV)}}$ WIDTH ${\mathrm {(MeV)}}$ DOCUMENT ID TECN
$2025 \pm30$ $330 \pm75$
1999 C
SPEC
References:
ANISOVICH 1999C
PL B452 173 ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \eta}}$ and ${{\mathit \pi}^{0}}$ ${{\mathit \eta}^{\,'}}$ from 600 to 1940 ${\mathrm {MeV}}/\mathit c$
| 2023-03-23T14:37:32 |
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https://pos.sissa.it/336/044/
|
Volume 336 - XIII Quark Confinement and the Hadron Spectrum (Confinement2018) - A: Vacuum structure and confinement
BRST invariant $d=2$ condensates in Gribov-Zwanziger theory
C. Felix*, D. Dudal, L. Palhares, F. Rondeau and D. Vercauteren
Full text: pdf
Pre-published on: September 12, 2019
Published on: September 26, 2019
Abstract
In this proceeding, $SU(N)$ Yang-Mills theory is quantized in the linear covariant gauges, while taking into account the issue of Gribov copies and we construct the one-loop effective potential for a set of mass dimension 2 condensates, including the Gribov parameter, that refines the infrared region of the Gribov-Zwanziger theory, whilst respecting renormalization group invariance and BRST symmetry.
DOI: https://doi.org/10.22323/1.336.0044
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
| 2023-02-09T12:03:51 |
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|
https://par.nsf.gov/biblio/10376230-gyr-dwarf-gyrochrone-from-cfht-megaprime-monitoring-open-cluster-m67
|
A 4 Gyr M-dwarf Gyrochrone from CFHT/MegaPrime Monitoring of the Open Cluster M67
Abstract
We present stellar rotation periods for late K- and early M-dwarf members of the 4 Gyr old open cluster M67 as calibrators for gyrochronology and tests of stellar spin-down models. Using Gaia EDR3 astrometry for cluster membership and Pan-STARRS (PS1) photometry for binary identification, we build this set of rotation periods from a campaign of monitoring M67 with the Canada–France–Hawaii Telescope’s MegaPrime wide-field imager. We identify 1807 members of M67, of which 294 are candidate single members with significant rotation period detections. Moreover, we fit a polynomial to the period versus color-derived effective temperature sequence observed in our data. We find that the rotation of very cool dwarfs can be explained by simple solid-body spin-down between 2.7 and 4 Gyr. We compare this rotational sequence to the predictions of gyrochronological models and find that the best match is Skumanich-like spin-down,Prott0.62, applied to the sequence of Ruprecht 147. This suggests that, for spectral types K7–M0 with near-solar metallicity, once a star resumes spinning down, a simple Skumanich-like relation is sufficient to describe their rotation evolution, at least through the age of M67. Additionally, for stars in the range M1–M3, our data show that spin-down must have resumed prior to the more »
Authors:
; ; ; ; ; ; ;
Publication Date:
NSF-PAR ID:
10376230
Journal Name:
The Astrophysical Journal
Volume:
938
Issue:
2
Page Range or eLocation-ID:
Article No. 118
ISSN:
0004-637X
Publisher:
DOI PREFIX: 10.3847
National Science Foundation
##### More Like this
1. Abstract
We present a study of the relationship between Galactic kinematics, flare rates, chromospheric activity, and rotation periods for a volume-complete, nearly all-sky sample of 219 single stars within 15 pc and with masses between 0.1 and 0.3Mobserved during the primary mission of TESS. We find all stars consistent with a common value ofα= 1.984 ± 0.019 for the exponent of the flare frequency distribution. Using our measured stellar radial velocities and Gaia astrometry, we determine GalacticUVWspace motions. We find 78% of stars are members of the Galactic thin disk, 7% belong to the thick disk, and for the remaining 15% we cannot confidently assign membership to either component. If we assume star formation has been constant in the thin disk for the past 8 Gyr, then based on the fraction that we observe to be active, we estimate the average age at which these stars transition from the saturated to the unsaturated flaring regime to be 2.4 ± 0.3 Gyr. This is consistent with the ages that we assign from Galactic kinematics: we find that stars with rotation periodProt< 10 days have an age of 2.0 ± 1.2 Gyr, stars with 10 days <Prot≤ 90 days have an agemore »
2. ABSTRACT
Age is a stellar parameter that is both fundamental and difficult to determine. Among middle-aged M dwarfs, the most prolific hosts of close-in and detectable exoplanets, gyrochronology is the most promising method to assign ages, but requires calibration by rotation-temperature sequences (gyrochrones) in clusters of known ages. We curated a catalogue of 249 late K- and M-type (Teff = 3200–4200 K) exoplanet host stars with established rotation periods, and applied empirical, temperature-dependent rotation–age relations based on relevant published gyrochrones, including one derived from observations of the 4-Gyr-old open cluster M67. We estimated ages for 227 of these stars, and upper limits for eight others, excluding 14 which are too rapidly rotating or are otherwise outside the valid parameter range of our gyrochronology. We estimated uncertainties based on observed scatter in rotation periods in young clusters, error in the gyrochrones, and uncertainties in temperature and non-solar metallicity. For those stars with measured metallicities, we provide but do not incorporate a correction for the effects of deviation from solar-metallicity. The age distribution of our sample declines to near zero at 10 Gyr, the age of the Galactic disc, with the handful of outliers explainable by large uncertainties. Continued addition or extension of cluster rotationmore »
3. Abstract
Current spectroscopic surveys are producing large catalogs of chemical abundances for stars of all types. The yttrium-to-magnesium ratio, [Y/Mg], has emerged as a candidate age indicator for solar twins in the local stellar neighborhood. However, it is unclear whether it is a viable age diagnostic for more diverse stellar types, so we investigate [Y/Mg] as an age indicator for the FGK-type planet host stars observed by Kepler. We find that the [Y/Mg] “Clock” is most precise for solar twins, with a [Y/Mg]/age slope ofm= −0.0370 ±0.0071 dex Gyr−1andσAge= 2.6 Gyr. We attribute the lower precision compared to literature results to nonsolar twins contaminating our solar twin sample and recommend a 1.5 Gyr systematic uncertainty for stellar ages derived with any [Y/Mg]–Age relation. We also analyzed the [Y/Mg] Clock as a function ofTeff,$logg$, and metallicity individually and find no strong trends, but we compute statistically significant [Y/Mg]–Age relations for subsamples defined by ranges inTeff,$logg$, and metallicity. Finally, we compare [Y/Mg] and rotation ages and find statistically similar trends as for isochrone ages, although we find that rotation ages perform better for GK dwarfs while isochrones perform better for FG subgiants. We conclude that themore »
4. Abstract
We observed HD 19467 B with JWST’s NIRCam in six filters spanning 2.5–4.6μm with the long-wavelength bar coronagraph. The brown dwarf HD 19467 B was initially identified through a long-period trend in the radial velocity of the G3V star HD 19467. HD 19467 B was subsequently detected via coronagraphic imaging and spectroscopy, and characterized as a late-T type brown dwarf with an approximate temperature ∼1000 K. We observed HD 19467 B as a part of the NIRCam GTO science program, demonstrating the first use of the NIRCam Long Wavelength Bar coronagraphic mask. The object was detected in all six filters (contrast levels of 2 × 10−4to 2 × 10−5) at a separation of 1.″6 using angular differential imaging and synthetic reference differential imaging. Due to a guide star failure during the acquisition of a preselected reference star, no reference star data were available for post-processing. However, reference differential imaging was successfully applied using synthetic point-spread functions developed from contemporaneous maps of the telescope’s optical configuration. Additional radial velocity data (from Keck/HIRES) are used to constrain the orbit of HD 19467 B. Photometric data from TESS are used to constrain the properties of the host star, particularly its age. NIRCammore »
5. Abstract
X-ray observations of low-mass stars in open clusters are critical to understanding the dependence of magnetic activity on stellar properties and their evolution. Praesepe and the Hyades, two of the nearest, most-studied open clusters, are among the best available laboratories for examining the dependence of magnetic activity on rotation for stars with masses ≲1M. We present an updated study of the rotation–X-ray activity relation in the two clusters. We updated membership catalogs that combine pre-Gaia catalogs with new catalogs based on Gaia Data Release 2. The resulting catalogs are the most inclusive ones for both clusters: 1739 Praesepe and 1315 Hyades stars. We collected X-ray detections for cluster members, for which we analyzed, re-analyzed, or collated data from ROSAT, the Chandra X-ray Observatory, the Neil Gehrels Swift Observatory, and XMM-Newton. We have detections for 326 Praesepe and 462 Hyades members, of which 273 and 164, respectively, have rotation periods—an increase of 6× relative to what was previously available. We find that at ≈700 Myr, only M dwarfs remain saturated in X-rays, with only tentative evidence for supersaturation. We also find a tight relation between the Rossby number and fractional X-ray luminosityLX/Lbolin unsaturated single members, suggesting a power-law index betweenmore »
| 2023-03-25T09:05:02 |
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|
https://phys.libretexts.org/Bookshelves/College_Physics/Book%3A_College_Physics_(OpenStax)/33%3A_Particle_Physics/33.0%3A_Prelude_to_Particle_Physics
|
$$\require{cancel}$$
# 33.0: Prelude to Particle Physics
Following ideas remarkably similar to those of the ancient Greeks, we continue to look for smaller and smaller structures in nature, hoping ultimately to find and understand the most fundamental building blocks that exist. Atomic physics deals with the smallest units of elements and compounds. In its study, we have found a relatively small number of atoms with systematic properties that explained a tremendous range of phenomena. Nuclear physics is concerned with the nuclei of atoms and their substructures. Here, a smaller number of components—the proton and neutron—make up all nuclei. Exploring the systematic behavior of their interactions has revealed even more about matter, forces, and energy.
Figure $$\PageIndex{1}$$: Part of the Large Hadron Collider at CERN, on the border of Switzerland and France. The LHC is a particle accelerator, designed to study fundamental particles. (credit: Image Editor, Flickr)
Particle physics deals with the substructures of atoms and nuclei and is particularly aimed at finding those truly fundamental particles that have no further substructure. Just as in atomic and nuclear physics, we have found a complex array of particles and properties with systematic characteristics analogous to the periodic table and the chart of nuclides. An underlying structure is apparent, and there is some reason to think that we are finding particles that have no substructure. Of course, we have been in similar situations before. For example, atoms were once thought to be the ultimate substructure. Perhaps we will find deeper and deeper structures and never come to an ultimate substructure. We may never really know, as indicated in Figure.
Figure $$\PageIndex{2}$$: The properties of matter are based on substructures called molecules and atoms. Atoms have the substructure of a nucleus with orbiting electrons, the interactions of which explain atomic properties. Protons and neutrons, the interactions of which explain the stability and abundance of elements, form the substructure of nuclei. Protons and neutrons are not fundamental—they are composed of quarks. Like electrons and a few other particles, quarks may be the fundamental building blocks of all there is, lacking any further substructure. But the story is not complete, because quarks and electrons may have substructure smaller than details that are presently observable.
This chapter covers the basics of particle physics as we know it today. An amazing convergence of topics is evolving in particle physics. We find that some particles are intimately related to forces, and that nature on the smallest scale may have its greatest influence on the large-scale character of the universe. It is an adventure exceeding the best science fiction because it is not only fantastic, it is real.
### Summary
• Particle physics is the study of and the quest for those truly fundamental particles having no substructure.
### Glossary
particle physics
the study of and the quest for those truly fundamental particles having no substructure
### Contributors
Paul Peter Urone (Professor Emeritus at California State University, Sacramento) and Roger Hinrichs (State University of New York, College at Oswego) with Contributing Authors: Kim Dirks (University of Auckland) and Manjula Sharma (University of Sydney). This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).
| 2019-05-20T13:11:03 |
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|
https://www.aimsciences.org/article/doi/10.3934/dcds.2020051
|
Article Contents
Article Contents
Existence and instability of some nontrivial steady states for the SKT competition model with large cross diffusion
• * Corresponding author: Yaping Wu
• This paper is concerned with the existence and stability of nontrivial positive steady states of Shigesada-Kawasaki-Teramoto competition model with cross diffusion under zero Neumann boundary condition. By applying the special perturbation argument based on the Lyapunov-Schmidt reduction method, we obtain the existence and the detailed asymptotic behavior of two branches of nontrivial large positive steady states for the specific shadow system when the random diffusion rate of one species is near some critical value. Further by applying the detailed spectral analysis with the special perturbation argument, we prove the spectral instability of the two local branches of nontrivial positive steady states for the limiting system. Finally, we prove the existence and instability of the two branches of nontrivial positive steady states for the original SKT cross-diffusion system when both the cross diffusion rate and random diffusion rate of one species are large enough, while the random diffusion rate of another species is near some critical value.
Mathematics Subject Classification: Primary: 35B35, 35B40, 35K20; Secondary: 35K57, 35P05.
Citation:
• Figure 1. (a): $B<C$ i.e. strong competition; (b): $B>C$ i.e. weak competition
Figure 2. (a): spiky steady state near positive constant steady states $(u^*, v^*)$ for small $d_2$, large enough $\rho_{12}$ and $\rho_{12}/d_1$, (b): large spiky steady state for small $d_2$, large enough $\rho_{12}$ and $\rho_{12}/d_1$, (c): positive steady state with singular bifurcation structure when $d_2$ is near $a_2/\pi^2$, $\rho_{12}$ and $\rho_{12}/d_1$ are large enough
Open Access Under a Creative Commons license
Figures(2)
| 2023-04-02T12:59:52 |
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https://publications.drdo.gov.in/ojs/index.php/dsj/article/download/651/4760
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Microstructural Evolution in Elastically-stressed Solids: A Phase-field Simulation
Simulation of microstructures under different processing conditions is important for fine- tuning the processing window as well as to understand the mechanisms. Phase field simulation has gained importance for problems with diffuse interfaces. Since in this simulation, thermodynamic driving forces (chemical as well as non-chemical) and kinetic constraints have been naturally incorporated, it has the potential to simulate microstructures under different processing and service conditions. In this paper, DMRL’s initiatives on using phase field simulations to understand microstructural evolution in both the phase separating and precipitating model systems have been presented. The influence of misfit stresses on the morphology of microstructures has been described. Output from actual thermodynamic calculations can be combined with these simulations to study systems of technological importance.
Technologically important materials such as Ni-base superalloys exhibit essentially two-phase microstructures. In Ni-base superalloys used for high temperature applications such as aeroengine turbine blades, the second phase (γ’) is precipitated through a solid solid transformation from the parent matrix phase (γ) through a multi-step solutionising and multi-step ageing process1-3. While the matrix has a disordered fcc structure, the precipitate has an ordered fcc (L12) structure and more often than not the compositions of the two phases are different. This difference in composition and structural arrangement results in a difference in the lattice parameters of the two phases. However, to keep the continuity of the lattice intact (i.e., to maintain coherency), the interface is strained (with the stresses within elastic limit) and such systems are called elastically-stressed solids.
Coherency stresses have a direct role in deciding the morphology of the precipitate phase4-7. In a two-phase system, the morphology of the second phase (minority phase) is decided by the sum of interfacial energy and the elastic energy8,9. In systems with isotropic interfacial energy, if the precipitate phase is completely coherent with the matrix (i.e., no lattice parameter misfit), then spherical shaped precipitates are expected.
In various misfit-controlled Ni-X alloys, it was found that the alloys with lower misfit had spherical precipitates whereas the alloys with higher misfit had cuboidal or elongated precipitates10. While the interfacial energy (which is more or less isotropic) drives a spherical shape, the elastic energy drives elongated shape and the precipitates acquire a shape for which the total energy is a minimum. The shapes corresponding to minimum energy are equilibrium shapes and the rate at which this shape is achieved is affected by kinetics of the transformation.
Phase-field simulation11-20 has emerged as a successful tool in predicting the morphology of microstructures considering both thermodynamical driving force as well as kinetic constraints. Its application spans a wide area of materials simulation, ranging from solidification microstructure, grain growth in single-phase and multi-phase materials, precipitation kinetics, effect of magnetic field on microstructures, electromigration, etc. An overview by Chen19 and the references therein have enormous information. Since tracking of interfaces is not required in phase-field simulations, it is more attractive and convenient to deal with problems involving interfaces in contrast to sharp interface model where it is very difficult to track interfaces11. Moreover, in these simulations, no assumption is made with regards to the thickness of interfaces, and hence, these are well-suited for studying this class of problems21. This method has the potential to predict the microstructural changes during the entire thermal treatment starting from dendrites arising during solidification, solutionising, precipitation during high temperature ageing, coarsening of precipitates and changes in the microstructures during service, especially arising due to externally applied stresses at high temperatures and dislocation interactions.
This study demonstrates the initiative in establishing expertise in phase-field simulation of microstructural evolution during solid → solid transformations. The paper covers essential mathematical background of phase-field simulation including the micromechanics of defects (specifically addressing solid-state precipitates). The application of phase-field simulation to microstructural evolution in a spinodally decomposing (2-D as well as 3-D) systems and a precipitating (2-D model Ni-Al) system has been demonstrated. The effect of elastic stresses on the morphological evolution has been shown qualitatively.
In a phase-field simulation, the energy of the system is expressed in terms of appropriate field variables and their derivatives11-20. There are two types of field variables: conserved and non-conserved. Composition is a conserved variable since the overall composition in a closed system has to be constant, whereas grain orientations (in grain growth problems), order-parameters (in solidification or precipitation problems) are non-conserved variables. The spatial derivatives of these variables account for changes wrt adjacent domain, and hence, represent interfacial contribution. Apart from these, long-range contribution such as elastic energy, magnetic energy (which themselves can be dependent on the field variables) can be added to the overall energy of the system. In a typical phase-field problem, the energy is expressed as a sum of chemical and non-chemical energies19. For example, in systems such as Ni-base superalloys, the non-chemical free energy is the elastic energy (Fel), and hence, the total energy, F, is expressed as
$F={F}_{ch}+{F}_{el}$ (1)
where, Fch is the chemical free energy given as
${F}_{ch}=\mathrm{\int }\left[\begin{array}{l}f\left({c}_{1},{c}_{2},\cdots {c}_{n},{\text{η}}_{1},{\text{η}}_{2},\cdots ,{\text{η}}_{m}\right)\\ +\sum _{i=1}^{n}{\text{α}}_{i}{\left(\nabla {c}_{i}\right)}^{2}+\sum _{i=1}^{m}{\text{β}}_{i}{\left(\nabla {\text{η}}_{i}\right)}^{2}\end{array}\right]\text{\hspace{0.17em}}d\mathbit{r}$ (2)
In Eqn (2), f is the local free energy density expressed as a function of conserved variables, c1, c2, …, cn (compositions in a multi-component alloy) and non-conserved variables, η1, η2,… ηm (order parameters indicating whether the location is matrix or precipitate and if precipitate, to which of the different possible orientations it belongs to). αi and βi are respectively the gradient energy coefficients for the conserved and the non-conserved variables. The functional form of local free energy functional is the key that would differentiate between different phase-field models.
2.1 Field Evolution
In a phase-field simulation, the microstructural evolution is obtained by solving Cahn-Hilliard and Allen-Cahn equations for the conserved and non-conserved variables, respectively19,21,22. These equations describe the time evolution of the field variables in terms of variational derivatives of the free energy functional wrt the field variables. Mathematically, these are stated as
$\frac{\partial {c}_{i}}{\partial t}=M{\nabla }^{2}\frac{\delta F}{\delta {c}_{i}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{for}\text{\hspace{0.17em}}i=1\cdots n$ (3)
$\frac{\partial {\text{η}}_{i}}{\partial t}=-L\frac{\delta F}{\delta {\text{η}}_{i}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{for}\text{\hspace{0.17em}}i=1\cdots m$ (4)
It is to be noted that both ci and ηi are functions of position and time. The coefficients M and L are the kinetic coefficients which would decide how fast the microstructures would evolve. Though, in general, these coefficients can be functions of field variables as well as can have directional dependence, here these are considered as isotropic scalar values and independent of concentration and order parameters.
2.2 Numerical Solution
It is convenient to solve the field kinetic equations in Fourier space. Assuming periodic boundary conditions (i.e., if we solve a 2-D problem, the problem space is repeated infinitely in both x and y directions filling the entire 2-D space), Fourier transformation (wrt position coordinates) of Eqns (3) and (4) will convert these into a set of algebraic equations19, as :
$\frac{{\stackrel{˜}{c}}_{i}^{t+\mathrm{\Delta }t}-{\stackrel{˜}{c}}_{i}^{t}}{\mathrm{\Delta }t}=-M{k}^{2}\left({\stackrel{˜}{g}}^{t}+2{k}^{2}{\text{α}}_{i}{\stackrel{˜}{c}}_{i}^{t+\mathrm{\Delta }t}\right)$ (5)
$\frac{{\stackrel{˜}{\eta }}_{i}^{t+\mathrm{\Delta }t}-{\stackrel{˜}{\eta }}_{i}^{t}}{\mathrm{\Delta }t}=-L\left({\stackrel{˜}{h}}^{t}+2{k}^{2}\beta {\stackrel{˜}{\eta }}_{\text{i}}^{t+\mathrm{\Delta }t}\right)$ (6)
In Eqns (5) and (6), the ~ above the quantities represent Fourier transforms, g and h are the derivatives of f wrt c and η, respectively, and k is the length of Fourier vector. The superscripts, t and tt represent the time at which the quantities are evaluated. In the above formalism, semi-implicit method has been used, wherein c and η occurring on the RHS of the equations are taken at time tt, whereas the nonlinear terms g and h are taken at time t.
2.3 Free Energy Functional
Two types of free energy functionals have been considered: (i) a spinodally decomposing system, and (ii) precipitating systems. For a binary spinodally decomposing system, simplest form of free energy is a double-well potential21. The double-well potential is mathematically represented as
$f={c}^{2}{\left(1-c\right)}^{2}$ (7)
where c is the concentration of the solute phase. This potential mimics a system with free energy minima at concentrations c = 0 and c = 1, as shown in Fig. 1. The physical implication is that in an A-B type of phase separating system, the two phases will have the compositions of that of pure A and pure B.
In case of precipitating system such as γ-γ’, the free energy functional is much more complicated, and involves a set of non-conserved variables (η1, η2, η3) apart from the conserved variable, c. A typical functional is given as20
$\begin{array}{l}f\left(c,{\text{η}}_{1},{\text{η}}_{2},{\text{η}}_{3}\right)={A}_{1}{\left(c-{c}_{1}\right)}^{2}+{A}_{2}\left({c}_{2}-c\right)+\left({\text{η}}_{1}^{2}+{\text{η}}_{2}^{2}+{\text{η}}_{3}^{2}\right)\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}-{A}_{3}{\text{η}}_{1}{\text{η}}_{2}{\text{η}}_{3}+{A}_{4}\left({\text{η}}_{1}^{4}+{\text{η}}_{2}^{4}+{\text{η}}_{3}^{4}\right)\end{array}$ (8)
where A1, A2, A3, A4, c1, c2 are constants for a particular system of interest. In this free energy functional, the disorderd γ region is represented by the order parameter set values (η1, η2, η3) = (0, 0, 0), whereas the four different variants of the ordered γ’ phase are represented by (1, 1, 1) η0, (1, -1, -1) η0, (-1, 1, -1) η0, (-1, -1, 1) η0, where η0 is the equilibrium value of the order parameter. Considering A1, A2, A3, A4, c1, c2 as 40.0, 17.0, 46.8, 15.0, 5.0, 0.05, 0.22 respectively and M = 4.0 and L = 4.0, the calculated free energy20 curve is shown in Fig. 2.
2.4 Elastic Energy
As noted earlier, two-phase Ni-base superalloys are under the influence of elastic stresses arising out of coherency strains (lattice misfit). The total elastic energy of the stressed system is given by22
${F}_{el}=\frac{1}{2}\underset{V}{\int }{\sigma }_{ij}^{el}\left(\mathbit{r}\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\epsilon }_{ij}^{el}\left(\mathbit{r}\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}d\mathbit{r}$ (9)
where, ${\epsilon }_{ij}^{el}\left(\mathbit{r}\right)={\epsilon }_{ij}\left(\mathbit{r}\right)-{\epsilon }_{ij}^{0}\left(\mathbit{r}\right)$ is the elastic strain (difference between the total strain and the misfit strain). The misfit strain itself is a function of composition and it can be assumed to vary linearly with composition (Vegard’s law). i.e., ${\epsilon }_{ij}^{0}\left(\mathbit{r}\right)={\epsilon }_{ij}^{0}\text{\hspace{0.17em}}\text{\hspace{0.17em}}c\left(\mathbit{r}\right)$ . Assuming homogeneous elasticity (i.e., elastic constants are independent of composition, and hence, position), the elastic stress is given by ${\sigma }_{ij}^{0}\left(\mathbit{r}\right)={C}_{ijkl}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\epsilon }_{kl}^{0}\left(\mathbit{r}\right)$ , where Cijkl are the elastic constants of the homogeneous system. In all these expressions, summation over repeated indices (where the indices vary from 1 to 3) is understood without explicitly stating. Though the Eqn (9) appears compact, evaluation of elastic strain is not straightforward. Considering, mechanical equilibrium of the system (Appendix 1), the final result (which is easily programmable) is given as20,22
${F}_{el}=\frac{1}{2}\underset{V}{\int }B\left(n\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}{|\stackrel{˜}{c}\left(\mathbit{r}\right)|}^{2}\frac{dk}{{\left(2\text{π}\right)}^{3}}$ (10)
where, $B\left(n\right)={C}_{ijkl}{\epsilon }_{ij}^{0}{\epsilon }_{kl}^{0}-{n}_{j}{\sigma }_{ij}^{0}{\text{Ω}}_{ki}\left(n\right){\sigma }_{kl}^{0}{n}_{l}$ and ${\text{Ω}}_{ik}^{\text{-}1}\left(n\right)={C}_{ijkl}{n}_{j}{n}_{l}$ is inverse Green function of anisotropic elasticity. Here, $n=k/|k|$ is the unit vector in Fourier space with k being the reciprocal vector. $\stackrel{˜}{c}\left(k\right)$ is the Fourier transform of the concentration field given as
$\stackrel{˜}{c}\left(k\right)=\underset{V}{\int }c\left(\mathbit{r}\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}{e}^{-ik\cdot \mathbit{r}}\text{\hspace{0.17em}}d\mathbit{r}$
The variational derivative of the elastic energy wrt to composition (all quantities in Fourier space) is given as $B\left(\mathbit{n}\right)\text{\hspace{0.17em}}B\left(\mathbit{n}\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\stackrel{˜}{c}\left(\mathbit{k}\right)$ . Incorporating the elastic energy, the semi-implicit equation for compositional evolution Eqn (5) is modified as
$\frac{{\stackrel{˜}{c}}_{i}^{t+\mathrm{\Delta }t}-{\stackrel{˜}{c}}_{i}^{t}}{\mathrm{\Delta }t}=-M{k}^{2}\left({\stackrel{˜}{g}}^{t}+\left[2{k}^{2}{\text{α}}_{i}+B\left(n\right)\right]{\stackrel{˜}{c}}_{i}^{t+\mathrm{\Delta }t}\right)$ (16)
The equation for order parameter evolution remains unchanged. Incorporating the elastic energy and the free energy functional of the precipitating system, a program in C has been developed by the author.
Here, application of the developed code has been demonstrated through simulations of 2-D and 3-D spinodally decomposing systems (using the free energy in Eqn (9)) and of 2-D precipitating systems (using the free energy in Eqn (10)). For the 2-D simulations of the spinodal decomposition, binary A-B systems with 0.25B and 0.5B have been considered. The effect of elastic (both isotropic and anisotropic) stresses on the microstructural evolution has been dealt with. For the 3-D spinodal decomposition, binary A-B system with 0.3B and 0.5B, both in the absence and presence of elastic stresses have been considered. Precipitating system has been simulated for 2-D model Ni-Al systems with 15 per cent and 18 per cent Al, in the presence of elastic stresses. These demonstrations serve a pedagogical role in understanding the individual effect of different factors that affect microstructural morphology.
3.1 Microstructural Evolution in Phase Separating System
3.1.1 Two Dimensional Systems
The microstructural evolution in a spinodally decomposing system as a function of time has been studied in the absence as well as presence of misfit stresses. The system size in each case is 1024 x 1024. Starting configurations for these simulations are generated by introducing a random fluctuation (to a maximum extent of 1 per cent of desired composition) at every point of the simulation system. This has been done to mimic the compositional fluctuations that trigger spinodal decomposition. Microstructural evolution has been tracked using free energy functional in Eqn (9) and using Eqn (8) (evolution of composition field as a function of time).
System with 25 per cent B: Figure 3 shows the microstructural evolution for a binary A-B alloy of composition c = 0.25B as a function of time. The gray areas represent regions that are richer in B. The segregation of second phase starts appearing around t = 1000 [Fig. 3(a)]. Well developed particles can be seen in Fig. 3(b) corresponding to a time of t = 2000. As the system evolves further, coarsening as well as coalescence of the second phase particles is evident from the decrease in the number density and increase in the size of particles. It can be seen that most of the particles have circular morphology due to the isotropic nature of the interfacial energy. Some particles are seen to have an elongated morphology, which is due to coalescence; eventually these particles also acquire circular morphology through redistribution of the solute atoms.
System with 50 per cent B: Figure 4 shows the microstructural evolution as a function of time in a system with composition c = 0.5B. Even from early times of evolution, the microstructure is an interconnected structure of A-rich (dark) and B-rich (bright) phases. The microstructure evolves in a self-similar fashion with increasing time. As time progresses, the phases can be seen to coarsen. Isolated particles with convex shapes are seen to disappear to the benefit of growth of lobe-like features of adjacent regions due to curvature effect or Ostwald ripening24. The chemical potential of solute around a particle scales as inverse of its radius of curvature. Hence, the chemical potential of solute around a smaller particle is higher compared to that around a bigger particle. As diffusion occurs down the chemical potential gradient, solute atoms diffuse from smaller particles to their bigger counterparts. This leads to eventual disappearance of smaller particles and coarsening of the larger ones.
Effect of isotropic elastic stress: Figures 5 and 6 show the evolution of microstructures in systems with composition 0.25B and 0.5B, respectively, but now with isotropic elastic stress arising due to lattice parameter misfit strain of 0.01 (i.e., lattice parameter of B differs from that of A by 1 per cent). The shear modulus and Poisson’s ratio considered are 400 (non-dimensional units) and 0.3, respectively. Comparing Fig. 3 (corresponding to t = 2000) with Fig. 5 (corresponding to t = 4000), it is clear that the nucleation is delayed in the later case. In contrast, for a composition of c = 0.5 B, there is no appreciable delay in the initiation of phase separation. This is easy to understand as this composition lies well within the coherent spinodal whereas a composition of c = 0.25B is presumably near the edge of coherent spinal (the edge of chemical spinodal being at c = 0.21B). It is to be noted that the phase boundaries of coherent spinodal (due to coherency stresses) occur within the chemical spinodal, and hence, the coexisting two-phase filed is narrowed24. The incorporation of elastic energy provides a barrier to the spontaneously evolving system, and hence, demands more fluctuations to induce phase separation. However, once the phase separation sets in, further growth is a spontaneous process. Accordingly, during late stages of evolution, there is no appreciable difference in the morphologies of microstructures of systems with and without elastic stresses.
Effect of anisotropic elastic stress: Figures 7 and 8 show the microstructural evolution in systems with composition 0.25B and 0.5B, respectively, in the presence of cubic elastic misfit (effective shear modulus of 400, effective Poisson’s ratio of 0.3 and Zener anisotropy factor of 3.0 were chosen). From Fig. 7, the effect of elastic stress is evident even during the early stages of phase separation. Since elastic stresses are of long range in nature, the second phase particles are aligned along the x- and y- axes (which are softer directions for the particular set of elastic constants chosen). During late stages, bigger second phase particles are elongated along the x- and y- axes. In the case of precipitates with cubic misfit, elastic energy is minimum for needle shaped particles. When the interfacial energy is isotropic, it is minimum for circular shapes. In the presence of both elastic and interfacial energies, for small sizes, interfacial energy is dominant, and hence, the particles are circular in nature, and for large sizes, elastic energy contribution is more, and hence, the shapes are elongated with edges along the x and y axes, with curved corners. In the case of c = 0.5B, the interconnected microstructures are elongated along the x- and y- axes.
3.1.2 Three-dimensional Systems
Three dimensional (3-D) microstructural evolution in binary phase separating systems has been presented in Figs 9-12, for different cases similar to those presented for 2-D systems. OpenDX program25 has been used to render these plots. A system size of 128 x 128 x 128 has been chosen, since study of higher sizes requires more memory and is time-consuming as well. However, it should be noted that for a qualitative study, this system size is adequate to discern different microstructural features. For studying the influence of coherency stresses, similar parameters as in 2-D cases have been chosen, except that the effective shear modulus is considered as 200. In the concentration maps, red corresponds to pure B and blue corresponds to 50 per cent B. Isoconcentration maps corresponding to 50 per cent B have also been shown to clearly delineate boundaries of solute-rich regions (in these maps, green and grey correspond to outer and inner surfaces, respectively). The results are qualitatively similar to those explained in the two dimensional cases. The complexity of interconnected microstructures in 3-D cases is quite evident from these figures. Two-dimensional sections of these microstructures can however produce artifacts such as circular and elongated morphologies depending on the orientation of the cutting plane. In other words, it is important to use 3-D visualisation techniques for analysing 3-D simulation results.
3.2 Microstructures in Model Ni-Al System
Microstructural evolution in a model Ni-Al system has been studied using free energy expression given in Eqn (10). While in the case of phase separating system, microstructural evolution is tracked using Eqn. (7) (corresponding to composition), in this case, equations corresponding to order parameters [(Eqn. (8)] have also been solved. In this system, since there is a barrier for forming nuclei of second phase, sustained noise in composition as well as order parameters (mimicking fluctuations) has been introduced till some incubation time. Care has been taken to keep the overall composition at the initially desired level, since it is a conserved variable. For times greater than the incubation time, the incorporation of noise has been stopped. In some literature, noise is incorporated adhering to fluctuation-dissipation theorem26.
In Fig. 13, microstructural evolution corresponding to a composition of 15 per cent Al has been shown as a function of time. The incubation time in this case been chosen as 10 units. After t = 15, the precipitates (γ’) are well isolated and mostly have a circular morphology, due to the dominant nature of (isotropic) interfacial energy. Solute depletion in matrix near the precipitate-matrix interface is evident. After t = 50, the precipitates have square morphology, driven by the elastic energy arising due to misfit. Further, alignment and elongation of precipitates, both driven by long-range elastic energy, can be seen after t = 400. The four different colours of the precipitates correspond to the four possible variants of γ’ precipitates. Comparing the figures corresponding to t = 50 with t = 400, it can be seen that two particles (at top left corner) have coalesced to form a single particle. Since these two particles belong to the same variant, there is no antiphase boundary separating them, and hence, coalescence has taken place. Other particles, even if they are spatially located nearby, cannot undergo coalescence because they belong to different variants. Such particles can grow only through coarsening.
Microstructural evolution in model Ni-Al system containing 18 per cent Al is shown in Fig. 14. Here, because of large supersaturation of solute Al atoms, it was suffi cient to provide an incubation period of 2 time units, at which point of time, enough nuclei had formed. The circular precipitates at early stages (t = 7) grow in size by acquiring solute atoms from the matrix. The coalescence of precipitates belonging to the same variant leads to precipitates having non-circular morphology (Figs. 14(b) and 14(c)). Towards the late stage (t > 500), most of the precipitates have straight edges parallel to the x- and y- axes in accordance with the cubic anisotropic condition. Further, due to the long-range nature of elastic energy, the precipitates are aligned along the x- and y- axes. The microstructure mimics a typical fully aged microstructure of nickel base superalloy, wherein cuboidal precipitates are embedded in a disordered matrix.
Microstructural simulation using phase-field method is fast gaining importance. In this paper, DMRL’s initiatives in using phase-field simulations have been described. Detailed description of phase-field simulation methodology has been given. Results of case studies concerning phase separating system and precipitating system have been presented. Influence of elastic stresses arising due to difference in lattice parameter between two phases has been shown. Delay in initiation of phase separation due to the barrier imposed by elastic stresses has been shown. With the incorporation of elastic anisotropy, alignment and elongation of precipitates have been observed. Simulated microstructures for model Ni-Al system resemble experimentally observed γ-γ’ microstructures.
This study forms a part of DMRL’s effort on multiscale simulation of microstructural evolution. This will be further taken forward by incorporating input from thermodynamic calculations of real systems (free energies calculated from ThermoCalc software which is available in DMRL will be used for this). The presently developed code can handle only homogeneous elasticity problem (i.e., elastic constants of the precipitate and matrix are equal). Extension of this code to handle elastic inhomogeneity and effect of externally applied stresses is underway. The present code for two-dimensional systems for the precipitating system will be extended to three-dimensional systems.
The author thanks Director, DMRL for allowing him to carry out this work and Dr M. Vijayakumar, Sc G, for his support and encouragement. The author also thanks Prof T.A. Abinandanan, IISc, Bengaluru, for providing the kernel of the phase field simulation code for simulating microstructural evolution of incoherent miscibility gap system and for detailed discussions on the fundamentals of micromechanics of defects.
1. Das, N.; Singh, S.; Hazari, N.; Chatterjee, D. & Praveen, V.V.N.S.S.C. Indigenous cast superalloys and investment casting technology for gas turbine components. Metals, Mater. Proce., 2007, 19, 189-202.
2. Reed, Roger C. The superalloys fundamentals and applications. Cambridge University Press, Cambridge, 2006.
3. Durant-Charre, Madeline. The microstructure of superalloys. Gordon Breach Science Publishers, Amsterdam, 1997.
4. Johnson, W.C. Influence of elastic stress on phase transformations, In Lectures on the theory of phase transformations, edited by H.I. Aaronson. TMS, Warrendale, Pennsylvania, 1999. pp. 35-134.
5. Doi, M. Elasticity effects on the microstructure of alloys containing coherent precipitates. Prog. Mater. Sci., 1996, 40, 79-180.
6. Fratzl, P; Penrose, O & Lebowitz, J.L. Modelling of phase separation in alloys with coherent elastic misfit. J. Stat. Phy., 1999, 95(5/6), 1429-503.
7. Voorhees, P.W. & Johnson, W.C. The thermodynamics of elastically stressed crystals. In Solid State Physics: Advances in Research and Applications. Vol 59. Elsevier Academic Press, 2004. pp. 1-201.
8. Johnson, W.C. & Cahn, J.W. Elastically induced shape bifurcations of inclusions. Acta Metallurgica, 1984. 32, 1925-933.
9. Sankarasubramanian, R.; Jog, C.S. & Abinandanan, T.A. Symmetry-breaking transitions in equilibrium shapes of coherent precipitates: Effect of elastic anisotropy and inhomogeneity. Metall. Mater. Trans. A, 2002, 33A, 1083-1090.
10. Li, F.; Prikhodko, S.V.; Ardell, A.J. & Kim, D. Morphological evolution of γ’-type particles in Ni-base alloys: shape characterisation. In Twelth Proceedings of the International Conference on Solid-Solid Transformations. The Japan Institute of Metals, 1999. pp. 545-52.
11. Leo, P.H.; Lowengrub, J.S. & Jou, H.J. A diffuse interface model for microstructural evolution in elastically stressed solids. Acta Materialia, 1998, 46, 2113-130.
12. Zhu, J.; Chen, L.Q.; & Shen, J. Morphological evolution during phase separation and coarsening with strong inhomogeneous elasticity. Modell. Simul. Mat. Sci. Engg., 2001, 9, 499-511.
13. Hu, S.Y.; & Chen, L.Q.; A phase-field model for evolving microstructures with strong elastic inhomogeneity. Acta Materialia, 2001, 49, 1879-890.
14. Jin, Y.M.; & Wang, Y.U. & Khachaturyan, A.G. Three-dimensional phase field microelasticity theory and modeling of multiple cracks and voids. App. Phy. Lett., 2001, 79, 3071-073.
15. Wang, Y.U.; Jin, Y.M. & Khachaturyan, A.G. Phase field microelasticity theory and simulation of multiple voids and cracks in single crystals and polycrystals under applied stress. J. Appl. Phy., 2001, 91, 6435-451.
16. Wang, Y.U.; Jin, Y.M. & Khachaturyan, A.G. Three-dimensional phase field microelasticity theory of a complex elastically inhomogeneous solid. Appl. Phy. Lett., 2002, 80, 4513-515.
17. Wang, Y.U.; Jin, Y.M. & Khachaturyan, A.G. Phase field microelasticity theory and modeling of elastically and structurally inhomogeneous solid. J. Appl. Phy., 2002, 92, 1351-360.
18. Gururajan, M.P. Elastic inhomogeneity effects on microstructures – A phase field study. Indian Institute of Science, Bengaluru, 2006. PhD Thesis.
19. Chen, L.Q. Phase field models for microstructure evolution. Ann. Rev. Mater. Res., 2002, 32, 113-40.
20. Li, D.Y. & Chen, L.Q., Shape evolution and splitting of coherent particles under applied stresses. Acta Materialia, 1999, 47, 247-57.
21. Cahn, J.W. & Hilliard, J.E. Free energy of a nonuniform system I, Interfacial free energy. J. Chem. Phy., 1958, 28, 258-67.
22. Allen, S.M. & Cahn, J.W. Mechanisms of phase transformations within the miscibility gap of Fe-rich Fe-Al alloys. Acta Metallurgica, 1976, 24, 425-37.
23. Khachaturyan, A.G. Theory of structural transformations in solids. John Wiley & Sons, Chicago, 1983.
24. Porter, D.A., & Easterling, K.E. Phase transformations in metals and alloys. Nelson Thornes Ltd, Cheltenham, UK, 2001.
25. http://www.opendx.org/ (Assessed on in 2007)
26. Lifshitz, E.M. & Pitaevskii, L.P. Statistical physics, Pt-I: Landau and Lifshitz course on theoretical physics. Pergamon Press, Oxford, 1980, 5.
Dr R. Sankarasubramanian completed his integrated ME and PhD from the Department of Metallurgy, Indian Institute of Science, Bengaluru, in 1994 and 2000, respectively. Presently, he is working as Scientist D at the Defence Metallurgical Research Laboratory (DMRL), Hyderabadand his research interest is multi-scale materials modelling and simulation.
# Appendix-1
To find out the elastic energy of coherent system, we start from the equation of mechanical equilibrium.
${\sigma }_{ij,j}\left(\mathbit{r}\right)=0,$ (A.1)
where, σij (r) are stress components and the subscript, j represents derivative of the quantity along the direction rj. Here, Einstein’s summation notation over repeated indices (all indices ranging from 1 to 3) has been followed. Assuming, the coherency strains to be in the linear elastic regime, the stress is related to strain through constitutive relation as
${\sigma }_{ij}={C}_{ijkl}\left({u}_{k,l}\left(\mathbit{r}\right)-{\epsilon }_{kl}^{0}\left(\mathbit{r}\right)\right),$ (A.2)
where, Cijkl are the elastic constants, uk,l (r) are the displacement gradients and ${\text{ε}}_{kl}^{0}\left(\mathbit{r}\right)$ are the components of the transformation strain or eigen strain. Following Vegard’s law, the transformation strain can be assumed to scale linearly with compostion, c(r), and is given as
${\text{ε}}_{kl}^{0}\left(\mathbit{r}\right)={\text{ε}}_{kl}^{0}\text{\hspace{0.17em}}\text{\hspace{0.17em}}c\left(\mathbit{r}\right)$ (A.3)
Substituting Eqn (2) in Eqn (1),
$\begin{array}{l}{C}_{ijkl}{\left({u}_{k,l}\left(\mathbit{r}\right)-{\text{ε}}_{kl}^{0}\left(\mathbit{r}\right)\right)}_{,j}=0\\ \text{or}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{C}_{ijkl}{u}_{k,lj}\left(\mathbit{r}\right)={C}_{ijkl}{\text{ε}}_{kl,j}^{0}\left(\mathbit{r}\right)\end{array}$ (A.4)
Using Fourier transform of the displacement field, the above equation can be simplified. Fourier transform is given by
$F\left({u}_{i}\left(\mathbit{r}\right)\right)={\stackrel{˜}{u}}_{i}\left(k\right)=\underset{-\infty }{\overset{\infty }{\int }}{u}_{i}\left(\mathbit{r}\right){e}^{-ik\cdot \mathbit{r}}d\mathbit{r}$ (A.5)
where, k is the Fourier vector and the ~ indicates Fourier transform.
It is easy to see that
$F\left({u}_{k,lj}\left(\mathbit{r}\right)\right)=\left(i{k}_{l}\right)\left(i{k}_{j}\right){\stackrel{˜}{u}}_{k}\left(k\right)=-{k}_{l}{k}_{j}{\stackrel{˜}{u}}_{k}\left(k\right)$ (A.6)
$\mathrm{and} F\left({\epsilon }_{kl,j}^{0}\left(\mathbit{r}\right)\right)=i{k}_{j}{\stackrel{˜}{\epsilon }}_{kl}^{0}\left(k\right)=i{k}_{j}{\epsilon }_{kl}^{0}\stackrel{˜}{c}\left(k\right)$ (A.7)
where, c(k) is the Fourier transform of the composition c(r). Applying Fourier transform to equation (A.4) and using equations (A.6) and (A.7),
$-{k}_{l}{k}_{j}{C}_{ijkl}{\stackrel{˜}{u}}_{k}\left(k\right)=i{k}_{j}{C}_{ijkl}\text{\hspace{0.17em}}{\epsilon }_{kl}^{0}\stackrel{˜}{c}\left(k\right)$
Writing in terms of unit vector in Fourier space ${n}_{i}={k}_{i}/|k|$
$-{|k|}^{2}{n}_{l}{n}_{j}{C}_{ijkl}{\stackrel{˜}{u}}_{k}\left(k\right)=i{n}_{j}|k|{C}_{ijkl}{\text{ε}}_{kl}^{0}\stackrel{˜}{c}\left(\mathbit{r}\right)$ (A.8)
Writing ${n}_{l}{n}_{j}{C}_{ijkl}={\text{Ω}}_{ik}^{-1}\left(n\right)$ and ${C}_{ijkl}{\text{ε}}_{kl}^{0}={\text{σ}}_{kl}^{0}$ , the displacement field can be written from Eqn (A.8) as:
${\stackrel{˜}{u}}_{k}\left(k\right)=-i{n}_{j}{\sigma }_{ij}^{0}{\text{Ω}}_{ik}\left(n\right)\stackrel{˜}{c}\left(k\right){|k|}^{-1}$ (A.9)
where, Ωik (n) is the inverse of ${\text{Ω}}_{ik}^{-1}\left(n\right)$ . Displacement gradient can be obtained by taking the derivative of Eqn (A.9) as:
${\stackrel{˜}{u}}_{k,l}\left(k\right)={\stackrel{˜}{u}}_{k}\left(k\right)i{k}_{l}={n}_{j}{n}_{l}{\text{σ}}_{ij}^{0}{\text{Ω}}_{ik}\left(n\right)\stackrel{˜}{c}\left(k\right)$ (A.10)
Strain is given by
${\text{ε}}_{ij}=\frac{1}{2}\left({u}_{i,j}+{u}_{j,i}\right)$ (A.11)
The elastic energy, Fel, is given by,
${F}_{el}=\frac{1}{2}\underset{V}{\int }{C}_{ijkl}\left({\text{ε}}_{ij}\left(\mathbit{r}\right)-{\text{ε}}_{ij}^{0}\left(\mathbit{r}\right)\right)\left({\text{ε}}_{kl}\left(\mathbit{r}\right)-{\text{ε}}_{kl}^{0}\left(\mathbit{r}\right)\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}d\mathbit{r}$ (A.12)
where, the integration is performed over the volume, V, of the system. Exploiting the symmetries of the components Cijkl,
$\begin{array}{l}{F}_{el}=\frac{1}{2}\underset{V}{\int }{C}_{ijkl}{\text{ε}}_{ij}\left(\mathbit{r}\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\text{ε}}_{kl}\left(\mathbit{r}\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}d\mathbit{r}-\underset{V}{\int }{C}_{ijkl}{\text{ε}}_{ij}\left(\mathbit{r}\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\text{ε}}_{kl}^{0}\left(\mathbit{r}\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}d\mathbit{r}\text{\hspace{0.17em}}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}+\frac{1}{2}\underset{V}{\int }{C}_{ijkl}{\text{ε}}_{ij}^{0}\left(\mathbit{r}\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\text{ε}}_{kl}^{0}\left(\mathbit{r}\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}d\mathbit{r}\end{array}$ (A.13)
Now, we can use Parseval’s theorem which is an identity relating integrals over real space to that over Fourier space.
$\int f\left(\mathbit{r}\right){g}^{*}\left(\mathbit{r}\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}d\mathbit{r}=\frac{1}{{\left(2\text{π)}}^{\text{3}}}\int \stackrel{˜}{f}\left(k\right)\text{\hspace{0.17em}}{\stackrel{˜}{g}}^{*}\left(k\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}dk$ (A.14)
where, the superscript * represents complex conjugate. Applying Parseval’s theorem to Eqn (A.13) and making use of the fact that the strains in that equation are real valued functions (and therefore the complex conjugates are the strains themselves), one gets
$\begin{array}{l}{F}_{el}=\frac{1}{2}\underset{-\infty }{\overset{\infty }{\int }}{C}_{ijkl}{\stackrel{˜}{\epsilon }}_{ij}\left(k\right){\left[{\stackrel{˜}{\epsilon }}_{kl}\left(k\right)\right]}^{*}\frac{dk}{{\left(2\pi \right)}^{3}}-\underset{-\infty }{\overset{\infty }{\int }}{C}_{ijkl}{\stackrel{˜}{\epsilon }}_{ij}\left(k\right){\left[{\stackrel{˜}{\epsilon }}_{kl}^{0}\left(k\right)\right]}^{*}\frac{dk}{{\left(2\pi \right)}^{3}}\\ +\frac{1}{2}\underset{-\infty }{\overset{\infty }{\int }}{C}_{ijkl}{\stackrel{˜}{\epsilon }}_{ij}^{0}\left(k\right){\left[{\stackrel{˜}{\epsilon }}_{kl}\left(k\right)\right]}^{*}\frac{dk}{{\left(2\pi \right)}^{3}}\end{array}$ (A.15)
or Fel = I1 + I2 + I3. We will show simplification of each of the above terms.
${I}_{1}=\frac{1}{2}\underset{-\infty }{\overset{\infty }{\int }}{C}_{ijkl}{\stackrel{˜}{\epsilon }}_{ij}\left(k\right) {\stackrel{˜}{\epsilon }}_{kl}^{*}\left(k\right)\frac{dk}{{\left(2\pi \right)}^{3}}=\frac{1}{2}\underset{-\infty }{\overset{\infty }{\int }}{C}_{ijkl}{\stackrel{˜}{u}}_{i,j}\left(k\right){\stackrel{˜}{u}}_{k,l}^{*}\left(k\right)$ (A.16)
While writing the above, the symmetry property that Cijkl = Cklij, has been exploited. Substituting the expression for ũi, j from Eqn (A.10) gives
${I}_{1}=\frac{1}{2}\underset{-\infty }{\overset{\infty }{\int }}{C}_{ijkl}{n}_{j}{\text{σ}}_{mn}^{0}{n}_{n}{\text{Ω}}_{mi}\left(n\right)\stackrel{˜}{c}\left(k\right){n}_{l}{\sigma }_{pq}^{0}{n}_{q}{\text{Ω}}_{pk}\left(n\right){\stackrel{˜}{c}}^{*}\left(k\right)\frac{dk}{{\left(2\pi \right)}^{3}}$ (A.17)
Using the relation ${C}_{ijkl}{n}_{j}{n}_{l}={\text{Ω}}_{ik}^{-1}\left(n\right)$ and the identity ${\text{Ω}}_{ik}^{-1}\left(n\right){\text{Ω}}_{mi}\left(n\right)={\delta }_{km}$ , Eqn (A.17) can be simplified as
$\begin{array}{l}{I}_{1}=\frac{1}{2}\underset{-\infty }{\overset{\infty }{\int }}{\delta }_{km}{\text{σ}}_{mn}^{0}{n}_{n}{\text{σ}}_{pq}^{0}{n}_{q}{\text{Ω}}_{pk}\left(n\right){|\stackrel{˜}{c}\left(k\right)|}^{2}\frac{dk}{{\left(2\pi \right)}^{3}}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\frac{1}{2}\underset{-\infty }{\overset{\infty }{\int }}{n}_{n}{\text{σ}}_{kn}^{0}{\text{Ω}}_{pk}\left(n\right){\text{σ}}_{pq}^{0}{n}_{q}{|\stackrel{˜}{c}\left(k\right)|}^{2}\frac{dk}{{\left(2\pi \right)}^{3}}\end{array}$
Changing the dummy (or repeated) indices,
$\begin{array}{l}{I}_{1}=\frac{1}{2}\underset{-\infty }{\overset{\infty }{\int }}{n}_{j}{\sigma }_{ij}^{0}{\text{Ω}}_{ki}\left(n\right){\sigma }_{kl}^{0}{n}_{l}{|\stackrel{˜}{c}\left(k\right)|}^{2}\frac{dk}{{\left(2\pi \right)}^{3}}\\ {I}_{2} =-\underset{-\infty }{\overset{\infty }{\int }}{C}_{ijkl}{\stackrel{˜}{\epsilon }}_{ij}\left(k\right){\left[{\stackrel{˜}{\epsilon }}_{kl}^{0}\left(k\right)\right]}^{*}\frac{dk}{{\left(2\pi \right)}^{3}}=\underset{-\infty }{\overset{\infty }{\int }}{C}_{ijkl}{\stackrel{˜}{u}}_{i,j}\left(k\right){\text{ε}}_{kl}^{0}{\stackrel{˜}{c}}^{*}\left(k\right)\frac{dk}{{\left(2\pi \right)}^{3}}\\ =-\underset{-\infty }{\overset{\infty }{\int }}{\text{σ}}_{ij}^{0}{n}_{j}{\text{σ}}_{mn}^{0}{n}_{n}{\text{Ω}}_{mi}\left(n\right)\stackrel{˜}{c}\left(k\right){\stackrel{˜}{c}}^{*}\left(k\right)\frac{dk}{{\left(2\pi \right)}^{3}}\\ =-\underset{-\infty }{\overset{\infty }{\int }}{n}_{j}{\text{σ}}_{ij}^{0}{\text{Ω}}_{ki}\left(n\right){\text{σ}}_{kl}^{0}{n}_{l}{|\stackrel{˜}{c}\left(k\right)|}^{2}\frac{dk}{{\left(2\pi \right)}^{3}}\end{array}$ (A.18)
$\begin{array}{l}{I}_{3}=\frac{1}{2}\underset{-\infty }{\overset{\infty }{\int }}{C}_{ijkl}{\stackrel{˜}{\epsilon }}_{ij}^{0}\left(k\right){\left[{\stackrel{˜}{\epsilon }}_{kl}^{0}\left(k\right)\right]}^{*}\frac{dk}{{\left(2\pi \right)}^{3}}\\ =\frac{1}{2}\underset{-\infty }{\overset{\infty }{\int }}{C}_{ijkl}{\epsilon }_{ij}^{0}{\epsilon }_{kl}^{0}\stackrel{˜}{c}\left(k\right){\stackrel{˜}{c}}^{*}\left(k\right)\frac{dk}{{\left(2\pi \right)}^{3}}\end{array}$ (A.19)
$=\frac{1}{2}\underset{-\infty }{\overset{\infty }{\int }}{C}_{ijkl}{\epsilon }_{ij}^{0}{\epsilon }_{kl}^{0}{|\stackrel{˜}{c}\left(k\right)|}^{2}\frac{dk}{{\left(2\pi \right)}^{3}}$ (A.20)
Adding I1, I2 and I3, the elastic energy in Eqn (A.15) is simplified as
$\begin{array}{c}{F}_{el}=\frac{1}{2}\underset{-\infty }{\overset{\infty }{\int }}\left[{C}_{ijkl}{\epsilon }_{ij}^{0}{\epsilon }_{kl}^{0}-{n}_{j}{\text{σ}}_{ij}^{0}{\text{Ω}}_{ki}\left(n\right){\text{σ}}_{kl}^{0}{n}_{l}\right]{|\stackrel{˜}{c}\left(k\right)|}^{2}\frac{dk}{{\left(2\pi \right)}^{3}}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\frac{1}{2}\underset{-\infty }{\overset{\infty }{\int }}B\left(n\right){|\stackrel{˜}{c}\left(k\right)|}^{2}\frac{dk}{{\left(2\pi \right)}^{3}}\end{array}$ (A.21)
where,
$B\left(n\right)={C}_{ijkl}{\epsilon }_{ij}^{0}{\epsilon }_{kl}^{0}-{n}_{j}{\text{σ}}_{ij}^{0}{\text{Ω}}_{ki}\left(n\right){\text{σ}}_{kl}^{0}{n}_{l}$
| 2021-10-27T21:54:56 |
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https://par.nsf.gov/biblio/10225264-maps-from-feigin-odesskii-elliptic-algebras-twisted-homogeneous-coordinate-rings
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Maps from Feigin and Odesskii's elliptic algebras to twisted homogeneous coordinate rings
Abstract The elliptic algebras in the title are connected graded $\mathbb {C}$ -algebras, denoted $Q_{n,k}(E,\tau )$ , depending on a pair of relatively prime integers $n>k\ge 1$ , an elliptic curve E and a point $\tau \in E$ . This paper examines a canonical homomorphism from $Q_{n,k}(E,\tau )$ to the twisted homogeneous coordinate ring $B(X_{n/k},\sigma ',\mathcal {L}^{\prime }_{n/k})$ on the characteristic variety $X_{n/k}$ for $Q_{n,k}(E,\tau )$ . When $X_{n/k}$ is isomorphic to $E^g$ or the symmetric power $S^gE$ , we show that the homomorphism $Q_{n,k}(E,\tau ) \to B(X_{n/k},\sigma ',\mathcal {L}^{\prime }_{n/k})$ is surjective, the relations for $B(X_{n/k},\sigma ',\mathcal {L}^{\prime }_{n/k})$ are generated in degrees $\le 3$ and the noncommutative scheme $\mathrm {Proj}_{nc}(Q_{n,k}(E,\tau ))$ has a closed subvariety that is isomorphic to $E^g$ or $S^gE$ , respectively. When $X_{n/k}=E^g$ and $\tau =0$ , the results about $B(X_{n/k},\sigma ',\mathcal {L}^{\prime }_{n/k})$ show that the morphism $\Phi _{|\mathcal {L}_{n/k}|}:E^g \to \mathbb {P}^{n-1}$ embeds $E^g$ as a projectively normal subvariety that is a scheme-theoretic intersection of quadric and cubic hypersurfaces.
Authors:
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Publication Date:
NSF-PAR ID:
10225264
Journal Name:
Forum of Mathematics, Sigma
Volume:
9
ISSN:
2050-5094
1. Abstract We prove an inequality that unifies previous works of the authors on the properties of the Radon transform on convex bodies including an extension of the Busemann–Petty problem and a slicing inequality for arbitrary functions. Let $K$ and $L$ be star bodies in ${\mathbb R}^n,$ let $0<k<n$ be an integer, and let $f,g$ be non-negative continuous functions on $K$ and $L$, respectively, so that $\|g\|_\infty =g(0)=1.$ Then \begin{align*} & \frac{\int_Kf}{\left(\int_L g\right)^{\frac{n-k}n}|K|^{\frac kn}} \le \frac n{n-k} \left(d_{\textrm{ovr}}(K,\mathcal{B}\mathcal{P}_k^n)\right)^k \max_{H} \frac{\int_{K\cap H} f}{\int_{L\cap H} g}, \end{align*}where $|K|$ stands for volume of proper dimension, $C$ is an absolute constant, the maximum is taken over all $(n-k)$-dimensional subspaces of ${\mathbb R}^n,$ and $d_{\textrm{ovr}}(K,\mathcal{B}\mathcal{P}_k^n)$ is the outer volume ratio distance from $K$ to the class of generalized $k$-intersection bodies in ${\mathbb R}^n.$ Another consequence of this result is a mean value inequality for the Radon transform. We also obtain a generalization of the isomorphic version of the Shephard problem.
2. Abstract Inspired by Lehmer’s conjecture on the non-vanishing of the Ramanujan $$\tau$$ τ -function, one may ask whether an odd integer $$\alpha$$ α can be equal to $$\tau (n)$$ τ ( n ) or any coefficient of a newform f ( z ). Balakrishnan, Craig, Ono and Tsai used the theory of Lucas sequences and Diophantine analysis to characterize non-admissible values of newforms of even weight $$k\ge 4$$ k ≥ 4 . We use these methods for weight 2 and 3 newforms and apply our results to L -functions of modular elliptic curves and certain K 3 surfaces with Picard number $$\ge 19$$ ≥ 19 . In particular, for the complete list of weight 3 newforms $$f_\lambda (z)=\sum a_\lambda (n)q^n$$ f λ ( z ) = ∑ a λ ( n ) q n that are $$\eta$$ η -products, and for $$N_\lambda$$ N λ the conductor of some elliptic curve $$E_\lambda$$ E λ , we show that if $$|a_\lambda (n)|<100$$ | a λ ( n ) | < 100 is odd with $$n>1$$ n > 1 and $$(n,2N_\lambda )=1$$ ( n , 2 N λ ) = 1 , then \begin{aligned} a_\lambda (n) \in&\{-5,9,\pm 11,25,more »
Let $S$ be a scheme and let $\pi : \mathcal{G} \to S$ be a ${\mathbb{G}}_{m,S}$-gerbe corresponding to a torsion class $[\mathcal{G}]$ in the cohomological Brauer group ${\operatorname{Br}}^{\prime}(S)$ of $S$. We show that the cohomological Brauer group ${\operatorname{Br}}^{\prime}(\mathcal{G})$ of $\mathcal{G}$ is isomorphic to the quotient of ${\operatorname{Br}}^{\prime}(S)$ by the subgroup generated by the class $[\mathcal{G}]$. This is analogous to a theorem proved by Gabber for Brauer–Severi schemes.
Let $k$ be an algebraically closed field of characteristic $p$, and let ${\mathcal{O}}$ be either $k$ or its ring of Witt vectors $W(k)$. Let $G$ be a finite group and $B$ a block of ${\mathcal{O}} G$ with normal abelian defect group and abelian $p^{\prime}$ inertial quotient $L$. We show that $B$ is isomorphic to its second Frobenius twist. This is motivated by the fact that bounding Frobenius numbers is one of the key steps towards Donovan’s conjecture. For ${\mathcal{O}}=k$, we give an explicit description of the basic algebra of $B$ as a quiver with relations. It is a quantized version of the group algebra of the semidirect product $P\rtimes L$.
5. Abstract Let X be a simply connected closed oriented manifold of rationally elliptic homotopy type. We prove that the string topology bracket on the $S^1$ -equivariant homology ${\overline {\text {H}}}_\ast ^{S^1}({\mathcal {L}} X,{\mathbb {Q}})$ of the free loop space of X preserves the Hodge decomposition of ${\overline {\text {H}}}_\ast ^{S^1}({\mathcal {L}} X,{\mathbb {Q}})$ , making it a bigraded Lie algebra. We deduce this result from a general theorem on derived Poisson structures on the universal enveloping algebras of homologically nilpotent finite-dimensional DG Lie algebras. Our theorem settles a conjecture of [7].
| 2022-11-26T09:13:51 |
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https://peterjamesthomas.com/glimpses-of-symmetry/chapter-24-emmy/
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# 24 – Emmy
< ρℝεν | ℂσητεητs | ℕεχτ >
“In the judgment of the most competent living mathematicians, Fräulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began. In the realm of algebra, in which the most gifted mathematicians have been busy for centuries, she discovered methods which have proved of enormous importance in the development of the present-day younger generation of mathematicians” – Albert Einstein
Out of the pantheon of Gods [1] involved in both the development of Group Theory and its application to Standard Model of Particle Physics, I have seen fit to take just two biographical detours to cover specific individuals. In Chapter 12 we met the “Father of Group Theory”, here we will spend some time on someone who could lay claim to being the “Mother of Symmetry’s role in Physics”. While Symmetry had been a guiding force in developing an understanding of the Natural World for many years, if not centuries, this person put these endeavours on a rigorous basis, unveiling a fundamental truth about reality. The remarkable woman we are talking about is Amalie Emmy Noether, always known as Emmy.
We will cover Emmy’s highly significant contributions to Physics in this Chapter, but she was first and foremost a Mathematician. While she can certainly be described as the greatest female Mathematician of all time, the adjective is superfluous. Emmy was simply one of the greatest Mathematicians of all time, with no need for gender-based modification. To build on my “Mother of…” theme, in 1972, acclaimed abstract algebraist Irving Kaplansky had this to say about Emmy:
It surely is not much of an exaggeration to call her the mother of modern algebra.
And for a perspective from the overlapping worlds of Mathematics and Theoretical Physics, we can turn to the incomparable, Herman Weyl in 1935:
Her strength lay in her ability to operate abstractly with concepts. It was not necessary for her to allow herself to be led to new results on the leading strings of known concrete examples. She was sometimes but incompletely cognizant of the specific details of the more interesting applications of her general theories. She possessed a most vivid imagination, with the aid of which she could visualize remote connections; she constantly strove toward unification. In this she sought out the essentials in the known facts, brought them into order by means of appropriate general concepts, espied the vantage point from which the whole could best be surveyed, cleansed the object under consideration of superfluous dross, and thereby won through to so simple and distinct a form that the venture into new territory could be undertaken with the greatest prospect of success.
Bringing things more up to date, Physicist, author and Science populariser, Brian Greene, tweeted the following:
Before looking at Noether’s work, it is instructive to cover some elements of her life and – in particular – the challenges she faced; ones that were exclusively due to her parents’ neglect. First, they unaccountably did not provide her with a Y chromosome, a prerequisite for any career in academia at the time. Second, they failed to ensure that Emmy was not of Jewish extraction, another oversight that is hard to understand in people who otherwise appeared as competent and caring parents.
Emmy’s Life and Hard Times
For a fuller biography of Emmy Noether, I would refer readers to a range of books, either dedicated biographies [2] or more general works in which she is featured [3]. Here I will simply sketch some salient details.
Emmy was born in 1882 in the German town of Erlangen, the oldest of four children. Her Father, Max, was an algebraic geometer, with (somewhat confusingly) both his own eponymous and shared-credit theorems. Her Mother, Ida Amalia, was born into a wealthy Cologne family. Both parents were supportive of all their children (regardless of gender) having the benefit of an advanced education. Two of her brothers achieved this goal. Alfred received a doctorate in Chemistry, though he unfortunately died just nine years later. Fritz became an Applied Mathematician, but left Germany for Russia when – as a Jew – he was unable to work. Unfortunately, while in Russia, he fell victim to one of the pogroms and was executed; though later formally exonerated of any crime. Perhaps most tragically in this family of academic achievers, her youngest brother Gustav suffered from intellectual disability and died before his fortieth birthday.
From one perspective, it could be argued that Emmy’s path ran smoother than her brothers during this turbulent time in European history. However, as a woman, it was much harder for Emmy to pursue her parents’ academic dreams in 1900s Germany. She showed no special aptitude for Mathematics early in life. Indeed her talents seemed rather to lie in English and French. Given this, Noether initially prepared herself for a career as a language teacher; suitable employment for a young lady. However, thankfully for the disciplines of Mathematics and Physics, she changed her mind and, in 1900, enlisted in an undergraduate course in Mathematics at her hometown University of Erlangen.
While between 1861 and 1885 women had been admitted to full academic life in each of France, the United Kingdom and Italy, turn of the Century Germany was much less open to embracing the intellectual potential of half of its population. So, when I say “enlisted”, this was not entirely true. At this point, women were allowed to attend lectures, but not to be formally registered as students, or to be awarded degrees. Emmy was one of only two women amongst a University of 986 students. In 1903-04 Emmy spent a term at the famous University of Göttingen, seat of German Mathematical excellence. On returning to Erlangen, she found that miraculously the restrictions on at least undergraduate female students has been relaxed, allowing her to first graduate and then obtain her doctorate in 1907. However at this point the doors to an academic career were firmly flung shut in Noether’s face. Women in Germany were simply not allowed to progress to be full academics.
For the next seven years Emmy taught at her father’s University, sometimes standing in for him when he was ill, but she was never formally a member of staff and never paid. Despite her unofficial status, Noether’s work began to speak for itself. As a result, in 1915, David Hilbert and another renowned Mathematician Felix Klein, invited her back to Göttingen. These two gentlemen then fought a lengthy battle to have Emmy registered as a full member of the academic staff, one that they eventually won four years later in 1919. A famous quote from Hilbert dates to this time:
I do not see that the sex of the candidate is an argument against her admission as Privatdozent [teaching assistant]. After all, we are a university and not a bathing establishment.
Hilbert, never one for respecting authority, used to arrange courses to be taught in his name and got Emmy to deliver them herself, despite her having no actual standing at the University.
It was also around this period that Hilbert was taking a parallel path to Einstein towards the goal of General Relativity. The two men’s relationship was sometimes collaborative, sometimes combative, sometimes even acrimonious, but both recognised the influence that the other’s ideas had on their work. Hilbert wanted expert help and it was to Noether that he turned. One almost immediate result of this was Noether’s Theorem, filling an important gap in General Relativity, but also establishing a broader Scientific principle. This breakthrough work of almost endless influence was carried out by someone whose gender barred them from being a member of the Göttingen staff at the time.
I will neither pursue this biography further here, nor attempt to catalogue Emmy’s many other cutting-edge contributions to Mathematics. I will however add a couple of sad footnotes. In 1933, as part of the Nazi party’s purging of non-Aryan influence from accademia, Noether – like many others with a Jewish background – was dismissed from the position at Göttingen that she had spent so long achieving and cherished so much. Unlike many, she was able to relocate to the United States where she lectured for a short while until her untimely death in 1935 at the age of only 53. One of the great voices of both Mathematics and Science, a voice that had refused to be quieted by the social strictures of her time, finally fell silent. But, while remaining close to unknown to the general public, Emmy’s legacy has resonated ever more loudly in Scientific and Mathematical circles ever since.
It is the component of Emmy’s legacy which relates to both Symmetry and Physics that I plan to cover in the rest of this Chapter. As ever, we first need to lay some groundwork.
Lights… Camera… Action!
Note: The groundwork I refer to above is predominantly Mathematical apparatus relating to a variety of situations in Physics, e.g. the evolution of N-body systems under either non-relativistic or relativistic conditions, or the behaviour of fields (in the Physics sense of force fields rather than the Mathematical one of algebraic objects). This is not my area of expertise, so I am going to take a 30,000 foot approach with apologies to any Physicists reading (and indeed to the Mathematicians who created the apparatus in the first place, notably Euler and Lagrange).
Our first new concepts here are the Lagrangian of a system, the Action of the same system and the Principle of Least Action. The first two are related inasmuch as the second is the integral of the first between two points in time. The Principle of Least Action, when applied to – for example – a set of particles, enables the equations of motion of the particles to be determined by working out those equations which minimise the Action. Adjustments can allow the same approach to be used in General Relativity (indeed it was Hilbert who discovered this approach) and later Paul Dirac and then Julian Schwinger and Richard Feynman extended the Principle of Least Action into the realm of Quantum Mechanics. It has even been applied in String Theory.
I am not going to get into the details here, for those who are interested, I provide an extremely useful reference in the footnotes [4]. Instead I wanted to first provide an analogy that perhaps captures the essence of the area. This is not a novel analogy and indeed appears in many works. I am unclear as to who originated it.
So consider a lifeguard on a beach. Her tower is 10 m from the edge of the water. She spots a swimmer in trouble in the water 10 m from the shore and 20 m to the right of where her tower is situated. The lifeguard can run at 5 ms-1 on the sand and can swim at 2 ms-1 in the water. What is the optimum path for her to take to get to the swimmer most quickly? As ever a picture paints a thousand words:
It may seem that the obvious thing is for the lifeguard to move directly towards the swimmer, taking the straight line $ABC$, which is the shortest distance between points $A$ and $B$. However, this has the guard traversing as far in the water as on the land and she goes much slower in the water. Indeed, we can work out the time she takes to reach the swimmer as follows:
Distance travelled on land $= \sqrt{10^2+10^2}=\sqrt{200}\approx 14.14\text{ m}$
Time spent on land $\approx \dfrac{14.14\text{ m}}{5\text{ ms}^{-1}}\approx 2.83\text{ s}$
The distance travelled in the water is the same as that on land.
Time spent in the water $\approx \dfrac{14.14\text{ m}}{2\text{ ms}^{-1}}\approx 7.07\text{ s}$
Total time $\approx 2.83\text{ s} + 7.07\text{ s}\approx 9.9\text {s}$
A way to speed things up might be to spend the least possible time in the water. This approach is shown by the dog-leg line $AB^{\prime}C$. Here are elapsed time calculations are as follows:
Distance travelled on land $= \sqrt{10^2+20^2}=\sqrt{500}\approx 23.36\text{ m}$
Time spent on land $\approx \dfrac{23.36\text{ m}}{5\text{ ms}^{-1}}\approx 4.67\text{ s}$
The distance travelled in the water is just $10\text{ m}$
Time spent in the water $\approx \dfrac{10\text{ m}}{2\text{ ms}^{-1}}= 5\text{ s}$
Total time $\approx 4.67\text{ s} + 5\text{ s}\approx 9.67\text {s}$
This is a small improvement, but can we do better?
Let’s consider a path which goes through some intermediate point, $B^{\prime \prime}$, forming the dog-leg line $AB^{\prime \prime} C$. Furthermore, let’s assume that the point $B^{\prime \prime}$ is $x\text{ m}$ sideways from the lifeguard. That is the length of line $DB^{\prime}$ is $x\text{ m}$ and, by the magic of subtraction, the length of the line $B^{\prime}B^{\prime \prime}$ is $20-x\text{ m}$.
Applying Pythagoras we get:
Distance travelled on land $= \sqrt{10^2+x^2}\text{ m}$
So the time spent on land $= \dfrac{\sqrt{10^2+x^2}}{5}\text{ s}$
The distance travelled in the water $= \sqrt{10^2+(20-x)^2}$
So the time spent in the water $= \dfrac{\sqrt{10^2+(20-x)^2}}{2}\text{ s}$
Thus the total time $= \dfrac{\sqrt{10^2+x^2}}{5}+\dfrac{\sqrt{10^2+(20-x)^2}}{2}\text{ s}$
We want to find for what value of $x$ the time is least and so employ the time honoured approach of differentiating the expression. Without going through the gory details, we get:
$\dfrac{d}{dx}\bigg(\dfrac{\sqrt{10^2+x^2}}{5}+\dfrac{\sqrt{10^2+(20-x)^2}}{2}\bigg)=\text{ }$ $\dfrac{x-20}{5\sqrt{x^2-40x+500}}+\dfrac{x}{2\sqrt{x^2+100}}$
We get the minimum (or maximum) value of our original expression when its derivative is equal to zero. Again sparing the reader the details, the answer we arrive at is $x\approx16.37\text{ m}$ which gives a minimum (and it is a minimum in this case) time of approximately $9.16\text{ s}$.
Thus the minimum time for the lifeguard to get to the swimmer is a path somewhere in between the one that is of minimum distance and that in which she spends the minimum time in the water. Of interest here is that the way that light is refracted when it moves between two media of different densities (e.g.air and water) can be calculated in precisely the same way. That is – given that light travels at different speeds in different media [5] – the angle of refraction may be calculated by determining which angle yields the least time of transit. The lifeguard diagram could be a picture of light being refracted.
So that was meant to be an impressionistic painting of the Principle of Least Action, the elements don’t precisely line up, but hopefully you get the idea. If we now more realistically consider a system of particles and forces acting on them in Classical Mechanics. Then the Principle of Least Action tells us that the equations of motion of the particles are precisely those which minimise the Action of the system. Somehow Nature knows that – of all possible paths that the particles could take – she must select the one that minimises Action [6].
Well that’s great, what have we achieved. Well Newton’s approach would be to apply his famous $\text{Force}=\text{Mass}\times\text{Acceleration}$ equation many times to all the particles and forces in the system and then solve the resulting (differential) equations. Taking a Least Action approach, we would first of all define the system’s Lagrangian as its total Kinetic Energy (energy due to motion) less its total Potential Energy (energy due to forces [7]), noting that both of these will vary as a function of time [8]. The Action of the system is then the integral of the Lagrangian between the starting and ending times. We set the expression for the Action that we have calculated to zero and then work from there. This is not magic, we still end up calculating a bunch of (differential) equations. However often we can eliminate complexities inherent in Newton’s approach and we can also judiciously select a generalised coordinate system so as to reduce complexity, which is often a very valuable thing to do.
Here I have referred to Classical Mechanics, for Relativistic Mechanics or Quantum Mechanics there are modifications to the details (e.g.how the Lagrangian is defined and the presence of other functions in equations defining the Action), but the shape of the approach remains the same. The Principle of Least Action has proved to be an invaluable tool for Physicists and Mathematicians alike.
Having hopefully given you some ideas about these concepts, I’ll now move on to the next one, Conservation Laws. After some arduous work, the next section will go much quicker I promise!
Going Green
In Physics, a Conservation Law is not a regulation about pollution, but instead a statement that some property of a system remains invariant over time. One obvious example is that the total energy of a closed system remains constant; energy is neither created nor destroyed, though it may change form. A somewhat related example is the conservation of linear momentum. If two particles are both travelling with specified speeds and directions and then elastically collide, their post-collision speeds and directions will most likely be radically different. However the total linear momentum of the two particles will be precisely the same post-collision and pre-collision.
However there can be more recherché types of conservation, in the world of Particle Physics, certain types of particle interactions or transformations can conserve strangeness, or spin or parity (whereas other interactions or transformations may not conserve these). A Conservation Law tells us a lot about the system we are studying. In particular it restricts the system’s behaviour – certain things cannot happen as they would break the Conservation Law.
Well I told you that this would be short! The only other concept we need to cover before stating Noether’s Theorem is that of Symmetry. We may have covered some of this already in the preceding 23 Chapters, so let’s plunge in.
The Amazing Theorem
Emmy’s theorem states the following (omitting some technical language):
For a given system, which has an Action, if there exists a Symmetry of the Action [9], then there will exist a related Conservation Law, and vice versa.
A Symmetry of the Action means that the Action is invariant under some transformation of the system. Let’s cover some basic examples:
• If we move the system in some direction and the Action is constant, then this is a spatial translation Symmetry. This implies that Linear Momentum will being conserved in the system.
• If a mirror version of the system has the same Action, then this is a spatial reflection Symmetry. This implies that Parity will being conserved in the system.
• If the whole system is rotated by an angle and the Action remains the same, this is a rotational Symmetry. In this case, Angular Momentum will be conserved.
• If the Action of a system is the same when time is run backwards, then this is a temporal reflection Symmetry and implies that Entropy is conserved [10].
• If the Action of a system is the same if we jump forward 10 seconds (or back 10 seconds), then this is a temporal translation Symmetry. This implies that Energy is conserved.
Why is this important? Well if we want to understand a system’s behaviour (for example a number of sub-atomic particles interacting) then any observable symmetries will lead us inevitably to some quantity that is conserved. Equally, if we want some new theory to conserve a given quantity, we can formulate Lagrangians that do this and use these to figure out if we are on the right track, e.g. that things remain consistent. Obviously, with the emphasis on symmetry as a fundamental part of Physical Law, we can see why Group Theory is of such interest to Physicists.
This is all thanks to Emmy Noether and her truly fundamental insights. As Brian Greene notes, maybe this remarkable woman should be more celebrated outside of technical circles than she is.
[Segue to next Chapter – To be completed when Chapter has been decided upon]
Concepts Introduced in this Chapter Lagrangian A function which captures the essential elements of the dynamics of a system and how it evolves. It thus generally contains information about the position of elements (coordinates) and how these are changing (derivative with respect to time). Action The integral of a Lagrangian between a start and end time. The Action distills down information inherent in the Lagrangain to generate a single Real Number. Principle of Least Action The actual paths taken by elements of a system as the system evolves will be precisely those that give the minimal value for the Action. Conservation Law A statement about physical quantities that remain constant as a system evolves over time. Noether’s Theorem Every differential Symmetry of the Action of a system corresponds one-to-one to a Conservation Law of that system.
< ρℝεν | ℂσητεητs | ℕεχτ >
Chapter 24 – Notes
[1] All of whom were obviously very human. An entirely non-exhaustive list of important early contributors to Group Theory might include (in alphabetical order): Abel Burnside Cartan Cauchy Cayley Frobenius Galois Hermite Jordan Killing Klein Kummer Lagrange Lie Poincaré Schur Sylow In Group Theory, it helps to have a surname that starts with with either a ‘C’ or a ‘K’. [2] For example: The Washington Post also provides a brief overview for those with less time on their hands. As do those twin bastions of the Scientific Community, Nature and Science. [3] These include: [4] A wonderful introduction to the area (though admittedly one that becomes more technical as it progresses) was given by Feynman himself in his famous lecture series at the California Institute of Technology. [5] The speed of light is only invariant when travelling through a media with a constant refractive index and is typically quoted for a vacuum. [6] It is not quite as mystical as that, indeed the link to Feynman’s lecture on the subject (see Note 4) above provides a proof of why this happens. [7] Readers are no doubt familiar with Potential Energy relating to Gravity, but the concept applies to any forces. [8] I should probably state that Kinetic Energy minus Potential energy is a Lagrangian, not the Lagrangian, other functions may be chosen, so long as they adhere to required properties. [9] Technically a differentiable Symmetry. Astute readers may begin to think of Lie Groups at this point. [10] And, given that entropy always increases, we have just demonstrated why there is an arrow of time!
Text: © Peter James Thomas 2016-18. Images: © Peter James Thomas 2016-18, unless stated otherwise. Published under a Creative Commons Attribution 4.0 International License.
| 2019-09-15T16:23:08 |
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https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Map%3A_University_Physics_II_-_Thermodynamics%2C_Electricity%2C_and_Magnetism_(OpenStax)/3%3A_The_First_Law_of_Thermodynamics/3.S%3A_The_First_Law_of_Thermodynamics_(Summary)
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# 3.S: The First Law of Thermodynamics (Summary)
## Key Terms
adiabatic process process during which no heat is transferred to or from the system boundary imagined walls that separate the system and its surroundings closed system system that is mechanically and thermally isolated from its environment cyclic process process in which the state of the system at the end is same as the state at the beginning environment outside of the system being studied equation of state describes properties of matter under given physical conditions equilibrium thermal balance established between two objects or parts within a system extensive variable variable that is proportional to the amount of matter in the system first law of thermodynamics the change in internal energy for any transition between two equilibrium states is $$ΔE_{int}=Q−W$$ intensive variable variable that is independent of the amount of matter in the system internal energy average of the total mechanical energy of all the molecules or entities in the system isobaric process process during which the system’s pressure does not change isochoric process process during which the system’s volume does not change isothermal process process during which the system’s temperature remains constant molar heat capacity at constant pressure quantifies the ratio of the amount of heat added removed to the temperature while measuring at constant pressure molar heat capacity at constant volume quantifies the ratio of the amount of heat added removed to the temperature while measuring at constant volume open system system that can exchange energy and/or matter with its surroundings quasi-static process evolution of a system that goes so slowly that the system involved is always in thermodynamic equilibrium reversible process process that can be reverted to restore both the system and its environment back to their original states together surroundings environment that interacts with an open system thermodynamic process manner in which a state of a system can change from initial state to final state thermodynamic system object and focus of thermodynamic study
## Key Equations
Equation of state for a closed system $$f(p,V,T)=0$$ Net work for a finite change in volume $$W=∫^{V_2}_{V_1}pdV$$ Internal energy of a system (average total energy) $$E_{int}=\sum_i(\bar{K_i}+\bar{U_i})$$, Internal energy of a monatomic ideal gas $$E_{int}=nN_A(\frac{3}{2}k_BT)=\frac{3}{2}nRT$$ First law of thermodynamics $$ΔE_{int}=Q−W$$ Molar heat capacity at constant pressure $$C_p=C_V+R$$ Ratio of molar heat capacities $$γ=C_p/C_V$$ Condition for an ideal gas in a quasi-static adiabatic process $$pV^γ=constant$$
### 3.1 Thermodynamic Systems
• A thermodynamic system, its boundary, and its surroundings must be defined with all the roles of the components fully explained before we can analyze a situation.
• Thermal equilibrium is reached with two objects if a third object is in thermal equilibrium with the other two separately.
• A general equation of state for a closed system has the form $$f(p,V,T)=0$$, with an ideal gas as an illustrative example.
### 3.2 Work, Heat, and Internal Energy
• Positive (negative) work is done by a thermodynamic system when it expands (contracts) under an external pressure.
• Heat is the energy transferred between two objects (or two parts of a system) because of a temperature difference.
• Internal energy of a thermodynamic system is its total mechanical energy.
### 3.3 First Law of Thermodynamics
• The internal energy of a thermodynamic system is a function of state and thus is unique for every equilibrium state of the system.
• The increase in the internal energy of the thermodynamic system is given by the heat added to the system less the work done by the system in any thermodynamics process.
### 3.4 Thermodynamic Processes
• The thermal behavior of a system is described in terms of thermodynamic variables. For an ideal gas, these variables are pressure, volume, temperature, and number of molecules or moles of the gas.
• For systems in thermodynamic equilibrium, the thermodynamic variables are related by an equation of state.
• A heat reservoir is so large that when it exchanges heat with other systems, its temperature does not change.
• A quasi-static process takes place so slowly that the system involved is always in thermodynamic equilibrium.
• A reversible process is one that can be made to retrace its path and both the temperature and pressure are uniform throughout the system.
• There are several types of thermodynamic processes, including (a) isothermal, where the system’s temperature is constant; (b) adiabatic, where no heat is exchanged by the system; (c) isobaric, where the system’s pressure is constant; and (d) isochoric, where the system’s volume is constant.
• As a consequence of the first law of thermodymanics, here is a summary of the thermodymaic processes:
• (a) isothermal: $$ΔE_{int}=0,Q=W$$;
• (b) adiabatic: $$Q=0,ΔE_{int}=−W$$ ;
• (c) isobaric: $$ΔE_{int}=Q−W$$; and
• (d) isochoric: $$W=0,ΔE_{int}=Q$$.
### 3.5 Heat Capacities of an Ideal Gas
• For an ideal gas, the molar capacity at constant pressure $$C_p$$ is given by $$C_p=C_V+R=dR/2+R$$, where d is the number of degrees of freedom of each molecule/entity in the system.
• A real gas has a specific heat close to but a little bit higher than that of the corresponding ideal gas with $$C_p≃C_V+R$$.
### 3.6 Adiabatic Processes for an Ideal Gas
• A quasi-static adiabatic expansion of an ideal gas produces a steeper pV curve than that of the corresponding isotherm.
• A realistic expansion can be adiabatic but rarely quasi-static.
## Contributors
Paul Peter Urone (Professor Emeritus at California State University, Sacramento) and Roger Hinrichs (State University of New York, College at Oswego) with Contributing Authors: Kim Dirks (University of Auckland) and Manjula Sharma (University of Sydney). This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).
| 2019-01-20T13:55:52 |
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|
https://www.anl.gov/article/sustainability-at-scale-argonnes-green-commitment
|
# Argonne National Laboratory
Feature Story | Argonne National Laboratory
# Sustainability at scale: Argonne’s ‘green’ commitment
Argonne’s commitment to green technologies, conservation and recycling make every day an Earth Day
Argonne National Laboratory’s sustainability efforts extend well beyond its cutting-edge research to the daily operation of the campus itself, where conservation is key.
The lab’s pioneering leadership — reflected in its battery-recycling program, electric vehicle recharging stations, extensive composting and water-saving measures — have had high-level impacts both fiscally and environmentally in recent years. Taken together, they have dramatically increased the laboratory’s efficiency, meeting or exceeding federal guidelines and embodying the Earth Day spirit.
Catherine Hurley, Sustainability Program Manager at Argonne, credits staff throughout the laboratory for her program’s success.
This truly is a team effort,” Hurley said. Argonne is a wonderful place to do this work: Our goals are in line with the science already taking place at the laboratory, so there is tremendous buy-in for the programs we’ve already rolled out and enthusiasm for future initiatives.”
Argonne has garnered high praise from the U.S. Department of Energy (DOE) for its efforts.
Argonne’s constant focus on conservation builds on its legacy as America’s first national laboratory. Ever since it was born out of the University of Chicago’s work on the Manhattan Project in the 1940s, Argonne’s goal has been to make an impact — from the atomic to the global scale. Its ongoing collaboration with the University of Chicago, other government agencies, institutions and industry has cemented its role as a leader in green technology and innovation.
## Battery recycling
Argonne was chosen by DOE last January to house the ReCell Center, aimed at profitably recovering materials from spent lithium-ion batteries. The National Renewable Energy Laboratory and Oak Ridge National Laboratory are participating in the program alongside the University of California San Diego, Worcester Polytechnic Institute and Michigan Technological University and industry partners.
Argonne was a great choice for leading the initiative,” said Jeff Spangenberger, director of the ReCell Center. The lab has long been a leader in advanced battery technology and materials recycling. We are proud to coordinate this multi-pronged effort.”
The ReCell Center will play a critical role in national security by reducing the nation’s dependence on foreign countries for its energy needs.
## Smart energy
Also in 2018, Argonne completed the second phase of construction for its Smart Energy Plaza, transforming a former on-site gas station to a green energy transportation hub and research space.
The plaza now has the capacity to charge 14 electric vehicles at once, boosting the number of lab-wide charging stations by an impressive 46 percent.
Its solar canopies have increased Argonne’s solar-energy production by a whopping 73 percent. DOE’s Sustainability Performance Office has commended the laboratory for its efforts.
Jason Harper, Argonne principal electrical engineer, praised the Smart Energy Plaza for providing researchers a platform to assess the current state of electric vehicle (EV) charging, grid storage and distributed energy resources.
The majority of research in this area is done in simulation,” Harper said. The Smart Energy Plaza allows researchers to use real-world hardware to address critical energy needs. We are very happy with the results.”
## Campus conservation
Years of sustainability planning culminated in the 2018 rollout of Argonne’s vast composting program. The effort kicked off last July in 10 buildings and collected some 10.7 tons of organic materials in its first several months.
Another 10 buildings are slated to join the program in 2019.
In fiscal year 2018, Argonne purchased and generated 50 percent more renewable energy compared to the year before and decreased its fleet of traditionally-fueled internal combustion engines by more than 66 percent.
Its 120 bicycles continue to provide convenient transportation across its 3-square-mile campus, improving air quality by reducing Argonne’s reliance on traditional vehicles.
In the area of water conservation, the laboratory recently completed two projects that deliver 4.5 million gallons of potable water savings each year by using canal water instead of drinking water.
Argonne’s canal water system taps a regional wastewater source and helps meet the cooling demand generated by laboratory processes. Site-wide, the canal water system saves 190 million gallons of potable water each year.
Also in 2018, Argonne’s Energy and Water Reinvestment program celebrated its 10-year anniversary. Its cumulative initiatives have saved the laboratory a total of $6.7 million — an average of$600,000 annually — in electricity, natural gas and potable water.
The grassroots efficiency effort accepts new projects on an ongoing basis: most are suggested by Argonne’s own building engineers, building managers and custodial staff.
The laboratory’s Disposal Days clean-up program collected and properly disposed of more than 90 tons of material spread across 35 buildings during a week-long period in July 2018. Obsolete industrial or laboratory equipment, furniture, electronics and scrap metal accounted for much of the haul.
The effort led to the processing of 30 metric tons of electronics along with 36 metric tons of scrap metal, enough to fill 17 dumpsters. More than 70 percent of the material was recycled.
DOE granted Argonne a Silver Level GreenBuy award for 2018 for its effort to purchase products — including locally produced food, carpeting, toner, packaging and shipping materials and pest-management services — that met tough environmental standards.
Hurley said she hopes Argonne can serve as a model for other organizations looking to achieve similar environmental goals.
All of our actions have an impact on the environment,” she said. If we want to live, work, play and grow on this great planet, we need to minimize impact and maximize livability and enjoyability for everyone. With strategic effort and consistent planning and investment, you really can make a difference.”
Argonne National Laboratory seeks solutions to pressing national problems in science and technology. The nation’s first national laboratory, Argonne conducts leading-edge basic and applied scientific research in virtually every scientific discipline. Argonne researchers work closely with researchers from hundreds of companies, universities, and federal, state and municipal agencies to help them solve their specific problems, advance America’s scientific leadership and prepare the nation for a better future. With employees from more than 60 nations, Argonne is managed by UChicago Argonne, LLC for the U.S. Department of Energy’s Office of Science.
The U.S. Department of Energy’s Office of Science is the single largest supporter of basic research in the physical sciences in the United States and is working to address some of the most pressing challenges of our time. For more information, visit https://energy.gov/science.
| 2020-06-05T10:53:49 |
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http://www.itl.nist.gov/div898/handbook/eda/section3/eda33a1.htm
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1. Exploratory Data Analysis
1.3. EDA Techniques
1.3.3. Graphical Techniques: Alphabetic
1.3.3.10. Contour Plot
## DOE Contour Plot
DOE Contour Plot: Introduction The DOE contour plot is a specialized contour plot used in the analysis of full and fractional experimental designs. These designs often have a low level, coded as "-1" or "-", and a high level, coded as "+1" or "+" for each factor. In addition, there can optionally be one or more center points. Center points are at the mid-point between the low and high level for each factor and are coded as "0".
The DOE contour plot is generated for two factors. Typically, this would be the two most important factors as determined by previous analyses (e.g., through the use of the DOE mean plots and an analysis of variance). If more than two factors are important, you may want to generate a series of DOE contour plots, each of which is drawn for two of these factors. You can also generate a matrix of all pairwise DOE contour plots for a number of important factors (similar to the scatter plot matrix for scatter plots).
The typical application of the DOE contour plot is in determining settings that will maximize (or minimize) the response variable. It can also be helpful in determining settings that result in the response variable hitting a pre-determined target value. The DOE contour plot plays a useful role in determining the settings for the next iteration of the experiment. That is, the initial experiment is typically a fractional factorial design with a fairly large number of factors. After the most important factors are determined, the DOE contour plot can be used to help define settings for a full factorial or response surface design based on a smaller number of factors.
Construction of DOE Contour Plot The following are the primary steps in the construction of the DOE contour plot.
1. The x and y axes of the plot represent the values of the first and second factor (independent) variables.
2. The four vertex points are drawn. The vertex points are (-1,-1), (-1,1), (1,1), (1,-1). At each vertex point, the average of all the response values at that vertex point is printed.
3. Similarly, if there are center points, a point is drawn at (0,0) and the average of the response values at the center points is printed.
4. The linear DOE contour plot assumes the model:
$$Y = \mu + \beta_1 \cdot U_1 + \beta_2 \cdot U_2 + \beta_{12} \cdot U_1 \cdot U_2$$
where μ is the overall mean of the response variable. The values of β1, β2, β12, and μ are estimated from the vertex points using least squares estimation.
In order to generate a single contour line, we need a value for Y, say Y0. Next, we solve for U2 in terms of U1 and, after doing the algebra, we have the equation:
$$\displaystyle{U_2 = \frac{(Y_0 - \mu) - \beta_1 \cdot U_1} {\beta_2 + \beta_{12} \cdot U_1}}$$
We generate a sequence of points for U1 in the range -2 to 2 and compute the corresponding values of U2. These points constitute a single contour line corresponding to Y = Y0.
The user specifies the target values for which contour lines will be generated.
The above algorithm assumes a linear model for the design. DOE contour plots can also be generated for the case in which we assume a quadratic model for the design. The algebra for solving for U2 in terms of U1 becomes more complicated, but the fundamental idea is the same. Quadratic models are needed for the case when the average for the center points does not fall in the range defined by the vertex point (i.e., there is curvature).
Sample DOE Contour Plot The following is a DOE contour plot for the data used in the Eddy current case study. The analysis in that case study demonstrated that X1 and X2 were the most important factors.
Interpretation of the Sample DOE Contour Plot From the above DOE contour plot we can derive the following information.
1. Interaction significance;
2. Best (data) setting for these two dominant factors;
Interaction Significance Note the appearance of the contour plot. If the contour curves are linear, then that implies that the interaction term is not significant; if the contour curves have considerable curvature, then that implies that the interaction term is large and important. In our case, the contour curves do not have considerable curvature, and so we conclude that the X1*X2 term is not significant.
Best Settings To determine the best factor settings for the already-run experiment, we first must define what "best" means. For the Eddy current data set used to generate this DOE contour plot, "best" means to maximize (rather than minimize or hit a target) the response. Hence from the contour plot we determine the best settings for the two dominant factors by simply scanning the four vertices and choosing the vertex with the largest value (= average response). In this case, it is (X1 = +1, X2 = +1).
As for factor X3, the contour plot provides no best setting information, and so we would resort to other tools: the main effects plot, the interaction effects matrix, or the ordered data to determine optimal X3 settings.
Case Study The Eddy current case study demonstrates the use of the DOE contour plot in the context of the analysis of a full factorial design.
Software DOE Contour plots are available in many statistical software programs that analyze data from designed experiments.
| 2016-09-28T17:07:08 |
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|
http://www.itl.nist.gov/div898/handbook/mpc/section3/mpc3312.htm
|
2. Measurement Process Characterization
2.3. Calibration
2.3.3. What are calibration designs?
2.3.3.1. Elimination of special types of bias
## Bias caused by instrument drift
Bias caused by linear drift over the time of measurement The requirement that reference standards and test items be stable during the time of measurement cannot always be met because of changes in temperature caused by body heat, handling, etc.
Representation of linear drift Linear drift for an even number of measurements is represented by
..., -5d, -3d, -1d, +1d, +3d, +5d, ...
and for an odd number of measurements by
..., -3d, -2d, -1d, 0d, +1d, +2d, +3d, ... .
Assumptions for drift elimination The effect can be mitigated by a drift-elimination scheme (Cameron/Hailes) which assumes:
• Linear drift over time
• Equally spaced measurements in time
Example of drift-elimination scheme An example is given by substitution weighing where scale deflections on a balance are observed for X, a test weight, and R, a reference weight. \begin{eqnarray} Y_1 = X - 3d_1 + error_1 \\ Y_2 = R - 1d_2 + error_2 \\ Y_3 = R + 1d_3 + error_3 \\ Y_4 = X + 3d_4 + error_4 \end{eqnarray}
Estimates of drift-free difference and size of drift The drift-free difference between the test and the reference is estimated by $$D = \frac{1}{2} \left[(Y_1 - Y_2) - (Y_3 - Y_4)\right]$$ and the size of the drift is estimated by $$\widehat{d} = \frac{1}{4} \left( -Y_1 + Y_2 - Y_3 + Y_4 \right)$$
Calibration designs for eliminating linear drift This principle is extended to create a catalog of drift-elimination designs for multiple reference standards and test items. These designs are listed under calibration designs for gauge blocks because they have traditionally been used to counteract the effect of temperature build-up in the comparator during calibration.
| 2018-01-18T02:09:14 |
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https://www.usgs.gov/center-news/volcano-watch-geologic-map-hawaii-island-available-electronic-format
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# Volcano Watch — Geologic Map of Hawaii Island available in electronic format
Release Date:
The U.S. Geological Survey recently made available the digital geologic map for the Island of Hawaii. Compiled by Frank Trusdell of the Hawaiian Volcano Observatory, this map is the electronic equivalent of a printed map that first appeared in 1996.
Geologic map of the Island of Hawaii
(Public domain.)
The 1996 full-color map by Edward Wolfe and Jean Morris shows the numerous lava-flow layers, vents, and earthquake faults of the Big Island. The paper map has already gone through two printings, owing to its popularity among visitors to Hawaii Volcanoes National Park and in bookstores in Hilo.
The digital version is made for computer-based applications, using Geographic Information Systems (GIS) software. It allows a user to quickly gather information not readily available from the paper version. For example, the area covered by all lava flows younger than 200 years in age can be determined by a few keystrokes. In the not-so-olden days, an analyst would laboriously trace each outline with a planimeter to obtain the areas, spending a day or a week in the process to gather the same information.
GIS analysis, however, offers far greater advantage than determining the size or shape of geological things. It allows numerous kinds of information to be superimposed. For civil-defense purposes, the relation of roads and utilities to young vents is readily determined. A biologist might compare his or her information about bird nesting sites with the age or type of lava (aa or pahoehoe), thereby finding a new correlation that might lead to enhanced management of Hawaii's natural resources.
Archaeologists have plotted the position of ancestral homesites and heiau (temples) on digital versions of island geologic maps for Kohala and Haleakalā volcanoes, leading to insights about the shrewd use of land by early Polynesians as they experimented with agriculture in their newly found Hawaiian island homes. The power of GIS is limited only by our ability to phrase questions judiciously.
Given the advantage offered by digitized electronic maps, why aren't they always made available in that format, from the get-go? The answer is simple: now they are. The Geological Survey requires digital version of all published maps, in order to increase the usefulness of its products.
The problem has been catching up with vintage maps produced prior to the widespread use of GIS technology. The most important of the older maps will be brought into the electronic age sooner than others, but the task requires diligence and hard work. That's Trusdell's contribution-a gigantic boost for those involved in private- and public-sector work along the island chain.
If you choose to visit the USGS publication page, here's how to do it and what you'll find. You're looking for a product entitled "Digital Database of the Geologic Map of the Island of Hawaii"
The meat of the electronic publication is GIS-based files in a format that can be used by many kinds of software. But PDF versions for some of the files are available, too, as small and intermediate-scale images of the geologic map and explanatory text. Those readers not inclined toward the GIS aspect might find these latter files a useful source of information.
One of the PDF files shows the geologic map draped over a shaded-relief topographic base. By using the clip-and-paste power of a computer, it's possible to capture small areas that will fit on a printed page. But be forewarned; some of the files are probably too large for dial-up connections.
————————————————————————————————————————————————————————————————
### Volcano Activity Update
Activity at the summit of Kīlauea Volcano has returned to low levels this past week. The number of earthquakes in the summit area has decreased. Inflation of the summit caldera continues but at a noticeably slower rate than over the past two months.
Eruptive activity at Puu Oo continues. On clear nights, glow is visible from several vents within the crater and on the southwest side of the cone. Lava continues to flow through the PKK lava tube from its source on the flank of Puu Oo to the ocean, with occasional surface flows breaking out of the tube. In the past week, surface flows were active on the coastal plain below Paliuli, 0.6 km (0.4 mi) inland of the coast at Kamoamoa, about 5.5 km (3.4 mi) from the end of Chain of Craters Road.
As of March 23, lava is entering the ocean at East Laeapuki, in Hawaii Volcanoes National Park. The active lava bench continues to grow following the major collapse of November 28 and is now approximately 1,100 m (3,600 ft) long by 250 m (820 ft) wide. Access to the ocean entry and the surrounding area remains closed, due to significant hazards. If you visit the eruption site, check with the rangers for current updates, and remember to carry lots of water when venturing out onto the flow field.
There were two earthquakes beneath Hawaii Island reported felt within the past week. A magnitude-3.1 earthquake occurred on Friday, March 17, at 8:10 p.m. and was located 3 km (2 miles) south of Kīlauea summit at a depth of 3 km (2 miles). A magnitude-3.4 earthquake occurred on Wednesday, March 22, at 4:38 a.m. and was located 5 km (3 miles) southwest of Waimea at a depth of 16 km (10 miles).
Mauna Loa is not erupting. During the past week, earthquake activity remained low beneath the volcano's summit. Inflation continues, but at a rate that has slowed since early October 2005.
| 2021-02-27T04:10:40 |
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https://rulb.org/ru/article/varianty-optimizacii-morfemnogo-razbora-slovoform-na-osnove-statisticheskix-dannyx/
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Art#: 2724
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Fadeev S.G. OPTIMIZATION OPTIONS OF WORD FORMS MORPHEMIC ANALYSIS ON THE BASIS OF STATISTICAL KNOWLEDGE / S.G. Fadeev, P.V. Zheltov // Russian Linguistic Bulletin. — 2016. — № 3 (7). — С. 15—17. — URL: https://rulb.org/ru/article/varianty-optimizacii-morfemnogo-razbora-slovoform-na-osnove-statisticheskix-dannyx/ (дата обращения: 08.12.2021. ). doi:10.18454/RULB.7.33
Fadeev S.G. OPTIMIZATION OPTIONS OF WORD FORMS MORPHEMIC ANALYSIS ON THE BASIS OF STATISTICAL KNOWLEDGE / S.G. Fadeev, P.V. Zheltov // Russian Linguistic Bulletin. — 2016. — № 3 (7). — С. 15—17. doi:10.18454/RULB.7.33
#### Импортировать
Фадеев С.Г.1, Желтов П.В.2
1аспирант, 2кандидат технических наук, кандидат филологических наук, Чувашский государственный университет им. И.Н.Ульянова
The publication was made in the scope of the scientific project №15-04-00532 supported by the Russian Foundation for Humanities (RFH)
ВАРИАНТЫ ОПТИМИЗАЦИИ МОРФЕМНОГО РАЗБОРА СЛОВОФОРМ НА ОСНОВЕ СТАТИСТИЧЕСКИХ ДАННЫХ
Аннотация
В статье предложен подход к оптимизации морфемного разбора словоформ. Словоформа представляется в виде последовательности 3-х морфемных групп – префиксной группы, группы основы и постфиксной группы. Каждая из этих групп имеет свои особенности, учитываемые при выполнении морфемного разбора. Перечислены статистические особенности естественных языков, позволяющие оптимизировать морфемный разбор префиксной и постфиксной групп. Рассмотрена проблема омонимов, препятствующая внедрению оптимизации на основе статистической информации в морфемный разбор. Для решения этой проблемы введен параметр «глубина морфемного разбора», позволяющий найти компромисс и управлять скоростью и точностью морфемного разбора на основе статистической информации.
Ключевые слова: морфемный анализ, словоформа, морф, оптимизация.
Страницы: 15 - 17
1postgraduate student, 2PhD in Technics, PhD in Philology, Chuvash State University named after I.N.Ulyanov
The publication was made in the scope of the scientific project №15-04-00532 supported by the Russian Foundation for Humanities (RFH)
OPTIMIZATION OPTIONS OF WORD FORMS MORPHEMIC ANALYSIS ON THE BASIS OF STATISTICAL KNOWLEDGE
Abstract
The article proposes an optimization approach of the morphological analysis of word forms. A word form is a sequence of 3 morphemic groups – the prefix group, the stem group and the postfix group. Each group has its own peculiarities, which are considered when performing the morphological analysis. The statistical characteristics of natural languages which provide means of optimization of the morphological analysis of the prefix and postfix groups are represented in the article. The author contemplates the problem of homonyms, which prevents the implementation of the optimization based on statistical information in the morphological analysis. To resolve this issue, the parameter of "the depth of the morphological analysis" is introduced, which allows to find a compromise and control the speed and accuracy of the morphological analysis based on statistical information.
Keywords: morphemic analysis, word form, morph, optimization.
Pages: 15 - 17
Почта авторов / Author Email: [email protected], [email protected]
Morphemic analysis of word forms
Word forms are composed of 2 types of morphs – roots and affixes. Some affixes can be found only before roots, some — only after roots and some of the affixes – within roots. Within this framework word form can be represented by a sequence of 3 groups of morphs:
1. The prefix group consists of a sequence of affixes, which can be found only before roots (prefixes, the left part of confixes).
2. The postfix group consists of a sequence of affixes, which can be found only after roots (suffixes, the right part of confixes).
3. The stem group consists of a sequence of stems, and possibly affixes, which can be interchange with stems (infixes, interfixes, etc.)
The morphs set of the prefix group stands for $\Delta =\left \{ \delta _{1},\delta _{2},..., \delta _{N} \right\}$, the morphs set of the stem group – $\Psi =\left \{\psi _{1}, \psi _{2}, ..., \psi _{M}\right \}$, the morphs set of the postfix group – $\Omega =\left \{\omega _{1}, \omega _{2}, ..., \omega _{K} \right \}$, wherein $N, M, K$ – are respectively the number of morphs of the prefix group, the stem group, and the postfix group for a given natural language. Each natural language has its own sets $\Delta ,\Psi ,\Omega$ and its own amount of $N, M, K$ determined by its morphology.
Let us consider the analysis on the example of the prefix group. There may be more than one prefix morph in a word, that is why even after the first successful check, one should move to the next step, preceding the analysis of the rest of the word form, and repeat these steps for as long as the inclusions will no longer be detected. In general, each of the morphs set $\Delta$ can be found both at the beginning, at the end and in the middle of the prefix group. Therefore, every step should contain verification of inclusions in the word form each of the morphs set $\Delta$.
The disadvantage of this approach is the necessity of looking over all the elements of set $\Delta$ at each step sequentially. And while at the first step the number of verifications is equal to $N$, then amount of verifications at the next steps becomes equal to $k*N$, where $k$ — the number of ways of analysis found at the previous step.
The postfix group has the similar way of analysis; with the only difference that it is more convenient to begin the analysis in the end of the word form and the analysis involves morphs from the set $\Omega$.
The reiterated complete verification of all elements of set slows down work on the analysis of text.
Optimization of the analysis
There are peculiarities in natural languages that can help in acceleration of analysis.
The 1st peculiarity. The probabilities $P()$ of coming across different morphs in a group differ from each other.
The 2nd peculiarity. The probability $P()$ of coming across a morph in a word form depends on the location in the group.
The 3rd peculiarity. The probabilities $P()$ of coming across different combinations of morphs differ from each other.
The 4st peculiarity. The probabilities $P()$ of coming across different combinations of morphs depends on the location in the group.
Considering these statistics features, it is possible to accelerate the analysis. However, this would require collecting statistics on the specific natural language, upon which primarily perform verification of that morphs and their combinations, which are more common in this place of analysis.
Possible solutions of optimization based on statistics
Solution for the 1st peculiarity. Instead of disordered set of morphs it is possible to use their one-dimensional ordered array, in which a morph with a higher probability of coming across has a lower index, than a morph with a lower probability. Verification of morphs for presence in word form should be performed in ascending order of their index. In this case, the morphs with the greatest probability will be checked first.
Solution for the 2nd peculiarity. It is possible to use two-dimensional ordered array. The 1st row of array includes morphs in order of descending of their probability of coming across at the 1st step. The 2nd row of array includes morphs in order of descending of their probability of coming across at the 2nd step, etc. Each step of analysis has its own corresponding number of the array row. As a result, at each step, the morphs with the highest probability of coming across will be checked first at this step.
Solution for the 3rd peculiarity. One-dimensional ordered array used as the solution for the 1st peculiarity can be supplemented with the combinations of morphs with a higher probability of coming across. The higher probability of coming across the lower index in the array. The verification is performed in order of increasing of element’s index. In this case, the morphs (combinations) with the highest probability will be checked first.
Solution for the 4st peculiarity. Two-dimensional ordered array used as the solution for the 2nd peculiarity can be supplemented with the combinations of morphs with a higher probability of coming across. Morphs and their combinations in each row are sorted in descending order of probability of their coming across. In this case, the morphs (combinations) with the highest probability will be checked first.
These solutions with the corresponding change of analysis algorithms will enable to find ways to the final result much faster. After receiving the result, one can discard the remaining verifications, thereby reducing the time of analysis.
These solutions are a practical approach for use with the prefix and postfix groups, since the number of elements is relatively small and the arrays will not be too cumbersome in them.
The problem of analysis based on statistics
The main problem is existence of homonyms. Homonyms are identical in spelling but different in their meanings, thus the analysis of a homonym should give several results instead of one. Therefore the analysis should not terminate at the first found result; it should pass on, since there is a possibility of finding another option for the analysis and possibly not even one.
The consequence of the requirement to continue the analysis after finding the first option is the necessity for a complete search of all morphs, and combinations thereof. If so, there is no point in their arrangement – they still have to be looked through in any case, therefore, time spent on analysis, will be the same one way or another.
In order to get out of this situation, we shall consider 3 situations:
1. The element $\delta _{i}$ in its order of appearance has already come across during the set of statistics in this language $(P(\delta _{i})>0)$.
2. The element $\delta _{i}$ in its order of appearance cannot be come across, since the language morphology does not allow its appearance in the current location (for example, the verb endings cannot be found together, when examining the location, far from the end of the postfix group).
3. Other situations, which are not related to par. 1 и 2. Here $P(\delta _{i})=0$.
In the 1st situation the searching of elements should be continued, since a common situation has already occurred in a given language.
In the 2nd situation the searching of elements should be ceased and then a shift should be produced.
In the 3rd situation it is not clear whether the searching of elements should be continued a shift should be produced. If continued then there is another question – how many elements of the set from с $P(\delta _{i})=0$ should be searched before ceasing and moving to another step?
To implement a flexible solution that can carry into effect the ceasing of searching as well as its continuation, an additional numerical parameter $D$ is introduced, which will determine the actions in the 3rd situation. Let us call it “the depth of the morphemic analysis”. It will determine number of the ordered set elements which are to be processed after elements with $P(\delta _{i})=0$ have proceeded. When $D=0$ such elements are not processed (with the exception of cases described below), when $D=1$, one element is processed, upon which the shift to the following step is produced. Accordingly, when $D=2$, 2 elements are processed, etc.
It should be noted that when $D=0$, there may be cases where processing elements with $P(\delta _{i})=0$ is still necessary. For example, if the analysis is over, but no final alternative was found. In such cases, it is necessary go back to the step at which the analysis was interrupted, and continue with the interrupted point. In order to make it possible, it is necessary to be remembered all the states in which the analysis was interrupted.
It is more sensible to define parameter $D$ outside the decomposition algorithm, so that the user could choose the behavior of the analysis. During initial set-up of the model the larger value of $D$ is more appropriate, since the statistics has not been collected yet and almost all the elements have $P(\delta _{i})=0$. According to continuation, the values of $D$ can be gradually reduced, looking for a compromise between performance and accuracy of the analysis.
Conclusion
The proposed optimization options can reduce time on morphemic analysis of word forms. This will require a preliminary collection of statistics on the basis of a language corpus. Moreover, the presence of suffixes and roots’ dictionaries of this language is a necessary condition as well.
Список литературы / References:
1. Желтов П.В. Лингвистические процессоры, формальные модели и методы: теория и практика. – Чебоксары: Изд-во Чуваш. ун-та, 2006. – 208 с.
2. Желтов П.В. Формальные методы в сравнительно-сопоставительном языкознании. – Чебоксары: Изд-во Чуваш. ун-та, 2006. – 252 с.
3. Желтов П.В. Лингвистические процессоры в системах искусственного интеллекта. – Чебоксары: Изд-во Чуваш. ун-та, 2007. – 100 с.
4. Zheltov, Pavel. Morphological markup system for the national corpora of the Chuvash language / Pavel Zheltov // Proceedings of the International conference “Turkic Languages Processingz: TurkLang 2015”. – Kazan: Academy of Sciences of the Republic of Tatarstan Press, 2015. – pp. 328-330.
Список литературы на английском / References in English:
1. Zheltov P.V. Lingvisticheskie processory, formal’nye modeli i metody: teorija i praktika [Linguistic processors, the formal models and methods: theory and practice]. – Cheboksary: Izd-vo Chuvash. un-ta, 2006. – 208 p. [In Russian]
2. Zheltov P.V. Formal’nye metody v sravnitel’no-sopostavitel’nom jazykoznanii [Formal methods in comparative linguistics]. – Cheboksary: Izd-vo Chuvash. un-ta, 2006. – 252 p. [In Russian]
3. Zheltov P.V. Lingvisticheskie processory v sistemah iskusstvennogo intellekta [Linguistic processors in systems of artificial intelligence]. – Cheboksary: Izd-vo Chuvash. un-ta, 2007. – 100 p. [In Russian]
4. Zheltov, Pavel. Morphological markup system for the national corpora of the Chuvash language / Pavel Zheltov // Proceedings of the International conference “Turkic Languages Processingz: TurkLang 2015”. – Kazan: Academy of Sciences of the Republic of Tatarstan Press, 2015. – pp. 328-330.
Это произведение доступно по – This material is available under Creative Commons «Attribution» («Атрибуция») 4.0 Всемирная
| 2021-12-08T05:45:10 |
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http://pavpanchekha.com/esp/physics-c-2011/ps12.html
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## By Pavel Panchekha, Jeffrey Prouty
Share under CC-BY-SA.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.
# Problem Set 12 (Given 02/12/12)
## Level I
1. A constant $$B$$ field is defined by $$\mathbf{B} = B_0 {\hat z}$$. An electron moving with velocity $$\mathbf{v} = v_x {\hat x} + v_y {\hat y} + v_z {\hat z}$$. As discussed in class, the electron will move in a helix (spiral). Find how far the electron will move in one rotation around its spiral.
A railgun works as follows. Two long, parallel rails are made of a conductive metal, and a conductive projectile is placed on them so that it can move along the rails while maintaining electric contact. The other ends of the rails are connected to a voltage source. As current flows along the rails, it creates a magnetic field between the rails.
1. Find the magnetic field in the middle of the two rails if the current along the rails is $$I$$ and the distance between the rails is $$2r$$. What is the magnitude and direction of the $$B$$ field?
2. Find and explain any forces on the projectile. Ignore gravity.
3. The resistance of steel, as might be used for the rails, is $$2 \cdot 10^-5 \Omega / m$$ (that is, per meter of rail). If the rails are ten meters long, and the current one mega-ampere, find the energy lost to heat.
## Level II
1. Two long parallel wires have current $$I$$ flowing in the same direction along them. Each wire lies along the center of a pipe of radius $$r$$. The two wires are $$d$$ distance apart. What is the average magnetic field between the two wires in their plane?
2. A wire consists of two parallel half-infinite wires connected by a half-circle. Using the Biot-Savart law, find the magnetic field in the center of the half-circle.
## Level III
1. The Biot-Savart law allows us to find magnetic field contribution of an infinitesimal piece of wire. On the other hand, recall that in class we found the magnetic field due to a plane of current; we couldn't use the plain Biot-Savart law for this job, since it is a piece of plane, not wire. By integrating in the correct way, derive a modified form of the Biot-Savart law suitable for finding the magnetic field due to a surface along which current flows.
| 2018-09-22T03:05:47 |
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https://large-numbers.fandom.com/wiki/Enneadecation
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## FANDOM
1,078 Pages
Enneadecation refers to the 19th hyperoperation starting from addition. It is equal to $$a \uparrow^{17} b$$ in Knuth's up-arrow notation.
Enneadecation can be written in array notation as $$\{a,b,17\}$$ and in chained arrow notation as $$a \rightarrow b \rightarrow 17$$.
Enneadecational growth rate is equivalent to $$f_18(n)$$ in the fast-growing hierarchy.
Community content is available under CC-BY-SA unless otherwise noted.
| 2019-12-10T13:32:06 |
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https://invernessgangshow.net/which-energy-level-requires-the-most-energy-to-remove-an-electron/
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## Ionization Energy
Ionization energy (IE) is the energy required to remove an electron from a neutral atom or cation in its gaseous phase. IE is also known as ionization potential.
You are watching: Which energy level requires the most energy to remove an electron?
\
Conceptually, ionization energy is the affinity of an element for its outermost electron (an electron it already has in its valence shell).
### 1st, 2nd, and 3rd Ionization Energies
The symbol $$I_1$$ stands for the first ionization energy (energy required to take away an electron from a neutral atom, where $$n=0$$). The symbol $$I_2$$ stands for the second ionization energy (energy required to take away an electron from an atom with a +1 charge, $$n=2$$.)
First Ionization Energy, $$I_1$$ (general element, A): $$A_{(g)} \rightarrow A^{1+}_{(g)} + e^-$$
Second Ionization Energy, $$I_2$$ (general element, A): $$A^{1+}_{(g)} \rightarrow A^{2+}_{(g)} + e^-$$
Third Ionization Energy, $$I_3$$ (general element, A): $$A^{2+}_{(g)} \rightarrow A^{3+}_{(g)} + e^-$$
Each succeeding ionization energy is larger than the preceding energy. This means that $$I_1 ### General periodic trends in electron affinity In general, ionization energies increase from left to right and decrease down a group; however there are variations in these trends that would be expected from the effects of penetration and shielding. The trends in first ionization energy are shown in Figure \(\PageIndex{1}$$ and are summarized below.
See more: Give The Hybridization For The O In H3O+., Chem 105 Test 3 Rowland Flashcards
Across a period: As Z* increases across a period, the ionization energy of the elements generally increases from left to right. However there are breaks or variation in the trends in the following cases: IE is especially low when removal of an electron creates a newly empty p subshell (examples include $$I_1$$ of B, Al, Sc) IE energy is especially low where removal of an electron results in a half-filled p or d subshell (examples include $$I_1$$ of O, S) IE increases more gradually across the d- and f-subshells compared to s- and p- subshells. This is because d- and f- electrons are weakly penetrating and experience especially low Z*. From one period to the next: There is an especially large decrease in IE with the start of every new period (from He to Li or from Ne to Na for example). This is consistent with the idea that IE is especially low when removal of an electron creates a newly empty s-subshell. Nobel gases: The noble gases posses very high ionization energies. Note that helium has the highest ionization energy of all the elements. Down a group: Although Z* increases going down a group, there is no reliable trend in IE going down any group; in some cases IE increases going down a group, while in other cases IE decreases going down a group.
Figure $$\PageIndex{2}$$. The first ($$I_1$$), second ($$I_2$$), and third ($$I_3$$) ionization energies are plotted for elements with Z = 1 to 36 (H to Kr). The position of each element in its atomic form is indicated as s- p- or d-block. (CC-BY-NC-SA; Kathryn Haas)
| 2023-03-31T02:27:12 |
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https://www.linuxtopia.org/online_books/office_guides/openoffice_3_getting_started_guide/openoffice_starter_Getting_Started_with_Math.html
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OpenOffice 3.x Getting Started Guide
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This is Chapter 9 of Getting Started with OpenOffice.org 3.x, produced by the OOoAuthors group. A PDF of this chapter is available from Documentation at OpenOffice.org.
# Introduction
OpenOffice.org (OOo) has a component for mathematical equations. It is most commonly used as an equation editor for text documents, but it can also be used with other types of documents or stand-alone. When used inside Writer, the equation is treated as an object inside the text document.
The equation editor is for writing equations in symbolic form (as in equation 1). If you want to evaluate a numeric value, see the Calc Guide.
$\frac {df(x)}{dx} = \ln(x)+\tan^{-1}(x^2)$ (1)
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| 2021-04-20T12:58:58 |
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https://zbmath.org/authors/?q=ai%3Aatabekyan.varuzhan-s
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# zbMATH — the first resource for mathematics
## Atabekyan, Varuzhan S.
Compute Distance To:
Author ID: atabekyan.varuzhan-s Published as: Atabekyan, V. S.; Atabekyan, Varujan; Atabekyan, Varuzhan S. Homepage: http://www.ysu.am/faculties/en/Mathematics-and-Mechanics/section/staff/person/p9... External Links: MGP · Math-Net.Ru · Wikidata
Documents Indexed: 38 Publications since 1987
all top 5
#### Co-Authors
23 single-authored 8 Adyan, Sergeĭ Ivanovich 4 Aslanyan, Haika T. 2 Gevorgyan, Amirjan L. 2 Grigoryan, A. E. 1 Grigoryan, Hayk A. 1 Pahlevanian, A. S. 1 Stepanyan, Sh. A.
all top 5
#### Serials
8 Mathematical Notes 7 Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences 4 Izvestiya: Mathematics 4 Proceedings of the Yerevan State University. Physical and Mathematical Sciences 3 International Journal of Algebra and Computation 2 Uchenye Zapiski Erevanskogo Gosudarstvennogo Universiteta. Estestvennye Nauki 2 Sbornik: Mathematics 2 Armenian Journal of Mathematics 1 Moscow University Mathematics Bulletin 1 Algebra and Logic 1 Vestnik Moskovskogo Universiteta. Seriya I. Matematika, Mekhanika 1 Journal of Mathematical Sciences (New York) 1 Proceedings of the Steklov Institute of Mathematics
#### Fields
37 Group theory and generalizations (20-XX) 4 Abstract harmonic analysis (43-XX) 3 Topological groups, Lie groups (22-XX) 1 Functional analysis (46-XX) 1 General topology (54-XX)
#### Citations contained in zbMATH
29 Publications have been cited 91 times in 32 Documents Cited by Year
Normal automorphisms of free Burnside groups. Zbl 1227.20030
Atabekyan, V. S.
2011
On periodic groups of odd period $$n\geq 1003$$. Zbl 1152.20034
Atabekyan, V. S.
2007
On simple and free periodic groups. Zbl 0661.20027
Atabekyan, V. S.
1987
Uniform nonamenability of subgroups of free Burnside groups of odd period. Zbl 1213.20036
Atabekyan, V. S.
2009
On free groups in the infinitely based varieties of S. I. Adian. Zbl 1436.20044
Adian, Sergey I.; Atabekyan, Varuzhan S.
2017
Non-$$\varphi$$-admissible normal subgroups of free Burnside groups. Zbl 1299.20046
Atabekyan, V. S.
2010
On subgroups of free Burnside groups of odd exponent $$n\geqslant 1003$$. Zbl 1226.20029
Atabekyan, V. S.
2009
Characteristic properties and uniform non-amenability of $$n$$-periodic products of groups. Zbl 1360.20018
Adian, Sergey I.; Atabekyan, Varuzhan S.
2015
The Hopfian property of $$n$$-periodic products of groups. Zbl 1326.20040
Adian, S. I.; Atabekyan, V. S.
2014
On normal subgroups in the periodic products of S. I. Adyan. Zbl 1297.20035
Atabekyan, V. S.
2011
Monomorphisms of free Burnside groups. Zbl 1200.20028
Atabekyan, V. S.
2009
The groups of automorphisms are complete for free Burnside groups of odd exponents $$n\geq 1003$$. Zbl 1283.20039
Atabekyan, V. S.
2013
Splitting automorphisms of free Burnside groups. Zbl 1282.20025
Atabekyan, Varuzhan S.
2013
Central extensions of free periodic groups. Zbl 07025721
Adian, Sergeĭ I.; Atabekyan, Varuzhan S.
2018
The automorphisms of endomorphism semigroups of relatively free groups. Zbl 1384.20033
Atabekyan, V. S.; Aslanyan, Haika T.
2018
The unique trace property of $$n$$-periodic product of groups. Zbl 1378.20041
Atabekyan, V. S.; Gevorgyan, A. L.; Stepanyan, Sh. A.
2017
Periodic products of groups. Zbl 1377.20026
Adian, S. I.; Atabekyan, V. S.
2017
The automorphisms of endomorphism semigroups of free Burnside groups. Zbl 1318.20038
Atabekyan, V. S.
2015
On outer normal automorphisms of periodic products of groups. Zbl 1299.20047
Atabekyan, V. S.; Gevorgyan, A. L.
2011
Normal subgroups in free Burnside groups of odd period. Zbl 1281.20042
Atabekyan, Varujan
2008
$$n$$-torsion groups. Zbl 1435.20050
Adian, S. I.; Atabekyan, V. S.
2019
Analogues of Nielsen’s and Magnus’s theorems for free Burnside groups of period 3. Zbl 1386.20022
Atabekyan, V. S.; Aslanyan, H. T.; Grigoryan, H. A.; Grigoryan, A. E.
2017
$$C^\ast$$-simplicity of $$n$$-periodic products. Zbl 1358.20033
Adyan, S. I.; Atabekyan, V. S.
2016
Automorphism groups and endomorphism semigroups of groups $$B(m,n)$$. Zbl 1323.20031
Atabekyan, V. S.
2015
Splitting automorphisms of order $$p^k$$ of free Burnside groups are inner. Zbl 1315.20030
Atabekyan, V. S.
2014
Splitting automorphisms of free Burnside groups. Zbl 1309.20027
Atabekyan, V. S.
2011
On CEP-subgroups of $$n$$-periodic products. Zbl 1299.20056
Atabekyan, V. S.
2011
The normalizers of free subgroups in free Burnside groups of odd period $$n\geq 1003$$. Zbl 1288.20049
Atabekyan, V. S.
2010
Simple and free periodic groups. Zbl 0794.20049
Atabekyan, V. S.
1987
$$n$$-torsion groups. Zbl 1435.20050
Adian, S. I.; Atabekyan, V. S.
2019
Central extensions of free periodic groups. Zbl 07025721
Adian, Sergeĭ I.; Atabekyan, Varuzhan S.
2018
The automorphisms of endomorphism semigroups of relatively free groups. Zbl 1384.20033
Atabekyan, V. S.; Aslanyan, Haika T.
2018
On free groups in the infinitely based varieties of S. I. Adian. Zbl 1436.20044
Adian, Sergey I.; Atabekyan, Varuzhan S.
2017
The unique trace property of $$n$$-periodic product of groups. Zbl 1378.20041
Atabekyan, V. S.; Gevorgyan, A. L.; Stepanyan, Sh. A.
2017
Periodic products of groups. Zbl 1377.20026
Adian, S. I.; Atabekyan, V. S.
2017
Analogues of Nielsen’s and Magnus’s theorems for free Burnside groups of period 3. Zbl 1386.20022
Atabekyan, V. S.; Aslanyan, H. T.; Grigoryan, H. A.; Grigoryan, A. E.
2017
$$C^\ast$$-simplicity of $$n$$-periodic products. Zbl 1358.20033
Adyan, S. I.; Atabekyan, V. S.
2016
Characteristic properties and uniform non-amenability of $$n$$-periodic products of groups. Zbl 1360.20018
Adian, Sergey I.; Atabekyan, Varuzhan S.
2015
The automorphisms of endomorphism semigroups of free Burnside groups. Zbl 1318.20038
Atabekyan, V. S.
2015
Automorphism groups and endomorphism semigroups of groups $$B(m,n)$$. Zbl 1323.20031
Atabekyan, V. S.
2015
The Hopfian property of $$n$$-periodic products of groups. Zbl 1326.20040
Adian, S. I.; Atabekyan, V. S.
2014
Splitting automorphisms of order $$p^k$$ of free Burnside groups are inner. Zbl 1315.20030
Atabekyan, V. S.
2014
The groups of automorphisms are complete for free Burnside groups of odd exponents $$n\geq 1003$$. Zbl 1283.20039
Atabekyan, V. S.
2013
Splitting automorphisms of free Burnside groups. Zbl 1282.20025
Atabekyan, Varuzhan S.
2013
Normal automorphisms of free Burnside groups. Zbl 1227.20030
Atabekyan, V. S.
2011
On normal subgroups in the periodic products of S. I. Adyan. Zbl 1297.20035
Atabekyan, V. S.
2011
On outer normal automorphisms of periodic products of groups. Zbl 1299.20047
Atabekyan, V. S.; Gevorgyan, A. L.
2011
Splitting automorphisms of free Burnside groups. Zbl 1309.20027
Atabekyan, V. S.
2011
On CEP-subgroups of $$n$$-periodic products. Zbl 1299.20056
Atabekyan, V. S.
2011
Non-$$\varphi$$-admissible normal subgroups of free Burnside groups. Zbl 1299.20046
Atabekyan, V. S.
2010
The normalizers of free subgroups in free Burnside groups of odd period $$n\geq 1003$$. Zbl 1288.20049
Atabekyan, V. S.
2010
Uniform nonamenability of subgroups of free Burnside groups of odd period. Zbl 1213.20036
Atabekyan, V. S.
2009
On subgroups of free Burnside groups of odd exponent $$n\geqslant 1003$$. Zbl 1226.20029
Atabekyan, V. S.
2009
Monomorphisms of free Burnside groups. Zbl 1200.20028
Atabekyan, V. S.
2009
Normal subgroups in free Burnside groups of odd period. Zbl 1281.20042
Atabekyan, Varujan
2008
On periodic groups of odd period $$n\geq 1003$$. Zbl 1152.20034
Atabekyan, V. S.
2007
On simple and free periodic groups. Zbl 0661.20027
Atabekyan, V. S.
1987
Simple and free periodic groups. Zbl 0794.20049
Atabekyan, V. S.
1987
all top 5
#### Cited by 26 Authors
19 Atabekyan, Varuzhan S. 6 Adyan, Sergeĭ Ivanovich 3 Gevorgyan, Amirjan L. 2 Aslanyan, Haika T. 1 Araújo, João 1 Bardakov, Valeriĭ Georgievich 1 Bentz, Wolfram 1 Button, Jack Oliver 1 Cameron, Peter Jephson 1 Coulon, Rémi 1 Coulon, Rémi B. 1 Gevorgyan, Garnik Gurgenovich 1 Grigoryan, A. E. 1 Gruber, Dominik 1 Kunyavskiĭ, Boris Èmmanuilovich 1 Mikaelian, Vahagn H. 1 Minasyan, Ashot 1 Ol’shanskiĭ, Aleksandr Yur’evich 1 Pahlevanyan, A. S. 1 Pajlevanyan, Ashot S. 1 Rostami, Hamid Reza 1 Sonkin, Dmitry M. 1 Stepanyan, Sh. A. 1 Vesnin, Andrei Yu. 1 Yadav, Manoj Kumar 1 Zusmanovich, Pasha
all top 5
#### Cited in 17 Serials
8 Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences 6 Mathematical Notes 3 International Journal of Algebra and Computation 2 Proceedings of the Steklov Institute of Mathematics 1 Communications in Algebra 1 Advances in Mathematics 1 Algebra and Logic 1 Journal of Algebra 1 Siberian Mathematical Journal 1 Transactions of the American Mathematical Society 1 Expositiones Mathematicae 1 Journal of Mathematical Sciences (New York) 1 Sbornik: Mathematics 1 Algebraic & Geometric Topology 1 Groups, Geometry, and Dynamics 1 Armenian Journal of Mathematics 1 RAIRO. Theoretical Informatics and Applications
all top 5
#### Cited in 9 Fields
31 Group theory and generalizations (20-XX) 3 Topological groups, Lie groups (22-XX) 3 Abstract harmonic analysis (43-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 General algebraic systems (08-XX) 1 Functional analysis (46-XX) 1 Manifolds and cell complexes (57-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2021-02-28T17:15:32 |
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|
https://pdglive.lbl.gov/DataBlock.action?node=M106W&home=MXXX005
|
# ${{\boldsymbol f}_{{2}}{(2010)}}$ WIDTH INSPIRE search
VALUE (MeV) DOCUMENT ID TECN COMMENT
$202$ ${}^{+67}_{-62}$ 1
1988
MPS 22 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \phi}}{{\mathit \phi}}{{\mathit n}}$
• • • We do not use the following data for averages, fits, limits, etc. • • •
$209$ $\pm32$
2006
SPEC 40 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}_S^0}$ ${{\mathit n}}$
$145$ $\pm50$ 2
1988
SPEC 40 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}_S^0}$ ${{\mathit n}}$
$200$ ${}^{+160}_{-50}$
1985
MPS 22 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ 2 ${{\mathit \phi}}{{\mathit n}}$
$300$ ${}^{+150}_{-50}$
1984
RVUE
$310$ $\pm70$
1982
MPS 22 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ 2 ${{\mathit \phi}}{{\mathit n}}$
1 Includes data of ETKIN 1985 .
2 Statistically very weak, only $1.4$ s.d.
References:
PAN 69 493 Analysis of the ${{\mathit K}_S^0}$ ${{\mathit K}_S^0}$ System from the Reaction ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}_S^0}$ ${{\mathit n}}$ at 40 GeV
BOLONKIN 1988
NP B309 426 ${{\mathit \theta}{(1700)}}$ and ${{\mathit \xi}{(2230)}}$ Resonances in the ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}_S^0}$ ${{\mathit n}}$ Reaction at Momentum 40 ${\mathrm {GeV/}}\mathit c$
ETKIN 1988
PL B201 568 Increased Statistics and Observation of $\mathit g_{{{\mathit T}}}$, $\mathit g_{{{\mathit T}^{\,'}}}$ and $\mathit g_{{{\mathit T}^{"}}}$ $2+{}^{+}{}^{}$ Resonances in Glueball Enhanced Channel ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \phi}}{{\mathit \phi}}{{\mathit n}}$
ETKIN 1985
PL 165B 217 Observation of Three $2+{}^{+}{}^{}$ Resonances in the Glueball Enhanced Channel ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \phi}}{{\mathit \phi}}{{\mathit n}}$
LINDENBAUM 1984
CNPP 13 285 Production of Glueballs
ETKIN 1982
PRL 49 1620 Reaction ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \phi}}{{\mathit \phi}}{{\mathit n}}$ and Evidence for Glueballs
| 2020-10-31T05:13:00 |
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|
https://par.nsf.gov/biblio/10318266-search-charginoneutralino-pair-production-final-states-three-leptons-missing-transverse-momentum-sqrt-tev-pp-collisions-atlas-detector
|
Search for chargino–neutralino pair production in final states with three leptons and missing transverse momentum in $$\sqrt{s} = 13$$ TeV pp collisions with the ATLAS detector
Abstract A search for chargino–neutralino pair production in three-lepton final states with missing transverse momentum is presented. The study is based on a dataset of $$\sqrt{s} = 13$$ s = 13 TeV pp collisions recorded with the ATLAS detector at the LHC, corresponding to an integrated luminosity of 139 $$\hbox {fb}^{-1}$$ fb - 1 . No significant excess relative to the Standard Model predictions is found in data. The results are interpreted in simplified models of supersymmetry, and statistically combined with results from a previous ATLAS search for compressed spectra in two-lepton final states. Various scenarios for the production and decay of charginos ( $${\tilde{\chi }}^\pm _1$$ χ ~ 1 ± ) and neutralinos ( $${\tilde{\chi }}^0_2$$ χ ~ 2 0 ) are considered. For pure higgsino $${\tilde{\chi }}^\pm _1{\tilde{\chi }}^0_2$$ χ ~ 1 ± χ ~ 2 0 pair-production scenarios, exclusion limits at 95% confidence level are set on $${\tilde{\chi }}^0_2$$ χ ~ 2 0 masses up to 210 GeV. Limits are also set for pure wino $${\tilde{\chi }}^\pm _1{\tilde{\chi }}^0_2$$ χ ~ 1 ± χ ~ 2 0 pair production, on $${\tilde{\chi }}^0_2$$ χ ~ 2 0 masses up to 640 GeV for decays via on-shell W and Z bosons, up more »
| 2022-07-07T01:29:15 |
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|
http://gams.cam.nist.gov/15.7
|
# §15.7 Continued Fractions
If $|\mathop{\mathrm{ph}\/}\nolimits\!\left(1-z\right)|<\pi$, then
15.7.1 $\frac{\mathop{\mathbf{F}\/}\nolimits\!\left(a,b;c;z\right)}{\mathop{\mathbf{F}% \/}\nolimits\!\left(a,b+1;c+1;z\right)}=t_{0}-\cfrac{u_{1}z}{t_{1}-\cfrac{u_{2% }z}{t_{2}-\cfrac{u_{3}z}{t_{3}-\cdots}}},$
where
15.7.2 $\displaystyle t_{n}$ $\displaystyle=c+n,$ $\displaystyle u_{2n+1}$ $\displaystyle=(a+n)(c-b+n),$ $\displaystyle u_{2n}$ $\displaystyle=(b+n)(c-a+n).$
If $|z|<1$, then
15.7.3 $\frac{\mathop{\mathbf{F}\/}\nolimits\!\left(a,b;c;z\right)}{\mathop{\mathbf{F}% \/}\nolimits\!\left(a,b+1;c+1;z\right)}=v_{0}-\cfrac{w_{1}}{v_{1}-\cfrac{w_{2}% }{v_{2}-\cfrac{w_{3}}{v_{3}-\cdots}}},$
where
15.7.4 $\displaystyle v_{n}$ $\displaystyle=c+n+(b-a+n+1)z,$ $\displaystyle w_{n}$ $\displaystyle=(b+n)(c-a+n)z.$
If $\realpart{z}<\tfrac{1}{2}$, then
15.7.5 $\frac{\mathop{\mathbf{F}\/}\nolimits\!\left(a,b;c;z\right)}{\mathop{\mathbf{F}% \/}\nolimits\!\left(a+1,b+1;c+1;z\right)}={x_{0}+\cfrac{y_{1}}{x_{1}+\cfrac{y_% {2}}{x_{2}+\cfrac{y_{3}}{x_{3}+\cdots}}}},$
where
15.7.6 $\displaystyle x_{n}$ $\displaystyle=c+n-(a+b+2n+1)z,$ $\displaystyle y_{n}$ $\displaystyle=(a+n)(b+n)z(1-z).$
| 2016-10-21T13:00:21 |
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|
https://scaron.info/publications/humanoids-2016.html
|
# Multi-contact Walking Pattern Generation based on Model Preview Control of 3D COM Accelerations
Stéphane Caron and Abderrahmane Kheddar. Humanoids 2016, Cancún, Mexico, November 2016.
## Abstract
We present a multi-contact walking pattern generator based on preview-control of the 3D acceleration of the center of mass (COM). A key point in the design of our algorithm is the calculation of contact-stability constraints. Thanks to a mathematical observation on the algebraic nature of the frictional wrench cone, we show that the 3D volume of feasible COM accelerations is a always an upward-pointing cone. We reduce its computation to a convex hull of (dual) 2D points, for which optimal $${\cal O}(n \log n)$$ algorithms are readily available. This reformulation brings a significant speedup compared to previous methods, which allows us to compute time-varying contact-stability criteria fast enough for the control loop. Next, we propose a conservative trajectory-wide contact-stability criterion, which can be derived from COM-acceleration volumes at marginal cost and directly applied in a model-predictive controller. We finally implement this pipeline and exemplify it with the HRP-4 humanoid model in multi-contact dynamically walking scenarios.
## BibTeX
@inproceedings{caron2016humanoids,
title = {Multi-contact Walking Pattern Generation based on Model Preview Control of 3D COM Accelerations},
author = {Caron, St{\'e}phane and Kheddar, Abderrahmane},
booktitle = {Proceedings of the 2016 IEEE-RAS International Conference on Humanoid Robots},
year = {2016},
month = nov,
organization = {IEEE},
url = {https://hal.archives-ouvertes.fr/hal-01349880},
doi = {10.1109/HUMANOIDS.2016.7803329},
}
## Q & A
Feel free to write me directly about any question you have on this work.
In the abstract, you mention a "significant speedup compared to previous methods". How much is that exactly? Is it quantified in the paper?
The main benefit and the real novelty of the algorithms introduced in Section IV (for the ZMP support area and COM acceleration volume) is that they only recompute the time-varying part of these stability criteria. This is e.g. quantified by the computation times in Table III: even using state-of-the-art algorithms, computing the whole criterion from scratch takes 10 times longer than computing only its time-varying part.
Pages of this website are under the CC-BY 4.0 license.
| 2018-06-18T07:11:50 |
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|
https://wiki.bnl.gov/eic/index.php?title=Simulations
|
# Simulations
The EIC task force has a large number of simulation tools available for investigating different types of physics processes. Unless noted otherwise, these can be accessed from /afs/rhic.bnl.gov/eic/PACKAGES.
## Event Generators
The following event generators are currently available:
• ep
• DJANGOH: (un)polarised DIS generator with QED and QCD radiative effects for NC and CC events.
• MILOU: A generator for deeply virtual Compton scattering (DVCS), the Bethe-Heitler process and their interference.
• PYTHIA: A general-purpose high energy physics event generator.
• PEPSI: A generator for polarised leptoproduction.
• RAPGAP: A generator for deeply inelastic scattering (DIS) and diffractive e + p events.
• eA
• BeAGLE: Benchmark eA Generator for LEptoproduction - a generator to simulate ep/eA DIS events including nuclear shadowing effects (based on DPMJetHybrid)
• eSTARlight: Monte Carlo that simulates coherent vector meson photo- and electro-production in electron-ion collisions.
These generators are not part of the current distribution but can be installed upon request:
• ep
• gmc_trans: A generator for semi-inclusive DIS with transverse-spin- and transverse-momentum-dependent distributions.
• LEPTO: A leptoproduction generator - used as a basis for PEPSI and DJANGOH
• LEPTO-PHI: A version of LEPTO with "Cahn effect" (azimuthal asymmetry) implemented
• eA
• DPMJet: a generator for very low Q2/real photon physics in eA
• DPMJetHybrid: an obsolete buggy beta version of BeAGLE: a generator to simulate ep/eA DIS events by employing PYTHIA in DPMJet. Not supported in any way. No physics should be published with it.
• Sartre is an event generator for exclusive diffractive vector meson production and DVCS in ep and eA collisions based on the dipole model.
There is code provided to convert the output from most of these generators into a ROOT format. It is distributed as part of eic-smear, the Monte Carlo smearing package.
## Detector simulations
The following programs are available for simulating detector geometry and response:
• eic-smear A package to apply very fast detector smearing to Monte Carlo events.
More details on detector simulations can be found here.
## Manuals
See the pages of the programmes listed above for their documentation. Other useful references are:
• BASES/SPRING v1 and v5.1: Cross section integration and Monte Carlo event generation. Used in Rapgap and MILOU.
The following pages provide useful general information for Monte Carlo simulations:
• MC programs:
• A list of Monte Carlo programmes
• HepForge, high-energy physics development environment, which includes many Monte Carlo generators.
• Lecture slides from a course on QCD and Monte Carlos
• Parton Distribution Function Interfaces:
• LHAPDF, the Les Houches Accord PDF Interface.
• By default, programs are linked to version 5.9.1, pointed to by $LHAPDF5. • You can adapt your LD_LIBRARY_PATH to point to$LHAPDF6 instead. This is a more modern version but lacks support for some EIC-relevant PDFs.
• The PDF-Grids can be accessed via /gpfs01/eic/data/LHAPDF59SHARE/lhapdf/PDFsets, or more generally via /cvmfs/sft.cern.ch/lcg/external/lhapdfsets. These should be found automatically if using the system-default version of LHAPDF.
• The users' manual of the CERN PDFLIB
## MC Analysis Techniques
##### How to get a cross section (for non-BeAGLE MC)
to normalize your counts to cross section you need two pieces of information
• the total number of trials, it is printed to the screen/logfile if all our MC finish
• the total integrated cross section, the unit is in general microbarn, it is printed to the screen/logfile if all our MC finish
Counts = Luminosity x Cross Section
==> count * total integrated cross section /total number of trials
to calculate the corresponding MC luminosity
==> total number of trials/ total integrated cross section
There are some handy ROOT functions available to get the total number of trials, the total integrated MC cross section and the total number of events in the Tree
These work on Pythia, Pepsi, Djangoh and Milou event-wise root trees
• total number of trials:
TObjString* nEventsString(NULL)
file.GetObject("nEvents", nEventsString);
• total integrated MC cross section
TObjString* crossSectionString(NULL);
file.GetObject("crossSection", crossSectionString);
• total number of events in the tree:
TTree* tree(NULL);
file.GetObject("EICTree", tree);
##### How to get a cross-section for BeAGLE
Note: This refers to standalone BeAGLE using internal e+N event generation (Pythia or optionally RAPGAP (when available)). For BeAGLE+GCF see below.
When BeAGLE simulates electron-nucleus (eA) collisions, it tags each event as scattering either from a proton or from a neutron in the nucleus. The stdout (which can be redirected to a log file) contains the total electron-proton cross section, σep, and the total electron-neutron cross section, σen, for the beam energies and kinematic ranges over which we choose to generate events. As long as we simulate enough events so that the cross sections can be effectively sampled (using sequential mode), these two values (σep and σen) will be independent of the number of events generated.
It should be noted that as long as σep and σen are equal to the desired precision, which is often the case at low x (high energy), then the simpler "non-BeAGLE" cross-section method above can be used with the exception that "number of events" should be used instead of "number of trials". For the most precise approach, we must correct for the fact that BeAGLE assumes equal ep and en cross-sections when selecting whether the struck nucleon is a proton or neutron, which is not quite right.
For a given electron-nucleon integrated luminosity, lumeic, the predicted number of events is
numeic = [ (Z×σep + N×σen) / A ] × lumeic
Here, for the nucleus being simulated, A = Z + N, Z, and N are the number of nucleons, protons, and neutrons, respectively. From the predicted total number of events, numeic, and the individual cross sections, we can calculate the ratio of the number originating from an electron-proton scattering to those originating from an electron-neutron scattering:
numeic = numprot + numneut = [ (Z×σep + N×σen) / A ] × lumeic = (Z/A)×σep×lumeic + (N/A)×σen×lumeic
This gives
numprot = (Z/A)×σep×lumeic
numneut = (N/A)×σen×lumeic
From where we calculate the following ratio:
numprot / numneut = (σep / σen) × (Z/N)
This means that if we simulate a certain number of events, numsim, the ratio of the simulated events which should come from a proton scattering to those which should come from a neutron scattering is given by the above equation. However, since the cross-section ratio depends strongly on the kinematic range we choose to generate over, using the true ratio is impractical. In practice, BeAGLE simulates proton and neutron scattering events according to the ratio of protons to neutrons in the nucleus under consideration.
So if we generate a total number of events, numsim, and then apply cuts (and/or binning), we end up with a final number of events, numsim,cut. Then we can ask, for a given electron-nucleon integrated luminosity, lumeic, how many events are predicted with that cut, numeic,cut. In order calculate this accurately, we first define the following:
numsim = numsimprot + numsimneut
lumsimprot = numsimprot / σep
lumsimneut = numsimneut / σen
In the above equations, numsimprot and numsimneut are the total number of proton and neutron scattering events generated, respectively. These numbers can be found in the output log file, or in the output ROOT file by seeing how many events are tagged as coming from a nucleon==2212 (proton) or a nucleon==2112 (neutron).
Next, after applying the cuts (and/or binning) mentioned above, we can write
numsim,cut = numsim,cutprot + numsim,cutneut
Again, using the output ROOT file, we can determine the number of proton-tagged events and neutron-tagged events which pass the cut. Then we can calculate the expected number of events:
numeic,cut = lumeic × ( [ Z×(numsim,cutprot/lumsimprot) + N×(numsim,cutneut/lumsimneut) ] / A )
As a specific example, we can consider the case where the 'cut' is simply a range in x and Q2 (i.e. a x-Q2 bin). We use the above result to calculate the inclusive (per-nucleon) differential cross section as
d2σ/dxdQ2 = numeic,cut / ( lumeic × Δx × ΔQ2) = ( [ Z×(numsim,cutprot/lumsimprot) + N×(numsim,cutneut/lumsimneut) ] / A ) / (Δx × ΔQ2)
In the above equation, Δx × ΔQ2 gives the area of the x-Q2 bin.
##### How to get a cross-section for BeAGLE+GCF
GCF (Generalized Contact Formalism) is a package which calculates cross-sections in e+A collisions with Short-Range Correlations (SRCs) for a variety of specific processes: Quasi-elastic, vector-meson diffraction, DIS. In many cases, BeAGLE can read these events in and handle the nuclear response. GCF generates events which are flat or gaussian in a variety of variables and then reports a weight which can be used to convert this to a cross-section.
The weight is carried in the "RAevt" variable and has units nb (some older versions used cm2).
##### How to scale to the MC luminosity to the luminosity we want for the measurement
Very often it is impossible to generate so many events that the MC luminosity would correspond to one month of EIC running.
For this case we generate so much MC events that all distributions are smooth and scale the uncertainties.
The factor needed to scale is the ratio lumi-scale-factor = EIC-luminosity / generated MC luminosity. If we have this factor there are 2 ways to scale.
• scaling of counts in histogram by
h11->Scale(lumi-scale-factor);
this will scale the number of counts in each bin of the histogram to what you would get for the EIC-luminosity
statistical uncertainties can then be calculated simply by sqrt(counts)
• scaling the statistical uncertainties only
sqrt(counts)/sqrt(lumi-scale-factor)
##### Example: reduced cross section
This example shows how to calculate the reduced cross section need to extract F_2 and F_L and how to scale the statistical uncertainties to a certain integrated luminosity
sigma_reduced = prefactor * dsigma/dx/dQ2 with prefactor = Q^4 * x / (2*pi*alpha_em^2*(1+(1-y)^2)
this cross section would have the unit barn * GeV^2, to make it dimensionless you need to use a conversion factor for barn to 1/GeV^2 (h^2c^2/GeV^2 = 0.3894 millibarn)
sigma_reduced = counts(x,Q^2) * prefactor * total integrated MC cross section /total number of trials/ conversion-barn-to-GeV /x-binsize/Q2-binsize
if the root function Scale was used the statistical uncertainty is
delta sigma_reduced = sqrt(counts(x,Q^2)) * prefactor * total integrated MC cross section /total number of trials/ conversion-barn-to-GeV /x-binsize/Q2-binsize
in the other case it is
delta sigma_reduced = sqrt(counts(x,Q^2)) * prefactor * total integrated MC cross section /total number of trials/ conversion-barn-to-GeV /x-binsize/Q2-binsize/ sqrt(lumi-scale-factor)
Attention: all luminosities and cross section must be in the same unit (pb or fb or ...)
##### High-Statistics BeAGLE Simulation
Multiple BeAGLE simulation jobs can submitted to the BNL batch farm using the condor utility. A simple submission file to run 10 jobs simultaneously is shown below.
Universe = vanilla
Executable = run_eAu.sh
GetEnv = True
Input = /dev/null
Arguments = "$(Process)" Output = jobout/eAujob.out.$(Process)
Error = jobout/eAujob.err.$(Process) Log = jobout/eAujob.log.$(Process)
Queue 10
This now works fine. Random # seeds are now taken from /dev/urandom inside of BeAGLE automatically. If that is unavailable a more complicated calculation is done which includes the time AND the process id. There is no longer any problem with identical seeds on parallel farm jobs occurring at the same time.
THE REST OF THIS SECTION IS OBSOLETE
If using the standard BeAGLE random number seeding, however, many of the seeds can be identical if the jobs start at the same second. An example is given below. Running this command on the output log files:
grep -i "SEED = " eAu_*.log
displays the random number seeds:
eAu_0.log: SEED = 2411
eAu_1.log: SEED = 2421
eAu_2.log: SEED = 2296
eAu_3.log: SEED = 2296
eAu_4.log: SEED = 2421
eAu_5.log: SEED = 2136
eAu_6.log: SEED = 2321
eAu_7.log: SEED = 2136
eAu_8.log: SEED = 2391
eAu_9.log: SEED = 2391
As can be seen, several of the jobs have the same seed, and therefore the output of the simulation will be identical. A simple workaround is to use the "/dev/urandom" pseudo-random number generator in a shell script to set the seed directly in the BeAGLE input file. This is done in the following shell script, which is the executable in the condor submission file.
#!/usr/bin/bash
if [ -z "$1" ] then echo "No job number set." echo "Please run as ./run_eAu.sh jobnumber" echo "Exiting..." exit 1 fi echo "-----------------------------------" echo "Running BeAGLE Simulation for eAu Collider!!!" echo "-----------------------------------" echo "Performing Job$1"
echo "..."
echo ""
VAR1=$1 PythiaCard="s/eAu.txt/eAu_${VAR1}.txt/g"
BeAGLECard="s/S3ALL002/InpAu_${VAR1}/g" sed "${PythiaCard}" S3ALL002 > InpAu_$1 sed "${BeAGLECard}" ./inputFiles/eAu.inp > ./inputFiles/eAu_$1.inp SEED=od -vAn -N2 -tu2 < /dev/urandom echo "The Random SEED is${SEED// /}"
echo ""
sed -i "s/1234567/${SEED// /}/g" InpAu_$1
echo "Running BeAGLE..."
$BEAGLESYS/BeAGLE < inputFiles/eAu_$1.inp > logs/eAu_$1.log echo "Completed Simulation!!!" echo "" echo "Making Output ROOT File..." root -l -b -q "make_tree.C(\"eAu_$1.txt\")"
echo "Done!!!"
echo ""
echo "Cleaning up..."
rm -vf ./outForPythiaMode/eAu_$1.txt rm -vf InpAu_$1
rm -vf inputFiles/eAu_\$1.inp
echo "Done!!!"
echo ""
This script makes use of this line in the Pythia input card that is called by BeAGLE:
FSEED 1234567
Using the above script, the seeds for the simultaneously run jobs should differ. An example of the set seeds for 10 jobs is shown below.
eAu_0.log: SEED = 14473
eAu_1.log: SEED = 30550
eAu_2.log: SEED = 55545
eAu_3.log: SEED = 4022
eAu_4.log: SEED = 28238
eAu_5.log: SEED = 36662
eAu_6.log: SEED = 12502
eAu_7.log: SEED = 57292
eAu_8.log: SEED = 29721
eAu_9.log: SEED = 37451
As can be seen, all the random seeds are different. A larger test was performed where 100 jobs were submitted simultaneously, each job simulating 100k events (10 million events in total). The jobs were all found to have different seeds, and all the jobs completed within 5 hours of submission.
| 2022-11-29T10:43:15 |
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https://www.zbmath.org/authors/?q=ai%3Asulem.catherine
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## Sulem, Catherine
Compute Distance To:
Author ID: sulem.catherine Published as: Sulem, Catherine; Sulem, C. Homepage: https://www.math.toronto.edu/cms/people/faculty/sulem-catherine/ External Links: MGP · Wikidata · dblp · GND · IdRef · theses.fr
Documents Indexed: 76 Publications since 1977, including 1 Book 7 Contributions as Editor Co-Authors: 53 Co-Authors with 79 Joint Publications 2,003 Co-Co-Authors
all top 5
### Co-Authors
2 single-authored 28 Sulem, Pierre-Louis 19 Craig, Walter 13 Guyenne, Philippe 7 Perry, Peter A. 6 Bardos, Claude Williams 6 Liu, Jiaqi 6 Papanicolaou, George C. 5 Pelinovsky, Dmitry Efimovich 4 LeMesurier, Brenton J. 4 Passot, Thierry 4 Simpson, Gideon 3 Buslaev, Vladimir Savel’evich 3 Colliander, James E. 3 Golse, François 3 Liu, Xiao 3 Nicholls, David P. 2 Coron, François 2 Frisch, Uriel 2 Landman, Michael J. 2 Meneguzzi, Maurice 2 Saut, Jean-Claude 2 Thual, Olivier 1 Balabane, Mikhael 1 Brandenberger, Robert H. 1 Cher, Yuri 1 Czubak, Magdalena 1 de Bouard, Anne 1 Díaz-Espinosa, Oliver 1 Fokas, Athanassios S. 1 Fournier, Jean-Daniel 1 Frisch, Helene 1 Frisch, Ulem 1 Gazeau, Maxime 1 Greiner, Peter C. 1 Hammack, Joseph L. 1 Henderson, Diane M. 1 Ivrii, Victor Ja. 1 Kuksin, Sergeĭ B. 1 Lacave, Christophe 1 Lannes, David 1 Laveder, Dimitri 1 Lochak, Pierre 1 Miller, Peter D. 1 Oh, Tadahiro 1 Patera, Anthony T. 1 Perthame, Benoît 1 Schanz, Ulrich 1 Seco, Luis Angel 1 Sidi, Avram 1 Sigal, Israel Michael 1 Sulem, Pl. 1 Wang, Xueping 1 Wayne, Clarence Eugene
all top 5
### Serials
9 Physica D 5 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 4 Communications in Mathematical Physics 4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 Journal of Fluid Mechanics 3 Fields Institute Communications 2 Communications on Pure and Applied Mathematics 2 Journal of Computational Physics 2 Nonlinearity 2 Quarterly of Applied Mathematics 2 Transactions of the American Mathematical Society 2 Communications in Partial Differential Equations 2 SIAM Journal on Mathematical Analysis 2 Journal of Hyperbolic Differential Equations 2 CRM Proceedings & Lecture Notes 2 Water Waves 1 Archive for Rational Mechanics and Analysis 1 Inverse Problems 1 Journal of Mathematical Physics 1 Wave Motion 1 Canadian Journal of Mathematics 1 Mathematics and Computers in Simulation 1 Acta Applicandae Mathematicae 1 Asymptotic Analysis 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Journal de Mécanique Théorique et Appliquée 1 Notices of the American Mathematical Society 1 Journal of Nonlinear Science 1 Physics of Fluids 1 Mathematical Research Letters 1 Discrete and Continuous Dynamical Systems 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 European Journal of Mechanics. B. Fluids 1 SIAM Journal on Applied Dynamical Systems 1 Communications in Mathematical Sciences 1 Journal de Mécanique 1 Applied Mathematical Sciences 1 Lecture Notes in Physics 1 Analysis & PDE 1 Kyoto Journal of Mathematics 1 Nonlinear Analysis. Theory, Methods & Applications 1 Bollettino dell’Unione Matematica Italiana
all top 5
### Fields
66 Partial differential equations (35-XX) 42 Fluid mechanics (76-XX) 25 Dynamical systems and ergodic theory (37-XX) 8 Numerical analysis (65-XX) 7 General and overarching topics; collections (00-XX) 7 Statistical mechanics, structure of matter (82-XX) 4 Mechanics of particles and systems (70-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Quantum theory (81-XX) 2 History and biography (01-XX) 2 Geophysics (86-XX) 1 Ordinary differential equations (34-XX) 1 Integral equations (45-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX) 1 Relativity and gravitational theory (83-XX)
### Citations contained in zbMATH Open
67 Publications have been cited 2,053 times in 1,642 Documents Cited by Year
The nonlinear Schrödinger equation. Self-focusing and wave collapse. Zbl 0928.35157
Sulem, Catherine; Sulem, Pierre-Louis
1999
Numerical simulation of gravity waves. Zbl 0778.76072
Craig, W.; Sulem, C.
1993
The focusing nonlinear Schrödinger equation: Effect of the coupling to a low frequency field. Zbl 0867.35094
Sulem, C.; Sulem, P. L.
1997
On asymptotic stability of solitary waves for nonlinear Schrödinger equations. Zbl 1028.35139
2003
On the continuous limit for a system of classical spins. Zbl 0614.35087
Sulem, P. L.; Sulem, C.; Bardos, C.
1986
A classification of well-posed kinetic layer problems. Zbl 0632.76088
Coron, François; Golse, François; Sulem, Catherine
1988
Nonlinear modulation of gravity waves: A region approach. Zbl 0742.76012
Craig, W.; Sulem, C.; Sulem, P. L.
1992
Tracing complex singularities with spectral methods. Zbl 0519.76002
Sulem, Catherine; Sulem, Pierre-Louis; Frisch, Helene
1983
The modulational regime of three-dimensional water waves and the Davey-Stewartson system. Zbl 0892.76008
Craig, Walter; Schanz, Ulrich; Sulem, Catherine
1997
Solitary water wave interactions. Zbl 1185.76463
Craig, W.; Guyenne, P.; Hammack, J.; Henderson, D.; Sulem, C.
2006
On a boundary layer problem for the nonlinear Boltzmann equation. Zbl 0668.76089
Golse, Francois; Perthame, Benoit; Sulem, Catherine
1988
Quelques résultats de régularité pour les équations de la turbulence de Langmuir. Zbl 0431.35077
Sulem, Catherine; Sulem, Pierre Louis
1979
Finite time analyticity for the two and three dimensional Kelvin- Helmholtz instability. Zbl 0476.76032
Sulem, C.; Sulem, P. L.; Bardos, C.; Frisch, U.
1981
Longtime dynamics of a conductive fluid in the presence of a strong magnetic field. Zbl 0696.35134
Bardos, C.; Sulem, C.; Sulem, P. L.
1988
Hamiltonian long-wave expansions for water waves over a rough bottom. Zbl 1145.76325
Craig, Walter; Guyenne, Philippe; Nicholls, David P.; Sulem, Catherine
2005
Interaction of lumps with a line soliton for the DSII equation. Zbl 0977.35132
Fokas, A. S.; Pelinovsky, D. E.; Sulem, C.
2001
Numerical simulation of singular solutions to the two-dimensional cubic Schrödinger equation. Zbl 0543.65081
Sulem, P. L.; Sulem, C.; Patera, A.
1984
The focusing singularity of the nonlinear Schrödinger equation. Zbl 0659.35020
LeMesurier, B.; Papanicolaou, G.; Sulem, C.; Sulem, P.-L.
1987
Local structure of the self-focusing singularity of the nonlinear Schrödinger equation. Zbl 0694.35206
LeMesurier, B. J.; Papanicolaou, G. C.; Sulem, C.; Sulem, P. L.
1988
Focusing and multi-focusing solutions of the nonlinear Schrödinger equation. Zbl 0694.35196
LeMesurier, B. J.; Papanicolaou, G.; Sulem, C.; Sulem, P. L.
1988
The focusing singularity of the Davey-Stewartson equations for gravity- capillary surface waves. Zbl 0815.35104
Papanicolaou, G. C.; Sulem, C.; Sulem, P. L.; Wang, X. P.
1994
Global existence for the derivative nonlinear Schrödinger equation by the method of inverse scattering. Zbl 1358.35173
Liu, Jiaqi; Perry, Peter A.; Sulem, Catherine
2016
Long-time behavior of solutions to the derivative nonlinear Schrödinger equation for soliton-free initial data. (Comportement aux temps longs des solutions de l’équation de Schrödinger nonlinéraire avec dérivée en l’absence de solitons.) Zbl 1382.35271
Liu, Jiaqi; Perry, Peter A.; Sulem, Catherine
2018
Stability of solitary waves for a generalized derivative nonlinear Schrödinger equation. Zbl 1271.35004
Liu, Xiao; Simpson, Gideon; Sulem, Catherine
2013
On the one-dimensional cubic nonlinear Schrödinger equation below $$L^{2}$$. Zbl 1258.35184
2012
Stability of isotropic singularities for the nonlinear Schrödinger equation. Zbl 0728.35116
Landman, M. J.; Papanicolaou, G. C.; Sulem, C.; Sulem, P. L.; Wang, X. P.
1991
Soliton resolution for the derivative nonlinear Schrödinger equation. Zbl 1408.35175
Jenkins, Robert; Liu, Jiaqi; Perry, Peter; Sulem, Catherine
2018
Water waves over a random bottom. Zbl 1183.76629
Craig, W.; Guyenne, P.; Sulem, C.
2009
The surface signature of internal waves. Zbl 1275.76059
Craig, W.; Guyenne, P.; Sulem, C.
2012
Three-dimensional numerical simulation of convection in low-Prandtl- number fluids. Zbl 0633.76049
Meneguzzi, Maurice; Sulem, C.; Sulem, P. L.; Thual, O.
1987
A Hamiltonian approach to nonlinear modulation of surface water waves. Zbl 1231.76028
Craig, Walter; Guyenne, Philippe; Sulem, Catherine
2010
Ground state mass concentration in the $$L^2$$-critical nonlinear Schrödinger equation below $$H^1$$. Zbl 1084.35088
Colliander, J.; Raynor, S.; Sulem, C.; Wright, J. D.
2005
Long wave expansions for water waves over random topography. Zbl 1228.76029
de Bouard, Anne; Craig, Walter; Díaz-Espinosa, Oliver; Guyenne, Philippe; Sulem, Catherine
2008
On the long time behavior of a generalized KdV equation. Zbl 0625.35072
Sidi, A.; Sulem, C.; Sulem, P. L.
1986
Mapping properties of normal forms transformations for water waves. Zbl 1382.37066
Craig, Walter; Sulem, Catherine
2016
Hamiltonian higher-order nonlinear Schrödinger equations for broader-banded waves on deep water. Zbl 1258.76035
Craig, Walter; Guyenne, Philippe; Sulem, Catherine
2012
Global well-posedness for the derivative non-linear Schrödinger equation. Zbl 1412.35309
Jenkins, Robert; Liu, Jiaqi; Perry, Peter A.; Sulem, Catherine
2018
Linear versus nonlinear dissipation for critical NLS equation. Zbl 1070.35091
Passot, T.; Sulem, C.; Sulem, P. L.
2005
Finite time analyticity for the two- and three-dimensional Rayleigh- Taylor instability. Zbl 0517.76051
Sulem, C.; Sulem, P. L.
1985
Eigenfunctions and eigenvalues for a scalar Riemann-Hilbert problem associated to inverse scattering. Zbl 0964.37044
Pelinovsky, Dmitry E.; Sulem, Catherine
2000
Local structure of singular profiles for a derivative nonlinear Schrödinger equation. Zbl 1434.35177
Cher, Yuri; Simpson, Gideon; Sulem, Catherine
2017
Normal form transformations for capillary-gravity water waves. Zbl 1331.35274
Craig, Walter; Sulem, Catherine
2015
Generation of acoustic fronts by focusing wave packets. Zbl 0902.76086
Passot, T.; Sulem, C.; Sulem, P. L.
1996
Bifurcations of new eigenvalues for the Benjamin-Ono equation. Zbl 0932.35183
Pelinovsky, Dmitry E.; Sulem, Catherine
1998
Water waves over a rough bottom in the shallow water regime. Zbl 1329.76069
Craig, Walter; Lannes, David; Sulem, Catherine
2012
The derivative nonlinear Schrödinger equation: global well-posedness and soliton resolution. Zbl 1434.35180
Jenkins, Robert; Liu, Jiaqi; Perry, Peter; Sulem, Catherine
2020
The well-posedness of two-dimensional ideal flow. Zbl 0561.76032
Sulem, C.; Sulem, Pl.
1983
Bloch theory and spectral gaps for linearized water waves. Zbl 1401.76035
Craig, Walter; Gazeau, Maxime; Lacave, Christophe; Sulem, Catherine
2018
Spectral decomposition for the Dirac system associated to the DSII equation. Zbl 0969.35118
Pelinovsky, Dmitry E.; Sulem, Catherine
2000
Global existence for the derivative nonlinear Schrödinger equation with arbitrary spectral singularities. Zbl 1451.35186
Jenkins, Robert; Liu, Jiaqi; Perry, Peter; Sulem, Catherine
2020
Internal waves coupled to surface gravity waves in three dimensions. Zbl 1327.76043
Craig, Walter; Guyenne, Philippe; Sulem, Catherine
2015
Focusing nonlinear Schrödinger equation and wave-packet collapse. Zbl 0886.35140
Sulem, Catherine; Sulem, Pierre-Louis
1997
Resonant tunneling of fast solitons through large potential barriers. Zbl 1247.35152
Salem, Walid K. Abou; Sulem, Catherine
2011
Numerical simulations of the energy-supercritical nonlinear Schrödinger equation. Zbl 1403.37082
Colliander, J.; Simpson, G.; Sulem, C.
2010
Focusing singularity in a derivative nonlinear Schrödinger equation. Zbl 1434.35183
Liu, Xiao; Simpson, Gideon; Sulem, Catherine
2013
Quelques résultats de régularité pour les équations de la magnetohydrodynamique. Zbl 0355.35073
Sulem, Catherine
1977
Asymptotic stability of solitary waves for nonlinear Schrödinger equations. Zbl 1017.35104
2002
Stochastic acceleration of solitons for the nonlinear Schrödinger equation. Zbl 1183.35254
Salem, Walid K. Abou; Sulem, Catherine
2009
Time-dependent Rayleigh-Benard convection in low Prandtl number fluids. Zbl 0588.76077
Meneguzzi, Maurice; Sulem, C.; Sulem, P. L.; Thual, O.
1985
Lower bound for the rate of blow-up of singular solutions of the Zakharov system in $$\mathbb R^{3}$$. Zbl 1277.35315
Colliander, James; Czubak, Magdalena; Sulem, Catherine
2013
Singular solutions of the cubic Schrödinger equation. Zbl 0712.35091
Landman, M. J.; LeMesurier, B. J.; Papanicolaou, G. C.; Sulem, C.; Sulem, P. L.
1989
Numerical simulation of resonant tunneling of fast solitons for the nonlinear Schrödinger equation. Zbl 1211.35253
Salem, Walid K. Abou; Liu, Xiao; Sulem, Catherine
2011
The water-wave problem and its long-wave and modulational limits. Zbl 0968.76009
Craig, Walter; Sulem, Catherine
2000
Remarques sur un modèle unidimensionnel pour la turbulence magnetohydrodynamique. Zbl 0409.76047
Sulem, Catherine; Fournier, Jean-Daniel; Frisch, Uriel; Sulem, Pierre- Louis
1979
Hamiltonian partial differential equations and applications. Selected papers based on the presentations at the conference on Hamiltonian PDEs: analysis, computations and applications, Toronto, Canada, January 10–12, 2014. Zbl 1333.35002
2015
Linear adiabatic dynamics generated by operators with continuous spectrum. I. Zbl 1152.35336
2008
Embedded solitons of the DSII equation. Zbl 0983.35134
Pelinovsky, Dmitri E.; Sulem, Catherine
2001
The derivative nonlinear Schrödinger equation: global well-posedness and soliton resolution. Zbl 1434.35180
Jenkins, Robert; Liu, Jiaqi; Perry, Peter; Sulem, Catherine
2020
Global existence for the derivative nonlinear Schrödinger equation with arbitrary spectral singularities. Zbl 1451.35186
Jenkins, Robert; Liu, Jiaqi; Perry, Peter; Sulem, Catherine
2020
Long-time behavior of solutions to the derivative nonlinear Schrödinger equation for soliton-free initial data. (Comportement aux temps longs des solutions de l’équation de Schrödinger nonlinéraire avec dérivée en l’absence de solitons.) Zbl 1382.35271
Liu, Jiaqi; Perry, Peter A.; Sulem, Catherine
2018
Soliton resolution for the derivative nonlinear Schrödinger equation. Zbl 1408.35175
Jenkins, Robert; Liu, Jiaqi; Perry, Peter; Sulem, Catherine
2018
Global well-posedness for the derivative non-linear Schrödinger equation. Zbl 1412.35309
Jenkins, Robert; Liu, Jiaqi; Perry, Peter A.; Sulem, Catherine
2018
Bloch theory and spectral gaps for linearized water waves. Zbl 1401.76035
Craig, Walter; Gazeau, Maxime; Lacave, Christophe; Sulem, Catherine
2018
Local structure of singular profiles for a derivative nonlinear Schrödinger equation. Zbl 1434.35177
Cher, Yuri; Simpson, Gideon; Sulem, Catherine
2017
Global existence for the derivative nonlinear Schrödinger equation by the method of inverse scattering. Zbl 1358.35173
Liu, Jiaqi; Perry, Peter A.; Sulem, Catherine
2016
Mapping properties of normal forms transformations for water waves. Zbl 1382.37066
Craig, Walter; Sulem, Catherine
2016
Normal form transformations for capillary-gravity water waves. Zbl 1331.35274
Craig, Walter; Sulem, Catherine
2015
Internal waves coupled to surface gravity waves in three dimensions. Zbl 1327.76043
Craig, Walter; Guyenne, Philippe; Sulem, Catherine
2015
Hamiltonian partial differential equations and applications. Selected papers based on the presentations at the conference on Hamiltonian PDEs: analysis, computations and applications, Toronto, Canada, January 10–12, 2014. Zbl 1333.35002
2015
Stability of solitary waves for a generalized derivative nonlinear Schrödinger equation. Zbl 1271.35004
Liu, Xiao; Simpson, Gideon; Sulem, Catherine
2013
Focusing singularity in a derivative nonlinear Schrödinger equation. Zbl 1434.35183
Liu, Xiao; Simpson, Gideon; Sulem, Catherine
2013
Lower bound for the rate of blow-up of singular solutions of the Zakharov system in $$\mathbb R^{3}$$. Zbl 1277.35315
Colliander, James; Czubak, Magdalena; Sulem, Catherine
2013
On the one-dimensional cubic nonlinear Schrödinger equation below $$L^{2}$$. Zbl 1258.35184
2012
The surface signature of internal waves. Zbl 1275.76059
Craig, W.; Guyenne, P.; Sulem, C.
2012
Hamiltonian higher-order nonlinear Schrödinger equations for broader-banded waves on deep water. Zbl 1258.76035
Craig, Walter; Guyenne, Philippe; Sulem, Catherine
2012
Water waves over a rough bottom in the shallow water regime. Zbl 1329.76069
Craig, Walter; Lannes, David; Sulem, Catherine
2012
Resonant tunneling of fast solitons through large potential barriers. Zbl 1247.35152
Salem, Walid K. Abou; Sulem, Catherine
2011
Numerical simulation of resonant tunneling of fast solitons for the nonlinear Schrödinger equation. Zbl 1211.35253
Salem, Walid K. Abou; Liu, Xiao; Sulem, Catherine
2011
A Hamiltonian approach to nonlinear modulation of surface water waves. Zbl 1231.76028
Craig, Walter; Guyenne, Philippe; Sulem, Catherine
2010
Numerical simulations of the energy-supercritical nonlinear Schrödinger equation. Zbl 1403.37082
Colliander, J.; Simpson, G.; Sulem, C.
2010
Water waves over a random bottom. Zbl 1183.76629
Craig, W.; Guyenne, P.; Sulem, C.
2009
Stochastic acceleration of solitons for the nonlinear Schrödinger equation. Zbl 1183.35254
Salem, Walid K. Abou; Sulem, Catherine
2009
Long wave expansions for water waves over random topography. Zbl 1228.76029
de Bouard, Anne; Craig, Walter; Díaz-Espinosa, Oliver; Guyenne, Philippe; Sulem, Catherine
2008
Linear adiabatic dynamics generated by operators with continuous spectrum. I. Zbl 1152.35336
2008
Solitary water wave interactions. Zbl 1185.76463
Craig, W.; Guyenne, P.; Hammack, J.; Henderson, D.; Sulem, C.
2006
Hamiltonian long-wave expansions for water waves over a rough bottom. Zbl 1145.76325
Craig, Walter; Guyenne, Philippe; Nicholls, David P.; Sulem, Catherine
2005
Ground state mass concentration in the $$L^2$$-critical nonlinear Schrödinger equation below $$H^1$$. Zbl 1084.35088
Colliander, J.; Raynor, S.; Sulem, C.; Wright, J. D.
2005
Linear versus nonlinear dissipation for critical NLS equation. Zbl 1070.35091
Passot, T.; Sulem, C.; Sulem, P. L.
2005
On asymptotic stability of solitary waves for nonlinear Schrödinger equations. Zbl 1028.35139
2003
Asymptotic stability of solitary waves for nonlinear Schrödinger equations. Zbl 1017.35104
2002
Interaction of lumps with a line soliton for the DSII equation. Zbl 0977.35132
Fokas, A. S.; Pelinovsky, D. E.; Sulem, C.
2001
Embedded solitons of the DSII equation. Zbl 0983.35134
Pelinovsky, Dmitri E.; Sulem, Catherine
2001
Eigenfunctions and eigenvalues for a scalar Riemann-Hilbert problem associated to inverse scattering. Zbl 0964.37044
Pelinovsky, Dmitry E.; Sulem, Catherine
2000
Spectral decomposition for the Dirac system associated to the DSII equation. Zbl 0969.35118
Pelinovsky, Dmitry E.; Sulem, Catherine
2000
The water-wave problem and its long-wave and modulational limits. Zbl 0968.76009
Craig, Walter; Sulem, Catherine
2000
The nonlinear Schrödinger equation. Self-focusing and wave collapse. Zbl 0928.35157
Sulem, Catherine; Sulem, Pierre-Louis
1999
Bifurcations of new eigenvalues for the Benjamin-Ono equation. Zbl 0932.35183
Pelinovsky, Dmitry E.; Sulem, Catherine
1998
The focusing nonlinear Schrödinger equation: Effect of the coupling to a low frequency field. Zbl 0867.35094
Sulem, C.; Sulem, P. L.
1997
The modulational regime of three-dimensional water waves and the Davey-Stewartson system. Zbl 0892.76008
Craig, Walter; Schanz, Ulrich; Sulem, Catherine
1997
Focusing nonlinear Schrödinger equation and wave-packet collapse. Zbl 0886.35140
Sulem, Catherine; Sulem, Pierre-Louis
1997
Generation of acoustic fronts by focusing wave packets. Zbl 0902.76086
Passot, T.; Sulem, C.; Sulem, P. L.
1996
The focusing singularity of the Davey-Stewartson equations for gravity- capillary surface waves. Zbl 0815.35104
Papanicolaou, G. C.; Sulem, C.; Sulem, P. L.; Wang, X. P.
1994
Numerical simulation of gravity waves. Zbl 0778.76072
Craig, W.; Sulem, C.
1993
Nonlinear modulation of gravity waves: A region approach. Zbl 0742.76012
Craig, W.; Sulem, C.; Sulem, P. L.
1992
Stability of isotropic singularities for the nonlinear Schrödinger equation. Zbl 0728.35116
Landman, M. J.; Papanicolaou, G. C.; Sulem, C.; Sulem, P. L.; Wang, X. P.
1991
Singular solutions of the cubic Schrödinger equation. Zbl 0712.35091
Landman, M. J.; LeMesurier, B. J.; Papanicolaou, G. C.; Sulem, C.; Sulem, P. L.
1989
A classification of well-posed kinetic layer problems. Zbl 0632.76088
Coron, François; Golse, François; Sulem, Catherine
1988
On a boundary layer problem for the nonlinear Boltzmann equation. Zbl 0668.76089
Golse, Francois; Perthame, Benoit; Sulem, Catherine
1988
Longtime dynamics of a conductive fluid in the presence of a strong magnetic field. Zbl 0696.35134
Bardos, C.; Sulem, C.; Sulem, P. L.
1988
Local structure of the self-focusing singularity of the nonlinear Schrödinger equation. Zbl 0694.35206
LeMesurier, B. J.; Papanicolaou, G. C.; Sulem, C.; Sulem, P. L.
1988
Focusing and multi-focusing solutions of the nonlinear Schrödinger equation. Zbl 0694.35196
LeMesurier, B. J.; Papanicolaou, G.; Sulem, C.; Sulem, P. L.
1988
The focusing singularity of the nonlinear Schrödinger equation. Zbl 0659.35020
LeMesurier, B.; Papanicolaou, G.; Sulem, C.; Sulem, P.-L.
1987
Three-dimensional numerical simulation of convection in low-Prandtl- number fluids. Zbl 0633.76049
Meneguzzi, Maurice; Sulem, C.; Sulem, P. L.; Thual, O.
1987
On the continuous limit for a system of classical spins. Zbl 0614.35087
Sulem, P. L.; Sulem, C.; Bardos, C.
1986
On the long time behavior of a generalized KdV equation. Zbl 0625.35072
Sidi, A.; Sulem, C.; Sulem, P. L.
1986
Finite time analyticity for the two- and three-dimensional Rayleigh- Taylor instability. Zbl 0517.76051
Sulem, C.; Sulem, P. L.
1985
Time-dependent Rayleigh-Benard convection in low Prandtl number fluids. Zbl 0588.76077
Meneguzzi, Maurice; Sulem, C.; Sulem, P. L.; Thual, O.
1985
Numerical simulation of singular solutions to the two-dimensional cubic Schrödinger equation. Zbl 0543.65081
Sulem, P. L.; Sulem, C.; Patera, A.
1984
Tracing complex singularities with spectral methods. Zbl 0519.76002
Sulem, Catherine; Sulem, Pierre-Louis; Frisch, Helene
1983
The well-posedness of two-dimensional ideal flow. Zbl 0561.76032
Sulem, C.; Sulem, Pl.
1983
Finite time analyticity for the two and three dimensional Kelvin- Helmholtz instability. Zbl 0476.76032
Sulem, C.; Sulem, P. L.; Bardos, C.; Frisch, U.
1981
Quelques résultats de régularité pour les équations de la turbulence de Langmuir. Zbl 0431.35077
Sulem, Catherine; Sulem, Pierre Louis
1979
Remarques sur un modèle unidimensionnel pour la turbulence magnetohydrodynamique. Zbl 0409.76047
Sulem, Catherine; Fournier, Jean-Daniel; Frisch, Uriel; Sulem, Pierre- Louis
1979
Quelques résultats de régularité pour les équations de la magnetohydrodynamique. Zbl 0355.35073
Sulem, Catherine
1977
all top 5
### Cited by 1,852 Authors
34 Sulem, Catherine 30 Guo, Boling 23 Komech, Alexander Ilich 22 Nicholls, David P. 21 Merle, Frank 20 Kopylova, Elena A. 19 Craig, Walter 19 Kevrekidis, Panayotis G. 17 Ozawa, Tohru 17 Yang, Tong 16 Alazard, Thomas 16 Guyenne, Philippe 15 Cuccagna, Scipio 15 Pelinovsky, Dmitry Efimovich 15 Pérez-García, Víctor Manuel 14 Klein, Christian 14 Raphael, Pierre 13 Lannes, David 13 Oh, Tadahiro 13 Saut, Jean-Claude 12 Hoshino, Gaku 12 Sulem, Pierre-Louis 11 Carles, Rémi 11 Dutykh, Denys 11 Fibich, Gadi 11 Kalisch, Henrik 11 Martel, Yvan 11 Sparber, Christof 11 Takata, Shigeru 11 Zhang, Jian 10 Feng, Binhua 10 Ionescu, Alexandru D. 10 Sigal, Israel Michael 9 Biswas, Anjan 9 Groves, Mark D. 9 Konotop, Vladimir V. 9 Masmoudi, Nader 9 Sciacca, Vincenzo 9 Soffer, Avraham 9 Wang, Youde 9 Wang, Zhan 9 Weinstein, Michael I. 9 Yan, Zhenya 8 Belmonte-Beitia, Juan 8 Colin, Thierry 8 Deconinck, Bernard 8 Gargano, Francesco 8 Kenig, Carlos Eduardo 8 Malomed, Boris A. 8 Pusateri, Fabio 8 Roudenko, Svetlana 8 Schneider, Guido 8 Wu, Jiahong 8 Zhao, Huijiang 7 Berti, Massimiliano 7 Burq, Nicolas 7 Cho, Yonggeun 7 Fan, Engui 7 Frantzeskakis, Dimitri J. 7 Gan, Zaihui 7 Golse, François 7 Granero Belinchón, Rafael 7 He, Jingsong 7 Mitsotakis, Dimitrios E. 7 Nakanishi, Kenji 7 Ponce, Gustavo 7 Sammartino, Marco Maria Luigi 7 Simpson, Gideon 7 Sone, Yoshio 7 Stefanov, Atanas G. 7 Tataru, Daniel 7 Yang, Xiongfeng 7 Zhang, Jingjun 7 Zhu, Shihui 6 Aoki, Kazuo 6 Bardos, Claude Williams 6 Colliander, James E. 6 Debussche, Arnaud 6 Germain, Pierre 6 Gustafson, Stephen J. 6 Liu, Jiaqi 6 Lushnikov, Pavel Mikhaĭlovich 6 Mantzavinos, Dionyssios 6 Perry, Peter A. 6 Pu, Xueke 6 Rao, Jiguang 6 Shatah, Jalal 6 Torres, Pedro José 6 Tzvetkov, Nikolay 6 Wang, Yuzhao 6 Wilkening, Jon A. 6 Xu, Guixiang 5 Ablowitz, Mark Jay 5 Baldi, Pietro 5 Bao, Weizhu 5 Bejenaru, Ioan 5 Belić, Milivoj R. 5 Bernhoff, Niclas 5 Caflisch, Russel E. 5 Comech, Andrew ...and 1,752 more Authors
all top 5
### Cited in 260 Serials
91 Physica D 77 Journal of Differential Equations 57 Journal of Fluid Mechanics 55 Journal of Computational Physics 54 Communications in Mathematical Physics 40 Archive for Rational Mechanics and Analysis 40 Journal of Mathematical Analysis and Applications 39 Journal of Mathematical Physics 31 Physics Letters. A 30 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 30 SIAM Journal on Mathematical Analysis 28 Communications in Partial Differential Equations 26 Journal of Functional Analysis 24 European Journal of Mechanics. B. Fluids 22 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 22 Physics of Fluids 21 Applied Mathematics and Computation 21 Journal of Nonlinear Science 20 Communications on Pure and Applied Analysis 19 Wave Motion 18 Journal of Statistical Physics 18 Discrete and Continuous Dynamical Systems 18 Water Waves 17 Nonlinearity 17 Mathematics and Computers in Simulation 16 Communications on Pure and Applied Mathematics 16 Applied Numerical Mathematics 15 Chaos, Solitons and Fractals 15 Advances in Mathematics 15 Inventiones Mathematicae 15 Calculus of Variations and Partial Differential Equations 14 Transactions of the American Mathematical Society 14 Nonlinear Dynamics 14 Acta Mathematica Sinica. English Series 13 Computers & Mathematics with Applications 13 Quarterly of Applied Mathematics 12 Studies in Applied Mathematics 11 Applied Mathematics Letters 11 Journal of Scientific Computing 10 Science China. Mathematics 9 Applicable Analysis 9 Journal of Computational and Applied Mathematics 9 Journal de Mathématiques Pures et Appliquées. Neuvième Série 9 NoDEA. Nonlinear Differential Equations and Applications 9 Journal of Mathematical Fluid Mechanics 9 Communications in Nonlinear Science and Numerical Simulation 9 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 8 Theoretical and Mathematical Physics 8 Journal of Dynamics and Differential Equations 8 Journal of Evolution Equations 7 Journal of Engineering Mathematics 7 ZAMP. Zeitschrift für angewandte Mathematik und Physik 7 Mathematics of Computation 7 Nonlinear Analysis. Real World Applications 7 Analysis and Applications (Singapore) 7 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 6 Computer Physics Communications 6 Letters in Mathematical Physics 6 Reviews in Mathematical Physics 6 Duke Mathematical Journal 6 Numerical Methods for Partial Differential Equations 6 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 6 Numerical Algorithms 6 Abstract and Applied Analysis 6 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 6 Communications in Contemporary Mathematics 6 Annales Henri Poincaré 6 Journal of Nonlinear Mathematical Physics 6 Discrete and Continuous Dynamical Systems. Series S 6 Annals of PDE 6 Séminaire Laurent Schwartz. EDP et Applications 5 Computers and Fluids 5 Transport Theory and Statistical Physics 5 Physics of Fluids, A 5 Proceedings of the American Mathematical Society 5 Chinese Annals of Mathematics. Series B 5 Acta Applicandae Mathematicae 5 Journal of the American Mathematical Society 5 SIAM Journal on Applied Mathematics 5 Journal of Mathematical Sciences (New York) 5 Annals of Mathematics. Second Series 5 Boundary Value Problems 5 Frontiers of Mathematics in China 5 Nonlinear Analysis. Theory, Methods & Applications 4 Mathematical Methods in the Applied Sciences 4 Memoirs of the American Mathematical Society 4 Numerische Mathematik 4 SIAM Journal on Numerical Analysis 4 Acta Mathematicae Applicatae Sinica. English Series 4 Russian Journal of Mathematical Physics 4 St. Petersburg Mathematical Journal 4 Discrete and Continuous Dynamical Systems. Series B 4 Journal of Hyperbolic Differential Equations 4 Advances in Difference Equations 4 Evolution Equations and Control Theory 3 Modern Physics Letters B 3 Computer Methods in Applied Mechanics and Engineering 3 Journal d’Analyse Mathématique 3 Physica A 3 Rocky Mountain Journal of Mathematics ...and 160 more Serials
all top 5
### Cited in 42 Fields
1,321 Partial differential equations (35-XX) 600 Fluid mechanics (76-XX) 231 Dynamical systems and ergodic theory (37-XX) 222 Numerical analysis (65-XX) 138 Statistical mechanics, structure of matter (82-XX) 115 Quantum theory (81-XX) 86 Optics, electromagnetic theory (78-XX) 43 Geophysics (86-XX) 40 Ordinary differential equations (34-XX) 34 Global analysis, analysis on manifolds (58-XX) 29 Mechanics of deformable solids (74-XX) 28 Operator theory (47-XX) 25 Probability theory and stochastic processes (60-XX) 25 Mechanics of particles and systems (70-XX) 20 Harmonic analysis on Euclidean spaces (42-XX) 17 Functional analysis (46-XX) 15 Calculus of variations and optimal control; optimization (49-XX) 13 Differential geometry (53-XX) 12 Integral equations (45-XX) 12 Relativity and gravitational theory (83-XX) 11 Difference and functional equations (39-XX) 9 Approximations and expansions (41-XX) 9 Biology and other natural sciences (92-XX) 8 Systems theory; control (93-XX) 6 Real functions (26-XX) 6 Computer science (68-XX) 6 Classical thermodynamics, heat transfer (80-XX) 5 Astronomy and astrophysics (85-XX) 4 Special functions (33-XX) 3 General and overarching topics; collections (00-XX) 3 Measure and integration (28-XX) 3 Functions of a complex variable (30-XX) 3 Operations research, mathematical programming (90-XX) 2 Nonassociative rings and algebras (17-XX) 2 Potential theory (31-XX) 2 Integral transforms, operational calculus (44-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Information and communication theory, circuits (94-XX)
### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2022-05-24T19:09:30 |
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|
https://www.usgs.gov/media/images/another-look-margin-kahauale-a-2-flow-small-vegetat
|
Another look at the margin of the Kahauale‘a 2 flow. Small vegetat...
Detailed Description
Another look at the margin of the Kahauale‘a 2 flow. Small vegetation fires triggered by the active lava spread a short distance out from the flow margin.
Details
Image Dimensions: 4608 x 3456
Date Taken:
| 2019-12-09T13:07:26 |
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https://par.nsf.gov/biblio/10357941
|
Optical properties of elongated conducting grains
ABSTRACT Extremely elongated, conducting dust particles (also known as metallic ‘needles’ or ‘whiskers’) are seen in carbonaceous chondrites and in samples brought back from the Itokawa asteroid. Their formation in protostellar nebulae and subsequent injection into the interstellar medium have been demonstrated, both experimentally and theoretically. Metallic needles have been suggested to explain a wide variety of astrophysical phenomena, ranging from the mid-infrared interstellar extinction at $\sim \,$3–8$\, {\rm \mu m}$ to the thermalization of starlight to generate the cosmic microwave background. To validate (or invalidate) these suggestions, an accurate knowledge of the optics (e.g. the amplitude and the wavelength dependence of the absorption cross sections) of metallic needles is crucial. Here we calculate the absorption cross sections of iron needles of various aspect ratios over a wide wavelength range, by exploiting the discrete dipole approximation, the most powerful technique for rigorously calculating the optics of irregular or nonspherical grains. Our calculations support the earlier findings that the antenna theory and the Rayleigh approximation, which are often taken to approximate the optical properties of metallic needles, are indeed inapplicable.
Authors:
; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10357941
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
503
Issue:
3
Page Range or eLocation-ID:
4544 to 4550
ISSN:
0035-8711
| 2023-02-06T19:40:41 |
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https://cordis.europa.eu/project/id/221571/reporting
|
# Non perturbative effects in gauge and string theories
## Final Report Summary - NPEGST (Non perturbative effects in gauge and string theories)
Project context and objectives
The main objective of the current project was to investigate non-perturbative effects in Super-symmetric Yang-Mills theories from the purely field theoretical point of view as well as from the string theory perspective. In the framework of field theory we have intended also to extend the results concerning super-symmetric Yang-Mills theory on flat space-time to the cases of non-trivial gravitational background. On string theory side the main objective was to investigate stringy instanton effects, which besides purely theoretical significance also have phenomenological implications in all directions significant progress has been achieved during the realisation of the project. The results are presented in six scientific publications which we detail one by one.
1) A system of Bethe-Ansatz type equations, which specify a unique array of Young tableau responsible for the leading contribution to the Nekrasov partition function in the $\epsilon_2\rightarrow 0$ limit is derived. It is shown that the prepotential with generic $\epsilon_1$ is directly related to the (rescaled by $\epsilon_1$) number of total boxes of these Young tableau. Moreover, all the expectation values of the chiral fields $\langle tr \phi^J \rangle$ are simple symmetric functions of their column lengths. An entire function whose zeros are determined by the column lengths is introduced. It is shown that this function satisfies a functional equation, closely resembling Baxter's equation in 2d integratable models.
2) We revisit Kaluza-Klein compactification of 11-d supergravity on $S^7/Z_k$ using group theory techniques that may find application in other flux vacua with internal coset spaces. Among the SO(2) neutral states, we identify marginal deformations and fields that couple to the recently discussed world-sheet instanton of Type IIA on $CP^3. 3) We discuss a string model where a conformal four-dimensional N=2 gauge theory receives corrections to its gauge kinetic functions from "stringy" instantons. These contributions are explicitly evaluated by exploiting the localisation properties of the integral over the stringy instanton moduli space. The model we consider corresponds to a setup with D7/D3-branes in type I' theory compactified on T4/Z2 x T2, and possesses a perturbatively computable heterotic dual. 4) Based on prototypical example of Al.Zamolodchikov's recursion relations for the four point conformal block and using recently proposed Alday-Gaiotto-Tachikawa (AGT) conjecture, recursion relations are derived for the generalised prepotential of${\cal N}=2$SYM with$f=0,1,2,3,4\$ (anti) fundamental or an adjoint hypermultiplets. In all cases the large expectation value limit is derived explicitly. A precise relationship between generic 1-point conformal block on torus and specific 4-point conformal block on sphere is established.
5) We perform a study of the moduli space of framed torsion-free sheaves on Hirzebruch surfaces by using localisation techniques. We discuss some general properties of this moduli space by studying it in the framework of Huybrechts-Lehn theory of framed modules. We classify the fixed points under a toric action on the moduli space, and use this to compute the Poincare polynomial of the latter. This will imply that the moduli spaces we are considering are irreducible. We also consider fractional first Chern classes, which means that we are extending our computation to a stacky deformation of a Hirzebruch surface. From the physical viewpoint, our results provide the partition function of N=4 Vafa-Witten theory on total spaces of line bundles on P1.
6) We compute the partition functions of D(-1)D7 systems describing the multi-instanton dynamics of SO(N) gauge theories in eight dimensions. This is the simplest instance of the so-called exotic. In analogy with the Seiberg-Witten theory in 4 D space-time, the prepotential and correlators in the chiral ring are derived via localisation formulae.
| 2021-12-01T02:14:10 |
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|
https://www.usgs.gov/media/images/map-shows-lava-flows-erupted-during-1983-february-17-2003
|
# Map shows lava flows erupted during the 1983-February 17, 2003
## Detailed Description
Map shows lava flows erupted during the 1983-present activity of Puu Oo and Kupaianaha. The most recent--and ongoing--activity has produced the lender, dark red flow along western edge of flow field. This flow entered the sea late on Valentine's Day to form the Kohola ocean entry. Lava is actively widening the flow on February 17, and the western arm is nearing the Chain of Craters Road. Visitors now can drive to Holei Sea Arch, 1.1 km from the Kohola flow, and walk to see the new flow. The new flow is part of the Mother's Day flow, which began erupting on May 12, 2002.. Lava from the Mother's Day flow (broad red flow on west side of flow field) reached the sea at West Highcastle early on July 19, at Wilipea early on July 21, and at Highcastle on August 8. From near the southwest base of Puu Oo, the Mother's Day flow passes along the west side of the flow field and into the forest, where it started a large wildfire in May that continued into late July. By June 10, the Mother's Day flow had reached the base of Paliuli, the steep slope and cliff below Pulama pali and just above the coastal flat. At the base of Paliuli, the Mother's Day flow abruptly spread laterally in a series of small budding flows to cover an area nearly 2 km wide, gradually moving seaward until the West Highcastle and Wilipea lobes finally reached the ocean and started building benches. Activity at West Highcastle ended in early August, but entry began soon thereafter at Highcastle, eventually burying tiny kipuka of the Chain of Craters Road. The Wilipea entry died away slowly and had ended by mid-August. Highcastle and neighboring Highcastle Stairs entries ended on about August 23. For a time there were no active entries. Then Wilipea was reactivated on September 3 but stopped in December. West Highcastle likewise renewed its activity on September 16-17, died away during the night of September 18-19, and returned soon thereafter to continue to time of mapping. East arm of Mother's Day flow branched from Highcastle lobe in late October and sent three fingers into ocean at Highcastle on November 15, West Laeapuki on November 19, and Laeapuki on November 20. The Lae`apuki entries had stopped by November 29. If this sounds like a soap opera, the truth is even more confusing than the simplified version of activity given here.
## Details
Image Dimensions: 800 x 520
Date Taken:
Location Taken: US
| 2021-09-17T06:37:56 |
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|
https://par.nsf.gov/biblio/10187870-low-luminosity-type-ii-sn2016aqf-well-monitored-spectral-evolution-ni-fe-abundance-ratio
|
The low-luminosity Type II SN 2016aqf: a well-monitored spectral evolution of the Ni/Fe abundance ratio
ABSTRACT Low-luminosity Type II supernovae (LL SNe II) make up the low explosion energy end of core-collapse SNe, but their study and physical understanding remain limited. We present SN 2016aqf, an LL SN II with extensive spectral and photometric coverage. We measure a V-band peak magnitude of −14.58 mag, a plateau duration of ∼100 d, and an inferred 56Ni mass of 0.008 ± 0.002 M⊙. The peak bolometric luminosity, Lbol ≈ 1041.4 erg s−1, and its spectral evolution are typical of other SNe in the class. Using our late-time spectra, we measure the [O i] λλ6300, 6364 lines, which we compare against SN II spectral synthesis models to constrain the progenitor zero-age main-sequence mass. We find this to be 12 ± 3 M⊙. Our extensive late-time spectral coverage of the [Fe ii] λ7155 and [Ni ii] λ7378 lines permits a measurement of the Ni/Fe abundance ratio, a parameter sensitive to the inner progenitor structure and explosion mechanism dynamics. We measure a constant abundance ratio evolution of $0.081^{+0.009}_{-0.010}$ and argue that the best epochs to measure the ratio are at ∼200–300 d after explosion. We place this measurement in the context of a large sample of SNe II and compare against various physical, light-curve, and spectral parameters, in search of trends that might allow indirect ways of constraining more »
Authors:
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Award ID(s):
Publication Date:
NSF-PAR ID:
10187870
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
497
Issue:
1
Page Range or eLocation-ID:
361 to 377
ISSN:
0035-8711
2. ABSTRACT Photometric and spectroscopic data for two Low Luminosity Type IIP Supernovae (LL SNe IIP) 2020cxd and 2021aai are presented. SN 2020cxd was discovered 2 d after explosion at an absolute magnitude of Mr = −14.02 ± 0.21 mag, subsequently settling on a plateau which lasts for ∼120 d. Through the luminosity of the late light curve tail, we infer a synthesized 56Ni mass of (1.8 ± 0.5) × 10−3 M⊙. During the early evolutionary phases, optical spectra show a blue continuum ($T\, \gt$8000 K) with broad Balmer lines displaying a P Cygni profile, while at later phases, Ca ii, Fe ii, Sc ii, and Ba ii lines dominate the spectra. Hydrodynamical modelling of the observables yields $R\, \simeq$ 575 R⊙ for the progenitor star, with Mej = 7.5 M⊙ and $E\, \simeq$ 0.097 foe emitted during the explosion. This low-energy event originating from a low-mass progenitor star is compatible with both the explosion of a red supergiant (RSG) star and with an Electron Capture Supernova arising from a super asymptotic giant branch star. SN 2021aai reaches a maximum luminosity of Mr = −16.57 ± 0.23 mag (correcting for AV = 1.92 mag), at the end of its remarkably long plateau (∼140 d). The estimated 56Ni mass is (1.4 ± 0.5) × 10−2 M⊙. The expansion velocities are compatible with those of other LL SNe IIP (few 103 km s−1). The physicalmore »
3. ABSTRACT ASASSN-18am/SN 2018gk is a newly discovered member of the rare group of luminous, hydrogen-rich supernovae (SNe) with a peak absolute magnitude of MV ≈ −20 mag that is in between normal core-collapse SNe and superluminous SNe. These SNe show no prominent spectroscopic signatures of ejecta interacting with circumstellar material (CSM), and their powering mechanism is debated. ASASSN-18am declines extremely rapidly for a Type II SN, with a photospheric-phase decline rate of ∼6.0 mag (100 d)−1. Owing to the weakening of H i and the appearance of He i in its later phases, ASASSN-18am is spectroscopically a Type IIb SN with a partially stripped envelope. However, its photometric and spectroscopic evolution shows significant differences from typical SNe IIb. Using a radiative diffusion model, we find that the light curve requires a high synthesized 56Ni mass $M_{\rm Ni} \sim 0.4\, \rm {M_{\odot }}$ and ejecta with high kinetic energy Ekin = (7–10) × 1051 erg. Introducing a magnetar central engine still requires $M_{\rm Ni} \sim 0.3\, \rm {M_{\odot }}$ and Ekin = 3 × 1051 erg. The high 56Ni mass is consistent with strong iron-group nebular lines in its spectra, which are also similar to several SNe Ic-BL with high 56Ni yields. The earliest spectrum shows ‘flash ionization’ features, from which we estimatemore »
| 2022-10-04T17:46:17 |
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https://dlmf.nist.gov/25.19
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# §25.19 Tables
• Abramowitz and Stegun (1964) tabulates: $\zeta\left(n\right)$, $n=2,3,4,\dots$, 20D (p. 811); $\mathrm{Li}_{2}\left(1-x\right)$, $x=0(.01)0.5$, 9D (p. 1005); $f(\theta)$, $\theta=15^{\circ}(1^{\circ})30^{\circ}(2^{\circ})90^{\circ}(5^{\circ})180^{\circ}$, $f(\theta)+\theta\ln\theta$, $\theta=0(1^{\circ})15^{\circ}$, 6D (p. 1006). Here $f(\theta)$ denotes Clausen’s integral, given by the right-hand side of (25.12.9).
• Morris (1979) tabulates $\mathrm{Li}_{2}\left(x\right)$25.12(i)) for $\pm x=0.02(.02)1(.1)6$ to 30D.
• Cloutman (1989) tabulates $\Gamma\left(s+1\right)F_{s}(x)$, where $F_{s}(x)$ is the Fermi–Dirac integral (25.12.14), for $s=-\frac{1}{2},\frac{1}{2},\frac{3}{2},\frac{5}{2}$, $x=-5(.05)25$, to 12S.
• Fletcher et al. (1962, §22.1) lists many sources for earlier tables of $\zeta\left(s\right)$ for both real and complex $s$. §22.133 gives sources for numerical values of coefficients in the Riemann–Siegel formula, §22.15 describes tables of values of $\zeta\left(s,a\right)$, and §22.17 lists tables for some Dirichlet $L$-functions for real characters. For tables of dilogarithms, polylogarithms, and Clausen’s integral see §§22.84–22.858.
| 2018-04-24T17:58:31 |
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|
https://poritz.net/jonathan/share/CCL4COOERmay2019/index.html
|
Creative Commons Licensing — The Key Legal Technology Enabling OER
Jonathan A. Poritz
Eventually, I'll port this to HTML, but at the moment it is only available as PDF or, for those who want to remix, in the original LATEX source.
pdflatex CCL4COOERmay2019
| 2022-01-16T10:42:27 |
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|
https://par.nsf.gov/biblio/10358430
|
The Aligned Orbit of WASP-148b, the Only Known Hot Jupiter with a nearby Warm Jupiter Companion, from NEID and HIRES
Abstract We present spectroscopic measurements of the Rossiter–McLaughlin effect for WASP-148b, the only known hot Jupiter with a nearby warm-Jupiter companion, from the WIYN/NEID and Keck/HIRES instruments. This is one of the first scientific results reported from the newly commissioned NEID spectrograph, as well as the second obliquity constraint for a hot Jupiter system with a close-in companion, after WASP-47. WASP-148b is consistent with being in alignment with the sky-projected spin axis of the host star, with λ = − 8 .° 2 − 9 .° 7 + 8 .° 7 . The low obliquity observed in the WASP-148 system is consistent with the orderly-alignment configuration of most compact multi-planet systems around cool stars with obliquity constraints, including our solar system, and may point to an early history for these well-organized systems in which migration and accretion occurred in isolation, with relatively little disturbance. By contrast, previous results have indicated that high-mass and hot stars appear to more commonly host a wide range of misaligned planets: not only single hot Jupiters, but also compact systems with multiple super-Earths. We suggest that, to account for the high rate of spin–orbit misalignments in both compact multi-planet and isolated-hot-Jupiter systems orbiting high-mass and more »
Authors:
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Award ID(s):
Publication Date:
NSF-PAR ID:
10358430
Journal Name:
The Astrophysical Journal Letters
Volume:
926
Issue:
2
Page Range or eLocation-ID:
L8
ISSN:
2041-8205
National Science Foundation
##### More Like this
1. Abstract
The distribution of spin–orbit angles for systems with wide-separation, tidally detached exoplanets offers a unique constraint on the prevalence of dynamically violent planetary evolution histories. Tidally detached planets provide a relatively unbiased view of the primordial stellar obliquity distribution, as they cannot tidally realign within the system lifetime. We present the third result from our Stellar Obliquities in Long-period Exoplanet Systems (SOLES) survey: a measurement of the Rossiter–McLaughlin effect across two transits of the tidally detached warm Jupiter TOI-1478 b with the WIYN/NEID and Keck/HIRES spectrographs, revealing a sky-projected spin–orbit angle$λ=6.2−5.5+5.9°$. Combining this new measurement with the full set of archival obliquity measurements, including two previous constraints from the SOLES survey, we demonstrate that, in single-star systems, tidally detached warm Jupiters are preferentially more aligned than closer-orbiting hot Jupiters. This finding has two key implications: (1) planets in single-star systems tend to form within aligned protoplanetary disks, and (2) warm Jupiters form more quiescently than hot Jupiters, which, in single-star systems, are likely perturbed into a misaligned state through planet–planet interactions in the post-disk-dispersal phase. We also find that lower-mass Saturns span a wide range of spin–orbit angles, suggesting a prevalence of planet–planet scattering and/or secularmore »
2. Abstract
The obliquity of a star, or the angle between its spin axis and the average orbit normal of its companion planets, provides a unique constraint on that system’s evolutionary history. Unlike the solar system, where the Sun’s equator is nearly aligned with its companion planets, many hot-Jupiter systems have been discovered with large spin–orbit misalignments, hosting planets on polar or retrograde orbits. We demonstrate that, in contrast to stars harboring hot Jupiters on circular orbits, those with eccentric companions follow no population-wide obliquity trend with stellar temperature. This finding can be naturally explained through a combination of high-eccentricity migration and tidal damping. Furthermore, we show that the joint obliquity and eccentricity distributions observed today are consistent with the outcomes of high-eccentricity migration, with no strict requirement to invoke the other hot-Jupiter formation mechanisms of disk migration or in situ formation. At a population-wide level, high-eccentricity migration can consistently shape the dynamical evolution of hot-Jupiter systems.
3. Abstract
High-eccentricity migration is a likely formation mechanism for many observed hot Jupiters, particularly those with a large misalignment between the stellar spin axis and orbital angular momentum axis of the planet. In one version of high-eccentricity migration, an inclined stellar companion excites von Zeipel–Lidov–Kozai (ZLK) eccentricity oscillations of a cold Jupiter, and tidal dissipation causes the planet’s orbit to shrink and circularize. Throughout this process, the stellar spin can evolve chaotically, resulting in highly misaligned hot Jupiters (HJs). Previous population studies of this migration mechanism have assumed that the stellar spin is aligned with the planetary orbital angular momentum when the companion begins to induce ZLK oscillations. However, in the presence of a binary companion, the star’s obliquity may be significantly excited during the dissipation of its protoplanetary disk. We calculate the stellar obliquities produced in the protoplanetary disk phase and use these to perform an updated population synthesis of ZLK-driven high-eccentricity migration with an F-type host star. We find that the resulting obliquity distribution of HJ systems is predominantly retrograde with a broad peak near 90°. The distribution we obtain has intriguing similarities to the recently observed preponderance of perpendicular planets close to their host stars.
4. Abstract We confirm the planetary nature of two gas giants discovered by the Transiting Exoplanet Survey Satellite to transit M dwarfs. TOI-3714 ( V = 15.24, J = 11.74) is an M2 dwarf hosting a hot Jupiter ( M p = 0.70 ± 0.03 M J and R p = 1.01 ± 0.03 R J ) on an orbital period of 2.154849 ± 0.000001 days with a resolved white dwarf companion. TOI-3629 ( V = 14.63, J = 11.42) is an M1 dwarf hosting a hot Jupiter ( M p = 0.26 ± 0.02 M J and R p =0.74 ± 0.02 R J ) on an orbital period of 3.936551 − 0.000006 + 0.000005 days. We characterize each transiting companion using a combination of ground-based and space-based photometry, speckle imaging, and high-precision velocimetry from the Habitable-zone Planet Finder and the NEID spectrographs. With the discovery of these two systems, there are now nine M dwarfs known to host transiting hot Jupiters. Among this population, TOI-3714 b ( T eq = 750 ± 20 K and TSM = 98 ± 7) and TOI-3629 b ( T eq = 690 ± 20 K and TSM = 80 ± 9) are warmmore »
5. Abstract
The warm Neptune GJ 3470b transits a nearby (d= 29 pc) bright slowly rotating M1.5-dwarf star. Using spectroscopic observations during two transits with the newly commissioned NEID spectrometer on the WIYN 3.5 m Telescope at Kitt Peak Observatory, we model the classical Rossiter–McLaughlin effect, yielding a sky-projected obliquity of$λ=98−12+15◦$and a$vsini=0.85−0.33+0.27kms−1$. Leveraging information about the rotation period and size of the host star, our analysis yields a true obliquity of$ψ=95−8+9◦$, revealing that GJ 3470b is on a polar orbit. Using radial velocities from HIRES, HARPS, and the Habitable-zone Planet Finder, we show that the data are compatible with a long-term radial velocity (RV) slope of$γ̇=−0.0022±0.0011ms−1day−1$over a baseline of 12.9 yr. If the RV slope is due to acceleration from another companion in the system, we show that such a companion is capable of explaining the polar and mildly eccentric orbit of GJ 3470b using two different secular excitation models. The existence of an outer companion can be further constrained with additional RV observations, Gaia astrometry, and future high-contrast imaging observations. Lastly, we show that tidal heating frommore »
| 2023-02-08T11:56:09 |
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|
https://par.nsf.gov/biblio/10363195-investigation-geomagnetic-reference-models-based-iridium-circledr-constellation
|
Investigation of geomagnetic reference models based on the Iridium$$^{\circledR }$$ constellation
Abstract
The World Magnetic Model (WMM) is a geomagnetic main field model that is widely used for navigation by governments, industry and the general public. In recent years, the model has been derived using high accuracy magnetometer data from the Swarm mission. This study explores the possibility of developing future WMMs in the post-Swarm era using data from the Iridium satellite constellation. Iridium magnetometers are primarily used for attitude control, so they are not designed to produce the same level of accuracy as magnetic data from scientific missions. Iridium magnetometer errors range from 30 nT quantization to hundreds of nT errors due to spacecraft contamination and calibration uncertainty, whereas Swarm measurements are accurate to about 1 nT. The calibration uncertainty in the Iridium measurements is identified as a major error source, and a method is developed to calibrate the spacecraft measurements using data from a subset of the INTERMAGNET observatory network producing quasi-definitive data on a regular basis. After calibration, the Iridium data produced main field models with approximately 20 nT average error and 40 nT maximum error as compared to the CHAOS-7.2 model. For many scientific and precision navigation applications, highly accurate Swarm-like measurements are still necessary, however, the more »
Graphical Abstract
Authors:
; ; ; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10363195
Journal Name:
Earth, Planets and Space
Volume:
74
Issue:
1
ISSN:
1880-5981
Publisher:
3. Abstract The Electron Loss and Fields Investigation with a Spatio-Temporal Ambiguity-Resolving option (ELFIN-STAR, or heretoforth simply: ELFIN) mission comprises two identical 3-Unit (3U) CubeSats on a polar (∼93 ∘ inclination), nearly circular, low-Earth (∼450 km altitude) orbit. Launched on September 15, 2018, ELFIN is expected to have a >2.5 year lifetime. Its primary science objective is to resolve the mechanism of storm-time relativistic electron precipitation, for which electromagnetic ion cyclotron (EMIC) waves are a prime candidate. From its ionospheric vantage point, ELFIN uses its unique pitch-angle-resolving capability to determine whether measured relativistic electron pitch-angle and energy spectra within the loss cone bear the characteristic signatures of scattering by EMIC waves or whether such scattering may be due to other processes. Pairing identical ELFIN satellites with slowly-variable along-track separation allows disambiguation of spatial and temporal evolution of the precipitation over minutes-to-tens-of-minutes timescales, faster than the orbit period of a single low-altitude satellite (T orbit ∼ 90 min). Each satellite carries an energetic particle detector for electrons (EPDE) that measures 50 keV to 5 MeV electrons with $\Delta$ Δ E/E < 40% and a fluxgate magnetometer (FGM) on a ∼72 cm boom that measures magnetic field waves (e.g., EMIC waves) in the range from DC tomore »
| 2023-03-30T05:12:45 |
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|
http://legisquebec.gouv.qc.ca/en/showversion/cs/I-0.4?code=se:10_2&pointInTime=20210106
|
### I-0.4 - Mining Tax Act
10.2. The amount that an operator is required to include in computing its annual earnings from a mine for a particular fiscal year, under subparagraph e of subparagraph 1 of the fourth paragraph of section 8, in respect of class 1 property or class 2 property, is equal to the proportion of the amount determined under the second paragraph that the use of the property of the class that is reasonably attributable to the operation of the mine for the particular fiscal year is of the total use of that property in that fiscal year.
The amount referred to in the first paragraph is equal to the amount by which the aggregate of the amounts referred to in subparagraphs a to h of paragraph 2 of the definition of “undepreciated capital cost” in the first paragraph of section 9, in respect of the class, exceeds the aggregate of the amounts referred to in subparagraphs a to d of paragraph 1 of the definition of that expression.
1994, c. 47, s. 12; 2011, c. 6, s. 33; 2015, c. 21, s. 57.
10.2. The amount that an operator is required to include in computing its annual earnings from a mine for a particular fiscal year, under subparagraph e of subparagraph 1 of the fourth paragraph of section 8, in respect of class 1 property or class 2 property, is equal to the proportion of the amount determined under the second paragraph that the use of the property of the class that is reasonably attributable to the operation of the mine for the particular fiscal year is of the total use of that property in that fiscal year.
The amount referred to in the first paragraph is equal to the amount by which the aggregate of the amounts referred to in subparagraphs a to h of paragraph 2 of the definition of “undepreciated capital cost” in section 9, in respect of the class, exceeds the aggregate of the amounts referred to in subparagraphs a to d of paragraph 1 of the definition of that expression.
1994, c. 47, s. 12; 2011, c. 6, s. 33.
10.2. The amount that an operator is required to include in computing his annual profit for a particular fiscal year under subparagraph c of paragraph 1 of section 8 in respect of the first or second class, is the proportion of the amount determined under the second paragraph that the use of the property for the purposes of the operator’s mining operation for the particular fiscal year is of the total use of the property of the class in that fiscal year.
The amount referred to in the first paragraph is the amount by which the aggregate of the amounts referred to in subparagraphs a to h of paragraph 2 of the definition of “undepreciated capital cost” in section 9, in respect of the class, exceeds the aggregate of the amounts referred to in subparagraphs a to d of paragraph 1 of the definition of that expression.
1994, c. 47, s. 12.
| 2021-03-05T20:34:47 |
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|
https://pdglive.lbl.gov/Particle.action?init=0&node=M250&home=MXXX040
|
CHARMED, STRANGE MESONS($\mathit C$ = $\mathit S$ = $\pm1$)(including possibly non- ${\mathit {\mathit q}}$ ${\mathit {\overline{\mathit q}}}$ states) ${{\mathit D}_{{s}}^{+}}$ = ${\mathit {\mathit c}}$ ${\mathit {\overline{\mathit s}}}$, ${{\mathit D}_{{s}}^{-}}$ = ${\mathit {\overline{\mathit c}}}$ ${\mathit {\mathit s}}$, similarly for ${{\mathit D}_{{s}}^{*}}$'s INSPIRE search
#### ${{\boldsymbol X}_{{0}}{(2900)}}$
$I(J^P)$ = $?(0^{+})$
An exotic state with minimal quark content ${{\overline{\mathit c}}}{{\mathit d}}{{\overline{\mathit s}}}{{\mathit u}}$ . Observed by AAIJ 2020AI using full amplitude analysis of ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit D}^{+}}{{\mathit D}^{-}}{{\mathit K}^{+}}$ decays.
${{\mathit X}_{{0}}{(2900)}}$ MASS $2866 \pm7$ MeV
${{\mathit X}_{{0}}{(2900)}}$ WIDTH $57 \pm13$ MeV
$\Gamma_{1}$ ${{\mathit D}^{-}}{{\mathit K}^{+}}$ seen 711
FOOTNOTES
| 2022-01-18T19:21:46 |
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|
https://pos.sissa.it/320/024/
|
Volume 320 - 12th International Workshop on High-pT Physics in the RHIC/LHC Era (High-pT2017) - Direct photons, heavy flavor, quarkonia
Impact of the initial high gluon density on the prompt photon yield and $v2$ in heavy-ion collisions with magnetic fields
A. Ayala*, J. David Castaño-Yepes, C. Dominguez, L. Alberto Hernández, S. Hernández-Ortíz and M. Elena Tejeda-Yeomans
Full text: pdf
Pre-published on: June 20, 2019
Published on: October 09, 2019
Abstract
We compute prompt photon production from gluon fusion in the presence of a magnetic field in semi-central relativistic heavy-ion collisions. The main ingredient is the treatment of the high gluon density at early stages of the collision where intense magnetic fields are also present. The magnetic field opens new channels for photon production that are forbidden otherwise. The elliptic flow coefficient $v_2$ is also computed. The calculation takes into account the saturation scale and phenomenological factors. Overall, the treatment gives a good description of the excess photon yield and $v_2$, particularly at low values of photon transverse momentum.
DOI: https://doi.org/10.22323/1.320.0024
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
| 2022-11-28T01:52:27 |
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|
https://www.legisquebec.gouv.qc.ca/en/version/cr/S-3.1.01,%20r.%201?code=se:81&history=20221129
|
### S-3.1.01, r. 1 - Dam Safety Regulation
81. The first dam safety review for an existing dam must include the dam failure analysis, rough maps or characterization referred to in section 18, as required by the dam failure consequence category, unless the owner has provided the Minister with the document before the expiry of the time limit determined under section 78, 79 or 80 upon applying for a review of the classification assigned to the structure or for an authorization referred to in section 5 of the Act.
O.C. 300-2002, s. 81; O.C. 901-2014, s. 22.
81. The first dam safety review for an existing dam must include the dam failure analysis, rough maps or characterization referred to in section 18, as required by the dam failure consequence category determined under sections 17 and 18, unless the owner has provided the Minister with the document before the expiry of the time limit determined under section 78, 79 or 80 upon applying for a review of the classification assigned to the structure or for an authorization referred to in section 5 of the Act.
O.C. 300-2002, s. 81.
| 2023-02-07T02:48:48 |
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|
https://opus4.kobv.de/opus4-fau/frontdoor/index/index/docId/4039
|
## Optimization of Particle Synthesis - New Mathematical Concepts for a Controlled Production of Functional Nanoparticles
### Optimierung in der Partikelsynthese - Neue mathematische Konzepte für eine gezielte Herstellung funktionaler Nanopartikel
Please always quote using this URN: urn:nbn:de:bvb:29-opus4-40395
• Embedded in an interdisciplinary research project, the present work investigates the modeling, simulation, and optimization of specific processes for the production of functional nanoparticles. The examined material systems represent a selection of important core building blocks for future nanotechnologies. Depending on the application, a well-defined particle size distribution of the final product is required. The involved mechanisms (e.g. reaction, growth, ripening, and agglomeration) are described in the modeling by a hyperbolic partial integro-differential equation coupled to one or more ordinary differential equations. The successful validation against experimental data combined withEmbedded in an interdisciplinary research project, the present work investigates the modeling, simulation, and optimization of specific processes for the production of functional nanoparticles. The examined material systems represent a selection of important core building blocks for future nanotechnologies. Depending on the application, a well-defined particle size distribution of the final product is required. The involved mechanisms (e.g. reaction, growth, ripening, and agglomeration) are described in the modeling by a hyperbolic partial integro-differential equation coupled to one or more ordinary differential equations. The successful validation against experimental data combined with the techniques of optimal control theory thereby allow for a targeted manipulation of the underlying processes. The developed methods establish in many cases for the first time a systematic approach for the production of tailor-made nanoparticles.
Author: Michael Gröschel urn:nbn:de:bvb:29-opus4-40395 978-3-944057-12-5 FAU Studies Mathematics & Physics (2) FAU University Press Erlangen Günther Leugering, Wolfgang Peukert Doctoral Thesis English 2013 FAU University Press Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Naturwissenschaftliche Fakultät 2013/09/10 2013/12/10 Funktionale Nanopartikel; Integrodifferentialgleichung; Nichtlineare partielle Differentialgleichung; Partikelgrößenverteilung; Partikeltechnologie; Populationsbilanzgleichung Optimale Kontrolle; Nichtlineare Kontrolltheorie; Nichtlineare Optimierung; Numerische Mathematik; Mathematische Modellierung; Nanopartikel; Prozessoptimierung; Parameteridentifikation; Teilchentechnologie; Steife nichtlineare Differentialgleichung; Bilineares System; Adjungierte Differentialgleichung; Finite-Volumen-Methode; Verteilungsfunktion; Glattheit Mathematik VIII, 211 S. Parallel erschienen als Druckausgabe bei FAU University Press Naturwissenschaftliche Fakultät / Department Mathematik G. Mathematics of Computing 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik 35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Lxx Hyperbolic equations and systems [See also 58J45] / 35L65 Conservation laws 35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Qxx Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] / 35Q70 PDEs in connection with mechanics of particles and systems 35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Rxx Miscellaneous topics (For equations on manifolds, see 58Jxx; for manifolds of solutions, see 58Bxx; for stochastic PDE, see also 60H15) / 35R09 Integro-partial differential equations [See also 45Kxx] 74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Sxx Numerical methods [See also 65-XX, 74G15, 74H15] / 74S10 Finite volume methods 93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Cxx Control systems / 93C20 Systems governed by partial differential equations 70.00.00 CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES / 78.00.00 Optical properties, condensed-matter spectroscopy and other interactions of radiation and particles with condensed matter / 78.20.-e Optical properties of bulk materials and thin films (for optical properties related to materials treatment, see 81.40.Tv; for optical materials, see 42.70-a; for optical properties of superconductors, see 74.25.Gz; for optical properties of rocks and mine open_access Universität Erlangen-Nürnberg / FAU University Press Creative Commons - CC BY-NC-ND - Namensnennung - Nicht kommerziell - Keine Bearbeitungen 3.0
| 2019-06-25T04:00:23 |
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|
https://www.ctcms.nist.gov/fipy/documentation/numerical/discret.html
|
# Finite Volume Method¶
To use the FVM, the solution domain must first be divided into non-overlapping polyhedral elements or cells. A solution domain divided in such a way is generally known as a mesh (as we will see, a Mesh is also a FiPy object). A mesh consists of vertices, faces and cells (see Figure Mesh). In the FVM the variables of interest are averaged over control volumes (CVs). The CVs are either defined by the cells or are centered on the vertices.
## Cell Centered FVM (CC-FVM)¶
In the CC-FVM the CVs are formed by the mesh cells with the cell center “storing” the average variable value in the CV, (see Figure CV structure for an unstructured mesh). The face fluxes are approximated using the variable values in the two adjacent cells surrounding the face. This low order approximation has the advantage of being efficient and requiring matrices of low band width (the band width is equal to the number of cell neighbors plus one) and thus low storage requirement. However, the mesh topology is restricted due to orthogonality and conjunctionality requirements. The value at a face is assumed to be the average value over the face. On an unstructured mesh the face center may not lie on the line joining the CV centers, which will lead to an error in the face interpolation. FiPy currently only uses the CC-FVM.
### Boundary Conditions¶
The natural boundary condition for CC-FVM is no-flux. For (2), the boundary condition is
## Vertex Centered FVM (VC-FVM)¶
In the VC-FVM, the CV is centered around the vertices and the cells are divided into sub-control volumes that make up the main CVs (see Figure CV structure for an unstructured mesh). The vertices “store” the average variable values over the CVs. The CV faces are constructed within the cells rather than using the cell faces as in the CC-FVM. The face fluxes use all the vertex values from the cell where the face is located to calculate interpolations. For this reason, the VC-FVM is less efficient and requires more storage (a larger matrix band width) than the CC-FVM. However, the mesh topology does not have the same restrictions as the CC-FVM. FiPy does not have a VC-FVM capability.
# Discretization¶
The first step in the discretization of Equation (2) using the CC-FVM is to integrate over a CV and then make appropriate approximations for fluxes across the boundary of each CV. In this section, each term in Equation (2) will be examined separately.
## Transient Term ¶
For the transient term, the discretization of the integral over the volume of a CV is given by
(1)
where represents the average value of in a CV centered on a point and the superscript “” represents the previous time-step value. The value is the volume of the CV and is the time step size.
This term is represented in FiPy as
>>> TransientTerm(coeff=rho)
## Convection Term ¶
The discretization for the convection term is given by
(2)
where we have used the divergence theorem to transform the integral over the CV volume into an integral over the CV surface . The summation over the faces of a CV is denoted by and is the area of each face. The vector is the normal to the face pointing out of the CV into an adjacent CV centered on point . When using a first order approximation, the value of must depend on the average value in adjacent cell and the average value in the cell of interest , such that
The weighting factor is determined by the convection scheme, described in Numerical Schemes.
This term is represented in FiPy as
>>> <SpecificConvectionTerm>(coeff=u)
where <SpecificConvectionTerm> can be any of CentralDifferenceConvectionTerm, ExponentialConvectionTerm, HybridConvectionTerm, PowerLawConvectionTerm, UpwindConvectionTerm, ExplicitUpwindConvectionTerm, or VanLeerConvectionTerm. The differences between these convection schemes are described in Section Numerical Schemes. The velocity coefficient u must be a rank-1 FaceVariable, or a constant vector in the form of a Python list or tuple, e.g. ((1,), (2,)) for a vector in 2D.
## Diffusion Term ¶
The discretization for the diffusion term is given by
(3)
indicates recursive application of the specified operation on , depending on the order of the diffusion term. The estimation for the flux, , is obtained via
where the value of is the distance between neighboring cell centers. This estimate relies on the orthogonality of the mesh, and becomes increasingly inaccurate as the non-orthogonality increases. Correction terms have been derived to improve this error but are not currently included in FiPy [14].
This term is represented in FiPy as
>>> DiffusionTerm(coeff=Gamma1)
or
>>> ExplicitDiffusionTerm(coeff=Gamma1)
ExplicitDiffusionTerm is provided primarily for illustrative purposes, although examples.diffusion.mesh1D demonstrates its use in Crank-Nicolson time stepping. ImplicitDiffusionTerm is almost always preferred (DiffusionTerm is a synonym for ImplicitDiffusionTerm to reinforce this preference). One can also create an explicit diffusion term with
>>> (Gamma1 * phi.faceGrad).divergence
### Higher Order Diffusion¶
Higher order diffusion expressions, such as or for Cahn-Hilliard are represented as
>>> DiffusionTerm(coeff=(Gamma1, Gamma2))
The number of elements supplied for coeff determines the order of the term.
Note
While this multiple-coefficient form is still supported, Coupled and Vector Equations are the recommended approach for higher order expressions.
## Source Term¶
Any term that cannot be written in one of the previous forms is considered a source . The discretization for the source term is given by,
(4)
Including any negative dependence of on increases solution stability. The dependence can only be included in a linear manner so Equation (4) becomes
where is the source which is independent of and is the coefficient of the source which is linearly dependent on .
A source term is represented in FiPy essentially as it appears in mathematical form, e.g., would be written
>>> 3 * kappa**2 + b * numerix.sin(theta)
Note
Functions like sin() can be obtained from the fipy.tools.numerix module.
Warning
Generally, things will not work as expected if the equivalent function is used from the NumPy or SciPy library.
If, however, the source depends on the variable that is being solved for, it can be advantageous to linearize the source and cast part of it as an implicit source term, e.g., might be written as
>>> 3 * kappa**2 + ImplicitSourceTerm(coeff=sin(theta))
# Linear Equations¶
The aim of the discretization is to reduce the continuous general equation to a set of discrete linear equations that can then be solved to obtain the value of the dependent variable at each CV center. This results in a sparse linear system that requires an efficient iterative scheme to solve. The iterative schemes available to FiPy are currently encapsulated in the Pysparse and PyTrilinos suites of solvers and include most common solvers such as the conjugate gradient method and LU decomposition.
Combining Equations (1), (2), (3) and (4), the complete discretization for equation (2) can now be written for each CV as
(5)
Equation (5) is now in the form of a set of linear combinations between each CV value and its neighboring values and can be written in the form
(6)
where
The face coefficients, and , represent the convective strength and diffusive conductance respectively, and are given by
Last updated on Jun 15, 2022. Created using Sphinx 5.0.1.
| 2022-08-10T01:31:14 |
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|
https://par.nsf.gov/biblio/10367524-toi-toi-constraining-masses-two-mini-neptunes-habitable-zone-planet-finder
|
TOI-1696 and TOI-2136: Constraining the Masses of Two Mini-Neptunes with the Habitable-Zone Planet Finder
Abstract
We present the validation of two planets orbiting M dwarfs, TOI-1696b and TOI-2136b. Both planets are mini-Neptunes orbiting nearby stars, making them promising prospects for atmospheric characterization with the James Webb Space Telescope (JWST). We validated the planetary nature of both candidates using high-contrast imaging, ground-based photometry, and near-infrared radial velocities. Adaptive optics images were taken using the ShARCS camera on the 3 m Shane Telescope. Speckle images were taken using the NN-Explore Exoplanet Stellar Speckle Imager on the WIYN 3.5 m telescope. Radii and orbital ephemerides were refined using a combination of the Transiting Exoplanet Survey Satellite, the diffuser-assisted Astrophysical Research Consortium (ARC) Telescope Imaging Camera (ARCTIC) imager on the 3.5 m ARC telescope at Apache Point Observatory, and the 0.6 m telescope at Red Buttes Observatory. We obtained radial velocities using the Habitable-Zone Planet Finder on the 10 m Hobby–Eberly Telescope, which enabled us to place upper limits on the masses of both transiting planets. TOI-1696b (P= 2.5 days;Rp= 3.24R;Mp< 56.6M) falls into a sparsely populated region of parameter space considering its host star’s temperature (Teff= 3168 K, M4.5), as planets of its size are quite rare around mid- to late-M dwarfs. On the other hand, TOI-2136b more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Award ID(s):
Publication Date:
NSF-PAR ID:
10367524
Journal Name:
The Astronomical Journal
Volume:
163
Issue:
6
Page Range or eLocation-ID:
Article No. 286
ISSN:
0004-6256
Publisher:
DOI PREFIX: 10.3847
National Science Foundation
##### More Like this
1. Abstract
We detail the follow-up and characterization of a transiting exo-Venus identified by TESS, GJ 3929b (TOI-2013b), and its nontransiting companion planet, GJ 3929c (TOI-2013c). GJ 3929b is an Earth-sized exoplanet in its star’s Venus zone (Pb= 2.616272 ± 0.000005 days; Sb=$17.3−0.7+0.8$S) orbiting a nearby M dwarf. GJ 3929c is most likely a nontransiting sub-Neptune. Using the new, ultraprecise NEID spectrometer on the WIYN 3.5 m Telescope at Kitt Peak National Observatory, we are able to modify the mass constraints of planet b reported in previous works and consequently improve the significance of the mass measurement to almost 4σconfidence (Mb= 1.75 ± 0.45M). We further adjust the orbital period of planet c from its alias at 14.30 ± 0.03 days to the likely true period of 15.04 ± 0.03 days, and we adjust its minimum mass to$msini$= 5.71 ± 0.92M. Using the diffuser-assisted ARCTIC imager on the ARC 3.5 m telescope at Apache Point Observatory, in addition to publicly available TESS and LCOGT photometry, we are able to constrain the radius of planet b toRp= 1.09 ± 0.04R. GJ 3929b is a top candidate for transmission spectroscopy in its size regime (TSM = 14more »
2. Abstract
Populating the exoplanet mass–radius diagram in order to identify the underlying relationship that governs planet composition is driving an interdisciplinary effort within the exoplanet community. The discovery of hot super-Earths—a high-temperature, short-period subset of the super-Earth planet population—has presented many unresolved questions concerning the formation, evolution, and composition of rocky planets. We report the discovery of a transiting, ultra-short-period hot super-Earth orbitingTOI-1075(TIC351601843), a nearby (d= 61.4 pc) late-K/early-M-dwarf star, using data from the Transiting Exoplanet Survey Satellite. The newly discovered planet has a radius of 1.791$−0.081+0.116$Rand an orbital period of 0.605 day (14.5 hr). We precisely measure the planet mass to be 9.95$−1.30+1.36$Musing radial velocity measurements obtained with the Planet Finder Spectrograph mounted on the Magellan II telescope. Our radial velocity data also show a long-term trend, suggesting an additional planet in the system. While TOI-1075 b is expected to have a substantial H/He atmosphere given its size relative to the radius gap, its high density ($9.32−1.85+2.05$g cm−3) is likely inconsistent with this possibility. We explore TOI-1075 b’s location relative to the M-dwarf radius valley, evaluate the planet’s prospects for atmospheric characterization, andmore »
3. Abstract
We present the discovery of TYC9191-519-1b (TOI-150b, TIC 271893367) and HD271181b (TOI-163b, TIC 179317684), two hot Jupiters initially detected using 30-min cadence Transiting Exoplanet Survey Satellite (TESS) photometry from Sector 1 and thoroughly characterized through follow-up photometry (CHAT, Hazelwood, LCO/CTIO, El Sauce, TRAPPIST-S), high-resolution spectroscopy (FEROS, CORALIE), and speckle imaging (Gemini/DSSI), confirming the planetary nature of the two signals. A simultaneous joint fit of photometry and radial velocity using a new fitting package juliet reveals that TOI-150b is a $1.254\pm 0.016\ \rm {R}_ \rm{J}$, massive ($2.61^{+0.19}_{-0.12}\ \rm {M}_ \rm{J}$) hot Jupiter in a 5.857-d orbit, while TOI-163b is an inflated ($R_ \rm{P}$ = $1.478^{+0.022}_{-0.029} \,\mathrm{ R}_ \rm{J}$, $M_ \rm{P}$ = $1.219\pm 0.11 \, \rm{M}_ \rm{J}$) hot Jupiter on a P = 4.231-d orbit; both planets orbit F-type stars. A particularly interesting result is that TOI-150b shows an eccentric orbit ($e=0.262^{+0.045}_{-0.037}$), which is quite uncommon among hot Jupiters. We estimate that this is consistent, however, with the circularization time-scale, which is slightly larger than the age of the system. These two hot Jupiters are both prime candidates for further characterization – in particular, both are excellent candidates for determining spin-orbit alignments via the Rossiter–McLaughlin (RM) effect and for characterizing atmosphericmore »
4. Abstract
We present the validation of a transiting low-density exoplanet orbiting the M2.5 dwarf TOI 620 discovered by the NASA Transiting Exoplanet Survey Satellite (TESS) mission. We utilize photometric data from both TESS and ground-based follow-up observations to validate the ephemerides of the 5.09 day transiting signal and vet false-positive scenarios. High-contrast imaging data are used to resolve the stellar host and exclude stellar companions at separations ≳0.″2. We obtain follow-up spectroscopy and corresponding precise radial velocities (RVs) with multiple precision radial velocity (PRV) spectrographs to confirm the planetary nature of the transiting exoplanet. We calculate a 5σupper limit ofMP< 7.1MandρP< 0.74 g cm−3, and we identify a nontransiting 17.7 day candidate. We also find evidence for a substellar (1–20MJ) companion with a projected separation ≲20 au from a combined analysis of Gaia, adaptive optics imaging, and RVs. With the discovery of this outer companion, we carry out a detailed exploration of the possibilities that TOI 620 b might instead be a circum-secondary planet or a pair of eclipsing binary stars orbiting the host in a hierarchical triple system. We find, under scrutiny, that we can exclude both of these scenarios from the multiwavelength transit photometry, thus validating TOI 620more »
5. ABSTRACT
We report the discovery and characterization of a pair of sub-Neptunes transiting the bright K-dwarf TOI-1064 (TIC 79748331), initially detected in the Transiting Exoplanet Survey Satellite (TESS) photometry. To characterize the system, we performed and retrieved the CHaracterising ExOPlanets Satellite (CHEOPS), TESS, and ground-based photometry, the High Accuracy Radial velocity Planet Searcher (HARPS) high-resolution spectroscopy, and Gemini speckle imaging. We characterize the host star and determine $T_{\rm eff, \star }=4734\pm 67\,\mathrm{ K}$, $R_{\star }=0.726\pm 0.007\, \mathrm{ R}_{\odot }$, and $M_{\star }=0.748\pm 0.032\, \mathrm{ M}_{\odot }$. We present a novel detrending method based on point spread function shape-change modelling and demonstrate its suitability to correct flux variations in CHEOPS data. We confirm the planetary nature of both bodies and find that TOI-1064 b has an orbital period of Pb = 6.44387 ± 0.00003 d, a radius of Rb = 2.59 ± 0.04 R⊕, and a mass of $M_{\rm b} = 13.5_{-1.8}^{+1.7}$ M⊕, whilst TOI-1064 c has an orbital period of $P_{\rm c} = 12.22657^{+0.00005}_{-0.00004}$ d, a radius of Rc = 2.65 ± 0.04 R⊕, and a 3σ upper mass limit of 8.5 M⊕. From the high-precision photometry we obtain radius uncertainties of ∼1.6 per cent, allowing us to conduct internal structure and atmospheric escape modelling. TOI-1064 b is one of the densest, well-characterized sub-Neptunes, withmore »
| 2023-01-27T04:24:51 |
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|
http://specs.openstack.org/openstack/qa-specs/specs/tempest/implemented/resource-cleanup.html
|
## Resource Cleanup
This work is licensed under a Creative Commons Attribution 3.0 Unported License.
# Resource Cleanup¶
Tempest test resource cleanup
## Problem description¶
The cleanup/release of test resources created/allocated in the class level test fixtures is invoked in the class level tearDown fixture. However tearDownClass is invoked by the unittest framework only in case setUpClass is successful. This is causing resources being leaked when:
• a skip exception is raised after resources (typically test accounts) have already been allocated
• there is a temporary failure in the system under test which causes the setUpClass to fail
The test-accounts bp introduces the possibility to run parallel tests using a configured list of pre-provisioned test accounts. Test accounts are allocated and released by each test class, and a failure to release leads to exhaustion of test accounts.
## Proposed change¶
Disallow overriding setUpClass defined in BaseTestCase with a hacking rule. Define setUpClass so that it calls one (or more) other methods to be overridden by descendants. Decorate it with the @safe_setup decorator. This way tearDownClass will always be invoked.
@classmethod
@safe_setup
def setUpClass(cls):
cls.setUpClassCalled = True
cls.resource_setup()
While doing this change, an extra benefit can be gained by structuring the setup in a series of methods, to enforce the least possible resource allocation before failure and thus quick cleanup as well.
PoC for this is available here: https://review.openstack.org/#/c/115353.
@classmethod
@safe_setup
def setUpClass(cls):
cls.setUpClassCalled = True
# All checks that may generate a skip
cls.setup_skip_checks()
# Any setup code that does not require / generate test resources
cls.setup_pre_resources()
# Allocation of all required credentials
cls.setup_allocate_credentials()
# Shortcuts to clients
cls.setup_clients()
# Allocation of shared test resources
cls.setup_create_resources()
# Any setup code to be run after resource allocation
cls.setup_post_resources()
The tearDownClass fixture requires fixing in several places, because several tearDownClass implementation would become unsafe, as they expect attributes defined during setUpClass, which may not be there anymore.
Disallow overriding tearDownClass defined in BaseTestCase with an hacking rule. Define tearDownClass so that it invokes a descendant specific cleanup code, and finally cleans-up credentials.
@classmethod
def tearDownClass(cls):
try:
cls.resource_cleanup()
finally:
cls._cleanup_credentials() # Defined in BaseTestCase
### Alternatives¶
Two alternatives have been identified.
### Massive fixture decoration¶
Decorate all setUpClass implementation with @safe_setup and all tearDownClass implementation with @safe_teardown. This approach requires a mass change to tempest, which as the benefit of being almost scriptable (PoC: https://review.openstack.org/#/c/115123/). It has the downfall of requiring every new test class to add those two decorators.
### Migrate to TestResources¶
This may still be an option on the long term, but at the moment the effort of the migration would be more than the benefit from it. Additional work to ensure cleanup of resources would still be required anyways.
## Implementation¶
### Assignee(s)¶
Andrea Frittoli <[email protected]>
### Milestones¶
Target Milestone for completion:
Juno-final
None
| 2018-12-15T10:26:34 |
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|
https://www.usgs.gov/center-news/volcano-watch-k-lauea-and-mars
|
# Volcano Watch — Kīlauea and Mars
Release Date:
One of the most highly watched events recently on television occurred on the Fourth of July when the U.S. Mars Pathfinder mission successfully transmitted images from the red planet back to Earth. The panorama of the Martian landing site had a striking semblance to the boulder-strewn field south of Halemaumau crater.
One of the most highly watched events recently on television occurred on the Fourth of July when the U.S. Mars Pathfinder mission successfully transmitted images from the red planet back to Earth. The panorama of the Martian landing site had a striking semblance to the boulder-strewn field south of Halemaumau crater. This similarity probably did not surprise the planetary geologists, for they have long recognized that the closest earthly counterparts of Martian volcanic landforms are found in Hawaii.
In February 1995, a prototype Mars robotic vehicle, the Marsokhod Rover, was field-tested in the martian-like terrain south of Halemaumau. The vehicle was teleoperated by engineers who issued commands from the NASA Ames Research Center in California. The Kīlauea tests provided invaluable information to NASA.
Whenever the Sojourner Rover encounters a problem on Mars, NASA simulates the situation, using a model to attain a solution. The red ash seen in the NASA model is from a Mauna Kea cinder cone off the Saddle Road. NASA believes that this ash has similar properties to the ash found on Mars.
Preliminary analyses by instruments on Sojourner indicate that the two rocks, Yogi and Barnacle Bill, are volcanic. Yogi is a basalt, like the lavas of Mauna Loa and Kīlauea. Barnacle Bill is an andesite, a rock similar to basalt but containing less iron and more silica. This rock indicates that igneous activity on Mars may have been more complex than originally thought. Research conducted by USGS petrologists (geologists who study the composition, origin, occurrence, and structure of rocks) at HVO will help unravel the past volcanic processes of Mars.
This close relationship between NASA and the USGS at HVO is not new. Early in 1965, Neil Armstrong and 15 other astronauts spent two weeks at HVO learning about volcanic structures and rocks. These training sessions were repeated in 1967 and in 1969. One of the exercises was to drive a vehicle similar to the lunar buggy around a course in the Kau desert.
In the early '70s, photographs from the Mariner and Viking missions to Mars revealed the similarities between Martian and Hawaiian volcanic features. NASA researchers working with these images routinely spent part of their time in Hawaii to improve their interpretation of the structures.
More recently, remote sensing instruments on NASA shuttles and satellites have been able to detect surface deformation, gas emissions, and temperature changes of our volcanoes. HVO provides ìground truthî or confirmation of these observations. Some day, through the efforts of NASA, USGS, and the University of Hawaii 's Space Grant Consortium, the volcanoes of the world will be monitored by our assets in the sky.
### Volcano Activity Update
Kīlauea's east rift zone eruptive activity continued during the past week with cyclic filling and lowering of the lava pond within Puu Oo crater. Sporatic fountaining was observed from the crater cone and the 55 spatter cone vents. During the early morning hours of August 11, lava flowed into the Wahaula heiau complex and completely inundated the structures. A corner of the Royal Gardens access road was covered by the same flow which entered the ocean near Wahaula. Another lobe of the flow entered the ocean in the Kamokuna area, 900 meters to the west of Wahaula. The public is reminded that the ocean entry areas are extremely hazardous, with explosions accompanying frequent collapses of the lava delta. The steam cloud is highly acidic and laced with glass particles.
Several earthquakes were felt during the past week. The largest was felt island-wide on Thursday afternoon at 3:54 p.m. and originated from the south flank of Kīlauea. The temblor was located 7 km (4 mi) southwest of Puu O`o at a depth of 5 km (3 mi.) and had a magnitude between 4.5 and 4.8. The epicenter is in the same general area as the magnitude 5.3 earthquake felt earlier this summer on June 30th. A resident of Pahala felt two earthquakes on Friday, August 8 at 11:03 a.m. and 3:24 p.m., respectively, and one on Sunday, August 10 at 7:39 p.m. The earthquakes were located 8 km (4.8 mi) northeast of Pahala at a depth of 6 km (3.6 mi). The first temblor had a magnitude of 3.3, the second had a magnitude of 2.7, and the third registered at 2.8.
| 2021-06-19T12:17:33 |
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|
https://conference.sns.gov/event/186/
|
# Workshop on Lateral Membrane Heterogeneity
16-17 October 2019
US/Eastern timezone
### Shull Wollan Center (ORNL Building 8630) - Room A202
Functional heterogeneities, or so-called “rafts” in biological membranes, have proven difficult to study systematically owing in part, to their chemical complexity that is manifested, in part, by the hundreds of distinct lipid species that are contained within them. Different model systems [1,2] provide a bottom-up approach to the study of membranes and have proven to be valuable tools for understanding membrane structure and function. For example, x-ray and neutron scattering from spherical vesicles has provided a better understanding of lateral bilayer structure [2], and its dependence on headgroup and acyl chain properties of individual lipids. However, key aspects of lateral organization, including the coexistence of ordered and disordered fluid phases, their functionalities and physiological significance in the presence of transmembrane proteins, peptides and hormones, to name a few, remain to be addressed [3]. Another fundamental question is how the two lipid bilayer leaflets interact and influence each other’s structure and dynamics. A related open question is the extent to which membrane heterogeneities function under different physiological conditions [4,5]. A powerful means by which the lateral organization of rafts can be studied is through the analysis of their functionalized conditions via a combination of new theoretical/computational frameworks and state-of-the-art experimental techniques. Importantly, these functional rafts must be consistent with the physics and chemistry of the heterogeneous lipid composition, including any microscale phase separation processes.
The purpose of this workshop will be to bring together experts in both the biological function of membrane heterogeneities and in the physical and chemical properties of these materials in an effort to build new collaborations and encourage new interdisciplinary interactions.
### Organizing Committee
• John Katsaras (Oak Ridge National Laboratory/University of Tennessee)
• Maxim Lavrentovich (University of Tennessee)
• Dima Bolmatov (University of Tennessee)
References
1. M. Lavrentovich et al., First-order patterning transitions on a sphere as a route to cell morphology, Proc. Natl. Acad. Sci. U.S.A. 113(19), 5189-5194 (2016).
2. V. N. P. Anghel, D. Bolmatov, and J. Katsaras, Models for randomly distributed nanoscopic domains on spherical vesicles, Phys. Rev. E 97, 062405 (2018).
3. K. Jacobson, O. G. Mouritsen, and R. G. W. Anderson, Lipid rafts: at a crossroad between cell biology and physics, Nature Cell Biol. 9, 7-14 (2007)
4. J. C. Stachowiak et al., Phase-Separated Liposomes Enhance the Efficiency of Macromolecular Delivery to the Cellular Cytoplasm, Cellular and Molecular Bioengineering 10, 387-403 (2017)
5. L. J. Pike, Lipid rafts: heterogeneity on the high seas, Biochem. J. 378, 281-292 (2004)
Starts
Ends
US/Eastern
| 2021-06-23T06:20:02 |
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|
https://pos.sissa.it/414/599/
|
Volume 414 - 41st International Conference on High Energy physics (ICHEP2022) - Neutrino Physics
Latest results from CUPID-0
G. Fantini*, O. Azzolini, J.W. Beeman, F. Bellini, M. Beretta, M. Biassoni, C. Brofferio, C. Bucci, S. Capelli, V. Caracciolo, L. Cardani, P. Carniti, N. Casali, E. Celi, D. Chiesa, M. Clemenza, I. Colantoni, O. Cremonesi, A. Cruciani, A. D’Addabbo, I. Dafinei, S. DiDomizio, V. Dompè, F. Ferroni, L. Gironi, A. Giuliani, P. Gorla, C. Gotti, G. Keppel, J. Kotila, M. Martinez, S. Nagorny, M. Nastasi, S. Nisi, C. Nones, D. Orlandi, L. Pagnanini, M. Pallavicini, L. Pattavina, M. Pavan, G. Pessina, V. Pettinacci, S. Pirro, S. Pozzi, E. Previtali, A. Puiu, A. Ressa, C. Rusconi, K. Schäffner, C. Tomei, M. Vignati and A.S. Zolotarovaet al. (click to show)
Full text: pdf
Pre-published on: December 22, 2022
Published on:
Abstract
CUPID-0 is a pilot experiment in scintillating cryogenic calorimetry for the search of neutrino-less double beta decay. 26 ZnSe crystals were operated continuously in the first project phase (March 2017 - December 2018), demonstrating unprecedented low levels of background in the region of interest at the Q-value of $^{82}\rm{Se}$. From this successful experience comes a demonstration of full alpha to beta/gamma background separation, the most stringent limits on the $^{82}\rm{Se}$ neutrino-less double beta decay, as well as the most precise measurement of the $^{82}$Se half-life. After a detector upgrade, CUPID-0 began its second and last phase (June 2019 - February 2020). We present the latest results on the neutrino-less double beta decay of $^{82}\rm{Se}$ with the full isotope exposure of $8.82~\rm{kg}\times\rm{yr}$. We set a lower bound to the ground state half life $\rm{T}_{1/2}( ^{82}\rm{Se})>4.6\times10^{24}$ yr (90 % C.I.). We review the most recent results from a Bayesian search for spectral distortions to the $^{82}\rm{Se}$ double-beta decay spectrum due to exotic decay modes.
DOI: https://doi.org/10.22323/1.414.0599
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
| 2023-01-30T20:32:03 |
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|
http://dlmf.nist.gov/14.11
|
# §14.11 Derivatives with Respect to Degree or Order
14.11.1 $\frac{\partial}{\partial\nu}\mathop{\mathsf{P}^{\mu}_{\nu}\/}\nolimits\!\left(% x\right)=\pi\mathop{\cot\/}\nolimits\!\left(\nu\pi\right)\mathop{\mathsf{P}^{% \mu}_{\nu}\/}\nolimits\!\left(x\right)-\frac{1}{\pi}\mathsf{A}_{\nu}^{\mu}(x),$
14.11.2 $\frac{\partial}{\partial\nu}\mathop{\mathsf{Q}^{\mu}_{\nu}\/}\nolimits\!\left(% x\right)=-\tfrac{1}{2}\pi^{2}\mathop{\mathsf{P}^{\mu}_{\nu}\/}\nolimits\!\left% (x\right)+\frac{\pi\mathop{\sin\/}\nolimits\!\left(\mu\pi\right)}{\mathop{\sin% \/}\nolimits\!\left(\nu\pi\right)\mathop{\sin\/}\nolimits\!\left((\nu+\mu)\pi% \right)}\mathop{\mathsf{Q}^{\mu}_{\nu}\/}\nolimits\!\left(x\right)-\tfrac{1}{2% }\mathop{\cot\/}\nolimits\!\left((\nu+\mu)\pi\right)\mathsf{A}_{\nu}^{\mu}(x)+% \tfrac{1}{2}\mathop{\csc\/}\nolimits\!\left((\nu+\mu)\pi\right)\mathsf{A}_{\nu% }^{\mu}(-x),$
where
14.11.3 $\mathsf{A}_{\nu}^{\mu}(x)=\mathop{\sin\/}\nolimits\!\left(\nu\pi\right)\left(% \frac{1+x}{1-x}\right)^{\mu/2}\*\sum_{k=0}^{\infty}\frac{\left(\frac{1}{2}-% \frac{1}{2}x\right)^{k}\mathop{\Gamma\/}\nolimits\!\left(k-\nu\right)\mathop{% \Gamma\/}\nolimits\!\left(k+\nu+1\right)}{k!\mathop{\Gamma\/}\nolimits\!\left(% k-\mu+1\right)}\*\left(\mathop{\psi\/}\nolimits\!\left(k+\nu+1\right)-\mathop{% \psi\/}\nolimits\!\left(k-\nu\right)\right).$
14.11.4 $\displaystyle\left.\frac{\partial}{\partial\mu}\mathop{\mathsf{P}^{\mu}_{\nu}% \/}\nolimits\!\left(x\right)\right|_{\mu=0}$ $\displaystyle=\left(\mathop{\psi\/}\nolimits\!\left(-\nu\right)-\pi\mathop{% \cot\/}\nolimits\!\left(\nu\pi\right)\right)\mathop{\mathsf{P}_{\nu}\/}% \nolimits\!\left(x\right)+\mathop{\mathsf{Q}_{\nu}\/}\nolimits\!\left(x\right),$ 14.11.5 $\displaystyle\left.\frac{\partial}{\partial\mu}\mathop{\mathsf{Q}^{\mu}_{\nu}% \/}\nolimits\!\left(x\right)\right|_{\mu=0}$ $\displaystyle=-\tfrac{1}{4}\pi^{2}\mathop{\mathsf{P}_{\nu}\/}\nolimits\!\left(% x\right)+\left(\mathop{\psi\/}\nolimits\!\left(-\nu\right)-\pi\mathop{\cot\/}% \nolimits\!\left(\nu\pi\right)\right)\mathop{\mathsf{Q}_{\nu}\/}\nolimits\!% \left(x\right).$
(14.11.1) holds if $\mathop{\mathsf{P}^{\mu}_{\nu}\/}\nolimits\!\left(x\right)$ is replaced by $\mathop{P^{\mu}_{\nu}\/}\nolimits\!\left(x\right)$, provided that the factor $(\ifrac{(1+x)}{(1-x)})^{\mu/2}$ in (14.11.3) is replaced by $(\ifrac{(x+1)}{(x-1)})^{\mu/2}$. (14.11.4) holds if $\mathop{\mathsf{P}^{\mu}_{\nu}\/}\nolimits\!\left(x\right)$, $\mathop{\mathsf{P}_{\nu}\/}\nolimits\!\left(x\right)$, and $\mathop{\mathsf{Q}_{\nu}\/}\nolimits\!\left(x\right)$ are replaced by $\mathop{P^{\mu}_{\nu}\/}\nolimits\!\left(x\right)$, $\mathop{P_{\nu}\/}\nolimits\!\left(x\right)$, and $\mathop{Q_{\nu}\/}\nolimits\!\left(x\right)$, respectively.
See also Szmytkowski (2006, 2009, 2011, 2012), Cohl (2010, 2011) and Magnus et al. (1966, pp. 177–178).
| 2014-09-02T02:01:10 |
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|
https://par.nsf.gov/biblio/10237586-unified-welfare-analysis-government-policies
|
A Unified Welfare Analysis of Government Policies*
Abstract We conduct a comparative welfare analysis of 133 historical policy changes over the past half-century in the United States, focusing on policies in social insurance, education and job training, taxes and cash transfers, and in-kind transfers. For each policy, we use existing causal estimates to calculate the benefit that each policy provides its recipients (measured as their willingness to pay) and the policy’s net cost, inclusive of long-term effects on the government’s budget. We divide the willingness to pay by the net cost to the government to form each policy’s Marginal Value of Public Funds, or its MVPF''. Comparing MVPFs across policies provides a unified method of assessing their effect on social welfare. Our results suggest that direct investments in low-income children’s health and education have historically had the highest MVPFs, on average exceeding 5. Many such policies have paid for themselves as the government recouped the cost of their initial expenditures through additional taxes collected and reduced transfers. We find large MVPFs for education and health policies among children of all ages, rather than observing diminishing marginal returns throughout childhood. We find smaller MVPFs for policies targeting adults, generally between 0.5 and 2. Expenditures on adults have exceeded more »
Authors:
;
Award ID(s):
Publication Date:
NSF-PAR ID:
10237586
Journal Name:
The Quarterly Journal of Economics
Volume:
135
Issue:
3
Page Range or eLocation-ID:
1209 to 1318
ISSN:
0033-5533
We estimate the climate value of offshore wind energy with a highly flexible, forward-looking method that estimates the value in a consistent manner under a range of policies, including carbon caps and taxes. Backward looking methods measure the damages avoided due to emissions reductions attributed to renewable energy under an existing policy structure. Under a carbon cap, however, the climate value of offshore wind energy comes entirely from reducing the cost of meeting the cap. Our method for estimating the prospective climate value compares bothclimate damagesandabatement costsin cases with and without offshore wind energy. This climate value can be compared to the costs of reducing barriers to new technologies, such as streamlining approval processes. The climate value depends on the cost of offshore wind technology, the climate policy under consideration, the severity of damages from climate change, and the discount rate. In the absence of a binding climate policy, the climate value of offshore wind energy ranges from $246 billion to$2.5 trillion under central assumptions about damages and discount rate, and can reach over \$30 trillion under certain assumptions (low discount rate, high damages, low technology costs). The value of technical change—of moving from the highest cost tomore »
| 2023-02-08T10:15:50 |
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https://pdglive.lbl.gov/Particle.action?node=B084&home=sumtabB
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${{\mathit \Delta}}$ BARYONS($\mathit S$ = 0, $\mathit I$ = 3/2) ${{\mathit \Delta}^{++}}$ = ${{\mathit u}}{{\mathit u}}{{\mathit u}}$ , ${{\mathit \Delta}^{+}}$ = ${\mathit {\mathit u}}$ ${\mathit {\mathit u}}$ ${\mathit {\mathit d}}$, ${{\mathit \Delta}^{0}}$ = ${\mathit {\mathit u}}$ ${\mathit {\mathit d}}$ ${\mathit {\mathit d}}$, ${{\mathit \Delta}^{-}}$ = ${\mathit {\mathit d}}$ ${\mathit {\mathit d}}$ ${\mathit {\mathit d}}$ INSPIRE search
#### ${{\mathit \Delta}{(2420)}}$
$I(J^P)$ = $3/2(11/2^{+})$
Older and obsolete values are listed and referenced in the 2014 edition, Chinese Physics C38 070001 (2014).
${{\mathit \Delta}{(2420)}}$ POLE POSITION
REAL PART $2300\text{ to }2500\text{ }(\approx2400)$ MeV
$-2{\times }$IMAGINARY PART $350\text{ to }550\text{ }(\approx450)$ MeV
${{\mathit \Delta}{(2420)}}$ ELASTIC POLE RESIDUE
MODULUS $\vert \mathit r\vert$ $20\text{ to }40\text{ }(\approx30)$ MeV
PHASE $\theta$ $-60\text{ to }20\text{ }(\approx-20)$ $^\circ{}$
${{\mathit \Delta}{(2420)}}$ BREIT-WIGNER MASS $2300\text{ to }2600\text{ }(\approx2450)$ MeV
${{\mathit \Delta}{(2420)}}$ BREIT-WIGNER WIDTH $300\text{ to }700\text{ }(\approx500)$ MeV
The following branching fractions are our estimates, not fits or averages.
$\Gamma_{1}$ ${{\mathit N}}{{\mathit \pi}}$ $5 - 10\%$ 1040
FOOTNOTES
| 2022-08-16T15:42:54 |
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http://dergipark.gov.tr/hujms/issue/38872/452963
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Yıl 2018, Cilt 47, Sayı 4, Sayfalar 821 - 833 2018-08-01
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## Univalence of certain integral operators involving generalized Struve functions
#### Muhey U Din [1] , Hari Mohan Srivastava [2] , Mohsan Raza [3]
##### 6 13
In this paper, we are mainly interested to fi nd suffi cient conditions for some integral operators de fined by generalized Struve functions. These operators are normalized and as well as univalent in the open unit disc $\mathcal{U}$. Some special cases of Struve functions and modi fied Struve functions are also a part of our investigations.
Univalence conditions, Integral operators, Generalized Struve functions, Modified Struve functions, Ahlfors-Becker and Becker univalence criteria, Schwarz lemma
• Abramowitz, M. and Stegun, I. A. Handbook of Mathematical Functions (Dover, New York, 1972).
• Arif, M. and Raza, M. Some properties of an integral operator defi ned by Bessel functions, Acta Universitatis Apulensis 26, 6974, 2011.
• Baricz, A., Dimitrov, D.K., Orhan, H. and Yagmur, N. Radii of starlikeness of some special functions, Proc. Amer. Math. Soc. 144(8) 33553367, 2016.
• Baricz, A. and Frasin, B.A. Univalence of integral operators involving Bessel functions, Appl. Math. Lett., 23, 371276, 2010.
• Breaz, D. Univalence properties for a general integral operator, Bull. Korean Math. Soc, 46(3), 439446, 2009.
• Breaz, D., Breaz, N. and Srivastava, H. M. An extension of the univalent condition for a family of integral operators, Appl. Math. Lett. 22, 4144, 2009.
• Breaz, D. and Güney, H.O. On the univalence criterion of a general integral operator, J. Inequal. Appl. Volume 2008, Article ID 702715, 8 pages, doi:10.1155/2008/702715.
• Breaz, D., Owa, S. and Breaz, N. A new integral univalent operator, Acta Univ. Apulensis Math. Inform., 16, 1116, 2008.
• Bulut, S. Univalence preserving integral operators defi ned by generalized Al-Oboudi dierential operators, An. St. Univ. Ovidius Constata 17, 3750, 2009.
• Deniz, E. Convexity of integral operators involving generalized Bessel functions, Integral Transforms Spec. Funct. 24(3), 201216, 2013.
• Deniz, E. On the univalence of two general integral operators, Filomat, 29(7), 15811586, 2015.
• Deniz, E. Univalence criteria for a general integral operator, Filomat 28(1), 1119, 2014.
• Deniz, E. and Orhan, H. Loewner chains and univalence criteria related with Ruscheweyh and Slgean derivatives, J. Appl. Anal. Comput. 5(3), 465478, 2015.
• Deniz, E. and Orhan, H. Some notes on extensions of basic univalence criteria, J. Korean Math. Soc. 48(1), 179189, 2011.
• Deniz, E. and Orhan, H. Univalence criterion for meromorphic functions and Loewner chains, Appl. Math. Comput. 218(6), 751755, 2011.
• Deniz, E., Orhan, H. and Srivastava, H.M. Some su fficient conditions for univalence of certain families of integral operators involving generalized Bessel functions, Taiwanese J. Math. 15(2), 883917, 2011.
• Frasin, B.A. Some su fficient conditions for certain integral operators, J. Math. Ineq. 2(4), 527535, 2008.
• Frasin, B.A. Su fficient conditions for integral operator defi ned by Bessel functions, J. Math. Ineq. 4(2), 301306, 2010.
• Frasin, B.A. Univalence criteria for general integral operator, Math. Commun. 16, 115124, 2011.
• Kanas, S. and Srivastava, H.M. Some criteria for univalence related to Ruscheweyh and Salagean derivatives, Complex Variables Theory Appl. 38, 263275, 1999.
• Kiryakova, V.S., Saigo, M., and Srivastava, H.M. Some criteria for univalence of analytic functions involving generalized fractional calculus operators, Fract. Calc. Appl. Anal. 1 , 79102, 1998.
• Nehari, Z. Conformal Mapping, (McGraw-Hill, 1952).
• Olver, F.W.J., Lozier, D.W., Boisvert, R.F. and Clark, C.W. (eds.) NIST Handbook of Mathematical Functions (Cambridge University Press, Cambridge, 2010).
• Orhan, H. and Yagmur, N. Geometric properties of generalized struve functions, An. Stiinµ. Univ. Al. I. Cuza Iasi. Mat. (N.S.), doi:10.2478/aicu-2014-0007.
• Pescar, V. Univalence of certain integral operators, Acta Univ. Apulensis Math. Inform., 12, 4348, 2006.
• Pescar, V. A new generalization of Ahlfors and Beckers criterion of univalence, Bull. Malaysian Math. Soc., 19, 5354, 1996.
• Pescar, V. On the univalence of an integral operator, Appl. Math. Lett. 23(5), 615619, 2010.
• Pescar, V. and Breaz, D. On an integral operator, Appl. Math. Lett. 23(5), 625629, 2010.
• Pascu, N.N. An improvement of Beckers univalence criterion, in: Proceedings of the Commemorative Session: Simion Stoilow (Brasov), 4348, 1987.
• Raza, M. and Yağmur, N. Some properties of a class of analytic functions defi ned by generalized Struve functions. Turkish Journal of Mathematics, 39(6), 931944, 2015.
• Struve, H. Beitrag zur Theorie der Diraction an Fernrö hren, Annalen der Physik und Chemie, 17(13), 10081016, 1882.
• Yagmur, N. and Orhan, H. Starlikeness and convexity of generalized Struve functions, Abstr. Appl. Anal., Volume 2013, Article ID: 954513, 6 pages, doi:10.1155/2013/954513.
• Zhang, S. and Jin, J. Computation of Special Functions, (Wiley, New york, 1996).
Birincil Dil en Matematik ve İstatistik Matematik Yazar: Muhey U Din Yazar: Hari Mohan Srivastava Yazar: Mohsan Raza (Sorumlu Yazar)
Bibtex @araştırma makalesi { hujms452963, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {1303-5010}, address = {Hacettepe Üniversitesi}, year = {2018}, volume = {47}, pages = {821 - 833}, doi = {}, title = {Univalence of certain integral operators involving generalized Struve functions}, key = {cite}, author = {U Din, Muhey and Raza, Mohsan and Srivastava, Hari Mohan} } APA U Din, M , Srivastava, H , Raza, M . (2018). Univalence of certain integral operators involving generalized Struve functions. Hacettepe Journal of Mathematics and Statistics, 47 (4), 821-833. Retrieved from http://dergipark.gov.tr/hujms/issue/38872/452963 MLA U Din, M , Srivastava, H , Raza, M . "Univalence of certain integral operators involving generalized Struve functions". Hacettepe Journal of Mathematics and Statistics 47 (2018): 821-833 Chicago U Din, M , Srivastava, H , Raza, M . "Univalence of certain integral operators involving generalized Struve functions". Hacettepe Journal of Mathematics and Statistics 47 (2018): 821-833 RIS TY - JOUR T1 - Univalence of certain integral operators involving generalized Struve functions AU - Muhey U Din , Hari Mohan Srivastava , Mohsan Raza Y1 - 2018 PY - 2018 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 821 EP - 833 VL - 47 IS - 4 SN - 1303-5010- M3 - UR - Y2 - 2017 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Univalence of certain integral operators involving generalized Struve functions %A Muhey U Din , Hari Mohan Srivastava , Mohsan Raza %T Univalence of certain integral operators involving generalized Struve functions %D 2018 %J Hacettepe Journal of Mathematics and Statistics %P 1303-5010- %V 47 %N 4 %R %U ISNAD U Din, Muhey , Srivastava, Hari Mohan , Raza, Mohsan . "Univalence of certain integral operators involving generalized Struve functions". Hacettepe Journal of Mathematics and Statistics 47 / 4 (Ağustos 2018): 821-833.
| 2018-09-19T01:43:07 |
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http://pdglive.lbl.gov/DataBlock.action?node=S060DMN&home=BXXX045
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# ${\boldsymbol m}_{{{\boldsymbol \Xi}_{{b}}^{0}}}–{\boldsymbol m}_{{{\boldsymbol \Lambda}_{{b}}^{0}}}$ INSPIRE search
VALUE (MeV) DOCUMENT ID TECN COMMENT
$\bf{ 172.5 \pm0.4}$ OUR AVERAGE
$174.8$ $\pm2.4$ $\pm0.5$
2014 H
LHCB ${{\mathit p}}{{\mathit p}}$ at 7 TeV
$172.44$ $\pm0.39$ $\pm0.17$ 1
2014 Z
LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8 TeV
1 Uses ${{\mathit \Xi}_{{b}}^{0}}$ $\rightarrow$ ${{\mathit \Xi}_{{c}}^{+}}{{\mathit \pi}^{-}}$ and ${{\mathit \Xi}_{{c}}^{+}}$ $\rightarrow$ ${{\mathit p}}{{\mathit K}^{-}}{{\mathit \pi}^{+}}$ decays.
References:
AAIJ 2014H
PR D89 032001 Studies of Beauty Baryon Decays to ${{\mathit D}^{0}}{{\mathit p}}{{\mathit h}^{-}}$ and ${{\mathit \Lambda}_{{c}}^{+}}{{\mathit h}^{-}}$ Final States
AAIJ 2014Z
PRL 113 032001 Precision Measurement of the Mass and Lifetime of the ${{\mathit \Xi}_{{b}}^{0}}$ Baryon
| 2020-04-05T20:06:42 |
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https://vizhub.ephi.gov.et/lan/index-pr.php
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Welcome to Perinatal Mortality Rate Analysis Platform!
Introduction
• Perinatal mortality is the sum of stillbirth (fetal death) and early neonatal death which is the death of a live newborn before the age of seven completed days.
• Ethiopia is one of the fast track sub-Saharan African countries in reducing under-five mortality. However, the reduction in neonatal and perinatal mortality continues to be a major challenge, and with a rate of 33 deaths per 1000 births, Ethiopia is one of the countries with the highest perinatal mortality rate in the world.
• It is an indicator of the social, economic and environmental conditions in which mother lives, including maternal health care utilization.
• This section shows the prevalence of perinatal mortality rate by background characteristics in Ethiopia.
Method
Data Source:
Ethiopian Demographic Health Survey (EDHS) 2000,2005,2011 and 2016 dataset.
Coverage:
Population base: Pregnancies of seven or more months to women age 15–49 at time of survey.
Time period: Five-year period preceding the survey.
Calculations:
Perinatal mortality rate = stillbirth rate + early neonatal death rate
Where,
NPSMD= Number of Pregnancies of More Than Seven Months Durations
$Stillbirth rate = {number of stillbirth \over NPSMD }*1000$
$Early Neonatal Death Rate= { Number of Early Neonatal Death \over NPSMD}*1000$
Key Findings
• Perinatal mortality rate declined from 52 to 33 deaths per 1,000 all births from 2000 to 2016.
• Perinatal mortality rate for the women age 20-29 and 40-49 were 28 and 63 deaths per 1,000 pregnancies in 2016 respectively. It shows that perinatal mortality rate among children born to women age 40-49 is more than twice as high as for women age 20-29.
| 2022-11-26T15:52:47 |
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http://hitchhikersgui.de/Talk:Directional_statistics
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# Talk:Directional statistics
WikiProject Statistics (Rated C-class, High-importance)
This article is within the scope of the WikiProject Statistics, a collaborative effort to improve the coverage of statistics on Wikipedia. If you would like to participate, please visit the project page or join the discussion.
C This article has been rated as C-Class on the quality scale.
High This article has been rated as High-importance on the importance scale.
## Circular standard deviation | Factor of 2
I noticed an oddity in the definition of the circular variance, which probably has historical reasons: While it is not generally true that the estimator of the circular standard deviation squared yields the circular standard deviation, I would have expected this equality to hold for very small values of the circular standard deviation, which recovers the linear case. However, there is a factor of 2 missing! You can test this numerically yourself with the following line of code
sigma=0.1
std_circ=sqrt(-2*log(abs(mean(exp(1i*sigma*randn(1e5,1))))))
var_circ=1-abs(mean(exp(1i*sigma*randn(1e5,1))))
I therefore added the following sentence to the article:
Note that for small ${\displaystyle S(z)}$, we have ${\displaystyle S(z)^{2}=2\mathrm {Var} (z)}$.
Does anybody know a reference for this?
Ben Benjamin.friedrich (talk) 20:39, 25 August 2014 (UTC)
## ?
The final step of the formula given for the example is unclear; apparently it is written for result in radians. Wouldn't it be better written this way:
Mean angle = arctangent (mean sine / mean cosine). If mean cosine < 0, add 180 degrees to the result. If mean sine <0 and mean cosine >= 0, add 360 degrees to the result.
Jim
## Modulus method
The modulus method only works in few specific cases (such as the example given).
Consider the same example but rotated further to the left so that the three angles are 330, 340 and 350 degrees. Taking the modulus 360 of the sum (1020) results in 2 remainder 280, which divided by 3 is clearly not 340.
As the remainder (in a modulus 360 operation) can only range from 0 to 360, the 'average' can only range from 0 to 360/n.
Unless I'm misunderstanding the procedure, I would suggest taking it out.
Fink3412 09:28, 20 August 2007 (UTC)
Agreed - I've removed it. Also, this article is about Directional statistics itself, not about various methods to calculate a circular average. Tomixdf 09:42, 20 August 2007 (UTC)
## wrapped normal
I've added the wrapped normal distribution as an example of the way a wrapped distribution can be made from the pdf of another distribution. I'm also redirecting the nonexistent wrapped normal distribution to this page. I hope this is considered useful! digfarenough (talk) 22:18, 11 November 2008 (UTC)
Good work, thanks. Tomixdf (talk) 07:07, 12 November 2008 (UTC)
## Should the Rayleigh test be mentioned
I started a new Goodness of fit section - in case it should be put elsewhere. - Rod57 (talk) 14:31, 6 April 2015 (UTC)
## Propose renaming of article
The current title of this article is directional statistics, which is a synonym of circular statistics. A quick search on Google Scholar and Google Books will show that the latter term, "circular statistics," is more widely used than "directional statistics". Here are the results.
• "Circular statistics": 9,670 results on Google Scholar and 811 results on Google Books
• "Directional statistics": 4,060 on Google Scholar and 766 results on Google Books
Thus, I would like to propose renaming this article to Circular statistics. Any thoughts? danielkueh (talk) 02:48, 28 August 2015 (UTC)
• Oppose: circular is 2D, a special case of spherical statistics or 3D directions. fgnievinski (talk) 03:10, 28 August 2015 (UTC)
Point taken. danielkueh (talk) 03:15, 28 August 2015 (UTC)
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| 2017-12-11T23:03:53 |
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https://conferences.lbl.gov/event/212/contributions/6022/
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# Nuclear Structure 2022
13-17 June 2022
Berkeley, CA
US/Pacific timezone
## Level lifetime measurements in neutron-rich Zr and Mo isotopes around A = 110 through in-beam gamma-ray spectroscopy
13 Jun 2022, 14:10
20m
Berkeley, CA
#### Berkeley, CA
Lawrence Berkeley National Laboratory
Oral Oral Presentations
### Speaker
Byul Moon (Center for Exotic Nuclear Studies, Institute for Basic Science)
### Description
Isotopes of zirconium (Zr) with semi-magic atomic number $40$ represent one of the most interesting cases of shape evolution in nuclei. The collective behavior of Zr nuclides is very much suppressed at neutron number $50$, where $^{90}$Zr exhibits properties of a doubly-magic nucleus. On the other hand, a sudden onset of nuclear deformation appears at $N = 40$ and $60$ due to the strong proton-neutron interaction between the overlapping partner $\pi 1g_{9/2}$ and $\nu 1g_{9/2}$ ($\nu 1g_{7/2}$) intruder orbitals. The strong shape transition at $N = 60$ happens in Zr ($Z = 40$) and Sr ($Z = 38$) nuclei which are located at the mid-shell between $N = 50$ to $82$. The abrupt shape transition is limited to the Sr and Zr nuclei, while the neighboring Kr ($Z = 36$) and Mo ($Z = 42$) show a smooth shape evolution pattern in terms of the quadrupole deformation.
Among Zr isotopes, $^{110}$Zr with $Z = 40$ and $N = 70$ shell closures of the harmonic oscillator potential could be another quasi doubly-magic nucleus. However, a previous SEASTAR experiment at the Radioactive Isotope Beam Factory (RIBF) provided evidence for rather well-deformed nature in this isotope by measuring the energy of the first excited state through in-beam gamma-ray spectroscopy [1]. Several questions then remain open, such as the possibility of shape coexistence or triaxial deformation in this $^{110}$Zr isotope as predicted by different theoretical models [2-4].
A high-resolution in-beam gamma-ray spectroscopy study of nuclei around $^{110}$Zr was performed within the HiCARI (High-resolution Cluster Array at RIBF) campaign at the RIBF to measure the level lifetimes [5]. The HiCARI array was comprised of several different types of high-purity germanium detectors, which were six Miniball triple clusters from the Miniball collaboration [6], four 4-fold segmented Clover detectors from the IMP [7], a quad-type 36-fold segmented tracking detector from the RCNP [8], and a triple 36-fold segmented tracking detector P3 from the LBNL [9]. This large array was installed at the F8 focus which is located between the BigRIPS and Zero Degree Spectrometer at the RIBF facility. From this experiment, $^{110}$Zr was populated through proton knockout reactions from $^{111}$Nb and $^{112}$Mo. In addition, states in $^{110}$Mo and $^{112}$Mo could be studied with significantly more statistics
In this talk, preliminary experimental results will be represented. Lifetimes of specific levels in $^{110}$Zr, $^{110}$Mo, and $^{112}$Mo are analyzed based on the line-shape method [10]. These experimental results will allow to distinguish between predictions of different nuclear models concerning the shape of $^{110}$Zr, the key isotope for the evolution of collective properties along the $N = 70$ isotones.
[1] N. Paul et al., Phys. Rev. Lett. 118, 032501 (2017).
[2] M. Borrajo et al., Phys. Lett. B 746, 341 (2015).
[3] J. Libert, Phys. Rev. C 60, 1 (1999).
[4] T. Togashi et al., Phys. Rev. Lett. 117, 172502 (2016).
[5] K. Wimmer et al., RIKEN Accel. Prog. Rep. 54, S27 (2021).
[6] N. Warr et al., Eur. Phys. J. A 49, 40 (2013).
[7] W. Hua et al., Nuclear Structure in China 2012, 98 (2013).
[8] D. Weisshaar et al., Nucl. Instrum. Methods Phys. Res. A 847, 187 (2017).
[9] T. Ross, Neutron damage tests of a highly segmented Germanium detector, Master Thesis, University of Surrey (2009).
[10] P. Doornenbal et al., Nucl. Instrum. Methods Phys. Res. A 613, 218 (2010).
### Primary author
Byul Moon (Center for Exotic Nuclear Studies, Institute for Basic Science)
### Co-authors
Dr Kathrin Wimmer (GSI) Wolfram KORTEN (CEA Saclay) Dr Pieter Doornenbal (RIKEN Nishina Center) Mr Jiseok Kim (Korea University)
| 2022-08-13T18:38:10 |
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https://www.aimsciences.org/article/doi/10.3934/proc.2015.1019
|
Article Contents
Article Contents
# Nonlinear Schrödinger equations with inverse-square potentials in two dimensional space
• Nonlinear Schrödinger equations with inverse-square potentials are considered in space dimension $N=2$. Stricharz estimates for (NLS)a are shown by Burq, Planchon, Stalker and Tahvildar-Zadeh [1] even when $N=2$. Here there seems not to be the study of solvability of (NLS)a when dimension is two. By virtue of the Hardy inequality the solvability is proved in Okazawa-Suzuki-Yokota, [3,4] if $N\ge 3$. Although strongly singular potential $a|x|^{-2}$ is available and the energy space is not exactly $H^{1}$ in (NLS)a, we can apply the energy methods established by Okazawa-Suzuki-Yokota [4].
Mathematics Subject Classification: Primary: 35Q55, 35Q40; Secondary: 81Q15.
Citation:
• [1] N.Burq, F.Planchon, J.Stalker, A.S.Tahvildar-Zadeh, Strichartz estimates for the wave and Schrödinger equations with the inverse-square potential, J. Funct. Anal., 203 (2003), 519-549. [2] T.Ogawa, A proof of Trudinger's inequality and its application to nonlinear Schrödinger equations, Nonlinear Anal., 14 (1990), 765-769. [3] N.Okazawa, T.Suzuki, T.Yokota, Cauchy problem for nonlinear Schrödinger equations with inverse-square potentials, Appl. Anal., 91 (2012), 1605-1629. [4] N.Okazawa, T.Suzuki, T.Yokota, Energy methods for abstract nonlinear Schrödinger equations, Evol. Equ. Control Theory, 1 (2012), 337-354. [5] T.Suzuki, Energy methods for Hartree type equation with inverse-square potentials, Evol. Equ. Control Theory, 2 (2013), 531-542. [6] T.Suzuki, Critical case of nonlinear Schrödinger equations with inverse-square potentials on bounded domains, Math. Bohemica, 139 (2014), 231-238. [7] T.Suzuki, Solvability of nonlinear Schrödinger equations with some critical singular potential via generalized Hardy-Rellich inequalities, Funkcial. Ekvac., to appear. [8] L.Wei, Z.Feng, Isolated singularity for semilinear elliptic equations, Discrete and Continuous Dynamical System-A, 35 (2015), 3239-3252.
Open Access Under a Creative Commons license
| 2022-12-03T10:22:58 |
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https://zbmath.org/authors/?q=ai%3Athomassen.carsten
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# zbMATH — the first resource for mathematics
## Thomassen, Carsten
Compute Distance To:
Author ID: thomassen.carsten Published as: Thomassen, C.; Thomassen, Carsten Homepage: http://www2.mat.dtu.dk/people/C.Thomassen/ External Links: MGP · Wikidata · ResearchGate · dblp · GND
Documents Indexed: 264 Publications since 1973, including 23 Books Reviewing Activity: 127 Reviews Biographic References: 1 Publication
all top 5
#### Co-Authors
168 single-authored 9 Aldred, Robert E. L. 8 Richter, Robert Bruce 5 Alahmadi, Adel N. 4 Gimbel, John G. 4 Häggkvist, Roland 4 Kündgen, André 4 Solé, Patrick 3 Andersen, Lars Døvling 3 Bang-Jensen, Jørgen 3 dela Cruz, Romar B. 3 Holton, Derek Allan 3 Jensen, Tommy René 3 Ok, Seongmin 3 Wu, Yezhou 3 Zhang, Cunquan 2 Bermond, Jean-Claude 2 Bollobás, Béla 2 Burger, Alewyn Petrus 2 Chia, Gek-Ling 2 Chvátal, Václav 2 Diestel, Reinhard 2 Dirac, Gabriel Andrew 2 Fellows, Michael Ralph 2 Fomin, Fedor V. 2 Frick, Marietjie 2 Kawarabayashi, Ken-ichi 2 Li, Binlong 2 Lokshtanov, Daniel 2 Markvorsen, Steen 2 McKay, Brendan D. 2 Mohar, Bojan 2 Petrović, Vojislav 2 Plummer, Michael D. 2 Reid, Kenneth Brooks 2 Rooney, Brendan 2 Rosamond, Frances A. 2 Saurabh, Saket 2 Seymour, Paul D. 2 Szeider, Stefan 2 Toft, Bjarne 2 van Aardt, Susan A. 2 Vestergaard, Preben Dahl 1 Aharoni, Ron 1 Alavi, Yousef 1 Albertson, Michael O. 1 Alishahi, Meysam 1 Alkenani, Ahmad N. 1 Alon, Noga M. 1 Alstrup, Stephen 1 Andersen, L. A. 1 Axenovich, Maria A. 1 Barát, János 1 Bensmail, Julien 1 Berman, David M. 1 Böhme, Thomas 1 Bondy, Adrian 1 Bondy, J. Adrian 1 Brouwer, Andries Evert 1 Cameron, Kathie 1 Davies, James 1 de Wet, Johan P. 1 Dejter, Italo Jose 1 Dunbar, Jean E. 1 Erdős, Pál 1 Fleischner, Herbert J. 1 Fraisse, Pierre 1 Georgakopoulos, Agelos 1 Gorbunov, Konstantin Yu. 1 Grötschel, Martin 1 Hahn, Gena 1 Hakimi, Seifollah Louis 1 Harary, Frank 1 Heydemann, Marie-Claude 1 Hijazi, Rola Asaad 1 Hjorth, Poul G. 1 Hliněný, Petr 1 Hutchinson, Joan P. 1 Jakobsen, Ivan Tafteberg 1 Jørgensen, Leif Kjær 1 Kleitman, Daniel J. 1 Langhede, Rikke 1 Leander, Gregor 1 Li, Jiaao 1 Lisoněk, Petr 1 Llano, Bernardo 1 Lovász, László Miklós 1 Malde, Paresh J. 1 Manoussakis, Yannis G. 1 McGuinness, Sean 1 Merker, Martin 1 Perrett, Thomas J. 1 Rotenberg, Eva 1 Sabidussi, Gert 1 Saks, Michael E. 1 Schade, Ursula 1 Schmeichel, Edward F. 1 Schwenk, Allen J. 1 Sheehan, John 1 Shen, Jian 1 Sorensen, Bo Aagaard ...and 10 more Co-Authors
all top 5
#### Serials
68 Journal of Combinatorial Theory. Series B 29 Journal of Graph Theory 21 Discrete Mathematics 20 Combinatorica 6 American Mathematical Monthly 5 European Journal of Combinatorics 5 Combinatorics, Probability and Computing 4 Discrete Applied Mathematics 4 Ars Combinatoria 4 Graphs and Combinatorics 4 The Electronic Journal of Combinatorics 3 Mathematische Annalen 3 Proceedings of the London Mathematical Society. Third Series 3 Transactions of the American Mathematical Society 3 Journal of Algorithms 3 SIAM Journal on Discrete Mathematics 3 Linear Algebra and its Applications 2 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 2 Proceedings of the American Mathematical Society 2 Journal of Combinatorics 1 Israel Journal of Mathematics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 The Annals of Probability 1 Archiv der Mathematik 1 Bulletin of the London Mathematical Society 1 Commentarii Mathematici Helvetici 1 Geometriae Dedicata 1 Journal of Combinatorial Theory. Series A 1 Journal of the London Mathematical Society. Second Series 1 Journal für die Reine und Angewandte Mathematik 1 Mathematische Nachrichten 1 Monatshefte für Mathematik 1 Normat 1 SIAM Journal on Computing 1 Order 1 Discrete & Computational Geometry 1 Information and Computation 1 Journal of the American Mathematical Society 1 Aequationes Mathematicae 1 Journal of Algebraic Combinatorics 1 Discrete Mathematics and Theoretical Computer Science. DMTCS 1 Annals of Discrete Mathematics 1 Nederlandse Akademie van Wetenschappen. Proceedings. Series A. Indagationes Mathematicae
all top 5
#### Fields
258 Combinatorics (05-XX) 11 Manifolds and cell complexes (57-XX) 11 Computer science (68-XX) 6 General topology (54-XX) 6 Information and communication theory, circuits (94-XX) 2 General and overarching topics; collections (00-XX) 2 Mathematical logic and foundations (03-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Geometry (51-XX) 2 Probability theory and stochastic processes (60-XX) 1 History and biography (01-XX) 1 Linear and multilinear algebra; matrix theory (15-XX)
#### Citations contained in zbMATH Open
223 Publications have been cited 3,792 times in 2,581 Documents Cited by Year
Graphs on surfaces. Zbl 0979.05002
Mohar, Bojan; Thomassen, Carsten
2001
Every planar graph is 5-choosable. Zbl 0805.05023
Thomassen, Carsten
1994
Thomassen, Carsten
1980
Cycles in digraphs. A survey. Zbl 0458.05035
Bermond, J. C.; Thomassen, C.
1981
Reflections on graph theory. Zbl 0614.05050
Thomassen, Carsten
1986
Planarity and duality of finite and infinite graphs. Zbl 0441.05023
Thomassen, Carsten
1980
3-list-coloring planar graphs of girth 5. Zbl 0822.05029
Thomassen, Carsten
1995
The graph genus problem is NP-complete. Zbl 0689.68071
Thomassen, Carsten
1989
The weak 3-flow conjecture and the weak circular flow conjecture. Zbl 1239.05083
Thomassen, Carsten
2012
Nonseparating cycles in k-connected graphs. Zbl 0498.05044
Thomassen, Carsten
1981
Nowhere-zero 3-flows and modulo $$k$$-orientations. Zbl 1301.05154
Lovász, László Miklós; Thomassen, Carsten; Wu, Yezhou; Zhang, Cun-Quan
2013
A theorem on paths in planar graphs. Zbl 0515.05040
Thomassen, Carsten
1983
Color-critical graphs on a fixed surface. Zbl 0883.05051
Thomassen, Carsten
1997
Five-coloring maps on surfaces. Zbl 0794.05026
Thomassen, Carsten
1993
Tilings of the torus and the Klein bottle and vertex-transitive graphs on a fixed surface. Zbl 0722.05031
Thomassen, Carsten
1991
Girth in graphs. Zbl 0537.05034
Thomassen, Carsten
1983
Hamiltonian-connected tournaments. Zbl 0435.05026
Thomassen, Carsten
1980
Grötzsch’s 3-color theorem and its counterparts for the torus and the projective plane. Zbl 0817.05024
Thomassen, Carsten
1994
Interval representations of planar graphs. Zbl 0595.05027
Thomassen, Carsten
1986
Embeddings of graphs with no short noncontractible cycles. Zbl 0704.05011
Thomassen, Carsten
1990
Highly connected sets and the excluded grid theorem. Zbl 0949.05075
Diestel, Reinhard; Jensen, Tommy R.; Gorbunov, Konstantin Yu.; Thomassen, Carsten
1999
Coloring graphs with fixed genus and girth. Zbl 0884.05039
Gimbel, John; Thomassen, Carsten
1997
On the presence of disjoint subgraphs of a specified type. Zbl 0662.05032
Thomassen, Carsten
1988
Plane representations of graphs. Zbl 0554.05021
Thomassen, C.
1984
Distances in orientations of graphs. Zbl 0311.05115
Chvátal, Václav; Thomassen, C.
1976
Non-separating induced cycles in graphs. Zbl 0456.05039
Thomassen, Carsten; Toft, Bjarne
1981
Claw-decompositions and Tutte-orientations. Zbl 1117.05088
Barát, János; Thomassen, Carsten
2006
Even cycles in directed graphs. Zbl 0606.05039
Thomassen, Carsten
1985
A short list color proof of Grötzsch’s theorem. Zbl 1025.05022
Thomassen, Carsten
2003
Path and cycle sub-Ramsey numbers and an edge-colouring conjecture. Zbl 0613.05044
Hahn, Geňa; Thomassen, Carsten
1986
Disjoint cycles in digraphs. Zbl 0527.05036
Thomassen, Carsten
1983
The zero-free intervals for chromatic polynomials of graphs. Zbl 0887.05020
Thomassen, Carsten
1997
Vertex-transitive graphs and accessibility. Zbl 0793.05073
Thomassen, Carsten; Woess, Wolfgang
1993
The even cycle problem for directed graphs. Zbl 0760.05051
Thomassen, Carsten
1992
Configurations in graphs of large minimum degree, connectivity, or chromatic number. Zbl 0709.05030
Thomassen, Carsten
1989
Graph decomposition with constraints on the connectivity and minimum degree. Zbl 0515.05045
Thomassen, Carsten
1983
Sign-nonsingular matrices and even cycles in directed graphs. Zbl 0589.05050
Thomassen, Carsten
1986
Rectilinear drawings of graphs. Zbl 0649.05051
Thomassen, Carsten
1988
On the complexity of some colorful problems parameterized by treewidth. Zbl 1223.05070
Fellows, Michael R.; Fomin, Fedor V.; Lokshtanov, Daniel; Rosamond, Frances; Saurabh, Saket; Szeider, Stefan; Thomassen, Carsten
2011
Graph decomposition with applications to subdivisions and path systems modulo k. Zbl 0515.05052
Thomassen, Carsten
1983
Planar and infinite hypohamiltonian and hypotraceable graphs. Zbl 0322.05130
Thomassen, Carsten
1976
The chromatic number of a graph of girth 5 on a fixed surface. Zbl 1020.05030
Thomassen, Carsten
2003
Two-coloring the edges of a cubic graph such that each monochromatic component is a path of length at most 5. Zbl 0930.05043
Thomassen, Carsten
1999
Kuratowski’s theorem. Zbl 0481.05023
Thomassen, Carsten
1981
Long cycles in digraphs. Zbl 0454.05029
Thomassen, Carsten
1981
Hypohamiltonian and hypotraceable graphs. Zbl 0278.05110
Thomassen, Carsten
1974
Finite metric spaces of strictly negative type. Zbl 0894.51003
Hjorth, Poul; Lisoněk, Petr; Markvorsen, Steen; Thomassen, Carsten
1998
The Jordan-Schönflies theorem and the classification of surfaces. Zbl 0773.57001
Thomassen, Carsten
1992
The Erdős-Pósa property for odd cycles in graphs of large connectivity. Zbl 0989.05062
Thomassen, Carsten
2001
A polynomial algorithm for the 2-path problem for semicomplete digraphs. Zbl 0759.05041
Bang-Jensen, Jørgen; Thomassen, Carsten
1992
Resistances and currents in infinite electrical networks. Zbl 0706.94029
Thomassen, Carsten
1990
Characterization of even directed graphs. Zbl 0607.05037
Seymour, Paul; Thomassen, Carsten
1987
Trees in triangulations. Zbl 0794.05027
Thomassen, Carsten
1994
Decompositions of highly connected graphs into paths of length 3. Zbl 1214.05134
Thomassen, Carsten
2008
Intersections of curve systems and the crossing number of $$C_ 5\times C_ 5$$. Zbl 0820.05015
Richter, R. B.; Thomassen, C.
1995
Five-coloring graphs on the torus. Zbl 0805.05022
Thomassen, Carsten
1994
Edge-decompositions of highly connected graphs into paths. Zbl 1181.05057
Thomassen, Carsten
2008
Graph-like continua, augmenting arcs, and Menger’s theorem. Zbl 1175.05045
Thomassen, Carsten; Vella, Antoine
2008
Highly connected non-2-linked digraphs. Zbl 0746.05030
Thomassen, Carsten
1991
When the sign pattern of a square matrix determines uniquely the sign pattern of its inverse. Zbl 0673.05067
Thomassen, Carsten
1989
Circuits through specified edges. Zbl 0488.05048
Haeggkvist, Roland; Thomassen, Carsten
1982
The 3-flow conjecture, factors modulo $$k$$, and the 1-2-3-conjecture. Zbl 1348.05085
Thomassen, Carsten; Wu, Yezhou; Zhang, Cun-Quan
2016
On the chromatic number of triangle-free graphs of large minimum degree. Zbl 1026.05042
Thomassen, Carsten
2002
Kings in $$k$$-partite tournaments. Zbl 0751.05047
Petrovic, Vojislav; Thomassen, Carsten
1991
Graphs with homeomorphically irreducible spanning trees. Zbl 0744.05013
Albertson, Michael O.; Berman, David M.; Hutchinson, Joan P.; Thomassen, Carsten
1990
Duality of infinite graphs. Zbl 0501.05054
Thomassen, Carsten
1982
Paths, circuits and subdivisions. Zbl 0659.05062
Thomassen, Carsten
1988
A nine point theorem for 3-connected graphs. Zbl 0488.05047
Holton, D. A.; McKay, B. D.; Plummer, M. D.; Thomassen, C.
1982
Edge-disjoint Hamiltonian paths and cycles in tournaments. Zbl 0486.05049
Thomassen, Carsten
1982
Some remarks on Hajós’ conjecture. Zbl 1061.05040
Thomassen, Carsten
2005
3-connected planar spaces uniquely embed in the sphere. Zbl 1010.57002
Richter, R. Bruce; Thomassen, Carsten
2002
Relations between crossing numbers of complete and complete bipartite graphs. Zbl 0872.05010
Richter, R. Bruce; Thomassen, Carsten
1997
On the number of Hamiltonian cycles in bipartite graphs. Zbl 0868.05034
Thomassen, Carsten
1996
Minimal graphs with crossing number at least $$k$$. Zbl 0733.05035
Richter, Bruce R.; Thomassen, Carsten
1993
The 2-linkage problem for acyclic digraphs. Zbl 0563.05027
Thomassen, Carsten
1985
On pancyclic digraphs. Zbl 0284.05110
Häggkvist, Roland; Thomassen, Carsten
1976
Independent dominating sets and a second hamiltonian cycle in regular graphs. Zbl 0895.05038
Thomassen, Carsten
1998
Decomposing a planar graph into degenerate graphs. Zbl 0840.05070
Thomassen, Carsten
1995
Infinite vertex-transitive, ege-transitive non-1-transitive graphs. Zbl 0677.05042
Thomassen, Carsten; Watkins, Mark E.
1989
Planar cubic hypohamiltonian and hypotraceable graphs. Zbl 0388.05033
Thomassen, Carsten
1981
Hypohamiltonian graphs and digraphs. Zbl 0371.05015
Thomassen, Carsten
1978
An Ore-type condition implying a digraph to be pancyclic. Zbl 0361.05034
Thomassen, Carsten
1977
Decomposing graphs into paths of fixed length. Zbl 1299.05270
Thomassen, Carsten
2013
Density conditions for triangles in multipartite graphs. Zbl 1174.05406
Bondy, Adrian; Shen, Jian; Thomassé, Steéphan; Thomassen, Carsten
2006
A simpler proof of the excluded minor theorem for higher surfaces. Zbl 0882.05053
Thomassen, Carsten
1997
Embeddings and minors. Zbl 0851.05043
Thomassen, Carsten
1995
Tight bounds on the chromatic sum of a connected graph. Zbl 0677.05028
Thomassen, Carsten; Erdős, Paul; Alavi, Yousef; Malde, Paresh J.; Schwenk, Allen J.
1989
The square of a planar cubic graph is 7-colorable. Zbl 1375.05110
Thomassen, Carsten
2018
On the chromatic number of pentagon-free graphs of large minimum degree. Zbl 1135.05303
Thomassen, Carsten
2007
Infinite, highly connected digraphs with no two arc-disjoint spanning trees. Zbl 0665.05023
Aharoni, Ron; Thomassen, Carsten
1989
A remark on the factor theorems of Lovasz and Tutte. Zbl 0465.05055
Thomassen, Carsten
1981
Hamiltonian paths in squares of infinite locally finite blocks. Zbl 0389.05043
Thomassen, Carsten
1978
A short proof of Meyniel’s theorem. Zbl 0368.05029
Bondy, J. A.; Thomassen, C.
1977
Chromatic roots and Hamiltonian paths. Zbl 1026.05048
Thomassen, C.
2000
Chords of longest cycles in cubic graphs. Zbl 0905.05047
Thomassen, Carsten
1997
Isoperimetric inequalities and transient random walks on graphs. Zbl 0756.60065
Thomassen, Carsten
1992
Three-regular subgraphs of four-regular graphs. Zbl 0427.05055
Chvatal, V.; Fleischner, H.; Sheehan, J.; Thomassen, C.
1979
Straight line representations of infinite planar graphs. Zbl 0373.05032
Thomassen, Carsten
1977
Some homeomorphism properties of graphs. Zbl 0272.05117
Thomassen, Carsten
1974
Decomposing a graph into bistars. Zbl 1301.05272
Thomassen, Carsten
2013
Cycles in 5-connected triangulations. Zbl 1430.05018
Alahmadi, A.; Aldred, R. E. L.; Thomassen, C.
2020
Group connectivity and group coloring: small groups versus large groups. Zbl 1435.05098
Langhede, Rikke; Thomassen, Carsten
2020
Planar Ramsey graphs. Zbl 1422.05066
Axenovich, Maria; Schade, Ursula; Thomassen, Carsten; Ueckerdt, Torsten
2019
Hamilton cycles in sparse locally connected graphs. Zbl 1406.05060
van Aardt, Susan A.; Burger, Alewyn P.; Frick, Marietjie; Thomassen, Carsten; de Wet, Johan P.
2019
The square of a planar cubic graph is 7-colorable. Zbl 1375.05110
Thomassen, Carsten
2018
The flow index and strongly connected orientations. Zbl 1384.05092
Li, Jiaao; Thomassen, Carsten; Wu, Yezhou; Zhang, Cun-Quan
2018
Chords in longest cycles. Zbl 1379.05032
Thomassen, Carsten
2018
A Hamiltonian cycle in the square of a 2-connected graph in linear time. Zbl 1403.05077
Alstrup, Stephen; Georgakopoulos, Agelos; Rotenberg, Eva; Thomassen, Carsten
2018
Decomposing graphs into a constant number of locally irregular subgraphs. Zbl 1348.05161
Bensmail, Julien; Merker, Martin; Thomassen, Carsten
2017
Cycles through all finite vertex sets in infinite graphs. Zbl 1369.05123
Kündgen, André; Li, Binlong; Thomassen, Carsten
2017
On the minimum number of spanning trees in $$k$$-edge-connected graphs. Zbl 1359.05023
Ok, S.; Thomassen, C.
2017
Infinitely connected subgraphs in graphs of uncountable chromatic number. Zbl 1413.05124
Thomassen, Carsten
2017
Spanning quadrangulations of triangulated surfaces. Zbl 1377.05040
Kündgen, André; Thomassen, Carsten
2017
The 3-flow conjecture, factors modulo $$k$$, and the 1-2-3-conjecture. Zbl 1348.05085
Thomassen, Carsten; Wu, Yezhou; Zhang, Cun-Quan
2016
Orientations of infinite graphs with prescribed edge-connectivity. Zbl 1399.05139
Thomassen, Carsten
2016
Group-colouring, group-connectivity, claw-decompositions, and orientations in 5-edge-connected planar graphs. Zbl 1360.05066
Richter, R. Bruce; Thomassen, Carsten; Younger, Daniel H.
2016
Strongly 2-connected orientations of graphs. Zbl 1302.05096
Thomassen, Carsten
2015
Extending a perfect matching to a Hamiltonian cycle. Zbl 1311.05157
2015
Destroying longest cycles in graphs and digraphs. Zbl 1311.05094
van Aardt, Susan A.; Burger, Alewyn P.; Dunbar, Jean E.; Frick, Marietjie; Llano, Bernardo; Thomassen, Carsten; Zuazua, Rita
2015
The minimum number of minimal codewords in an $$[n, k]$$-code and in graphic codes. Zbl 1311.05027
Alahmadi, A.; Aldred, R. E. L.; de la Cruz, R.; Ok, S.; Solé, P.; Thomassen, C.
2015
Group flow, complex flow, unit vector flow, and the $$(2 + \epsilon)$$-flow conjecture. Zbl 1297.05102
Thomassen, Carsten
2014
Graph factors modulo $$k$$. Zbl 1300.05262
Thomassen, Carsten
2014
Addendum: Commentary for “On planarity of compact, locally connected, metric spaces”. Zbl 1313.05357
Richter, R. Bruce; Rooney, Brendan; Thomassen, Carsten
2014
Nowhere-zero 3-flows and modulo $$k$$-orientations. Zbl 1301.05154
Lovász, László Miklós; Thomassen, Carsten; Wu, Yezhou; Zhang, Cun-Quan
2013
Decomposing graphs into paths of fixed length. Zbl 1299.05270
Thomassen, Carsten
2013
Decomposing a graph into bistars. Zbl 1301.05272
Thomassen, Carsten
2013
The maximum number of minimal codewords in long codes. Zbl 1254.05084
Alahmadi, A.; Aldred, R. E. L.; dela Cruz, R.; Solé, P.; Thomassen, C.
2013
The maximum number of minimal codewords in an $$[n,k]$$-code. Zbl 1281.94099
Alahmadi, A.; Aldred, R. E. L.; de la Cruz, R.; Solé, P.; Thomassen, C.
2013
The weak 3-flow conjecture and the weak circular flow conjecture. Zbl 1239.05083
Thomassen, Carsten
2012
From the plane to higher surfaces. Zbl 1244.05075
Kawarabayashi, Ken-Ichi; Thomassen, Carsten
2012
On the number of longest and almost longest cycles in cubic graphs. Zbl 1274.05254
Chia, Gek L.; Thomassen, Carsten
2012
On the complexity of some colorful problems parameterized by treewidth. Zbl 1223.05070
Fellows, Michael R.; Fomin, Fedor V.; Lokshtanov, Daniel; Rosamond, Frances; Saurabh, Saket; Szeider, Stefan; Thomassen, Carsten
2011
Rainbow paths with prescribed ends. Zbl 1218.05044
Alishahi, Meysam; Taherkhani, Ali; Thomassen, Carsten
2011
On planarity of compact, locally connected, metric spaces. Zbl 1249.05080
Richter, R. Bruce; Rooney, Brendan; Thomassen, Carsten
2011
Switchings, extensions, and reductions in central digraphs. Zbl 1232.05086
Kündgen, André; Leander, Gregor; Thomassen, Carsten
2011
Grinberg’s criterion applied to some non-planar graphs. Zbl 1265.05342
Chia, G. L.; Thomassen, C.
2011
Spanning trees and orientation of graphs. Zbl 1219.05044
Thomassen, Carsten
2010
Decomposing a planar graph of girth 5 into an independent set and a forest. Zbl 1184.05029
Kawarabayashi, Ken-ichi; Thomassen, Carsten
2009
The chromatic polynomial and list colorings. Zbl 1197.05061
Thomassen, Carsten
2009
Decompositions of highly connected graphs into paths of length 3. Zbl 1214.05134
Thomassen, Carsten
2008
Edge-decompositions of highly connected graphs into paths. Zbl 1181.05057
Thomassen, Carsten
2008
Graph-like continua, augmenting arcs, and Menger’s theorem. Zbl 1175.05045
Thomassen, Carsten; Vella, Antoine
2008
On the maximum number of cycles in a planar graph. Zbl 1140.05034
Aldred, R. E. L.; Thomassen, Carsten
2008
2-list-coloring planar graphs without monochromatic triangles. Zbl 1167.05029
Thomassen, Carsten
2008
On the chromatic number of pentagon-free graphs of large minimum degree. Zbl 1135.05303
Thomassen, Carsten
2007
Exponentially many 5-list-colorings of planar graphs. Zbl 1123.05043
Thomassen, Carsten
2007
Many 3-colorings of triangle-free planar graphs. Zbl 1118.05038
Thomassen, Carsten
2007
On the complexity of some colorful problems parameterized by treewidth. Zbl 1175.68292
Fellows, Michael; Fomin, Fedor V.; Lokshtanov, Daniel; Rosamond, Frances; Saurabh, Saket; Szeider, Stefan; Thomassen, Carsten
2007
Hajós’ conjecture for line graphs. Zbl 1114.05041
Thomassen, Carsten
2007
Claw-decompositions and Tutte-orientations. Zbl 1117.05088
Barát, János; Thomassen, Carsten
2006
Density conditions for triangles in multipartite graphs. Zbl 1174.05406
Bondy, Adrian; Shen, Jian; Thomassé, Steéphan; Thomassen, Carsten
2006
On the max-cut problem for a planar, cubic, triangle-free graph, and the Chinese postman problem for a planar triangulation. Zbl 1109.05039
Thomassen, Carsten
2006
The number of $$k$$-colorings of a graph on a fixed surface. Zbl 1200.05090
Thomassen, Carsten
2006
Some remarks on Hajós’ conjecture. Zbl 1061.05040
Thomassen, Carsten
2005
Edge-disjoint Hamiltonian cycles in hypertournaments. Zbl 1086.05046
Petrovic, Vojislav; Thomassen, Carsten
2005
Classification of locally 2-connected compact metric spaces. Zbl 1070.05034
Thomassen, Carsten
2005
The locally connected compact metric spaces embeddable in the plane. Zbl 1070.05033
Thomassen, Carsten
2004
Graphs with not all possible path-kernels. Zbl 1066.05107
Aldred, R. E. L.; Thomassen, Carsten
2004
Tutte’s spring theorem. Zbl 1038.05019
Thomassen, Carsten
2004
A short list color proof of Grötzsch’s theorem. Zbl 1025.05022
Thomassen, Carsten
2003
The chromatic number of a graph of girth 5 on a fixed surface. Zbl 1020.05030
Thomassen, Carsten
2003
On the chromatic number of triangle-free graphs of large minimum degree. Zbl 1026.05042
Thomassen, Carsten
2002
3-connected planar spaces uniquely embed in the sphere. Zbl 1010.57002
Richter, R. Bruce; Thomassen, Carsten
2002
Long cycles in graphs on a fixed surface. Zbl 1025.05035
Böhme, Thomas; Mohar, Bojan; Thomassen, Carsten
2002
Graphs on surfaces. Zbl 0979.05002
Mohar, Bojan; Thomassen, Carsten
2001
The Erdős-Pósa property for odd cycles in graphs of large connectivity. Zbl 0989.05062
Thomassen, Carsten
2001
Decomposing a planar graph into an independent set and a 3-degenerate graph. Zbl 1024.05075
Thomassen, Carsten
2001
Totally odd $$K_4$$-subdivisions in 4-chromatic graphs. Zbl 1012.05064
Thomassen, Carsten
2001
Chromatic roots and Hamiltonian paths. Zbl 1026.05048
Thomassen, C.
2000
The color space of a graph. Zbl 0957.05036
Jensen, Tommy R.; Thomassen, Carsten
2000
The rendezvous number of a symmetric matrix and a compact connected metric space. Zbl 1004.54020
Thomassen, Carsten
2000
Coloring triangle-free graphs with fixed size. Zbl 0948.05027
Gimbel, John; Thomassen, Carsten
2000
Highly connected sets and the excluded grid theorem. Zbl 0949.05075
Diestel, Reinhard; Jensen, Tommy R.; Gorbunov, Konstantin Yu.; Thomassen, Carsten
1999
Two-coloring the edges of a cubic graph such that each monochromatic component is a path of length at most 5. Zbl 0930.05043
Thomassen, Carsten
1999
On the Nelson unit distance coloring problem. Zbl 0986.05041
Thomassen, Carsten
1999
Parity, cycle space, and $$K_4$$-subdivisions in graphs. Zbl 0931.05041
Thomassen, C.
1999
Finite metric spaces of strictly negative type. Zbl 0894.51003
Hjorth, Poul; Lisoněk, Petr; Markvorsen, Steen; Thomassen, Carsten
1998
Independent dominating sets and a second hamiltonian cycle in regular graphs. Zbl 0895.05038
Thomassen, Carsten
1998
Color-critical graphs on a fixed surface. Zbl 0883.05051
Thomassen, Carsten
1997
Coloring graphs with fixed genus and girth. Zbl 0884.05039
Gimbel, John; Thomassen, Carsten
1997
The zero-free intervals for chromatic polynomials of graphs. Zbl 0887.05020
Thomassen, Carsten
1997
Relations between crossing numbers of complete and complete bipartite graphs. Zbl 0872.05010
Richter, R. Bruce; Thomassen, Carsten
1997
A simpler proof of the excluded minor theorem for higher surfaces. Zbl 0882.05053
Thomassen, Carsten
1997
Chords of longest cycles in cubic graphs. Zbl 0905.05047
Thomassen, Carsten
1997
On the complexity of finding a minimum cycle cover of a graph. Zbl 0870.05040
Thomassen, Carsten
1997
On the number of cycles in 3-connected cubic graphs. Zbl 0918.05068
Aldred, R. E. L.; Thomassen, Carsten
1997
The genus problem for cubic graphs. Zbl 0869.05024
Thomassen, Carsten
1997
Dirac’s conjecture on $$K_ 5$$-subdivisions. Zbl 0871.05052
Thomassen, Carsten
1997
On the number of Hamiltonian cycles in bipartite graphs. Zbl 0868.05034
Thomassen, Carsten
1996
$$K_5$$-subdivisions in graphs. Zbl 0948.05051
Thomassen, Carsten
1996
Directed cycles with two chords and strong spanning directed subgraphs with few arcs. Zbl 0842.05037
Thomassen, Carsten
1996
3-list-coloring planar graphs of girth 5. Zbl 0822.05029
Thomassen, Carsten
1995
Intersections of curve systems and the crossing number of $$C_ 5\times C_ 5$$. Zbl 0820.05015
Richter, R. B.; Thomassen, C.
1995
Decomposing a planar graph into degenerate graphs. Zbl 0840.05070
Thomassen, Carsten
1995
Embeddings and minors. Zbl 0851.05043
Thomassen, Carsten
1995
Every planar graph is 5-choosable. Zbl 0805.05023
Thomassen, Carsten
1994
Grötzsch’s 3-color theorem and its counterparts for the torus and the projective plane. Zbl 0817.05024
Thomassen, Carsten
1994
Trees in triangulations. Zbl 0794.05027
Thomassen, Carsten
1994
Five-coloring graphs on the torus. Zbl 0805.05022
Thomassen, Carsten
1994
Embeddings of graphs. Zbl 0797.05035
Thomassen, Carsten
1994
...and 123 more Documents
all top 5
#### Cited by 2,546 Authors
112 Thomassen, Carsten 72 Kawarabayashi, Ken-ichi 53 Mohar, Bojan 37 Bang-Jensen, Jørgen 37 Lai, Hong-Jian 32 Ozeki, Kenta 31 Chandran, L. Sunil 31 Thomas, Robin 30 Yu, Xingxing 24 Dvořák, Zdeněk 22 Kühn, Daniela 22 Wang, Wei-Fan 21 Thilikos, Dimitrios M. 21 Zhang, Cunquan 20 Diestel, Reinhard 20 Nakamoto, Atsuhiro 20 Raspaud, André 20 Richter, Robert Bruce 19 Osthus, Deryk 19 Zhu, Xuding 18 Lidický, Bernard 18 Liotta, Giuseppe 18 Salazar, Gelasio 17 Ren, Han 16 Kriesell, Matthias 16 Li, Jiaao 16 Seymour, Paul D. 15 Chen, Guantao 15 Fomin, Fedor V. 15 Kobayashi, Yusuke 15 Li, Xiangwen 15 Sudakov, Benny 15 Zamfirescu, Carol T. 14 Esperet, Louis 14 Fujita, Shinya 14 Havet, Frédéric 14 Hong, Seok-Hee 14 Král’, Daniel 14 Liu, Yanpei 14 Montassier, Mickaël 14 Montecchiani, Fabrizio 14 Ryjáček, Zdeněk 14 Vrána, Petr 14 Yeo, Anders 13 Borodin, Oleg Veniaminovich 13 Georgakopoulos, Agelos 13 Guo, Yubao 13 Koh, Khee Meng 13 Plummer, Michael D. 13 Postle, Luke 13 Reed, Bruce Alan 13 Wollan, Paul 13 Xu, Baogang 12 Bensmail, Julien 12 Broersma, Hajo J. 12 Bruhn, Henning 12 Chen, Min 12 Jendrol’, Stanislav 12 Li, Hao 12 Škrekovski, Riste 12 Thomassé, Stéphan 12 Wood, David Ronald 11 Ando, Kiyoshi 11 Francis, Mathew C. 11 Harant, Jochen 11 Kakimura, Naonori 11 Nagamochi, Hiroshi 11 Nešetřil, Jaroslav 11 Sau, Ignasi 10 Aldred, Robert E. L. 10 Ellingham, Mark Norman 10 Gutin, Gregory Z. 10 Hutchinson, Joan P. 10 Jackson, Bill 10 Joret, Gwenaël 10 Kostochka, Aleksandr Vasil’evich 10 Luo, Rong 10 Ma, Jie 10 Saito, Akira 10 Saurabh, Saket 10 Ye, Dong 10 Zhan, Mingquan 10 Zhang, Heping 9 Albertson, Michael O. 9 Alon, Noga M. 9 Bessy, Stéphane 9 Chiba, Shuya 9 DeVos, Matthew 9 Frick, Marietjie 9 Hliněný, Petr 9 Kaiser, Tomáš 9 Li, Binlong 9 Mader, Wolfgang 9 Ota, Katsuhiro 9 Sereni, Jean-Sébastien 9 Shao, Yehong 9 Sivadasan, Naveen 9 Stiebitz, Michael 9 Tuza, Zsolt 9 Yu, Gexin ...and 2,446 more Authors
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#### Cited in 206 Serials
492 Discrete Mathematics 342 Journal of Combinatorial Theory. Series B 187 Discrete Applied Mathematics 157 Journal of Graph Theory 147 Graphs and Combinatorics 123 European Journal of Combinatorics 64 SIAM Journal on Discrete Mathematics 58 Combinatorica 57 Theoretical Computer Science 49 Algorithmica 42 Linear Algebra and its Applications 33 Combinatorics, Probability and Computing 29 Discrete & Computational Geometry 26 The Electronic Journal of Combinatorics 25 Computational Geometry 22 Information Processing Letters 19 Applied Mathematics and Computation 18 Discussiones Mathematicae. Graph Theory 14 Journal of Combinatorial Theory. Series A 14 Transactions of the American Mathematical Society 14 Random Structures & Algorithms 12 Journal of Computer and System Sciences 12 Journal of Combinatorial Optimization 11 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 11 Topology and its Applications 11 Advances in Applied Mathematics 10 Czechoslovak Mathematical Journal 10 Journal of Mathematical Chemistry 10 Acta Mathematica Sinica. English Series 8 Bulletin of the Australian Mathematical Society 8 Advances in Mathematics 8 Mathematica Slovaca 8 Operations Research Letters 8 Acta Mathematicae Applicatae Sinica. English Series 8 Applied Mathematics Letters 8 Discrete Mathematics, Algorithms and Applications 7 Israel Journal of Mathematics 7 Networks 7 Proceedings of the American Mathematical Society 7 Information and Computation 7 Journal of Graph Algorithms and Applications 7 Science China. Mathematics 6 The Annals of Probability 6 Journal of Algebraic Combinatorics 6 Journal of Mathematical Sciences (New York) 6 Ars Mathematica Contemporanea 6 Computer Science Review 5 Linear and Multilinear Algebra 5 SIAM Journal on Computing 5 Science in China. Series A 5 The Australasian Journal of Combinatorics 5 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 5 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Journal of Mathematical Analysis and Applications 4 Journal of Statistical Physics 4 Rocky Mountain Journal of Mathematics 4 Inventiones Mathematicae 4 Order 4 International Journal of Computer Mathematics 4 Theory of Computing Systems 4 Annals of Combinatorics 4 Miscelánea Matemática 4 Journal of Applied Mathematics and Computing 4 Journal of Algebra and its Applications 4 Journal of Discrete Algorithms 4 Frontiers of Mathematics in China 3 Communications in Algebra 3 Communications in Mathematical Physics 3 Journal of Mathematical Biology 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Periodica Mathematica Hungarica 3 Geometriae Dedicata 3 Journal of Soviet Mathematics 3 Mathematische Zeitschrift 3 Monatshefte für Mathematik 3 Acta Mathematica Hungarica 3 Computers & Operations Research 3 Annals of Operations Research 3 Potential Analysis 3 Applied Mathematics. Series B (English Edition) 3 Opuscula Mathematica 3 Positivity 3 Journal of Commutative Algebra 3 Open Mathematics 2 Journal of Mathematical Physics 2 Mathematical Notes 2 Mathematics of Computation 2 Journal of Geometry and Physics 2 Beiträge zur Algebra und Geometrie 2 Annales de l’Institut Fourier 2 Journal of Functional Analysis 2 Journal of Pure and Applied Algebra 2 Mathematische Annalen 2 Rendiconti del Seminario Matemàtico e Fisico di Milano 2 Annals of Pure and Applied Logic 2 Probability Theory and Related Fields 2 Indagationes Mathematicae. New Series 2 Journal of Knot Theory and its Ramifications 2 Discrete Mathematics and Theoretical Computer Science. DMTCS 2 RAIRO. Operations Research ...and 106 more Serials
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#### Cited in 50 Fields
2,398 Combinatorics (05-XX) 316 Computer science (68-XX) 64 Operations research, mathematical programming (90-XX) 57 Manifolds and cell complexes (57-XX) 46 Convex and discrete geometry (52-XX) 45 Linear and multilinear algebra; matrix theory (15-XX) 37 Probability theory and stochastic processes (60-XX) 24 General topology (54-XX) 23 Functional analysis (46-XX) 23 Geometry (51-XX) 21 Group theory and generalizations (20-XX) 21 Biology and other natural sciences (92-XX) 21 Information and communication theory, circuits (94-XX) 19 Order, lattices, ordered algebraic structures (06-XX) 18 Mathematical logic and foundations (03-XX) 18 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 17 Statistical mechanics, structure of matter (82-XX) 13 Potential theory (31-XX) 12 Differential geometry (53-XX) 11 Functions of a complex variable (30-XX) 11 Dynamical systems and ergodic theory (37-XX) 11 Numerical analysis (65-XX) 8 Commutative algebra (13-XX) 8 Partial differential equations (35-XX) 8 Quantum theory (81-XX) 6 General and overarching topics; collections (00-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 History and biography (01-XX) 5 Number theory (11-XX) 5 Measure and integration (28-XX) 5 Operator theory (47-XX) 4 Topological groups, Lie groups (22-XX) 4 Abstract harmonic analysis (43-XX) 3 Associative rings and algebras (16-XX) 3 Algebraic topology (55-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Special functions (33-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 1 General algebraic systems (08-XX) 1 Algebraic geometry (14-XX) 1 Real functions (26-XX) 1 Ordinary differential equations (34-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Statistics (62-XX) 1 Fluid mechanics (76-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Geophysics (86-XX) 1 Systems theory; control (93-XX)
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65.484 Pages
Τελεστής Ανάδελτα
Nabla Del, Nabla, Αναδελτικός Τελεστής
Στην Διαφορική Ανάλυση, το "ανάδελτα" είναι ένας διανυσματικός, διαφορικός τελεστής.
## Ορισμοί
Σε ένα τρισδιάστατο Καρτεσιανό Σύστημα Συντεταγμένων (Cartesian coordinate system) ενός Ευκλείδειου Χώρου R3 με συνταταγμένες (x, y, z), ο τελεστής "ανάδελτα" μπορεί να ορισθεί ως εξής:
ή εναλλακτικά,
όπου:
είναι η πρότυπη βάση (standard basis) στον χώρο R3.
Del operator,
represented by
the nabla symbol
In vector calculus, del is a vector differential operator, usually represented by the nabla symbol . - When applied to a function defined on a one-dimensional domain, it denotes its standard derivative as defined in calculus. - When applied to a field (a function defined on a multi-dimensional domain), del may denote the gradient (locally steepest slope) of a scalar field, the divergence of a vector field, or the curl (rotation) of a vector field, depending on the way it is applied.
Strictly speaking, del is not a specific operator, but rather a convenient mathematical notation for those three operators, that makes many equations easier to write and remember. The del symbol can be interpreted as a vector of partial derivative operators, and its three possible meanings—gradient, divergence, and curl—can be formally viewed as the product of scalars, dot product, and cross product, respectively, of the del "operator" with the field. These formal products may not commute with other operators or products.
## Definition
In the three-dimensional Cartesian coordinate system R3 with coordinates (x, y, z), del is defined in terms of partial derivative operators as
where are the unit vectors in their respective directions. Though this page chiefly treats del in three dimensions, this definition can be generalized to the n-dimensional Euclidean space Rn. In the Cartesian coordinate system with coordinates (x1, x2, ..., xn), del is:
where is the standard basis in this space.
More compactly, using the Einstein summation notation, del is written as
Del can also be expressed in other coordinate systems, see for example del in cylindrical and spherical coordinates.
## Notational uses
Del is used as a shorthand form to simplify many long mathematical expressions. It is most commonly used to simplify expressions for the gradient, divergence, curl, directional derivative, and Laplacian.
The vector derivative of a scalar field f is called the gradient, and it can be represented as:
It always points in the direction of greatest increase of f, and it has a magnitude equal to the maximum rate of increase at the point—just like a standard derivative. In particular, if a hill is defined as a height function over a plane h(x,y), the 2d projection of the gradient at a given location will be a vector in the xy-plane (sort of like an arrow on a map) pointing along the steepest direction. The magnitude of the gradient is the value of this steepest slope.
In particular, this notation is powerful because the gradient product rule looks very similar to the 1d-derivative case:
However, the rules for dot products do not turn out to be simple, as illustrated by:
### Divergence
The divergence of a vector field is a scalar function that can be represented as:
The divergence is roughly a measure of a vector field's increase in the direction it points; but more accurately, it is a measure of that field's tendency to converge toward or repel from a point.
The power of the del notation is shown by the following product rule:
The formula for the vector product is slightly less intuitive, because this product is not commutative:
### Curl
The curl of a vector field is a vector function that can be represented as:
The curl at a point is proportional to the on-axis torque to which a tiny pinwheel would be subjected if it were centered at that point.
The vector product operation can be visualized as a pseudo-determinant:
Again the power of the notation is shown by the product rule:
Unfortunately the rule for the vector product does not turn out to be simple:
### Directional derivative
The directional derivative of a scalar field f(x,y,z) in the direction is defined as:
This gives the change of a field f in the direction of a. In operator notation, the element in parentheses can be considered a single coherent unit; fluid dynamics uses this convention extensively, terming it the convective derivative—the "moving" derivative of the fluid.
### Laplacian
The Laplace operator is a scalar operator that can be applied to either vector or scalar fields; it is defined as:
The Laplacian is ubiquitous throughout modern mathematical physics, appearing in Laplace's equation, Poisson's equation, the heat equation, the wave equation, and the Schrödinger equation—to name a few.
### Tensor derivative
Del can also be applied to a vector field with the result being a tensor. The tensor derivative of a vector field is a 9-term second-rank tensor, but can be denoted simply as , where represents the dyadic product. This quantity is equivalent to the Jacobian matrix of the vector field with respect to space.
## Second derivatives
When del operates on a scalar or vector, generally a scalar or vector is returned. Because of the diversity of vector products (scalar, dot, cross) one application of del already gives rise to three major derivatives: the gradient (scalar product), divergence (dot product), and curl (cross product). Applying these three sorts of derivatives again to each other gives five possible second derivatives, for a scalar field f or a vector field v; the use of the scalar Laplacian and vector Laplacian gives two more:
These are of interest principally because they are not always unique or independent of each other. As long as the functions are well-behaved, two of them are always zero:
Two of them are always equal:
The 3 remaining vector derivatives are related by the equation:
And one of them can even be expressed with the tensor product, if the functions are well-behaved:
## Precautions
Most of the above vector properties (except for those that rely explicitly on del's differential properties—for example, the product rule) rely only on symbol rearrangement, and must necessarily hold if del is replaced by any other vector. This is part of the tremendous value gained in representing this operator as a vector in its own right.
Though you can often replace del with a vector and obtain a vector identity, making those identities intuitive, the reverse is not necessarily reliable, because del does not often commute.
A counterexample that relies on del's failure to commute:
A counterexample that relies on del's differential properties:
Central to these distinctions is the fact that del is not simply a vector; it is a vector operator. Whereas a vector is an object with both a precise numerical magnitude and direction, del does not have a precise value for either until it is allowed to operate on something.
For that reason, identities involving del must be derived with care, using both vector identities and differentiation identities such as the product rule.
## Ιστογραφία
Κίνδυνοι Χρήσης
Αν και θα βρείτε εξακριβωμένες πληροφορίες
σε αυτήν την εγκυκλοπαίδεια
ωστόσο, παρακαλούμε να λάβετε σοβαρά υπ' όψη ότι
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την εγκυρότητα των πληροφοριών που περιλαμβάνει.
"Οι πληροφορίες αυτές μπορεί πρόσφατα
να έχουν αλλοιωθεί, βανδαλισθεί ή μεταβληθεί από κάποιο άτομο,
η άποψη του οποίου δεν συνάδει με το "επίπεδο γνώσης"
του ιδιαίτερου γνωστικού τομέα που σας ενδιαφέρει."
Πρέπει να λάβετε υπ' όψη ότι
όλα τα άρθρα μπορεί να είναι ακριβή, γενικώς,
και για μακρά χρονική περίοδο,
αλλά να υποστούν κάποιο βανδαλισμό ή ακατάλληλη επεξεργασία,
ελάχιστο χρονικό διάστημα, πριν τα δείτε.
Επίσης,
(όχι μόνον, της Sciencepedia
αλλά και κάθε διαδικτυακού ιστότοπου (ή αλλιώς site)),
αν και άκρως απαραίτητοι,
είναι αδύνατον να ελεγχθούν
(λόγω της ρευστής φύσης του Web),
και επομένως είναι ενδεχόμενο να οδηγήσουν
σε παραπλανητικό, κακόβουλο ή άσεμνο περιεχόμενο.
Ο αναγνώστης πρέπει να είναι
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αν διαφωνείτε με όσα αναγράφονται σε αυτήν
>>Διαμαρτυρία προς την wikia<<
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Community content is available under CC-BY-SA unless otherwise noted.
| 2021-06-25T10:11:39 |
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http://welding-inve.gov.petshoponline.me/post/series-rc-circuit-equations
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# series rc circuit equations
welding-inve.gov.petshoponline.me 9 out of 10 based on 800 ratings. 200 user reviews.
Analyze a Series RC Circuit Using a Differential Equation ... The RC series circuit is a first order circuit because it’s described by a first order differential equation. A circuit reduced to having a single equivalent capacitance and a single equivalent resistance is also a first order circuit. The circuit has an applied input voltage v T (t). Series RC circuit and its Design [A Low Pass Filter] Series RC Circuit The name defines itself, it is a series circuit comprising of a resistor (R) and capacitor (C). It is a first order differential circuit because by applying Kirchoff’s Laws, the circuit ends in a first order differential equation. Don’t be scared of these heavy words, they are very simple to understand. RC circuit These equations show that a series RC circuit has a time constant, usually denoted τ = RC being the time it takes the voltage across the component to either rise (across the capacitor) or fall (across the resistor) to within 1 e of its final value. What is RC Series Circuit? Phasor Diagram and Power Curve ... RC Series Circuit A circuit that contains pure resistance R ohms connected in series with a pure capacitor of capacitance C farads is known as RC Series Circuit. A sinusoidal voltage is applied to and current I flows through the resistance (R) and the capacitance (C) of the circuit.The RC Series circuit is shown in the figure below Application of ODEs: 6. Series RC Circuit A series RC circuit with R = 5 W and C = 0.02 F is connected with a battery of E = 100 V. At t = 0, the voltage across the capacitor is zero. (a) Obtain the subsequent voltage across the capacitor. RC Series Circuit Analysis | RC Time Constant Electrical ... The discharge equations are summarized in the following figure. You May Also Read: RC Circuit Analysis using Matlab; When a voltage is switched on to a series RC Circuit, V C increases exponentially toward the level of E over a time of 5RC. The current jumps to I=E R then decreases exponentially to zero. RC Charging Circuit Tutorial & RC Time Constant This then forms the basis of an RC charging circuit were 5T can also be thought of as “5 x RC”. RC Charging Circuit. The figure below shows a capacitor, ( C ) in series with a resistor, ( R ) forming a RC Charging Circuit connected across a DC battery supply ( Vs ) via a mechanical switch. When the switch is closed, the capacitor will ... The RC Circuit The RC Circuit The RC circuit is the electrical circuit consisting of a resistor of resistance R, a capacitor of capacitance C and a voltage source arranged in series. If the charge on the capacitor is Q and the C R V current flowing in the circuit is I, the voltage across R and C are RI and Q C respectively. By the Simple RC Series Circuit ** THIS VIDEO ASSUMES THAT YOU UNDERSTAND HOW TO SOLVE FIRST ORDER DIFFERENTIAL EQUATIONS AND HOW A CAPACITOR SHOULD BEHAVE IN A CIRCUIT ** This is just a short video on a series RC circuit. More ... Voltage and Current Calculations | RC and L R Time ... In a series RC circuit, the time constant is equal to the total resistance in ohms multiplied by the total capacitance in farads. For a series L R circuit, it is the total inductance in henrys divided by the total resistance in ohms. DC Circuit Equations and Laws | Useful Equations And ... NOTE: the symbol “V” (“U” in Europe) is sometimes used to represent voltage instead of “E”. In some cases, an author or circuit designer may choose to exclusively use “V” for voltage, never using the symbol “E.” Other times the two symbols are used interchangeably, or “E” is ... RC step response (article) | Khan Academy How does an RC circuit respond to a voltage step? We solve for the total response as the sum of the forced and natural response. The RC step response is a fundamental behavior of all digital circuits. Written by Willy McAllister. RC Circuits web.pa.msu.edu An RC circuit is a circuit with both a resistor (R) and a capacitor (C). RC circuits are freqent element in electronic devices. They also play an important role in the transmission of electrical signals in nerve cells. A capacitor can store energy and a resistor placed in series with it will control the rate at which it charges or discharges. RC Circuit Analysis (1 of 8) Voltage and Current Explains RC circuit analysis for voltage, charge and current. ... RC Circuits, Charging Capacitors and Equation Derivations ... Capacitors (5 of 11) in bination, Parallel and Series Capacitors ... Figure 1. Series RC circuit driven by a sinusoidal forcing ... Series RC circuit driven by a sinusoidal forcing function Our goal is to determine the voltages v c (t) and the current i(t) which will completely characterize the “Steady State” response of the circuit. The equation that describes the behavior of this circuit is obtained by applying KVL An RC Circuit: Charging physics.bu.edu I(t) = (Q o RC) e t τ = I o e t τ. where I o = ε R is the maximum current possible in the circuit. The time constant τ = RC determines how quickly the capacitor charges. If RC is small the capacitor charges quickly; if RC is large the capacitor charges more slowly. Analyze a First Order RC Circuit Using Laplace Methods ... Consider the simple first order RC series circuit shown here. To set up the differential equation for this series circuit, you can use Kirchhoff’s voltage law (KVL), which says the sum of the voltage rises and drops around a loop is zero. This circuit has the following KVL equation around the loop: v S (t) v r (t) v c (t) = 0 RC circuit equation derivation edaboard the equation i have shown is a very general equation which i can apply to any kind of RC circuit. so i wanted to understand the derivation of the equation. My general feeling was that if i have a source voltage and a series resistor and a capacitor it is always the case of energizing as the capacitor has no path for de energizing. RC Circuits | Boundless Physics differential equation : An equation involving the derivatives of a function. An RC circuit is one containing a resistor R and a capacitor C. The capacitor is an electrical component that houses electric charge. In this Atom, we will study how a series RC circuit behaves when connected to a DC voltage source. RC time constant The RC time constant, also called tau, the time constant (in seconds) of an RC circuit, is equal to the product of the circuit resistance (in ohms) and the circuit capacitance (in farads), i.e. τ = R C {\displaystyle \tau =RC} RC Circuit Calculator Omni RC circuit. The RC circuit is a basic electrical circuit in which a resistor of resistance R is connected in a series with a capacitor of capacitance C. Such circuit is characterized by a frequency f and has two primary applications: the RC circuit can be used as a filter, and the capacitor can be used to store the energy. Transient response of RC and RL circuits Transient response of RC and RL circuits ENGR40M lecture notes | July 26, 2017 Chuan Zheng Lee, Stanford University Resistor{capacitor (RC) and resistor{inductor (RL) circuits are the two types of rst order circuits: circuits either one capacitor or one inductor. In many applications, these circuits respond to a sudden change in an RL Series Circuit | Electrical4U The term L R in the equation is called the Time Constant, (τ) of the RL series circuit, and it is defined as time taken by the current to reach its maximum steady state value and the term V R represents the final steady state value of current in the circuit. Difference between RC and RL Circuit Electronics Coach The major difference between RC and RL circuits is that the RC circuit stores energy in the form of the electric field while the RL circuit stores energy in the form of magnetic field. The RC circuit is formed by connecting a resistance in series with the capacitor and a battery source is provided to charge the capacitor. Series RLC Circuit and RLC Series Circuit Analysis In a series RLC circuit containing a resistor, an inductor and a capacitor the source voltage V S is the phasor sum made up of three components, V R, V L and V C with the current common to all three. Since the current is common to all three components it is used as the horizontal reference when constructing a voltage triangle. 10.5: RC Circuits Physics LibreTexts Circuits with Resistance and Capacitance. An RC circuit is a circuit containing resistance and capacitance. As presented in Capacitance, the capacitor is an electrical component that stores electric charge, storing energy in an electric field.. Figure $$\PageIndex{1a}$$ shows a simple RC circuit that employs a dc (direct current) voltage source $$ε$$, a resistor $$R$$, a capacitor $$C$$, and ... Chapter 7 Response of First order RL and RC Circuits and RC Circuits 7.1 2 The Natural Response of RL and RC Circuits. 7.3 The Step Response of . RL . and . RC . Circuits. 7.4 A General Solution for Step and Natural Responses. 7.5 Sequential Switching. 7.6 Unbounded Response. 2 ... and RC Circuits 1. Differential equation & solution of a Passive ponents in AC Circuits with Equations ... There are three key passive elements used in many electrical and electronic circuits such as: Resistor, Inductor, and Capacitor. All these three elements limit the current flow but in a dissimilar manner. Series RC Circuit Impedance Calculator, Electrical, RF and ... A simple series RC or resistor capacitor circuit is composed of a resistor and a capacitor connected in series and driven by a voltage source. The current in both capacitor and resistor is the same because they are connected in series. The voltages across the resistor V R and the capacitor V C are shown in the diagram at the right angle to each ... AC RC CIRCUITS jick.net We begin by picturing a generic series RC circuit driven by a sinusoidal voltage E(t) = E0 cos(!t) = Solution of First Order Linear Differential Equation Solution of First Order Linear Differential Equation Thesolutiontoafirst orderlineardifferentialequationwithconstantcoefficients, a1 dX dt a0X =f(t), is X = Xn ... ACL2 Flashcards | Quizlet A parallel RC circuit has a resistance of 470 ohms, a reactance of 330 ohms, and an applied voltage of 470 volts. Solve for the impedance of the circuit by determining the branch currents and the total current. (Round the FINAL answer to one decimal place.) The values calculated for this question will be used for additional questions. First Order Circuits LSU Mathematics First Order Circuits We will consider a few simple electrical circuits that lead to ˝rst order linear di˙erential equations. These are sometimes referred to as ˝rst order circuits. The basic elements to be considered are: 1. Resistor 2. Inductor 3. Capacitor Thecurrent I(t), expressed inunitsofamperes, throughoneofthese elements
## series rc circuit equations Gallery
### electric currents and resistance
#### New Update
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| 2019-11-19T05:24:11 |
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https://tardis.fandom.com/wiki/1_(number)
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## FANDOM
86,635 Pages
1 was a prime number. (AUDIO: The Haunting)
According to the Tenth Doctor, "Any number that reduces to 1 when you take the sum of the square of its digits and continue iterating it until it yields 1 is a happy number; any number that doesn't, isn't." (TV: 42)
The Twelfth Doctor once proved that $\lim_{\theta\to 0} \frac {sin \theta} {\theta} = 1$. (TV: The Pilot)
Block Transfer Computation made use of 1s and 0s, as it was written in binary. (AUDIO: The Enchantress of Numbers)
According to the Second Doctor, a one in 13 chance was about 7.6923 percent, odds he didn't like. (COMIC: Card Conundrum)
The Twelfth Doctor once told Bill that "eleven plus two" was an anagram of "twelve plus one", to which Bill responded that both of these were equal to 13. (COMIC: Harvest of the Daleks)
## Behind the scenes Edit
Though AUDIO: The Haunting establishes that 1 is itself a prime number in the DWU, this is a point of contention among mathematicians.
Generally, 1 is considered neither prime nor composite. It would certainly have been considered a prime, however, in the story's time period of the 1890s. In particular, the entry for Number published in 1890 in the 9th edition of Encyclopædia Britannica stated that every positive number was either prime or composite, and explicitly listed 1 as prime.[1]
Though unremarked in PROSE: Daisy Chain, 1 is also the first and second Fibonacci number.
## Footnotes Edit
1. A. Reddick et al. The History of the Primality of One---A Selection of Sources. Accessed at http://primes.utm.edu/notes/one.pdf on 7.12.2015.
Community content is available under CC-BY-SA unless otherwise noted.
| 2020-10-01T05:49:29 |
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http://dlmf.nist.gov/7.20
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§7.20 Mathematical Applications
§7.20(i) Asymptotics
For applications of the complementary error function in uniform asymptotic approximations of integrals—saddle point coalescing with a pole or saddle point coalescing with an endpoint—see Wong (1989, Chapter 7), Olver (1997b, Chapter 9), and van der Waerden (1951).
The complementary error function also plays a ubiquitous role in constructing exponentially-improved asymptotic expansions and providing a smooth interpretation of the Stokes phenomenon; see §§2.11(iii) and 2.11(iv).
§7.20(ii) Cornu’s Spiral
Let the set $\{x(t),y(t),t\}$ be defined by $x(t)=\mathop{C\/}\nolimits\!\left(t\right)$, $y(t)=\mathop{S\/}\nolimits\!\left(t\right)$, $t\geq 0$. Then the set $\{x(t),y(t)\}$ is called Cornu’s spiral: it is the projection of the corkscrew on the $\{x,y\}$-plane. See Figure 7.20.1. The spiral has several special properties (see Temme (1996b, p. 184)). Let $P(t)=P(x(t),y(t))$ be any point on the projected spiral. Then the arc length between the origin and $P(t)$ equals $t$, and is directly proportional to the curvature at $P(t)$, which equals $\pi t$. Furthermore, because $\ifrac{dy}{dx}=\mathop{\tan\/}\nolimits\!\left(\frac{1}{2}\pi t^{2}\right)$, the angle between the $x$-axis and the tangent to the spiral at $P(t)$ is given by $\frac{1}{2}\pi t^{2}$.
§7.20(iii) Statistics
The normal distribution function with mean $m$ and standard deviation $\sigma$ is given by
7.20.1 $\frac{1}{\sigma\sqrt{2\pi}}\int_{-\infty}^{x}e^{-(t-m)^{2}/(2\sigma^{2})}dt=% \frac{1}{2}\mathop{\mathrm{erfc}\/}\nolimits\!\left(\frac{m-x}{\sigma\sqrt{2}}% \right)=Q\left(\frac{m-x}{\sigma}\right)=P\left(\frac{x-m}{\sigma}\right).$
For applications in statistics and probability theory, also for the role of the normal distribution functions (the error functions and probability integrals) in the asymptotics of arbitrary probability density functions, see Johnson et al. (1994, Chapter 13) and Patel and Read (1982, Chapters 2 and 3).
| 2016-07-26T08:22:02 |
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https://pdglive.lbl.gov/DataBlock.action?node=S070M0&home=BXXX045
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${{\boldsymbol \Xi}_{{b}}^{0}}$ MASS
VALUE (MeV) DOCUMENT ID TECN COMMENT
$\bf{ 5791.9 \pm0.5}$ OUR AVERAGE
$5794.3$ $\pm2.4$ $\pm0.7$
2014 H
LHCB ${{\mathit p}}{{\mathit p}}$ at 7 TeV
$5791.80$ $\pm0.39$ $\pm0.31$ 1
2014 Z
LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8 TeV
$5788.7$ $\pm4.3$ $\pm1.4$ 2
2014 B
CDF ${{\mathit p}}{{\overline{\mathit p}}}$ at 1.96 TeV
• • We do not use the following data for averages, fits, limits, etc. • •
$5787.8$ $\pm5.0$ $\pm1.3$ 3
2011 X
CDF Repl. by AALTONEN 2014B
1 Uses ${{\mathit \Xi}_{{b}}^{0}}$ $\rightarrow$ ${{\mathit \Xi}_{{c}}^{+}}{{\mathit \pi}^{-}}$ and ${{\mathit \Xi}_{{c}}^{+}}$ $\rightarrow$ ${{\mathit p}}{{\mathit K}^{-}}{{\mathit \pi}^{+}}$ decays. The measurement comes from the mass difference of ${{\mathit \Xi}_{{b}}^{0}}$ and ${{\mathit \Lambda}_{{b}}^{0}}$.
2 Uses ${{\mathit \Xi}_{{b}}^{0}}$ $\rightarrow$ ${{\mathit \Xi}_{{c}}^{+}}{{\mathit \pi}^{-}}$ decays.
3 Measured in ${{\mathit \Xi}_{{b}}^{0}}$ $\rightarrow$ ${{\mathit \Xi}_{{c}}^{+}}{{\mathit \pi}^{-}}$ with $25.3$ ${}^{+5.6}_{-5.4}$ candidates.
References:
AAIJ 2014H
PR D89 032001 Studies of Beauty Baryon Decays to ${{\mathit D}^{0}}{{\mathit p}}{{\mathit h}^{-}}$ and ${{\mathit \Lambda}_{{c}}^{+}}{{\mathit h}^{-}}$ Final States
AAIJ 2014Z
PRL 113 032001 Precision Measurement of the Mass and Lifetime of the ${{\mathit \Xi}_{{b}}^{0}}$ Baryon
AALTONEN 2014B
PR D89 072014 Mass and Lifetime Measurements of Bottom and Charm Baryons in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.96 TeV
AALTONEN 2011X
PRL 107 102001 Observation of the ${{\mathit \Xi}_{{b}}^{0}}$ Baryon
| 2022-01-24T03:49:57 |
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|
https://par.nsf.gov/biblio/10101025
|
α-Alumina and spinel react into single-phase high-alumina spinel in <3 seconds during flash sintering
In situ X-ray diffraction measurements at the Advanced Photon Source show that alpha-Al2O3 and MgAl2O4 react nearly instantaneously and completely, and nearly completely to form single-phase high-alumina spinel during voltage-to-current type of flash sintering experiments. The initial sample was constituted from powders of alpha-Al2O3, MgAl2O4 spinel, and cubic 8 mol% Y2O3-stabilized ZrO2 (8YSZ) mixed in equal volume fractions, the spinel to alumina molar ratio being 1:1.5. Specimen temperature was measured by thermal expansion of the platinum standard. These measurements correlated well with a black-body radiation model, using appropriate values for the emissivity of the constituents. Temperatures of 1600-1736 degrees C were reached during the flash, which promoted the formation of alumina-rich spinel. In a second set of experiments, the flash was induced in a current-rate method where the current flowing through the specimen is controlled and increased at a constant rate. In these experiments, we observed the formation of two different compositions of spinel, MgO center dot 3Al(2)O(3) and MgO center dot 1.5Al(2)O(3), which evolved into a single composition of MgO center dot 2.5Al(2)O(3) as the current continued to increase. In summary, flash sintering is an expedient way to create single-phase, alumina-rich spinel.
Authors:
; ; ; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10101025
Journal Name:
Journal of the American Ceramic Society
Volume:
102
Issue:
2
Page Range or eLocation-ID:
644-653
ISSN:
0002-7820
2. ABSTRACT ASASSN-18am/SN 2018gk is a newly discovered member of the rare group of luminous, hydrogen-rich supernovae (SNe) with a peak absolute magnitude of MV ≈ −20 mag that is in between normal core-collapse SNe and superluminous SNe. These SNe show no prominent spectroscopic signatures of ejecta interacting with circumstellar material (CSM), and their powering mechanism is debated. ASASSN-18am declines extremely rapidly for a Type II SN, with a photospheric-phase decline rate of ∼6.0 mag (100 d)−1. Owing to the weakening of H i and the appearance of He i in its later phases, ASASSN-18am is spectroscopically a Type IIb SN with a partially stripped envelope. However, its photometric and spectroscopic evolution shows significant differences from typical SNe IIb. Using a radiative diffusion model, we find that the light curve requires a high synthesized 56Ni mass $M_{\rm Ni} \sim 0.4\, \rm {M_{\odot }}$ and ejecta with high kinetic energy Ekin = (7–10) × 1051 erg. Introducing a magnetar central engine still requires $M_{\rm Ni} \sim 0.3\, \rm {M_{\odot }}$ and Ekin = 3 × 1051 erg. The high 56Ni mass is consistent with strong iron-group nebular lines in its spectra, which are also similar to several SNe Ic-BL with high 56Ni yields. The earliest spectrum shows ‘flash ionization’ features, from which we estimatemore »
| 2022-12-09T02:46:09 |
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|
https://pdglive.lbl.gov/DataBlock.action?node=B104D14&home=sumtabB
|
#### ${\mathit m}_{{{\mathit \Sigma}_{{c}}{(2455)}^{+}}}–{\mathit m}_{{{\mathit \Sigma}_{{c}}{(2455)}^{0}}}$
VALUE (MeV) DOCUMENT ID TECN COMMENT
$\bf{ -1.10 {}^{+0.16}_{-0.08}}$ OUR FIT
• • We do not use the following data for averages, fits, limits, etc. • •
$1.4$ $\pm0.5$ $\pm0.3$
1993
CLE2 See AMMAR 2001
References:
CRAWFORD 1993
PRL 71 3259 Observation of the Charmed Baryon ${{\mathit \Sigma}_{{c}}^{+}}$ and Measurement of the Isospin Mass Splitting of the ${{\mathit \Sigma}_{{c}}}$
| 2023-03-29T22:51:41 |
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|
https://linkeddata.tern.org.au/viewer/tern/id/http://linked.data.gov.au/def/tern-cv/0d748d470c37a8a98cb40302b8b238a6c2813165d96d3c63c69dfb59cd534a0b
|
# surface upwelling longwave flux in air
URI: http://linked.data.gov.au/def/tern-cv/0d748d470c37a8a98cb40302b8b238a6c2813165d96d3c63c69dfb59cd534a0b
Also known as surface_upwelling_longwave_flux_in_air
Date created: 2018-07-03
Date modified: 2022-06-10
Parameter Type
##### Definition
The surface called "surface" means the lower boundary of the atmosphere. The term "longwave" means longwave radiation. Upwelling radiation is radiation from below. It does not mean "net upward". The sign convention is that "upwelling" is positive upwards and "downwelling" is positive downwards. When thought of as being incident on a surface, a radiative flux is sometimes called "irradiance". In addition, it is identical with the quantity measured by a cosine-collector light-meter and sometimes called "vector irradiance". In accordance with common usage in geophysical disciplines, "flux" implies per unit area, called "flux density" in physics.
##### source
http://vocab.nerc.ac.uk/collection/P07/current/
##### notation
surface_upwelling_longwave_flux_in_air
##### note
This concept was harvested from the controlled vocabulary at http://vocab.nerc.ac.uk/collection/P07/current/ on 2022-06-10. Information was pulled as-is for the following properties: dcterms:created, skos:definition, skos:exactMatch, skos:related and skos:notation. The URI of the concept is generated using SHA256 on the CF standard name (in the skos:notation) and concatenated with the TERN controlled vocabularies' base URI (http://linked.data.gov.au/def/tern-cv/).
##### related
http://vocab.nerc.ac.uk/collection/P06/current/UFAA/
TERN is supported by the Australian Government through the National Collaborative Research Infrastructure Strategy, NCRIS.
| 2022-08-15T21:39:40 |
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|
https://www.zbmath.org/authors/?q=ai%3Awu.min.1
|
# zbMATH — the first resource for mathematics
## Wu, Min
Compute Distance To:
Author ID: wu.min.1 Published as: Wu, M.; Wu, Min Homepage: https://ece.umd.edu/~minwu/ External Links: MGP · Wikidata · ORCID
Documents Indexed: 167 Publications since 1993, including 1 Book
all top 5
#### Co-Authors
0 single-authored 1 Bloom, Jeffrey A. 1 Chen, Meng 1 Cox, Ingemar J. 1 Gou, Hongmei 1 Lin, Ching-Yung 1 Liu, Bede 1 Liu, K. J. Ray 1 Lui, Yui Man 1 Miller, Matt L. 1 Trappe, Wade 1 Wang, Z. Jane 1 Zheng, Yefeng
#### Serials
2 IEEE Transactions on Signal Processing 1 IEEE Transactions on Image Processing 1 EURASIP Journal on Applied Signal Processing
#### Fields
3 Information and communication theory, circuits (94-XX) 2 Computer science (68-XX)
#### Citations contained in zbMATH
81 Publications have been cited 370 times in 262 Documents Cited by Year
Stability analysis for neutral systems with mixed delays. Zbl 1120.34057
Liu, Xin-Ge; Wu, Min; Martin, Ralph; Tang, Mei-Lan
2007
Delay-dependent stability analysis for uncertain neutral systems with time-varying delays. Zbl 1128.34048
Liu, Xin-Ge; Wu, Min; Martin, Ralph; Tang, Mei-Lan
2007
Hausdorff dimensions of the divergence points of self-similar measures with the open set condition. Zbl 1236.28007
Li, Jinjun; Wu, Min; Xiong, Ying
2012
Rotation, scale, and translation resilient watermarking for images. Zbl 1037.68778
Lin, Ching-Yung; Wu, Min; Bloom, Jeffrey A.; Cox, Ingemar J.; Miller, Matt L.; Lui, Yui Man
2001
On exceptional sets in Erdős-Rényi limit theorem. Zbl 1408.11077
Li, Jinjun; Wu, Min
2016
The Hausdorff measure of a Sierpinski carpet. Zbl 0984.28005
Zhou, Zuoling; Wu, Min
1999
On exceptional sets in Erdős-Rényi limit theorem revisited. Zbl 1371.28022
Li, Jinjun; Wu, Min
2017
Topological pressure and topological entropy of a semigroup of maps. Zbl 1234.37011
Ma, Dongkui; Wu, Min
2011
Pointwise dimensions of general Moran measures with open set condition. Zbl 1219.28010
Li, Jinjun; Wu, Min
2011
Generic property of irregular sets in systems satisfying the specification property. Zbl 1280.54024
Li, Jinjun; Wu, Min
2014
The sets of divergence points of self-similar measures are residual. Zbl 1304.28008
Li, Jinjun; Wu, Min
2013
The multifractal spectrum of some Moran measures. Zbl 1126.28010
Wu, Min
2005
The singularity spectrum $$f(\alpha)$$ of some Moran fractals. Zbl 1061.28005
Wu, Min
2005
Picard-Vessiot extensions for linear functional systems. Zbl 1360.12005
Bronstein, Manuel; Li, Ziming; Wu, Min
2005
Divergence points of self-similar measures satisfying the OSC. Zbl 1223.28007
Xiao, Jia-Qing; Wu, Min; Gao, Fei
2011
Anti-collusion fingerprinting for multimedia. Zbl 1369.94591
Trappe, Wade; Wu, Min; Wang, Z. Jane; Liu, K. J. Ray
2003
Inference for accelerated competing failure models from Weibull distribution under type-I progressive hybrid censoring. Zbl 1381.62267
Wu, Min; Shi, Yimin; Sun, Yudong
2014
The effect of interstitial pressure on tumor growth: coupling with the blood and lymphatic vascular systems. Zbl 1406.92330
Wu, Min; Frieboes, Hermann B.; McDougall, Steven R.; Chaplain, Mark A. J.; Cristini, Vittorio; Lowengrub, John
2013
Divergence points in systems satisfying the specification property. Zbl 1271.37026
Li, Jinjun; Wu, Min
2013
On the longest block in Lüroth expansion. Zbl 1434.11153
Li, Jinjun; Wu, Min; Yang, Xiangfeng
2018
A note on the rate of returns in random walks. Zbl 1296.54034
Li, Jinjun; Wu, Min
2014
Quasisymmetric minimality on packing dimension for Moran sets. Zbl 1309.28004
Li, Yanzhe; Wu, Min; Xi, Lifeng
2013
The pointwise dimensions of Moran measures. Zbl 1200.28011
Lou, Manli; Wu, Min
2010
The multifractal dimension functions of homogeneous Moran measure. Zbl 1165.28005
Xiao, Jiaqing; Wu, Min
2008
Lower dimensions of some fractal sets. Zbl 1370.28004
Chen, Haipeng; Wu, Min; Wei, Chun
2017
Further results on delay-dependent stability criteria of discrete systems with an interval time-varying delay. Zbl 1367.93448
Wu, Min; Peng, Chen; Zhang, Jin; Fei, Minrui; Tian, Yuchu
2017
Limit theorems related to beta-expansion and continued fraction expansion. Zbl 1408.11076
Fang, Lulu; Wu, Min; Li, Bing
2016
Statistical inference for competing risks model in step-stress partially accelerated life tests with progressively type-I hybrid censored Weibull life data. Zbl 1327.62501
Zhang, Chunfang; Shi, Yimin; Wu, Min
2016
Generating invariants of hybrid systems via sums-of-squares of polynomials with rational coefficients. Zbl 1345.65046
Wu, Min; Yang, Zhengfeng
2011
Doubling measures with doubling continuous part. Zbl 1203.28012
Lou, Man-Li; Wu, Min
2010
Category and dimensions for cut-out sets. Zbl 1177.28027
Xiong, Ying; Wu, Min
2009
Two examples on atomic doubling measures. Zbl 1123.28004
Lou, Manli; Wen, Shengyou; Wu, Min
2007
A recursive method for determining the one-dimensional submodules of Laurent-Ore modules. Zbl 1356.12012
Li, Ziming; Singer, Michael F.; Wu, Min; Zheng, Dabin
2006
A note on Rényi’s ‘record’ problem and Engel’s series. Zbl 1419.60024
Fang, Lulu; Wu, Min
2018
Hausdorff dimension of certain sets arising in Engel expansions. Zbl 1437.11115
Fang, Lulu; Wu, Min
2018
Exact safety verification of hybrid systems using sums-of-squares representation. Zbl 1343.93051
Lin, Wang; Wu, Min; Yang, Zhengfeng; Zeng, Zhenbing
2014
A discrete-time global quasi-sliding mode control scheme with bounded external disturbance rejection. Zbl 1307.93106
Wu, M.; Chen, J. S.
2014
Optimal isolation strategies of emerging infectious diseases with limited resources. Zbl 1273.92063
Zhou, Yinggao; Wu, Jianhong; Wu, Min
2013
Liouvillian solutions of linear difference-differential equations. Zbl 1233.12004
Feng, Ruyong; Singer, Michael F.; Wu, Min
2010
On Assouad dimension and arithmetic progressions in sets defined by digit restrictions. Zbl 1414.28017
Li, Jinjun; Wu, Min; Xiong, Ying
2019
Beta-expansion and continued fraction expansion of real numbers. Zbl 1448.11150
Fang, Lulu; Wu, Min; Li, Bing
2019
Large and moderate deviation principles for Engel continued fractions. Zbl 1442.11112
Fang, Lulu; Wu, Min; Shang, Lei
2018
A note on correlation and local dimensions. Zbl 1380.28001
Yang, Jiaojiao; Käenmäki, Antti; Wu, Min
2017
Second-order integro-differential parabolic variational inequalities arising from the valuation of American option. Zbl 06408985
Sun, Yudong; Shi, Yimin; Wu, Min
2014
Transforming linear functional systems into fully integrable systems. Zbl 1252.68357
Li, Ziming; Wu, Min
2012
The singularity spectrum of some non-regularity Moran fractals. Zbl 1222.28020
Wu, Min; Xiao, Jiaqing
2011
On the pointwise densities of the Cantor measure. Zbl 1219.28007
Wang, Jun; Wu, Min; Xiong, Ying
2011
On Hausdorff dimension and topological entropy. Zbl 1206.28008
Ma, Dongkui; Wu, Min
2010
A new semi-local convergence theorem for the inexact Newton methods. Zbl 1160.65025
Wu, Min
2008
Lipschitz constant for bi-Lipschitz automorphism on Moran-like sets. Zbl 1133.28005
Guo, Qiu-Li; Wu, Min; Xi, Li-Feng
2007
A note on Whitney’s critical sets. Zbl 1036.28012
Xi, Lifeng; Wu, Min
2003
Multimedia data hiding. Zbl 1018.68027
Wu, Min; Liu, Bede
2003
Universal admissibility of linear estimators in multivariate linear models with respect to a restricted parameter set. Zbl 0995.62003
Qin, Hong; Wu, Min; Peng, Junhao
2002
On Hausdorff and Bouligand dimensions of a class of recurrent sets. Zbl 0824.28008
Wu, Min
1995
Slow growth rate of the digits in Engel expansions. Zbl 1434.11155
Shang, Lei; Wu, Min
2020
A game-based approximate verification of deep neural networks with provable guarantees. Zbl 1436.68199
Wu, Min; Wicker, Matthew; Ruan, Wenjie; Huang, Xiaowei; Kwiatkowska, Marta
2020
Improved stability criteria for the neural networks with time-varying delay via new augmented Lyapunov-Krasovskii functional. Zbl 1428.34101
Gao, Zhen-Man; He, Yong; Wu, Min
2019
The exceptional sets on the run-length function of $$\beta$$-expansions. Zbl 1432.11104
Zheng, Lixuan; Wu, Min; Li, Bing
2017
Statistical analysis of dependent competing risks model in accelerated life testing under progressively hybrid censoring using copula function. Zbl 1402.62244
Wu, Min; Shi, Yimin; Zhang, Chunfang
2017
The topological property of the irregular sets on the lengths of basic intervals in beta-expansions. Zbl 1401.37014
Zheng, Lixuan; Wu, Min; Li, Bing
2017
Level sets and equivalences of Moran-type sets. Zbl 1374.28006
Du, Yali; Miao, Junjie; Wu, Min
2016
A note on the distribution of the digits in Cantor expansions. Zbl 1339.11077
Li, Jinjun; Wang, Yi; Wu, Min
2016
Bayes estimation and expected termination time for the competing risks model from Gompertz distribution under progressively hybrid censoring with binomial removals. Zbl 1331.62390
Wu, Min; Shi, Yimin
2016
Establishing a dynamic self-adaptation learning algorithm of the BP neural network and its applications. Zbl 1334.68189
Li, Xiaofeng; Xiang, Suying; Zhu, Pengfei; Wu, Min
2015
Domain-of-attraction estimation for uncertain non-polynomial systems. Zbl 07175113
Wu, Min; Yang, Zhengfeng; Lin, Wang
2014
Generating exact nonlinear ranking functions by symbolic-numeric hybrid method. Zbl 1282.90123
Shen, Liyong; Wu, Min; Yang, Zhengfeng; Zeng, Zhenbing
2013
Exact asymptotic stability analysis and region-of-attraction estimation for nonlinear systems. Zbl 1271.93128
Wu, Min; Yang, Zhengfeng; Lin, Wang
2013
Finding positively invariant sets of a class of nonlinear loops via curve fitting. Zbl 1356.68147
Shen, Liyong; Wu, Min; Yang, Zhengfeng; Zeng, Zhenbing
2009
Fractional-moment capital asset pricing model. Zbl 1198.91249
Li, Hui; Wu, Min; Wang, Xiao-Tian
2009
The entropies and multifractal spectrum of some compact systems. Zbl 1146.37304
Ma, Dongkui; Wu, Min; Liu, Cuijun
2008
The exact rate of convergence of the $$L^q$$-spectra of self-similar measures for $$q<0$$. Zbl 1132.28002
Xiao, Jiaqing; Wu, Min; Olsen, L.
2008
A convergence theorem for the Newton-like methods under some kind of weak Lipschitz conditions. Zbl 1136.65059
Wu, Min
2008
Collaborative image coding and transmission over wireless sensor networks. Zbl 1168.94480
Wu, Min; Chen, Chang Wen
2007
Relations between packing premeasure and measure on metric space. Zbl 1125.28007
Wen, Shengyou; Wu, Min
2007
Data hiding in curves with application to fingerprinting maps. Zbl 1370.94034
Gou, Hongmei; Wu, Min
2005
On the factorization of differential modules. Zbl 1096.13526
Wu, Min
2005
Higher level orderings on modules. Zbl 1095.06012
Wu, Min; Zeng, Guangxing
2005
Hausdorff dimension of certain level sets associated with generalized Rademacher functions. Zbl 1039.28008
Wu, Min; Xi, Li-Feng
2002
The Hausdorff measure of a class of generalized Sierpiński sponges. Zbl 0988.28003
Zhou, Zuoling; Wu, Min; Zhao, Yanfen
2001
Hausdorff dimension of cutset of complex valued Rademacher series. Zbl 0960.28001
Wu, Min
2000
Hausdorff dimension of $$\alpha$$-cutset of some random series. Zbl 0862.28007
Wu, Min
1995
Slow growth rate of the digits in Engel expansions. Zbl 1434.11155
Shang, Lei; Wu, Min
2020
A game-based approximate verification of deep neural networks with provable guarantees. Zbl 1436.68199
Wu, Min; Wicker, Matthew; Ruan, Wenjie; Huang, Xiaowei; Kwiatkowska, Marta
2020
On Assouad dimension and arithmetic progressions in sets defined by digit restrictions. Zbl 1414.28017
Li, Jinjun; Wu, Min; Xiong, Ying
2019
Beta-expansion and continued fraction expansion of real numbers. Zbl 1448.11150
Fang, Lulu; Wu, Min; Li, Bing
2019
Improved stability criteria for the neural networks with time-varying delay via new augmented Lyapunov-Krasovskii functional. Zbl 1428.34101
Gao, Zhen-Man; He, Yong; Wu, Min
2019
On the longest block in Lüroth expansion. Zbl 1434.11153
Li, Jinjun; Wu, Min; Yang, Xiangfeng
2018
A note on Rényi’s ‘record’ problem and Engel’s series. Zbl 1419.60024
Fang, Lulu; Wu, Min
2018
Hausdorff dimension of certain sets arising in Engel expansions. Zbl 1437.11115
Fang, Lulu; Wu, Min
2018
Large and moderate deviation principles for Engel continued fractions. Zbl 1442.11112
Fang, Lulu; Wu, Min; Shang, Lei
2018
On exceptional sets in Erdős-Rényi limit theorem revisited. Zbl 1371.28022
Li, Jinjun; Wu, Min
2017
Lower dimensions of some fractal sets. Zbl 1370.28004
Chen, Haipeng; Wu, Min; Wei, Chun
2017
Further results on delay-dependent stability criteria of discrete systems with an interval time-varying delay. Zbl 1367.93448
Wu, Min; Peng, Chen; Zhang, Jin; Fei, Minrui; Tian, Yuchu
2017
A note on correlation and local dimensions. Zbl 1380.28001
Yang, Jiaojiao; Käenmäki, Antti; Wu, Min
2017
The exceptional sets on the run-length function of $$\beta$$-expansions. Zbl 1432.11104
Zheng, Lixuan; Wu, Min; Li, Bing
2017
Statistical analysis of dependent competing risks model in accelerated life testing under progressively hybrid censoring using copula function. Zbl 1402.62244
Wu, Min; Shi, Yimin; Zhang, Chunfang
2017
The topological property of the irregular sets on the lengths of basic intervals in beta-expansions. Zbl 1401.37014
Zheng, Lixuan; Wu, Min; Li, Bing
2017
On exceptional sets in Erdős-Rényi limit theorem. Zbl 1408.11077
Li, Jinjun; Wu, Min
2016
Limit theorems related to beta-expansion and continued fraction expansion. Zbl 1408.11076
Fang, Lulu; Wu, Min; Li, Bing
2016
Statistical inference for competing risks model in step-stress partially accelerated life tests with progressively type-I hybrid censored Weibull life data. Zbl 1327.62501
Zhang, Chunfang; Shi, Yimin; Wu, Min
2016
Level sets and equivalences of Moran-type sets. Zbl 1374.28006
Du, Yali; Miao, Junjie; Wu, Min
2016
A note on the distribution of the digits in Cantor expansions. Zbl 1339.11077
Li, Jinjun; Wang, Yi; Wu, Min
2016
Bayes estimation and expected termination time for the competing risks model from Gompertz distribution under progressively hybrid censoring with binomial removals. Zbl 1331.62390
Wu, Min; Shi, Yimin
2016
Establishing a dynamic self-adaptation learning algorithm of the BP neural network and its applications. Zbl 1334.68189
Li, Xiaofeng; Xiang, Suying; Zhu, Pengfei; Wu, Min
2015
Generic property of irregular sets in systems satisfying the specification property. Zbl 1280.54024
Li, Jinjun; Wu, Min
2014
Inference for accelerated competing failure models from Weibull distribution under type-I progressive hybrid censoring. Zbl 1381.62267
Wu, Min; Shi, Yimin; Sun, Yudong
2014
A note on the rate of returns in random walks. Zbl 1296.54034
Li, Jinjun; Wu, Min
2014
Exact safety verification of hybrid systems using sums-of-squares representation. Zbl 1343.93051
Lin, Wang; Wu, Min; Yang, Zhengfeng; Zeng, Zhenbing
2014
A discrete-time global quasi-sliding mode control scheme with bounded external disturbance rejection. Zbl 1307.93106
Wu, M.; Chen, J. S.
2014
Second-order integro-differential parabolic variational inequalities arising from the valuation of American option. Zbl 06408985
Sun, Yudong; Shi, Yimin; Wu, Min
2014
Domain-of-attraction estimation for uncertain non-polynomial systems. Zbl 07175113
Wu, Min; Yang, Zhengfeng; Lin, Wang
2014
The sets of divergence points of self-similar measures are residual. Zbl 1304.28008
Li, Jinjun; Wu, Min
2013
The effect of interstitial pressure on tumor growth: coupling with the blood and lymphatic vascular systems. Zbl 1406.92330
Wu, Min; Frieboes, Hermann B.; McDougall, Steven R.; Chaplain, Mark A. J.; Cristini, Vittorio; Lowengrub, John
2013
Divergence points in systems satisfying the specification property. Zbl 1271.37026
Li, Jinjun; Wu, Min
2013
Quasisymmetric minimality on packing dimension for Moran sets. Zbl 1309.28004
Li, Yanzhe; Wu, Min; Xi, Lifeng
2013
Optimal isolation strategies of emerging infectious diseases with limited resources. Zbl 1273.92063
Zhou, Yinggao; Wu, Jianhong; Wu, Min
2013
Generating exact nonlinear ranking functions by symbolic-numeric hybrid method. Zbl 1282.90123
Shen, Liyong; Wu, Min; Yang, Zhengfeng; Zeng, Zhenbing
2013
Exact asymptotic stability analysis and region-of-attraction estimation for nonlinear systems. Zbl 1271.93128
Wu, Min; Yang, Zhengfeng; Lin, Wang
2013
Hausdorff dimensions of the divergence points of self-similar measures with the open set condition. Zbl 1236.28007
Li, Jinjun; Wu, Min; Xiong, Ying
2012
Transforming linear functional systems into fully integrable systems. Zbl 1252.68357
Li, Ziming; Wu, Min
2012
Topological pressure and topological entropy of a semigroup of maps. Zbl 1234.37011
Ma, Dongkui; Wu, Min
2011
Pointwise dimensions of general Moran measures with open set condition. Zbl 1219.28010
Li, Jinjun; Wu, Min
2011
Divergence points of self-similar measures satisfying the OSC. Zbl 1223.28007
Xiao, Jia-Qing; Wu, Min; Gao, Fei
2011
Generating invariants of hybrid systems via sums-of-squares of polynomials with rational coefficients. Zbl 1345.65046
Wu, Min; Yang, Zhengfeng
2011
The singularity spectrum of some non-regularity Moran fractals. Zbl 1222.28020
Wu, Min; Xiao, Jiaqing
2011
On the pointwise densities of the Cantor measure. Zbl 1219.28007
Wang, Jun; Wu, Min; Xiong, Ying
2011
The pointwise dimensions of Moran measures. Zbl 1200.28011
Lou, Manli; Wu, Min
2010
Doubling measures with doubling continuous part. Zbl 1203.28012
Lou, Man-Li; Wu, Min
2010
Liouvillian solutions of linear difference-differential equations. Zbl 1233.12004
Feng, Ruyong; Singer, Michael F.; Wu, Min
2010
On Hausdorff dimension and topological entropy. Zbl 1206.28008
Ma, Dongkui; Wu, Min
2010
Category and dimensions for cut-out sets. Zbl 1177.28027
Xiong, Ying; Wu, Min
2009
Finding positively invariant sets of a class of nonlinear loops via curve fitting. Zbl 1356.68147
Shen, Liyong; Wu, Min; Yang, Zhengfeng; Zeng, Zhenbing
2009
Fractional-moment capital asset pricing model. Zbl 1198.91249
Li, Hui; Wu, Min; Wang, Xiao-Tian
2009
The multifractal dimension functions of homogeneous Moran measure. Zbl 1165.28005
Xiao, Jiaqing; Wu, Min
2008
A new semi-local convergence theorem for the inexact Newton methods. Zbl 1160.65025
Wu, Min
2008
The entropies and multifractal spectrum of some compact systems. Zbl 1146.37304
Ma, Dongkui; Wu, Min; Liu, Cuijun
2008
The exact rate of convergence of the $$L^q$$-spectra of self-similar measures for $$q<0$$. Zbl 1132.28002
Xiao, Jiaqing; Wu, Min; Olsen, L.
2008
A convergence theorem for the Newton-like methods under some kind of weak Lipschitz conditions. Zbl 1136.65059
Wu, Min
2008
Stability analysis for neutral systems with mixed delays. Zbl 1120.34057
Liu, Xin-Ge; Wu, Min; Martin, Ralph; Tang, Mei-Lan
2007
Delay-dependent stability analysis for uncertain neutral systems with time-varying delays. Zbl 1128.34048
Liu, Xin-Ge; Wu, Min; Martin, Ralph; Tang, Mei-Lan
2007
Two examples on atomic doubling measures. Zbl 1123.28004
Lou, Manli; Wen, Shengyou; Wu, Min
2007
Lipschitz constant for bi-Lipschitz automorphism on Moran-like sets. Zbl 1133.28005
Guo, Qiu-Li; Wu, Min; Xi, Li-Feng
2007
Collaborative image coding and transmission over wireless sensor networks. Zbl 1168.94480
Wu, Min; Chen, Chang Wen
2007
Relations between packing premeasure and measure on metric space. Zbl 1125.28007
Wen, Shengyou; Wu, Min
2007
A recursive method for determining the one-dimensional submodules of Laurent-Ore modules. Zbl 1356.12012
Li, Ziming; Singer, Michael F.; Wu, Min; Zheng, Dabin
2006
The multifractal spectrum of some Moran measures. Zbl 1126.28010
Wu, Min
2005
The singularity spectrum $$f(\alpha)$$ of some Moran fractals. Zbl 1061.28005
Wu, Min
2005
Picard-Vessiot extensions for linear functional systems. Zbl 1360.12005
Bronstein, Manuel; Li, Ziming; Wu, Min
2005
Data hiding in curves with application to fingerprinting maps. Zbl 1370.94034
Gou, Hongmei; Wu, Min
2005
On the factorization of differential modules. Zbl 1096.13526
Wu, Min
2005
Higher level orderings on modules. Zbl 1095.06012
Wu, Min; Zeng, Guangxing
2005
Anti-collusion fingerprinting for multimedia. Zbl 1369.94591
Trappe, Wade; Wu, Min; Wang, Z. Jane; Liu, K. J. Ray
2003
A note on Whitney’s critical sets. Zbl 1036.28012
Xi, Lifeng; Wu, Min
2003
Multimedia data hiding. Zbl 1018.68027
Wu, Min; Liu, Bede
2003
Universal admissibility of linear estimators in multivariate linear models with respect to a restricted parameter set. Zbl 0995.62003
Qin, Hong; Wu, Min; Peng, Junhao
2002
Hausdorff dimension of certain level sets associated with generalized Rademacher functions. Zbl 1039.28008
Wu, Min; Xi, Li-Feng
2002
Rotation, scale, and translation resilient watermarking for images. Zbl 1037.68778
Lin, Ching-Yung; Wu, Min; Bloom, Jeffrey A.; Cox, Ingemar J.; Miller, Matt L.; Lui, Yui Man
2001
The Hausdorff measure of a class of generalized Sierpiński sponges. Zbl 0988.28003
Zhou, Zuoling; Wu, Min; Zhao, Yanfen
2001
Hausdorff dimension of cutset of complex valued Rademacher series. Zbl 0960.28001
Wu, Min
2000
The Hausdorff measure of a Sierpinski carpet. Zbl 0984.28005
Zhou, Zuoling; Wu, Min
1999
On Hausdorff and Bouligand dimensions of a class of recurrent sets. Zbl 0824.28008
Wu, Min
1995
Hausdorff dimension of $$\alpha$$-cutset of some random series. Zbl 0862.28007
Wu, Min
1995
all top 5
#### Cited by 443 Authors
16 Li, Jinjun 16 Wu, Min 11 Wu, Min 9 Ma, Dongkui 9 Xi, Lifeng 8 Shi, Yimin 8 Wu, Min 7 Zhong, Shou-Ming 6 Cheng, Minquan 6 Jiang, Jing 5 Fang, Lulu 5 Li, Ziming 5 Singer, Michael F. 5 Xiong, Ying 5 Yang, Jiaojiao 4 Liu, Xinge 4 Lou, Manli 4 Park, Juhyun (Jessie) 4 Shu, Yanjun 4 Wang, Yupan 4 Xiong, Lianglin 4 Zhang, Fode 4 Zhou, Zuoling 3 Chen, Ercai 3 Chen, Haipeng 3 Chen, Shaoshi 3 Cheng, Jun 3 Cui, Baotong 3 Deng, Juan 3 Feng, Ruyong 3 Frieboes, Hermann B. 3 Ji, Yan 3 Kwon, O. M. 3 Li, Yanzhe 3 Lin, Wang 3 Liu, Chuntai 3 Miao, Ying 3 Qiu, Fang 3 Qu, Chengqin 3 Rakkiyappan, Rajan 3 Su, Weiyi 3 Tan, Bo 3 Tian, Xueting 3 Wen, Zhi-Ying 3 Xiao, Jiaqing 3 Xu, Shaoyuan 3 Yang, Zhengfeng 3 Zhan, Naijun 3 Zhou, Xiaoyao 2 Bai, Xuchao 2 Balasubramaniam, Pagavathigounder 2 Cha, E. J. 2 Chen, Huabin 2 Chen, Wenbin 2 Dai, Meifeng 2 Dong, Yiwei 2 Fei, Shumin 2 Gui, Wenhao 2 Hu, Xiaomei 2 Hui, Huihui 2 Käenmäki, Antti 2 Kauers, Manuel 2 Lakshmanan, Shanmugam 2 Li, Bing 2 Lin, Xiaogang 2 Liu, Gang 2 Liu, Jia 2 Liu, Juan 2 Liu, Xinzhi 2 Lü, Meiying 2 Ma, Chao 2 Min, Wu 2 Ni, Rongrong 2 Olsen, Lars Folke 2 Qian, Wei 2 Qiu, Saibing 2 Ruan, Qiuqi 2 Selmi, Bilel 2 Shang, Lei 2 Tang, Xiaohu 2 Wang, Jichun 2 Wang, Wen 2 Wen, Shengyou 2 Xiao, Dong 2 Yang, Xiangfeng 2 Zeng, Zhenbing 2 Zhang, Chunfang 2 Zhang, Mengjie 2 Zhang, Qingling 2 Zhang, Shangli 2 Zhang, Yiwei 2 Zhang, Zhenliang 2 Zhao, Hengjun 2 Zhou, Ji 2 Zhu, Hong 2 Zhu, Sanguo 1 Abdi, Hamid 1 Abraham, Ajith 1 Aldredge, Ralph C. 1 Ali, M. Syed ...and 343 more Authors
all top 5
#### Cited in 99 Serials
22 Journal of Mathematical Analysis and Applications 17 Fractals 11 Chaos, Solitons and Fractals 8 Journal of the Franklin Institute 8 Monatshefte für Mathematik 8 Mathematical Problems in Engineering 7 Journal of Computational and Applied Mathematics 7 Journal of Symbolic Computation 7 Pattern Recognition 6 Applied Mathematics and Computation 5 Designs, Codes and Cryptography 5 Journal of Inequalities and Applications 5 Advances in Difference Equations 5 Journal of Theoretical Biology 4 Archiv der Mathematik 4 Journal of Number Theory 4 Signal Processing 4 Applied Mathematical Modelling 4 Discrete and Continuous Dynamical Systems 4 Analysis in Theory and Applications 3 Journal of Algebra 3 Proceedings of the American Mathematical Society 3 Ergodic Theory and Dynamical Systems 3 Annales Academiae Scientiarum Fennicae. Mathematica 3 Abstract and Applied Analysis 3 Acta Mathematica Sinica. English Series 3 Nonlinear Analysis. Real World Applications 3 Dynamical Systems 3 Journal of Systems Science and Complexity 3 Science China. Mathematics 2 Mathematical Biosciences 2 Physica A 2 Czechoslovak Mathematical Journal 2 Information Sciences 2 Mathematics and Computers in Simulation 2 Results in Mathematics 2 Acta Mathematicae Applicatae Sinica. English Series 2 Science in China. Series A 2 Multidimensional Systems and Signal Processing 2 European Journal of Control 2 Nonlinear Dynamics 2 Wuhan University Journal of Natural Sciences (WUJNS) 2 International Journal of Number Theory 2 Cryptography and Communications 2 Asian Journal of Control 1 Communications in Algebra 1 International Journal of Control 1 Israel Journal of Mathematics 1 Journal d’Analyse Mathématique 1 Journal of Mathematical Physics 1 Mathematical Methods in the Applied Sciences 1 Nonlinearity 1 Arkiv för Matematik 1 Advances in Mathematics 1 Fuzzy Sets and Systems 1 Geometriae Dedicata 1 Illinois Journal of Mathematics 1 Journal of Differential Equations 1 Journal of the Korean Mathematical Society 1 Mathematische Annalen 1 Mathematische Zeitschrift 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Theoretical Computer Science 1 Theoretical Population Biology 1 Topology and its Applications 1 Optimal Control Applications & Methods 1 Statistics & Probability Letters 1 Circuits, Systems, and Signal Processing 1 Chinese Annals of Mathematics. Series B 1 Acta Mathematica Hungarica 1 Numerical Algorithms 1 Aequationes Mathematicae 1 Linear Algebra and its Applications 1 Journal of Mathematical Imaging and Vision 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Journal of Nonlinear Science 1 Computational Optimization and Applications 1 Computational and Applied Mathematics 1 The Journal of Fourier Analysis and Applications 1 Taiwanese Journal of Mathematics 1 Communications in Nonlinear Science and Numerical Simulation 1 Discrete and Continuous Dynamical Systems. Series B 1 Journal of the Australian Mathematical Society 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Stochastics and Dynamics 1 International Journal of Wavelets, Multiresolution and Information Processing 1 Journal of the Korean Statistical Society 1 Complex Analysis and Operator Theory 1 Frontiers of Mathematics in China 1 EURASIP Journal on Advances in Signal Processing 1 Asian-European Journal of Mathematics 1 Journal of Nonlinear Science and Applications 1 Advances in Mathematical Physics 1 Science China. Information Sciences 1 Frontiers of Computer Science in China 1 Frontiers of Computer Science 1 International Journal of Systems Science. Principles and Applications of Systems and Integration 1 Electronic Research Archive
all top 5
#### Cited in 30 Fields
102 Measure and integration (28-XX) 48 Systems theory; control (93-XX) 37 Ordinary differential equations (34-XX) 35 Dynamical systems and ergodic theory (37-XX) 26 Number theory (11-XX) 26 Computer science (68-XX) 23 Information and communication theory, circuits (94-XX) 16 Biology and other natural sciences (92-XX) 15 Statistics (62-XX) 13 General topology (54-XX) 8 Probability theory and stochastic processes (60-XX) 8 Operations research, mathematical programming (90-XX) 7 Field theory and polynomials (12-XX) 6 Numerical analysis (65-XX) 5 Commutative algebra (13-XX) 5 Special functions (33-XX) 5 Partial differential equations (35-XX) 4 Difference and functional equations (39-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Functions of a complex variable (30-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 2 Group theory and generalizations (20-XX) 2 Real functions (26-XX) 2 Sequences, series, summability (40-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 Mathematical logic and foundations (03-XX) 1 Operator theory (47-XX) 1 Differential geometry (53-XX) 1 Classical thermodynamics, heat transfer (80-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2021-01-28T03:36:37 |
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|
https://par.nsf.gov/biblio/10226045-review-particle-physics
|
Review of Particle Physics
Abstract The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 3,324 new measurements from 878 papers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. Particle properties and search limits are listed in Summary Tables. We give numerous tables, figures, formulae, and reviews of topics such as Higgs Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology, Particle Detectors, Colliders, Probability and Statistics. Among the 120 reviews are many that are new or heavily revised, including a new review on High Energy Soft QCD and Diffraction and one on the Determination of CKM Angles from B Hadrons. The Review is divided into two volumes. Volume 1 includes the Summary Tables and 98 review articles. Volume 2 consists of the Particle Listings and contains also 22 reviews that address specific aspects of the data presented in the Listings. The complete Review (both volumes) is published online on the website of the Particle Data Group (pdg.lbl.gov) and in a journal. Volume 1 is available more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Award ID(s):
Publication Date:
NSF-PAR ID:
10226045
Journal Name:
Progress of Theoretical and Experimental Physics
Volume:
2020
Issue:
8
ISSN:
2050-3911
2. Abstract A search for dark matter particles is performed using events with a Z boson candidate and large missing transverse momentum. The analysis is based on proton–proton collision data at a center-of-mass energy of 13 $$\,\text {Te}\text {V}$$ Te , collected by the CMS experiment at the LHC in 2016–2018, corresponding to an integrated luminosity of 137 $$\,\text {fb}^{-1}$$ fb - 1 . The search uses the decay channels $${\mathrm{Z}} \rightarrow {\mathrm{e}} {\mathrm{e}}$$ Z → e e and $${\mathrm{Z}} \rightarrow {{\upmu }{}{}} {{\upmu }{}{}}$$ Z → μ μ . No significant excess of events is observed over themore »
4. A bstract A search for nonresonant production of Higgs boson pairs via gluon-gluon and vector boson fusion processes in final states with two bottom quarks and two photons is presented. The search uses data from proton-proton collisions at a center-of-mass energy of $$\sqrt{s}$$ s = 13 TeV recorded with the CMS detector at the LHC, corresponding to an integrated luminosity of 137 fb − 1 . No significant deviation from the background-only hypothesis is observed. An upper limit at 95% confidence level is set on the product of the Higgs boson pair production cross section and branching fractionmore »
| 2022-06-26T20:16:21 |
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http://dergipark.gov.tr/ieja/issue/25194/266221
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Yıl 2015, Cilt 17, Sayı 17, Sayfalar 199 - 214 2015-06-01
| | | |
## ON RINGS WHERE LEFT PRINCIPAL IDEALS ARE LEFT PRINCIPAL ANNIHILATORS
#### Victor Camillo [1] , W. Keith Nicholson [2]
##### 188 245
The rings in the title are studied and related to right principally injective rings. Many properties of these rings (called left pseudo-morphic by Yang) are derived, and conditions are given that an endomorphism ring is left pseudo-morphic. Some particular results: (1) Commutative pseudo-morphic rings are morphic; (2) Semiprime left pseudo-morphic rings are semisimple; and (3) A left and right pseudo-morphic ring satisfying (equivalent) mild finiteness conditions is a morphic, quasi-Frobenius ring in which every onesided ideal is principal. Call a left ideal L a left principal annihilator if L = l(a) = {r ∈ R | ra = 0} for some a ∈ R. It is shown that if R is left pseudo-morphic, left mininjective ring with the ACC on left principal annihilators then R is a quasi-Frobenius ring in which every right ideal is principal and every left ideal is a left principal annihilator.
Regular rings, morphic rings, quasi-morphic rings, pseudo-morphic rings, artinian principal ideal rings, quasi-Frobenius rings
Konular JA77FH99TM Makaleler Yazar: Victor Camillo Yazar: W. Keith Nicholson
Bibtex @ { ieja266221, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2015}, volume = {17}, pages = {199 - 214}, doi = {10.24330/ieja.266221}, title = {ON RINGS WHERE LEFT PRINCIPAL IDEALS ARE LEFT PRINCIPAL ANNIHILATORS}, key = {cite}, author = {Nicholson, W. Keith and Camillo, Victor} } APA Camillo, V , Nicholson, W . (2015). ON RINGS WHERE LEFT PRINCIPAL IDEALS ARE LEFT PRINCIPAL ANNIHILATORS. International Electronic Journal of Algebra, 17 (17), 199-214. DOI: 10.24330/ieja.266221 MLA Camillo, V , Nicholson, W . "ON RINGS WHERE LEFT PRINCIPAL IDEALS ARE LEFT PRINCIPAL ANNIHILATORS". International Electronic Journal of Algebra 17 (2015): 199-214 Chicago Camillo, V , Nicholson, W . "ON RINGS WHERE LEFT PRINCIPAL IDEALS ARE LEFT PRINCIPAL ANNIHILATORS". International Electronic Journal of Algebra 17 (2015): 199-214 RIS TY - JOUR T1 - ON RINGS WHERE LEFT PRINCIPAL IDEALS ARE LEFT PRINCIPAL ANNIHILATORS AU - Victor Camillo , W. Keith Nicholson Y1 - 2015 PY - 2015 N1 - doi: 10.24330/ieja.266221 DO - 10.24330/ieja.266221 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 199 EP - 214 VL - 17 IS - 17 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.266221 UR - http://dx.doi.org/10.24330/ieja.266221 Y2 - 2019 ER - EndNote %0 International Electronic Journal of Algebra ON RINGS WHERE LEFT PRINCIPAL IDEALS ARE LEFT PRINCIPAL ANNIHILATORS %A Victor Camillo , W. Keith Nicholson %T ON RINGS WHERE LEFT PRINCIPAL IDEALS ARE LEFT PRINCIPAL ANNIHILATORS %D 2015 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 17 %N 17 %R doi: 10.24330/ieja.266221 %U 10.24330/ieja.266221 ISNAD Camillo, Victor , Nicholson, W. Keith . "ON RINGS WHERE LEFT PRINCIPAL IDEALS ARE LEFT PRINCIPAL ANNIHILATORS". International Electronic Journal of Algebra 17 / 17 (Haziran 2015): 199-214. http://dx.doi.org/10.24330/ieja.266221
| 2019-02-19T20:52:06 |
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|
https://www.federalreserve.gov/econres/notes/feds-notes/international-measures-of-common-inflation-20211105.html
|
November 05, 2021
### International Measures of Common Inflation
Eli Nir, Flora Haberkorn, and Danilo Cascaldi-Garcia1
#### 1. Introduction
A key challenge for monetary policymakers in achieving their inflation goals—particularly important at the current juncture—is to be able to distinguish between persistent inflationary changes and short-term idiosyncratic shocks. The most common approach for filtering out short-term price shocks from inflation is to focus on measures of "core" inflation, traditionally defined as the change in the consumer price index (CPI) excluding food and energy prices. However, this approach includes temporary shocks in other categories. For example, a temporary tax cut for a specific good, a short-term supply disruption, or a strike in a manufacturing industry would result in changes in core inflation that do not represent changes in underlying inflationary pressures. As such, core inflation is an imperfect measure of underlying inflation in that temporary shocks in sectors other than food and energy may be misunderstood as economy-wide shocks.
In this note, we propose alternative measures of inflation for selected advanced and emerging economies that better represent structural inflationary movements. The basic assumption is that each component of the inflation index combines two driving forces. The first is a trend that is common across all components. The second comes from idiosyncratic components that capture one-off changes, sector-specific developments, and measurement errors. From a policymaker point of view, disentangling these two forces is important, as the first may be sensitive to policy actions while the second may not. Following the approach developed by Luciani (2020) using U.S. data, we employ a dynamic factor model (DFM) to estimate these two forces and aggregate the effects of the first in what we call common inflation using data for selected advanced and emerging economies.
As it is less prone to temporary shocks and measurement errors, common inflation captures the connection between prices, the real economy, and monetary policy, qualifying it as a powerful concept for policymakers to focus on. We also show that these new measures perform better than traditional core inflation series in forecasting medium-term headline inflation (two to three years ahead). Of particular relevance to the current situation, the common inflation measures suggest that the deflationary period and eventual rebound due to the COVID-19 pandemic were mainly idiosyncratic factors with only muted effects on underlying structural inflation.
#### 2. Methodology
We provide common inflation measures for Canada, the Euro area, Japan, United Kingdom (UK), Brazil, and Mexico. For each economy, we calculate a common inflation estimate by applying a DFM to its disaggregated price series. The idiosyncratic inflation is then defined as the difference between the common inflation and traditional core inflation.
The DFM is designed to extract the common dynamics from a set of different time series variables. In this case, the time series are the disaggregated price series that make up a country's core consumer price index (CPI) or, in the case of the euro area, the harmonized index of consumer prices (HICP). The DFM identifies the common factor across all the series, as well as the influence of the common factor on the individual series (the factor loadings). For each period, the product of the common factor and factor loading for a price series is that individual series' common component.
We then employ CPI or HICP weights to generate the aggregate common inflation by calculating a weighted sum of the common components of each individual series. We exclude price series related to food and energy, so the common inflation is the common component of core inflation. In practice, we take the fully disaggregated list of price series and re-aggregate the series that shares a high correlation, resulting in a set of about 50 to 60 price series for each country.
The general specification and technical explanation of the model closely follows Luciani (2020), which produces a similar measure for the United States. Formally, for disaggregated price series $i$ at time $t$, the DFM2 can be summarized as
$$\pi_{it} = \chi_{it} + \xi_{it}$$
$$\chi_{it} = \lambda_i f_t$$
$$f_t = a f_{t-1} + b f_{t-2} + c f_{t-3} + d f_{t-4} + u_t \ \ \ \ \ \ \ \ \ \ \ u_t \sim N(0,Q) \ \ {i.i.d}$$
$$\xi_{it} = \rho_i \xi_{it-1} + e_{it} \ \ \ \ \ \ \ \ \ \ \ \boldsymbol{e}_t \sim N(0,\Gamma) \ \ {i.i.d}$$
where $\pi_{it}$ is the 12-month inflation rate, $\chi_{it}$ is the common component, $\xi_{it}$ is the idiosyncratic component, and $f_t$ is the common factor. $\lambda_i$ is the factor loading and $\boldsymbol{e}_t = (e_{1t}\dots e_{nt})^{\prime}$, where $n$ is the number of price series. The residuals in the last two equations are normally distributed with mean 0. $Q$ and $\Gamma$ are covariance matrices of full rank.
The aggregated common inflation is calculated as
$$\sum_{i\in{core}} w_{it} \chi_{it}$$
Where $w_{it}$ are the weights for the individual disaggregated price series based on the core inflation basket. The model is estimated using maximum likelihood, implemented through the expectation-maximization algorithm. Unobserved latent factors are predicted using past observations and a Kalman Smoother.
#### 3. Common inflation results
In this section we present the historical series of the estimated common inflation for each country and compare it with the traditional core and headline inflation. On average, the common inflation measures track traditional core inflation but are substantially less volatile than core and headline inflation. The high persistence of the common inflations indicate that they are indeed capturing slow moving structural changes in underlying inflation, instead of large swings originating from temporary shocks. Moreover, traditional core inflation tends to mean-revert to the common inflation in the medium-run, indicating where that series should converge when short-term shocks dissipate.
In what follows, we present the results3 for each of the selected advanced and emerging economies, focusing mainly on the historical experience. Later in section 4, we analyze the current situation during the pandemic in detail.
The common inflation (blue line) is clearly less volatile than core inflation (red solid line), but it still adheres to the long-term trends in inflation, as shown in Figure 1. Interestingly, our common inflation closely follows an equivalent measure (purple dashed line) calculated by the Bank of Canada (BoC), as described in Khan et. al. (2013). This result is reassuring since it demonstrates how our methodology employed for data from other countries aligns with those that are already considered informative for policymakers.
##### Figure 1. Canada common inflation
Some anecdotal evidence highlights the information uncovered by the common inflation in Canada. From December 2015 to March 2017, passenger vehicle purchase inflation and its contribution to core inflation was much higher than usual. The common component recognized this and kept its contribution relatively steady. From 2018 to 2019, common inflation was pinned down to the two percent inflation target established by the BoC even though headline inflation (black line) fluctuated above the target.
#### 3.2. Euro area
The common inflation for the euro area has been remarkably stable in recent years. Since 2016, core inflation (red line) has oscillated around a value a little under one percent, well below the two percent target established by the European Central Bank, as presented in Figure 2. Common inflation (blue line) remained steady at or just below 1 percent during this period until the COVID-19 pandemic. For example, in April 2017, air transportation prices had a major spike that quickly dissipated. Common inflation correctly classified this shock as idiosyncratic.
#### 3.3. Japan
Figure 3 shows that the common inflation (blue line) for Japan has been hovering around zero for years now, exacerbating the difficulty of the Bank of Japan to increase inflation towards its two percent target. In March 2017, the communications price index had a major spike and was the biggest contributor to the value of core inflation. However, the common component recognized the spike and filtered it out.
#### 3.4. United Kingdom
In Figure 4, common inflation (blue line) for the UK is substantially smoother and slower moving than the traditional core inflation (red line). It is also below the Bank of England's two percent target and correctly captures core inflation's acceleration up to 2018. Afterwards, core inflation starts to converge to the lower level of common inflation until the middle of 2019. July 2019 saw a positive spike in inflation for recreational items, which was also ignored by the common inflation.
#### 3.5. Brazil
We have also applied the common inflation method to selected emerging economies with much more volatile inflationary movements. Brazil's common core inflation (blue line) closely tracks the movements of core inflation (red line) with less volatility and short-term spikes, as seen in Figure 5. It showed a substantial slowdown from 2016 to mid-2018, converging to the 3-to-6 percent inflation target band set by the Central Bank of Brazil for that year. Brazil seems to be facing a stronger acceleration on common inflation with the rebound from the COVID-19 shock than the other countries considered in this note.
#### 3.6. Mexico
Figure 6 shows that Mexico's common core inflation (blue line) sits between headline (black line) and core inflation (red line). While both core and headline spiked in 2017, the common inflation showed a substantially more muted increase, treating most of the spike as temporary. Indeed, from 2018 onward, core inflation slowed down toward the lower level of the common inflation. Until the COVID-19 pandemic, common inflation has consistently remained above the mid-point 3 percent inflation target set by the Bank of Mexico, though inside its 2-to-4 percent band.
#### 4. The COVID-19 pandemic
Common inflation remained less volatile and fell substantially less during the onset of the COVID-19 pandemic than traditional core inflation (excluding food and energy). Figure 7 presents the evolution of the common component (red bars) and idiosyncratic component (white bars) of core inflation (black line) since January 2020.
Except for Mexico, every country saw steep drops in core inflation in the early months of 2020 while the common component decreased at a much slower rate. As businesses and sectors adapted to lockdown restrictions, trade disruptions, and less consumer spending, common inflation classified most of the big dips in core inflation as temporary shocks.
Indeed, the deflationary pressures did not last long, and by the beginning of 2021, most of the core inflation measures already converged back to the common inflation. In real-time, the discrepancy between common and the traditional core inflation over 2020 indicated that the large deflationary swings were temporary. With hindsight it is now possible to say that such evaluation was correct.
##### Figure 7. Decomposition of common inflation on the onset of the COVID-19 pandemic
More recently, some countries have experienced the opposite effect in mid-2021: Canada, the UK, and Brazil present core inflation measures above their central bank's mid-point inflation targets. For Canada and the UK, common inflation indicates that the upward swings are mainly due to temporary factors, such as base effects and side-effects of the economic re-opening.
The euro area is seeing a steady increase in the common inflation, reaching its highest point in the past seven years. While most of the increase is still temporary, there seems to be some structural pass-through in place. This increase may be a welcome development, as the common component still sits well below the 2 percent target set by the European Central Bank. For Brazil, the recent increase seems to be mainly structural, with its common inflation situating almost at the upper bound of the 2-to-5 percent inflation target band set by the Central Bank of Brazil for 2021.
#### 5. Using common inflation to forecast headline inflation
In this section, we show that common inflation is also useful for forecasting medium-term headline inflation with higher predictability than traditional core inflation measures. If the common inflation correctly distils the inflation measure from temporary shocks and measurement errors, it is expected that once these deviations dissipate, headline will converge back to the common inflation level.
We tested the forecast power of common inflation for each country and for forecast horizons (h) ranging from 1 to 36 months with the following regression
$$y_{t+h} = \alpha + \beta x_t + \varepsilon_{t+h}$$
Where $y_{t+h}$ is twelve-month headline inflation $h$ periods ahead, and $x_t$ is either the common inflation at time $t$ or the traditional core inflation at time $t$. We can then compare the in-sample root-mean-square deviation of the two regressions. For each $h$, we define $RMSD_{hCommon}$ and $RMSD_{hCore}$ as the root-mean-square deviation of the regression using common and traditional core inflation, respectively. The forecast power score of the common component for each $h$ is then calculated as
$${Score}_h = \frac{ RMSD_{hCommon}}{RMSD_{hCore}} \times 100 .$$
It follows that the score will be below 100 if the RMSD for the common inflation is lower than the traditional core inflation and above 100 otherwise. The lower the score, the better the predictive performance of common inflation over traditional core inflation at each $h$ horizon. Figure 8 presents the resulting forecast power scores for different countries.
##### Figure 8. Power of common inflation in forecasting headline inflation
For Canada, the UK, and Japan, the forecast power score stays below 100 for all forecast horizons, indicating a better performance for common inflation than traditional core. For every country except Japan, the forecast power sees a performance peak at around the two-year mark. Canada performs the best of all the countries at the one-year mark while the UK outperforms the other three at the two-year mark. Japan has relatively consistent performance until the three-year mark, where it sees a substantial boost in forecast power. As for the euro area, we see a crucial trough at the two-year mark, indicating that although it oscillates around the 100-mark threshold, it holds valuable forecasting power over the conventional core inflation.
Again, an important benchmark is the comparison of our Canada common inflation and the BoC's CPI-Common inflation. Our proposed measure performs as good or marginally better than the BoC's version for every forecast horizon.
For the emerging market economies, we see that the score shows strong forecasting performance in comparison to core for Mexico for all forecast horizons, peaking around 18 months. It also shows substantial gains for Brazil starting after 20 months. The forecast power of common inflation is undistinguishable or marginally lower than core inflation for Brazil in the short-term.
#### 6. Conclusion
In this note we present common inflation measures for selected advanced and emerging economies free of temporary factors and measurement errors. The proposed series are less volatile and better represent underlying inflationary forces than traditional core inflation measures. Common inflation is a powerful tool for inflation evaluation since it prevents researchers and policymakers from misleadingly interpreting short-term, temporary fluctuations as structural inflationary movements. It also provides an accurate medium-term forecast for headline inflation once the temporary factors dissipate. Anecdotally, common inflation correctly indicated that a large part of the deflationary pressures at the onset of the COVID-19 pandemic was temporary and mostly reverted by the early months of 2021.
#### 7. References
Khan, M., Morel, L., & Sabourin, P. (2013). "The Common Component of CPI: An Alternative Measure of Underlying Inflation for Canada," Staff Working Papers 13-35. Bank of Canada.
Luciani, M. (2020). "Common and idiosyncratic inflation," Finance and Economics Discussion Series 2020-024. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2020.024.
1. We thank Shaghil Ahmed, Harun Alp, Giuseppe Fiori, Joaquín García-Cabo, Anna Lipińska, Matteo Luciani, Andrea De Michelis, Hyunseung Oh, Musa Orak, Andrea Raffo, Patrice Robitaille, Samer Shousha, Mariano Somale, and Thiago Teixeira Ferreira for comments and suggestions. Return to text
2. We implement the DFM with four lags in the factor transition equation along with no factor lags in the observation equation for the common component. Return to text
3. The DFM is applied to data starting on January 1st of: 1996 for the Euro area, 1993 for the UK, 2000 for Japan, 1990 for Canada, 2010 for Mexico, and 2007 for Brazil. Return to text
| 2023-03-21T18:28:51 |
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|
https://confluence.ecmwf.int/display/UDOC/Confluence+Wiki
|
##### Page tree
Go to start of banner
# Accessing Confluence
## Default page
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1. A drop-down list listing all the spaces you have access to.
2. Other tabs at the top of the page are for other Atlassian products (JIRA, Fisheye, Bamboo, etc)
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# Wiki usages
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| 2019-10-19T16:58:14 |
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|
https://www.usgs.gov/center-news/erupting-lava-domes-create-thick-flows-and-glowing-rock-avalanches
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# Erupting lava domes create thick flows and glowing rock avalanches
Release Date:
Within the broad spectrum of volcanic activity that is possible on Earth, the eruption of lava domes is a common and frequently hazardous phenomenon. Volcanic domes are formed when sticky, high-silica lava piles up around a vent instead of flowing rapidly away, as in the case of low-silica basaltic lava erupted in Hawaii.
Pyroclastic flows from Montserrat dome collapses have flowed down the White River creating a new delta where they entered the sea. Photograph copyrighted by Steve O'Meara of Volcano Watch International. April 27, 2004.
(Public domain.)
Erupting domes are commonly associated with fast-moving pyroclastic flows, which form when either blocks of fresh lava break off from the dome and move rapidly downhill or when a lava dome is shattered during strong explosive activity.
At the present time, there are 4 major lava dome eruptions taking place in the world - Augustine and Mount St. Helens volcanoes in the U.S., Soufriere Hills Volcano on the Caribbean island of Montserrat, and Santa Maria in Guatemala.
The activity is not making headline news now, but the volcanoes deserve close watching, because each is capable of producing powerful explosive activity and dangerous pyroclastic flows. Of the four volcanoes, only Santa Maria is not intensely monitored by scientists.
Augustine is a beautiful cone-shaped volcanic island rising steeply 1,260 m (4134 ft) above sea level in southern Cook Inlet about 290 km (180 mi) southwest of Anchorage, Alaska. The volcano's summit consists of several domes, and the lower slopes are made chiefly of rock debris shed from these domes as pyroclastic flows and large landslides.
Augustine's current eruption began on January 11, 2006, with a series of explosions that generated ash columns as high as 15 km (50,000 ft). A few days later, viscous lava began erupting at the summit and eventually spread partway down the volcano's northern flank.
As the new lava crept down the steep side of the volcano, hot lava blocks from the leading edges broke away, generating pyroclastic flows that spread as far as about 3 km (2 mi) from the summit. Billowing volcanic ash rising from these pyroclastic flows has turned the usually brilliant white, snow-covered cone a dull brown. Photographs showing the red glow and pathways of the lava flows and pyroclastic flows can be seen at the Alaska Volcano Observatory's Web site.
At Mount St. Helens, a lava dome continues to grow inside the volcano's horseshoe-shaped crater. This dome began forming 17 months ago on the south side of an earlier dome that had erupted between 1980 and 1986.
In late February, scientists placed a new monitoring station called a "spider" on the active part of the dome to track its movement. For the past two weeks, the spider has moved westward nearly a meter (3 feet) per day. A year ago, the active part of the dome moved 7 to 10 m (20-30 feet) per day! Close-up photographs and time-lapse sequences from cameras located on the volcano show how the steady extrusion of lava is building the dome. (See the Cascades Volcano Observatory Web site for current images.)
The current dome of Soufriere Hills Volcano began growing in August 2005, the third such episode during an eruption that began in 1995. The active part of the dome is shedding frequent rockfalls and small pyroclastic flows down the sides of the volcano.
The largest recorded collapse of an active volcanic dome occurred at Soufriere Hills in 2003, when about 210 million cubic meters (275 million cubic yards) of dome rock slid away over an 18-hour period. This event triggered large pyroclastic flows that swept into the sea, and caused a local tsunami and an underwater explosion that sent hot water and debris back onshore.
The longest historical dome-building eruption is ongoing at Santiaguito dome, which is erupting on the southwest flank of Santa Maria Volcano in Guatemala. The eruption began in 1922 after a large explosive eruption in 1902 carved a 1.5 km- (1 mi) wide crater in the side of the volcano and killed more than 1,000 people.
Since early March, several moderate explosions produced pyroclastic flows down the active dome and formed an ash plume about 3 km (10,000 feet) above the volcano, typical of the activity for the past 84 years.
————————————————————————————————————————————————————————————————
### Volcano Activity Update
Eruptive activity at Puu Oo continues. On clear nights, glow is visible from several vents within the crater and on the southwest side of the cone. Lava continues to flow through the PKK lava tube from its source on the flank of Puu Oo to the ocean, with scattered surface flows breaking out of the tube. In the past week, surface flows were on the coastal plain below Paliuli, less than 0.75 km (0.5 mi) inland of the coast at Kamoamoa, about 5.5 km (3.4 mi) from the end of Chain of Craters Road.
As of March 16, lava is entering the ocean at East Laeapuki, in Hawaii Volcanoes National Park. The active lava bench continues to grow following the major collapse of November 28 and is now approximately 900 m long by 250 m wide. Access to the ocean entry and the surrounding area remains closed, due to significant hazards. If you visit the eruption site, check with the rangers for current updates, and remember to carry lots of water when venturing out onto the flow field.
There were no felt earthquakes beneath Hawaii Island reported within the past week.
Mauna Loa is not erupting and earthquake activity remained low beneath the volcano's summit. Inflation continues, but at a rate that has slowed since early October 2005.
| 2020-01-28T04:11:12 |
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|
https://www.eurocontrol.int/prudata/dashboard/metadata/additional-taxi-out-time/
|
## Contacts
Contact organisation EUROCONTROL: The European organisation for the safety of air navigation Contact organisation unit Directorate European Civil-Military Aviation - Performance Review Unit (DECMA/PRU) Contact name Performance Review Unit - EUROCONTROL Contact mail address 96 Rue de la Fusée1130 BrusselsBelgium Contact e-mail address [email protected]
## Statistical presentation
### Data description
The additional taxi-out time is a proxy for the average departure runway queuing time on the outbound traffic flow, during congestion periods at airports.
It is the difference between the actual taxi-out time of a flight and a statistically determined unimpeded taxi-out time based on taxi-out times in periods of low traffic demand (see also related methodology documentation).
Uncertainty of take-off clearance time and aircraft arriving time at runway holding stop bars makes traffic supply to runways a stochastic phenomenon. In order to ensure continuous traffic demand at runways and maximise runway usage, a minimum level of queuing is required. However, additional time is detrimental to taxi-out efficiency, fuel consumption and environment. Therefore, there exists a trade-off between taxi-out efficiency and runway throughput.
When monitoring taxi-out performance at airports, it is to be stressed that the goal is not to reduce taxi time to an unimpeded time - as this could negatively impact on runway throughput - but rather to reduce additional taxi-out time and associated fuel burn to the strict minimum.
As an output of the ATMAP Group, additional taxi-out time has been in use as a commonly agreed proxy for airport inefficiency in the taxi-out phase since 2008 and is compliant with the PI definition in the EU legislation.
### Classification system
Additional taxi-out time is classified per Member State, with a breakdown for each airport subject to performance monitoring within the SES performance scheme.
### Sector coverage
The measures pertain to the Air Transport and Air Traffic Management Sector of the economy.
### Statistical concepts and definitions
The Taxi-out time is defined as the time spent by a flight between its actual off-block time (AOBT) and actual take-off time (ATOT).
The Unimpeded taxi-out time is an average taxi-out time when there is no congestion. There is one unimpeded time by departure airport, departure runway and departure stand.
The Additional taxi-out time is the difference between the actual taxi-out time and the unimpeded taxi-out time.
### Statistical unit
The statistical unit is the airport. Airport level data is also aggregated to States.
### Statistical population
The statistical population is the set of airports subject to performance monitoring within the SES performance scheme.
### Reference area
The reference area is the Single European Sky Area.
### Time coverage
2011 is the first year for which data is presented.
Not applicable.
## Unit of Measure
The additional taxi-out time is measured in minutes per IFR departure [min/dep].
## Reference period
• The first reference period (RP1) covers the calendar years 2012 to 2014 inclusive.
• The second reference period (RP2) covers the calendar years 2015 to 2019 inclusive.
• The third reference period (RP3) covers the calendar years 2020 to 2024 inclusive.
Unless decided otherwise, the following reference periods shall be of five calendar years.
## Institutional Mandate
Legal acts and agreements are established in the EU IR691/2010|Performance Regulation (691 / 2010), Commission Implementing Regulation (EU) No 390 / 2013 and Commission Implementing Regulation (EU) 2019/317.
## Release policy
### Release calendar
Taxi-out additional time is released monthly with yearly aggregates.
Not applicable.
### User access
Information is disseminated to the general public via the SES Data Portal.
## Frequency of dissemination
Data is published monthly with the annual performance aggregate being available in January of the following year.
## Dissemination format
Information is disseminated to the general public via the SES Data Portal.
## Accessibility of documentation
### Documentation on methodology
As per the pertaining regulations (see Institutional Mandate).
Additional definitions of the terms used in the frame of the this KPI are available in the Metadata page.
### Quality documentation
There is no specific documentation on procedures applied for quality management and quality assessment.
## Quality Management
Although data providers are responsible for data quality, the EUROCONTROL Performance Review Unit performs data validation and quality checks.
### Quality assurance
Data validation is performed by the Central Office for Delay Analysis (CODA), on behalf of PRU, on each data delivery by airports, and data validation report are returned to the data providers.
### Quality assessment
Raw data is cross-checked with various sources (Network manager, ANSP’s, airport operators, airport coordinators and air carriers). A quality threshold is established, and data that does not pass the quality threshold is rejected.
If a field is found to be blank, it is tried to fill the missing value from an alternative data source (i.e. a missing aircraft type in the airport data flow can be filled with information from the Network manager.)
### Completeness
The data is collected for all airports subject to performance monitoring within the SES performance scheme. Data completeness is determined each month as per the above-mentioned quality checks. Any missing data is reported to the provider.
## Relevance
The information is published for performance monitoring purposes in accordance with the relevant EU legislation.
## Accuracy and reliability
### Overall accuracy
The accuracy of the measure is influenced by the availability of the stand/runway configuration and the type of AOBT recording at the airports (manual vs. automated).
### Sampling error
There is no sampling and therefore no sampling error.
## Timeliness and punctuality
### Timeliness
The information is published each month - in general around 30 days after the end of the month in question.
### Punctuality
The internal databases are updated daily. The statistical processing is performed once per month.
## Comparability
### Comparability — geographical
The data is collected centrally by the EUROCONTROL Performance Review Unit (PRU) with delegation to the Central Office for Delay Analysis (CODA) and computed consistently for all airports subject to performance monitoring within the SES performance scheme.
The interpretation of the measure and comparisons across airports require due consideration of prevailing local circumstances (airport infrastructure, etc.)
### Comparability over time
Comparisons over time are valid.
## Coherence
### Coherence — cross domain
Checks have been carried out with a number of airports and there is generally a good level of coherence between the indicator results and the results from performance measurement systems of airport operators.
### Coherence — internal
Data is fully coherent from an internal perspective.
Not available.
## Data revision
Subject to changes (i.e. infrastructure), there might be a need to change unimpeded times accordingly.
## Statistical processing
### Source data
In accordance with EU legislation, the data is collected centrally for all the airports subject to performance monitoring within the SES performance scheme.
The input variables used for the calculation are detailed in the Statistical concepts and definitions section.
### Frequency of data collection
The data is collected on a daily basis and transmitted for statistical processing on a monthly basis.
### Data collection
The data is collected by the EUROCONTROL Performance Review Unit (PRU) and the Central Office for Delay Analysis (CODA).
### Data validation
The data is validation as described in the Quality Management section.
### Data compilation
#### Calculation of the indicator
Let
• $$c$$, a combination of departure runway and group of stands, as described in the methodology for unimpeded taxi-out time,
• $$f(c)$$ a flight characterised by a combination $$c$$,
• $$\mathrm{AcTXOT}(f(c))$$ the actual taxi-out time for a flight $$f(c)$$, i.e. the elapsed time between the off-block time (AOBT) of the flight $$f(c)$$ and its actual take-off time (ATOT),
• $$\mathrm{UTXOT}(c)$$ the unimpeded taxi-out time for a combination $$c$$.
The additional taxi-out time $$\mathrm{AdTXOT}(f(c))$$ is calculated for each flight $$f(c)$$ as the difference between the actual taxi-out time $$\mathrm{AcTXOT}(f(c))$$ of the flight and the unimpeded taxi-out time $$\mathrm{UTXOT}(c)$$ :
$\mathrm{AdTXOT}(f(c)) = \mathrm{AcTXOT}(f(c)) - \mathrm{UTXOT}(c)$
The additional taxi-out time $$\mathrm{AdTXOT}(c)$$ for a given combination $$c$$ is the average of the additional taxi-out time $$\mathrm{AdTXOT}(f(c))$$ of all the flight $$f(c)$$ characterised by that combination $$c$$.
The additional taxi-out time $$\mathrm{AdTXOT}$$ for a given airport is the weighted average of the additional taxi-out time $$\mathrm{AdTXOT}(c)$$, for all the combinations $$c$$ at that airport with their probability of occurrence.
| 2021-08-03T01:45:22 |
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|
https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Map%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/2%3A_Geometric_Optics_and_Image_Formation
|
$$\require{cancel}$$
# 2: Geometric Optics and Image Formation
This chapter introduces the major ideas of geometric optics, which describe the formation of images due to reflection and refraction. It is called “geometric” optics because the images can be characterized using geometric constructions, such as ray diagrams. We have seen that visible light is an electromagnetic wave; however, its wave nature becomes evident only when light interacts with objects with dimensions comparable to the wavelength (about 500 nm for visible light). Therefore, the laws of geometric optics only apply to light interacting with objects much larger than the wavelength of the light.
• 2.0: Prelude to Geometric Optics and Image Formation
loud Gate is a public sculpture by Anish Kapoor located in Millennium Park in Chicago. Its stainless steel plates reflect and distort images around it, including the Chicago skyline. Dedicated in 2006, it has become a popular tourist attraction, illustrating how art can use the principles of physical optics to startle and entertain.
• 2.1: Images Formed by Plane Mirrors
The law of reflection tells us that the angle of incidence is the same as the angle of reflection. A plane mirror always forms a virtual image (behind the mirror). The image and object are the same distance from a flat mirror, the image size is the same as the object size, and the image is upright.
• 2.2: Spherical Mirrors
Spherical mirrors may be concave (converging) or convex (diverging). The focal length of a spherical mirror is one-half of its radius of curvature: $$f = \frac{R}{2}$$. The mirror equation and ray tracing allow you to give a complete description of an image formed by a spherical mirror. Spherical aberration occurs for spherical mirrors but not parabolic mirrors; comatic aberration occurs for both types of mirrors.
• 2.3: Images Formed by Refraction
When an object is observed through a plane interface between two media, then it appears at an apparent distance hi that differs from the actual distance $$h_0$$: $$h_i = \left(\frac{n_2}{n_1}\right)h_0$$. An image is formed by the refraction of light at a spherical interface between two media of indices of refraction n1 and $$n_2$$. Image distance depends on the radius of curvature of the interface, location of the object, and the indices of refraction of the media.
• 2.4: Thin Lenses
Two types of lenses are possible: converging and diverging. A lens that causes light rays to bend toward (away from) its optical axis is a converging (diverging) lens. By the end of this section, you will be able to use ray diagrams to locate and describe the image formed by a lens and employ the thin-lens equation to describe and locate the image formed by a lens.
• 2.5: The Eye
The human eye is perhaps the most interesting and important of all optical instruments. Our eyes perform a vast number of functions: They allow us to sense direction, movement, colors, and distance. In this section, we explore the geometric optics of the eye.
• 2.6: The Camera
Cameras use combinations of lenses to create an image for recording. By the end of this section, you will be able to: Describe the optics of a camera. Characterize the image created by a camera.
• 2.7: The Simple Magnifier
A simple magnifier is a converging lens and produces a magnified virtual image of an object located within the focal length of the lens. The magnification of an image when observed by the eye is the angular magnification M, which is defined by the ratio of the angle $$θ_{image}$$ subtended by the image to the angle $$θ_{object}$$ subtended by the object.
• 2.8: Microscopes and Telescopes
Many optical devices contain more than a single lens or mirror. These are analyzed by considering each element sequentially. The image formed by the first is the object for the second, and so on. The same ray-tracing and thin-lens techniques developed in the previous sections apply to each lens element. The overall magnification of a multiple-element system is the product of the linear magnifications of its individual elements times the angular magnification of the eyepiece.
• 2.A: Geometric Optics and Image Formation (Answers)
• 2.E: Geometric Optics and Image Formation (Exercises)
• 2.S: Geometric Optics and Image Formation (Summary)
Thumbnail: Rays reflected by a convex spherical mirror: Incident rays of light parallel to the optical axis are reflected from a convex spherical mirror and seem to originate from a well-defined focal point at focal distance f on the opposite side of the mirror. The focal point is virtual because no real rays pass through it.
### Contributors
• Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).
| 2019-03-21T08:55:34 |
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|
https://www.usgs.gov/center-news/volcano-watch-molokini-erupted-about-230000-years-ago
|
# Volcano Watch — Molokini erupted about 230,000 years ago
Release Date:
The tiny, crescent-shaped island of Molokini lies 4.2 km (3 miles) offshore of Haleakalā volcano, East Maui. Molokini is a volcanic cone that rises about 150 m (500 ft) from the submarine flank of Haleakalā to a summit only 49 m (162 ft) above sea level.
The cone is capped by a crater 540 m in diameter (1770 ft), although the northern rim is below sea level and the crater is flooded by the sea. It was active about 230,000 years ago--give or take 90,000 years--according to an age measured from lava fragments contained in the cone.
The age was obtained recently by Yoshitomo Nishimitsu, a graduate student at Kyoto University, Japan. Working in conjunction with scientists from the Hawaiian Volcano Observatory, he used the potassium-argon method of dating to measure ages from 60 lava flows on Haleakalā. The ages will improve our understanding of Haleakalā's volcanic history and the likelihood of future eruption along its rift zones.
Molokini lies along Haleakalā's southwest rift zone. Much of the rift zone is mantled with lava, cinders, and asherupted during the past 50,000 years. For that reason, geologists have always assumed that Molokini was a fairly young volcanic formation. But the 230,000-year age suggests that Molokini is much older, probably older than Haleakalā Crater itself.
Molokini would be similar to cinder cones elsewhere along the southwest rift zone except that it erupted through water. When magma erupts explosively in shallow water, the liquid water heats, expands rapidly, and changes to steam, adding to the eruptive force. The extra force shatters the extruded lava, which exposes more hot material--and hence more steam and more force as the eruption grows. Near-shore eruptions are some of the most dangerous that Hawaiian volcanoes can produce.
Shallow marine eruptions have two consequences for the appearance of the resulting cone. The first is grain size, because the ripping power of these marine eruptions leads to finer-grained deposits than in cinder cones onshore. The second is the abundance of volcanic glass, because the lava fragments are quickly cooled by water before crystals can form. Glass is a geologically unstable material. It alters rapidly to brownish-yellow clays, giving Molokini its earthy yellow color. In contrast, cinders erupted on land are reddish and black.
For those dying to know, the Molokini deposits are basanite, a type of basalt with fairly low amounts of silicon and high concentrations of sodium and potassium. (Geochemists would say it contains 45 percent SiO2, 4.4 percent Na2O, and 1.4 percent K2O.) Visible crystals are sparse, even under a magnifying glass. Lava like this is typical of Haleakalā's flows erupted during the past 500,000 years.
The ocean near Molokini is a popular skin-diving location reached easily by boat. The island itself is off limits, however, because it serves as a bird sanctuary. We at the Hawaiian Volcano Observatory take this opportunity to thank Drs. Fern Duvall (State of Hawaii's Department of Land and Natural Resources) and Marilet Zablan (U.S. Fish and Wildlife Service) for permission to collect geologic samples. The trip to Molokini was made possible through the expert piloting of Chief Petty Officer Robert Schmidt and Petty Officer Richard Magaa of the U.S. Coast Guard.
### Volcano Activity Update
Eruptive activity of Kīlauea Volcano continued unabated at the Puu Oo vent during the past week and provided participants and viewers of the JASON television program with spectacular surface flow activity on Pulama pali and on the coastal flats. HVO researchers and associates had a major role in nearly all of the 55 live broadcasts to schoolchildren throughout the United States, but the lava flow activity was the main attraction. Flows are active near the eastern boundary of Hawaii Volcanoes National Park adjacent to the Royal Gardens subdivision. Lava is pooling in the coastal flats and not entering the ocean at this time. The closest flow is 1.5 km (1 mi) away from the sea coast.
One earthquake was reported felt during the week ending on February 8. A resident of Volcano village felt an earthquake at 33 minutes after midnight on February 7. The magnitude-3.0 earthquake was located 28 km (16.8 mi) beneath Volcano village.
| 2021-05-08T16:47:27 |
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http://pdglive.lbl.gov/Particle.action?init=0&node=M213&home=MXXX025
|
${\boldsymbol {\boldsymbol c}}$ ${\boldsymbol {\overline{\boldsymbol c}}}$ MESONS(including possibly non- ${\boldsymbol {\boldsymbol q}}$ ${\boldsymbol {\overline{\boldsymbol q}}}$ states) INSPIRE search
# ${{\boldsymbol X}{(4020)}}$ $I^G(J^{PC})$ = $1^+(?^{? -})$
Properties incompatible with a ${{\mathit q}}{{\overline{\mathit q}}}$ structure (exotic state). See the review on non- ${{\mathit q}}{{\overline{\mathit q}}}$ states. Charged X(4020) seen by ABLIKIM 2013X from ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit h}_{{c}}{(1P)}}$ at c.m. energy from 3.90 to 4.42 GeV as a peak in the invariant mass distribution of the ${{\mathit \pi}^{\pm}}{{\mathit h}_{{c}}{(1P)}}$ system, and by ABLIKIM 2014B from ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ( ${{\mathit D}^{*}}{{\overline{\mathit D}}^{*}}){}^{+-}{{\mathit \pi}^{\mp}}$ events in ( ${{\mathit D}^{*}}{{\overline{\mathit D}}^{*}}$ )${}^{+-}$ mass. A neutral X(4020) seen by ABLIKIM 2014P at three c.m. energies in the same range in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit h}_{{c}}{(1P)}}$ as a peak in the larger of the two masses recoiling against a ${{\mathit \pi}^{0}}$. ABLIKIM 2015AA observes a 5.9 $\sigma$ signal in ( ${{\mathit D}^{*}}{{\overline{\mathit D}}^{*}}$ )${}^{0}$ in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ( ${{\mathit D}^{*}}{{\overline{\mathit D}}^{*}}$ )${}^{0}{{\mathit \pi}^{0}}$ events using collisions at two c.m. energies. Production rates and mass values support grouping neutral and charged X(4020) together as manifestations of a single $\mathit I =$ particle.
${{\mathit X}{(4020)}}$ MASS $4024.1 \pm1.9$ MeV
${{\mathit X}{(4020)}}$ WIDTH $13 \pm5$ MeV (S = 1.7)
| 2019-04-19T13:11:04 |
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|
https://pdglive.lbl.gov/ParticleGroup.action?node=MXXX025&init=0
|
#### ${\mathit {\mathit c}}$ ${\mathit {\overline{\mathit c}}}$ MESONS (including possibly non- ${\mathit {\mathit q}}$ ${\mathit {\overline{\mathit q}}}$ states)
Charmonium System Branching Ratios of ${{\mathit \psi}{(2S)}}$ and ${{\mathit \chi}}$ $_{c0,1,2}$ Spectroscopy of Mesons Containing Two Heavy Quarks
| 2023-03-29T23:19:03 |
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https://www.bnl.gov/event.php?q=14538
|
# HET Seminar
## "Matrix Elements for Neutrinoless Double Beta Decay from Lattice QCD"
#### Presented by David Murphy, MIT
Wednesday, January 30, 2019, 2:30 pm — Small Seminar Room, Bldg. 510
While neutrino oscillation experiments have demonstrated that neutrinos have small, nonzero masses, much remains unknown about their properties and decay modes. One potential decay mode —- neutrinoless double beta decay ($0 \nu \beta \beta$) —- is a particularly interesting target of experimental searches, since its observation would imply both the violation of lepton number conservation in nature as well as the existence of at least one Majorana neutrino, in addition to giving further constraints on the neutrino masses and mixing angles. Relating experimental constraints on $0 \nu \beta \beta$ decay rates to the neutrino masses, however, requires theoretical input in the form of non-perturbative nuclear matrix elements which remain difficult to calculate reliably. In this talk we will discuss progress towards first-principles calculations of relevant nuclear matrix elements using lattice QCD and effective field theory techniques, assuming neutrinoless double beta decay mediated by a light Majorana neutrino.
Hosted by: Aaron Meyer
14538 | INT/EXT | Events Calendar
| 2021-11-29T18:43:18 |
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|
https://par.nsf.gov/biblio/10346205-optimal-uniform-ope-model-based-offline-reinforcement-learning-time-homogeneous-reward-free-task-agnostic-settings
|
Optimal Uniform OPE and Model-based Offline Reinforcement Learning in Time-Homogeneous, Reward-Free and Task-Agnostic Settings
This work studies the statistical limits of uniform convergence for offline policy evaluation (OPE) problems with model-based methods (for episodic MDP) and provides a unified framework towards optimal learning for several well-motivated offline tasks. Uniform OPE supΠ|Qπ−Q̂ π|<ϵ is a stronger measure than the point-wise OPE and ensures offline learning when Π contains all policies (the global class). In this paper, we establish an Ω(H2S/dmϵ2) lower bound (over model-based family) for the global uniform OPE and our main result establishes an upper bound of Õ (H2/dmϵ2) for the \emph{local} uniform convergence that applies to all \emph{near-empirically optimal} policies for the MDPs with \emph{stationary} transition. Here dm is the minimal marginal state-action probability. Critically, the highlight in achieving the optimal rate Õ (H2/dmϵ2) is our design of \emph{singleton absorbing MDP}, which is a new sharp analysis tool that works with the model-based approach. We generalize such a model-based framework to the new settings: offline task-agnostic and the offline reward-free with optimal complexity Õ (H2log(K)/dmϵ2) (K is the number of tasks) and Õ (H2S/dmϵ2) respectively. These results provide a unified solution for simultaneously solving different offline RL problems.
Authors:
;
Award ID(s):
Publication Date:
NSF-PAR ID:
10346205
Journal Name:
Advances in neural information processing systems
Volume:
34
Page Range or eLocation-ID:
12890--12903
ISSN:
1049-5258
1. We study the \emph{offline reinforcement learning} (offline RL) problem, where the goal is to learn a reward-maximizing policy in an unknown \emph{Markov Decision Process} (MDP) using the data coming from a policy $\mu$. In particular, we consider the sample complexity problems of offline RL for the finite horizon MDPs. Prior works derive the information-theoretical lower bounds based on different data-coverage assumptions and their upper bounds are expressed by the covering coefficients which lack the explicit characterization of system quantities. In this work, we analyze the \emph{Adaptive Pessimistic Value Iteration} (APVI) algorithm and derive the suboptimality upper bound that nearly matches $O\left(\sum_{h=1}^H\sum_{s_h,a_h}d^{\pi^\star}_h(s_h,a_h)\sqrt{\frac{\mathrm{Var}_{P_{s_h,a_h}}{(V^\star_{h+1}+r_h)}}{d^\mu_h(s_h,a_h)}}\sqrt{\frac{1}{n}}\right).$ We also prove an information-theoretical lower bound to show this quantity is required under the weak assumption that $d^\mu_h(s_h,a_h)>0$ if $d^{\pi^\star}_h(s_h,a_h)>0$. Here $\pi^\star$ is a optimal policy, $\mu$ is the behavior policy and $d(s_h,a_h)$ is the marginal state-action probability. We call this adaptive bound the \emph{intrinsic offline reinforcement learning bound} since it directly implies all the existing optimal results: minimax rate under uniform data-coverage assumption, horizon-free setting, single policy concentrability, and the tight problem-dependent results. Later, we extend the result to the \emph{assumption-free} regime (where we make no assumption on $\mu$) and obtain the assumption-free intrinsicmore »
| 2022-10-05T08:06:11 |
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https://www.zbmath.org/authors/?q=ai%3Ashao.xuancheng
|
zbMATH — the first resource for mathematics
Shao, Xuancheng
Compute Distance To:
Author ID: shao.xuancheng Published as: Shao, X.; Shao, Xuancheng External Links: MGP · Wikidata
Documents Indexed: 26 Publications since 2008
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Co-Authors
11 single-authored 3 Granville, Andrew James 3 Matomäki, Kaisa Sofia 2 Drappeau, Sary 2 Johnson, Steven G. 1 Devadoss, Satyan Linus 1 Diaconis, Persi Warren 1 Kedlaya, Kiran Sridhara 1 Maynard, James 1 Shah, Rahul 1 Soundararajan, Kannan 1 Winston, Ezra M. 1 Xu, Wenqiang
all top 5
Serials
2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Signal Processing 2 IMRN. International Mathematics Research Notices 2 Algebra & Number Theory 2 Forum of Mathematics, Sigma 1 American Mathematical Monthly 1 Acta Arithmetica 1 Advances in Mathematics 1 American Journal of Mathematics 1 Bulletin of the London Mathematical Society 1 Compositio Mathematica 1 Duke Mathematical Journal 1 Journal für die Reine und Angewandte Mathematik 1 Mathematika 1 Proceedings of the London Mathematical Society. Third Series 1 Forum Mathematicum 1 Contributions to Discrete Mathematics 1 Discrete Analysis
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Fields
21 Number theory (11-XX) 2 Group theory and generalizations (20-XX) 2 Information and communication theory, circuits (94-XX) 1 Combinatorics (05-XX) 1 Convex and discrete geometry (52-XX) 1 Manifolds and cell complexes (57-XX) 1 Computer science (68-XX)
Citations contained in zbMATH
18 Publications have been cited 47 times in 40 Documents Cited by Year
Character sums over unions of intervals. Zbl 1326.11043
Shao, Xuancheng
2015
Smooth-supported multiplicative functions in arithmetic progressions beyond the $$x^{1/2}$$-barrier. Zbl 1428.11174
Drappeau, Sary; Granville, Andrew; Shao, Xuancheng
2017
Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations. Zbl 1186.94305
Shao, Xuancheng; Johnson, Steven G.
2008
Bombieri-Vinogradov for multiplicative functions, and beyond the $$x^{1/2}$$-barrier. Zbl 07066543
Granville, Andrew; Shao, Xuancheng
2019
When does the Bombieri-Vinogradov theorem hold for a given multiplicative function? Zbl 1451.11105
Granville, Andrew; Shao, Xuancheng
2018
Vinogradov’s theorem with almost equal summands. Zbl 1400.11132
Matomäki, Kaisa; Maynard, James; Shao, Xuancheng
2017
Vinogradov’s three primes theorem with almost twin primes. Zbl 1395.11120
Matomäki, Kaisa; Shao, Xuancheng
2017
Carries, group theory, and additive combinatorics. Zbl 1310.05210
Diaconis, Persi; Shao, Xuancheng; Soundararajan, Kannan
2014
A density version of the Vinogradov three primes theorem. Zbl 1330.11062
Shao, Xuancheng
2014
Deformations of associahedra and visibility graphs. Zbl 1317.52018
Devadoss, Satyan L.; Shah, Rahul; Shao, Xuancheng; Winston, Ezra
2012
Polynomial values modulo primes on average and sharpness of the larger sieve. Zbl 1331.11083
Shao, Xuancheng
2015
An $$L$$-function-free proof of Vinogradov’s three primes theorem. Zbl 1308.11087
Shao, Xuancheng
2014
Type-II/III DCT/DST algorithms with reduced number of arithmetic operations. Zbl 1186.94306
Shao, Xuancheng; Johnson, Steven G.
2008
A robust version of Freiman’s $$3k-4$$ theorem and applications. Zbl 07054515
Shao, Xuancheng; Xu, Wenqiang
2019
Gowers norms of multiplicative functions in progressions on average. Zbl 1416.11142
Shao, Xuancheng
2017
Weyl sums, mean value estimates, and Waring’s problem with friable numbers. Zbl 1385.11052
Drappeau, Sary; Shao, Xuancheng
2016
Finding linear patterns of complexity one. Zbl 1400.11023
Shao, Xuancheng
2015
Generalizations of product-free subsets. Zbl 1179.20025
Kedlaya, Kiran S.; Shao, Xuancheng
2009
Bombieri-Vinogradov for multiplicative functions, and beyond the $$x^{1/2}$$-barrier. Zbl 07066543
Granville, Andrew; Shao, Xuancheng
2019
A robust version of Freiman’s $$3k-4$$ theorem and applications. Zbl 07054515
Shao, Xuancheng; Xu, Wenqiang
2019
When does the Bombieri-Vinogradov theorem hold for a given multiplicative function? Zbl 1451.11105
Granville, Andrew; Shao, Xuancheng
2018
Smooth-supported multiplicative functions in arithmetic progressions beyond the $$x^{1/2}$$-barrier. Zbl 1428.11174
Drappeau, Sary; Granville, Andrew; Shao, Xuancheng
2017
Vinogradov’s theorem with almost equal summands. Zbl 1400.11132
Matomäki, Kaisa; Maynard, James; Shao, Xuancheng
2017
Vinogradov’s three primes theorem with almost twin primes. Zbl 1395.11120
Matomäki, Kaisa; Shao, Xuancheng
2017
Gowers norms of multiplicative functions in progressions on average. Zbl 1416.11142
Shao, Xuancheng
2017
Weyl sums, mean value estimates, and Waring’s problem with friable numbers. Zbl 1385.11052
Drappeau, Sary; Shao, Xuancheng
2016
Character sums over unions of intervals. Zbl 1326.11043
Shao, Xuancheng
2015
Polynomial values modulo primes on average and sharpness of the larger sieve. Zbl 1331.11083
Shao, Xuancheng
2015
Finding linear patterns of complexity one. Zbl 1400.11023
Shao, Xuancheng
2015
Carries, group theory, and additive combinatorics. Zbl 1310.05210
Diaconis, Persi; Shao, Xuancheng; Soundararajan, Kannan
2014
A density version of the Vinogradov three primes theorem. Zbl 1330.11062
Shao, Xuancheng
2014
An $$L$$-function-free proof of Vinogradov’s three primes theorem. Zbl 1308.11087
Shao, Xuancheng
2014
Deformations of associahedra and visibility graphs. Zbl 1317.52018
Devadoss, Satyan L.; Shah, Rahul; Shao, Xuancheng; Winston, Ezra
2012
Generalizations of product-free subsets. Zbl 1179.20025
Kedlaya, Kiran S.; Shao, Xuancheng
2009
Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations. Zbl 1186.94305
Shao, Xuancheng; Johnson, Steven G.
2008
Type-II/III DCT/DST algorithms with reduced number of arithmetic operations. Zbl 1186.94306
Shao, Xuancheng; Johnson, Steven G.
2008
all top 5
Cited by 62 Authors
5 Shao, Xuancheng 5 Shparlinski, Igor E. 3 Granville, Andrew James 2 Britaňák, Vladimír 2 Cetina, Mario 2 Chan, Tsz Ho 2 Dietmann, Rainer 2 Drappeau, Sary 2 Elsholtz, Christian 2 Leanos, Jesus 2 Roy, Arindam 2 Salazar, Gelasio 2 Vatwani, Akshaa 1 Ábrego, Bernardo Manuel 1 Aichholzer, Oswin 1 Arriëns, Huibert J. Lincklaen 1 Banks, William D. 1 Benedetto, Robert L. 1 Blanco-Velasco, Manuel 1 Bourgain, Jean 1 Braun, Benjamin 1 Cruz-Roldán, Fernando 1 Diaconis, Persi Warren 1 Ehrenborg, Richard 1 Fabila-Monroy, Ruy 1 Fulman, Jason E. 1 García, Juan Manuel 1 Ge, Gennian 1 Heath-Brown, David Roger 1 Hellus, Michael 1 Ingram, Patrick 1 Jones, Rafe 1 Kober, V. I. 1 Konyagin, Sergeĭ Vladimirovich 1 Liu, Jianhua 1 Manes, Michelle 1 Maynard, James 1 Melnikov, Alexander V. 1 Monopoli, Francesco 1 Mora-Mora, Higinio 1 Osés-del Campo, José David 1 Perera, Sirani M. 1 Pinto-Benel, Freddy A. 1 Rechenauer, Anton 1 Ruzsa, Imre Z. 1 Sagdeev, A. A. 1 Sanders, Tom 1 Shen, Quanli 1 Signes, María Teresa 1 Silverman, Joseph Hillel 1 Tao, Terence 1 Tărnăuceanu, Marius 1 Teräväinen, Joni 1 Tolev, Doychin I. 1 Topacogullari, Berke 1 Tucker, Thomas John 1 Urrutia Galicia, Jorge L. 1 Vokhmintcev, A. V. 1 Waldi, Rolf 1 Xu, Wenqiang 1 Xu, Zixiang 1 Zhu, Wenbin
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Cited in 28 Serials
5 Mathematika 2 Advances in Mathematics 2 Archiv der Mathematik 2 Transactions of the American Mathematical Society 2 Signal Processing 2 Integers 2 Proceedings of the Steklov Institute of Mathematics 2 Forum of Mathematics, Sigma 1 Information Processing Letters 1 Journal of the Franklin Institute 1 Mathematical Notes 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Mathematics of Computation 1 Canadian Journal of Mathematics 1 Journal of Combinatorial Theory. Series A 1 Journal of Computational and Applied Mathematics 1 Journal of Number Theory 1 Semigroup Forum 1 Advances in Applied Mathematics 1 Mathematical and Computer Modelling 1 SIAM Journal on Discrete Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 Indagationes Mathematicae. New Series 1 Doklady Mathematics 1 The Ramanujan Journal 1 International Journal of Number Theory 1 Algebra & Number Theory 1 Japanese Journal of Mathematics. 3rd Series
all top 5
Cited in 12 Fields
27 Number theory (11-XX) 6 Information and communication theory, circuits (94-XX) 5 Numerical analysis (65-XX) 3 Convex and discrete geometry (52-XX) 3 Computer science (68-XX) 2 Group theory and generalizations (20-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Systems theory; control (93-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Abstract harmonic analysis (43-XX) 1 Probability theory and stochastic processes (60-XX) 1 Operations research, mathematical programming (90-XX)
Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2021-03-04T22:48:15 |
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http://www.khronos.org/registry/vulkan/specs/1.1-extensions/man/html/VkPhysicalDevicePushDescriptorPropertiesKHR.html
|
## C Specification
The VkPhysicalDevicePushDescriptorPropertiesKHR structure is defined as:
typedef struct VkPhysicalDevicePushDescriptorPropertiesKHR {
VkStructureType sType;
void* pNext;
uint32_t maxPushDescriptors;
} VkPhysicalDevicePushDescriptorPropertiesKHR;
## Members
The members of the VkPhysicalDevicePushDescriptorPropertiesKHR structure describe the following implementation-dependent limits:
## Description
• sType is the type of this structure.
• pNext is NULL or a pointer to an extension-specific structure.
• maxPushDescriptors is the maximum number of descriptors that can be used in a descriptor set created with VK_DESCRIPTOR_SET_LAYOUT_CREATE_PUSH_DESCRIPTOR_BIT_KHR set.
If the VkPhysicalDevicePushDescriptorPropertiesKHR structure is included in the pNext chain of VkPhysicalDeviceProperties2, it is filled with the implementation-dependent limits.
Valid Usage (Implicit)
• sType must be VK_STRUCTURE_TYPE_PHYSICAL_DEVICE_PUSH_DESCRIPTOR_PROPERTIES_KHR
## Document Notes
For more information, see the Vulkan Specification at URL
This page is extracted from the Vulkan Specification. Fixes and changes should be made to the Specification, not directly.
Copyright (c) 2014-2019 Khronos Group. This work is licensed under a Creative Commons Attribution 4.0 International License.
| 2019-03-25T04:50:05 |
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https://www.usgs.gov/center-news/volcano-watch-mauna-loa-older-or-younger-k-lauea
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# Volcano Watch — Is Mauna Loa older or younger than Kīlauea?
Release Date:
In 1916, Thomas Jaggar, renowned scientist and founder of HVO, wrote, in a foreword to "Hawaiian Legends of Volcanoes" by Westervelt, that "Everything indicates that Kīlauea is older than Mauna Loa. Mauna Loa with its flows is tending through the ages to bury up Kīlauea?."
In 1916, Thomas Jaggar, renowned scientist and founder of HVO, wrote, in a foreword to "Hawaiian Legends of Volcanoes" by Westervelt, that "Everything indicates that Kīlauea is older than Mauna Loa. Mauna Loa with its flows is tending through the ages to bury up Kīlauea?." But for at least the past 40 years, volcanologists have unanimously agreed that Kīlauea is younger, not older, than Mauna Loa. What occasioned this remarkable about-face, and how secure is today's interpretation?
Jaggar was no dummy. He didn't develop his ideas out of thin air. He looked at the much greater lava-flow activity of Mauna Loa than of Kīlauea during the preceding 100 years and reasoned that Kīlauea was waning and Mauna Loa waxing. He thought that Mauna Loa had formed in a "long spoon-shaped valley between [Hualālai and Kīlauea]."
But careful observations by Polynesian settlers of Hawaii had noted that the islands become younger toward the southeast. J.D. Dana, a leading 19th-century naturalist, had concluded similarly on the basis of geologic evidence. Rather than building on these concepts and suggesting that Kīlauea was younger than its northwestern neighbor, Mauna Loa, Jaggar concluded that Mauna Loa must be younger because of its greater activity in the previous 100 years.
Since Jaggar wrote his words for Westervelt, the concepts and supporting data for plate tectonics and hot spots have changed the way that scientists view the earth. The case has been strongly made that the Pacific plate is moving northwestward over an immobile (or only slightly mobile) hot spot carrying magma up from the earth's mantle. A volcano begins to form as a point on the plate nears the hot spot; the volcano flourishes as it passes over the hot spot and slowly dies as it moves northwestward away from the spot. In this way the Hawaiian Islands in general---and each volcano on each island in particular---become younger toward the southeast. These concepts are supported by isotopic dating, landform development, and much other information. The Polynesians and Dana were right by modern thinking, and Jaggar wrong.
But what about the details of specific volcanoes? What is the "hard" evidence that Mauna Loa is older than Kīlauea? We cannot see the earliest lava flows erupted by each volcano; they are deeply buried. No geophysical techniques are capable of telling which volcano is on top of the other at depths of several kilometers. There are no deep drill holes that penetrate the two volcanoes to show that one started before the other. Even with such holes, it might be tough to distinguish flows from the two volcanoes; they don't talk to you and aren't color coded. Indirect geochemical methods would be needed to develop ways to tell old Mauna Loa flows from old Kīlauea flows.
You can, in places, see Mauna Loa flows on top of Kīlauea flows, and vice versa. These relations, however, simply tell us what we already know; the two volcanoes have each erupted many times in the past thousand years. The relations do not tell which volcano started first, some 100,000 or more years ago.
And so we're stuck. We really can't find proof that Mauna Loa began erupting before Kīlauea, yet all our concepts demand it, and there is no evidence against it. We disagree strongly with Jaggar, and, put to the test of a civil lawsuit, we would surely win a majority vote of the jury. Yet there is really no smoking gun. It is simply not possible, on the basis of what we know today, to say with absolute certainty that Mauna Loa is older than Kīlauea.
### Volcano Activity Update
Eruptive activity of Kīlauea Volcano continued unabated during the past week. Lava is erupting from Puu Oo and flowing through a tube to the southeast in the direction of the sea coast. The lava pond within Puu Oo occasionally drains, and gases jet from the vents with a loud roar. Lava leaves Puu Oo and flows through a tube southeastward to the 620-m (2050-ft) elevation, near the top of Pulama pali. There lava wells out to form a low shield with a perched pond on top. Since October 22, breakouts from the south side of the shield have been feeding a flow that has descended to the base of Pulama pali and spread part way across the coastal flat. By November 4, the distal end of the flow is about 1.6 km (1.0 mi) from the sea coast just west of the old Kamoamoa campground.
Two earthquakes were reported felt by a resident of Leilani Estates during the week ending on November 4. The first earthquake was at 10:06 p.m. on Sunday, October 31, and the second was at 12:28 p.m. on Monday, November 1. Both earthquakes were located 3 km (1.8 mi) south of Pu`ulena Crater at a shallow depth. The magnitudes of the two earthquakes were 2.2 and 2.5, respectively.
| 2021-03-08T16:30:09 |
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|
https://gea.esac.esa.int/archive/documentation/GDR2/Data_processing/chap_cu4sso/sec_cu4sso_QAV/ssec_cu4sso_QCatAstrometry.html
|
# 4.5.2 Quality control of Astrometry
Author(s): Thierry Pauwels, Federica Spoto, Paolo Tanga
## Comparing uncertainties with $O-C$s
During the validation process, we computed the best fitting orbit to Gaia data and the post-fit residuals ($O-C$) to each observation. We could thus check the coherence of the error model with the $O-C$s. For this purpose it was assumed that the errors on the positions from the orbit are negligible compared to the errors on individual positions, so that the $O-C$s reflect the real errors on the positions (except for possible systematics that might be present throughout the mission). In order to be able to validate the uncertainties, we separated the $O-C$s also in a systematic and random part. For the systematic part we took the average of all $O-C$s of the transit, and for the random part we took the difference between each individual $O-C$ and the average.
The left panels of Figure 4.21 and Figure 4.22 show the random part of $O-C$s in AL and AC respectively. As expected, we see that in AL the $O-C$s increase with increasing magnitude, due to the progressive deterioration in the centroiding performance. For brighter objects ($G$ $<\approx$16), the $O-C$s become independent of magnitude, since the errors from centroiding are smaller than those due to the attitude.
In AC the situation is different. For objects with G$>$13, with 1-D windows, the error comes from the fact that the window centre has been used as an estimate of the position of the object, and it is not dependent on magnitude. Minor variations are present, whose relevance is marginal, whose origin deserves further investigations. Objects brighter than magnitude 13 have 2-D windows (see the left panel of Figure 4.23 for a zoom of Figure 4.22). The situation is similar to AL, where the errors on the attitude dominate, and the $O-C$s are independent from magnitude.
The right panels of Figure 4.21 and Figure 4.22 give the same information, but divided by the computed uncertainties, with the correction $\sqrt{(n-1)/n}$, where $n$ is the number of positions in the transit after removal of the positions that were rejected. The figures show also the 2.3, 16, 50, 84 and 97.7 percentiles, which correspond to the $-2\sigma$, $-1\sigma$, median or mean, $+$1$\sigma$ and $+$2$\sigma$, respectively, under the hypothesis that the $O-C$s follow a Gaussian distribution.
In AL the $O-C$s behave as expected over the whole brightness range, with the percentiles following almost exactly the values $-2$, $-1$, 0, $+1$ and $+2\sigma$. In AC the situation is again different. For objects brighter than magnitude 13, the behaviour is similar to AL, but for fainter objects the real $O-C$s are a lot smaller than the computed uncertainties. This is explained by the fact that uncertainties are given as coming from a rectangular distribution over the complete transmitted window, while in reality a majority of objects will be closer to one of the central pixels, as explained in section 4.4.4.
Figure 4.24, Figure 4.25 and the right panel of Figure 4.23 for a zoom on Figure 4.25 represent the same for the systematic errors. Both in AL and AC we see a slightly less good agreement with the error model as the O-C are smaller than expected. This fact indicates that our model for systematic errors is rather conservative. We also note that in AC a bi-variate distribution for faint objects appears (at magnitudes fainter than $\sim$18).
| 2019-03-24T15:56:49 |
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|
https://www.federalreserve.gov/econres/notes/feds-notes/measurement-and-effects-of-supply-chain-bottlenecks-using-natural-language-processing-20230206.html
|
February 06, 2023
### Measurement and Effects of Supply Chain Bottlenecks Using Natural Language Processing1
Paul E. Soto
Supply chain bottlenecks can have significant impacts on the real economy. When firms experience shortages, shipping delays, or shutdowns, as occurred during the COVID-19 pandemic, they may be unable to produce, transport, and sell their products. This can lead to demand and supply mismatches, potentially resulting in price increases and requiring firms to make difficult decisions regarding their supply chain management or scaling down operations.
Quantifying supply chain bottlenecks can be challenging due to the complexity of a firm's input-output network. While traditional measures such as lead times, freight costs, and backorders provide insight into supply chain performance, new research in economics emphasizes the value of using narratives and anecdotes in forecasting major economic events (Shiller, 2018). This study proposes a novel approach to measuring supply chain bottlenecks by analyzing narratives from the Federal Reserve's Beige Books using machine learning and natural language processing techniques. The Beige Books are a valuable source for such anecdotes due to their predictive power for GDP and employment (Armesto et al., 2009).
This note builds on several notable measures of supply chain disruptions. The Global Supply Chain Pressure Index (GSCPI), created by the Applied Macroeconomics and Econometrics Center at the Federal Reserve Bank of New York (Benigno et al. 2022), uses quantitative transportation and manufacturing survey data to produce a global measure. Young et al. 2021 measure supply chain bottlenecks across firms and industries using quarterly earnings conference calls. Most similar to this note, Kliesen and Werner (2022) develop the Beige Book Supply Chain Disruption Index (BBSCDI) by counting the frequency of supply chain-related words in the Beige Books.2
This study introduces a new measure, the Supply Chain Bottleneck Sentiment (SCB Sentiment) index, which differs in two ways. First, the list of words related to supply chain bottlenecks is generated through unsupervised machine learning and natural language processing (similar to Soto, 2021), rather than being predetermined. For example, one could identify sentences containing "supply chain," "supply chains," or "bottlenecks" as indicative of supply chain bottlenecks. However, these tokens appear 689, 86, and 270 times, respectively, across all Beige Books. Other words referring to supply chain disruptions appear just as frequently or more often, such as "shortages" (2,733 occurrences), "delays" (552 occurrences), and "disruptions" (623 occurrences). Failing to account for other words related to supply chain disruptions may underestimate the attention Beige Books give to bottlenecks. By using unsupervised methods to identify semantically and syntactically similar words to "supply chain bottlenecks," subjectivity in the creation of the lexicon is minimized.
Second, the new index takes into account the sentiment of the supply chain text using deep learning techniques. While supply chain issues are often depicted negatively in media or narratives, it is important to consider instances in which supply chain improvements or resiliencies are mentioned. For example, in the October 2022 Beige Book report, the Federal Reserve Bank of Boston noted that "for retailers as well as manufacturers, supply chain issues appeared to be relenting and inventories approached desired levels." Using deep learning text analysis, the SCB Sentiment index would classify this sentence as positive, as the word "relenting" is used to describe the "supply chain issues." Text measures of supply chain bottlenecks that simply count the presence of supply chain-related words may overestimate the actual level of disruption.
#### Data
The Beige Book summarizes the economic condition of each of the twelve Federal Reserve districts. The report aggregates narratives that are collected from business contacts.3 I build a dataset where each row includes the month, year, and text of the Beige Book. In addition to the Beige Book text, I also include changes in logs of the levels of the Consumer Price Index, the price of Brent crude, and industrial production for each month-year.
#### Finding Words Related to Supply Chain Bottlenecks
The first step of creating the measure involves finding sentences related to supply chain bottlenecks. This process is done by estimating word embeddings, which are vector representations of words that preserve their syntactic and semantic nature. That is, a well estimated word embedding model will map words with similar meanings to the same area of the vector space.
I estimate word embeddings for every unique word, also known as a token, used throughout the Beige Books using the Word2Vec algorithm.4,5 Vector arithmetic can be used to validate the fit of Word2Vec models. For example, Mikolov et al. (2013) demonstrated that the sum of the vectors for "capital" and "vietnam" was closest to the word embedding for "hanoi" in their study using the first Word2Vec model trained on internal Google data. Similarly, the following examples show the semantic and syntactic understanding of language by the Beige Book Word2Vec model:
vec(chip)+vec(technology) = vec(semiconductor)
vec(loan)+vec(home) = vec(mortgage)
vec(december)+vec(holiday) = vec(christmas)
Since the sum of two words often yields coherent results (e.g. "chip" and "technology" is most similar to "semiconductor"), it is possible to create a vector representation for a specific theme by adding phrases or words. In this study, the list of words related to supply chain bottlenecks is defined as the set of tokens near the vector, vec("supply chain") + vec("bottlenecks"). Figure 1 presents this list of words, with the size of the word indicating its frequency across the corpus. The list covers various themes related to bottlenecks, such as material and labor shortages, delays, shutdowns, and capacity constraints.
#### Classifying the Sentiment of Sentences Mentioning Supply Chain Bottlenecks
Next, I estimate the sentiment of each sentence containing at least one of the supply chain bottleneck words by applying a BERT sentiment classifier to each sentence (Devlin et al. 2018). BERT models have been demonstrated to capture sentiment more effectively than lexicons, as they account for the complexities of language, such as negation and the range of synonyms for positive and negative sentiment. In addition, BERT models can be fine-tuned to consider the nuances of different domains. One widely available BERT model, FinBERT, was trained on a financial corpus and has been shown to improve the accuracy of sentiment classification for financial texts.6 Given the financial context of the Beige Book, I use FinBERT to classify the sentiment of supply chain bottleneck sentences.
Figure 2 shows the Supply Chain Bottleneck Sentiment Index (SCB Sentiment- total negative sentences minus total positive sentences, divided by total sentences) for each Beige Book publication. Supply chains were stressed in the 1970s after the oil embargo and increases in oil prices. Supply chain issues reappeared at the beginning of the millennium with chip shortages. Most recently, bottlenecks arose during the COVID-19 pandemic. The index suggests that the bottlenecks arising from the pandemic have been ebbing since the latter half of 2021. This is in line with other measures of supply chain bottlenecks, such as supplier delivery times and order backlogs provided by the Institute for Supply Management.
#### Supply Chain Bottlenecks and Inflation
Supply chain bottlenecks can impact the availability of goods and potentially result in higher inflation. I use the SCB Sentiment score to assess the link between supply chain bottlenecks and inflation. Table 1 shows how the new index at time t is associated with monthly inflation growth at t+1. Recall that higher values of the SCB Sentiment index correspond to more negative sentiment about supply chain bottlenecks. In column (1), we see a positive and significant relationship with SCB Sentiment and inflation after accounting for lagged changes in inflation and oil prices. Given that supply chain bottlenecks are related to industrial production, in column (2) I include the lagged changes in industrial production growth. Controlling for lagged CPI, oil, and IP dynamics do not seem to hamper the significance or magnitude of the coefficient on the new index. In columns (3) and (4), I include two prominent supply chain indices, the BBSCDI and GSCPI (available from 1998), resulting in little change to the coefficient. Figure 3 presents the time series of the SCB Sentiment, as well as the BBSCDI and GSCPI. All three indices show a rapid increase during the COVID-19 pandemic, but exhibit different tendencies earlier in the sample.
##### Table 1: Regressing CPI on Supply Chain Bottleneck Sentiment
(1) (2) (3) (4) Dependent Variable: Δlog(CPI)t+1 0.162** 0.181*** 0.178*** 0.175** -0.068 -0.067 -0.069 -0.082 0.003 0.022 -0.042 -0.06 0.137* -0.077 Y Y Y Y Y Y Y Y N Y Y Y 261 261 261 198 0.332 0.351 0.351 0.396
Notes: Robust standard errors in parentheses (∗ p < 0.1, ∗∗ p < 0.05, ∗∗∗ p < 0.01). This table reports the effect of supply chain bottleneck sentiment on inflation. The sample runs from 1991 to 2022 in columns (1) through (3) and from 1998 to 2022 in column (4). CPI, Oil and IP Lags are three lags of Δlog(CPI), Δlog(OIL), and Δlog(IP). SCB Sentimentt is the total number of negative sentences minus the total number of positive sentences about supply chain bottlenecks, divided by total number of supply chain bottleneck sentences reported in the Beige Book of month t. BBSCDIt and the GSCPIt are the Beige Book Supply Chain Disruption Index (Kliesen and Werner 2022) and the Global Supply Chain Pressure Index (Benigno et al. 2022).
##### Figure 3. Supply Chain Bottleneck Measures
To better understand the dynamics of a shock to supply chain bottlenecks, I estimate a Bayesian Vector Autoregression with IP, oil price and CPI growth. I include two lags for each of the four variables and allow for time-varying coefficients as in (Primiceri 2005).7
$$\left[\begin{matrix}SCDisruption_t\\\Delta{IP}_t\\\Delta O i l_t\\\Delta C P I_t\\\end{matrix}\right]=\mathbf{\alpha}_\mathbf{t}+\mathbf{\beta}_{\mathbf{1},\mathbf{t}}\left[\begin{matrix}SCDisruption_{t-1}\\\Delta{IP}_{t-1}\\\Delta O i l_{t-1}\\\Delta C P I_{t-1}\\\end{matrix}\right]+\mathbf{\beta}_{\mathbf{2},\mathbf{t}}\left[\begin{matrix}SCDisruption_{t-2}\\\Delta{IP}_{t-2}\\\Delta O i l_{t-2}\\\Delta C P I_{t-2}\\\end{matrix}\right]+\mathbf{\varepsilon}_\mathbf{t}$$
Where $\mathbf{\alpha}_\mathbf{t}$ and $\mathbf{\beta}_{\mathbf{k},\mathbf{t}}$ are time-varying parameters with $\mathbf{\alpha}_\mathbf{t}=\mathbf{\alpha}_{\mathbf{t}-\mathbf{1}}+\mathbf{\zeta}_\mathbf{t}$ and $\mathbf{\beta}_{\mathbf{k},\mathbf{t}}=\mathbf{\beta}_{\mathbf{k},\mathbf{t}-\mathbf{1}}+\mathbf{\nu}_\mathbf{t}$. $SCDisruption_t$ is one of three supply chain bottleneck measures: the new index, the BBSCDI, and the GSCPI.
In Figure 4, we see that a shock to SCB Sentiment significantly drives up the monthly inflation growth. The slow decay is consistent with the lasting effects of supply chain pressures that buildup and take time to manifest in prices. The BBSCDI does not exhibit similar nor significant movements in inflation, potentially due to the lexicon for supply chain words, or the ambiguity in whether mentions of supply chains is generally positive or negative. The GSCPI shock exhibits a more pronounced impact on inflation, and less swift return to the baseline. Considering that the new index focuses on the U.S. while the GSCPI has a global scope, the slower decay of the GSCPI shock illustrates the intricate nature and enduring effect of bottlenecks in global supply chains.
#### Conclusion
This note presented a new measure of supply chain bottlenecks, the Supply Chain Bottleneck Sentiment (SCB Sentiment) index, which utilizes unsupervised machine learning and natural language processing techniques to identify words related to supply chain bottlenecks in the Federal Reserve's Beige Book and uses deep learning to account for the sentiment of the identified supply chain text. The SCB Sentiment index was found to be positively and significantly associated with future inflation after controlling for lagged changes in inflation, oil prices, and industrial production. This new measure of supply chain bottlenecks adds to the existing literature by providing a more comprehensive and sentiment-aware approach to assessing the impact of supply chain disruptions on the economy.
#### References
Armesto, M.T., Hernández‐Murillo, R., Owyang, M.T. and Piger, J., 2009. Measuring the information content of the beige book: A mixed data sampling approach. Journal of Money, Credit and Banking, 41(1), pp.35-55.
Benigno, G., di Giovanni, J., Groen, J.J. and Noble, A.I., 2022. The GSCPI: A New Barometer of Global Supply Chain Pressures. FRB of New York Staff Report, (1017).
Devlin, J., Chang, M.W., Lee, K. and Toutanova, K., 2018. Bert: Pre-training of deep bidirectional transformers for language understanding. arXiv preprint arXiv:1810.04805.
Kliesen, K.L. and Werner, D., 2022. Using Beige Book Text Analysis to Measure Supply Chain Disruptions. Economic Synopses, (18).
Mikolov, T., Sutskever, I., Chen, K., Corrado, G.S. and Dean, J., 2013. Distributed representations of words and phrases and their compositionality. Advances in neural information processing systems, 26.
Primiceri, G.E., 2005. Time varying structural vector autoregressions and monetary policy. The Review of Economic Studies, 72(3), pp.821-852.
Soto, P.E., 2021. Breaking the Word Bank: Measurement and Effects of Bank Level Uncertainty. Journal of Financial Services Research, 59(1), pp.1-45.
Shiller, R.J., 2017. Narrative economics. American Economic Review, 107(4), pp.967-1004.
Young, H.L., Monken, A., Haberkorn, F. and Van Leemput, E., 2021. Effects of supply chain bottlenecks on prices using textual analysis.
1. The analysis and conclusions set forth are those of the author and do not indicate concurrence by other members of the research staff or the Board of Governors. I thank Flora Haberkorn and Isabel Kitschelt in the International Finance Division for providing the dataset on the Beige Book text. The note benefited from comments and suggestions by Tomaz Cajner, Christopher J. Kurz and Stacey Tevlin. Return to text
2. The index counts the frequency of the following words: "supply chain-," "bottleneck-," "bottle neck-," "backlog-," "port-," "unfilled order-," "delivery time-," "supply delay-," "truck-," "boat-," or "transportation." Return to text
3. See https://www.federalreserve.gov/monetarypolicy/beige-book-faqs.htm for further information on the Beige Books. Return to text
4. I preprocess the text by applying a sentence tokenizer to isolate individual sentences and remove any non-alphanumeric characters from each sentence. I also include bigrams, defined as any sequence of two words that appear at least five times throughout the corpus. I keep stopwords in the text to assist the Word2Vec algorithm in finding syntactically and semantically similar words. Return to text
5. The word embeddings are estimated using a window size of 10 and a dimension size of 300. For further details on Word2Vec, see Mikolov et al. 2013. Return to text
| 2023-03-20T13:23:34 |
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