The Experts below are selected from a list of 213 Experts worldwide ranked by ideXlab platform
Bhimsen K. Shivamoggi - One of the best experts on this subject based on the ideXlab platform.
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Thomas-Fermi Model: Nonextensive statistical mechanics approach
Physical Review A, 2004Co-Authors: Evgeny Martinenko, Bhimsen K. ShivamoggiAbstract:In this paper, the Thomas-Fermi Model for large atoms is reformulated by incorporating the nonextensive entropy prescription. The entropy nonextensivity contribution dominates the usual thermal correction term in the ``low-temperature'' limit. On the other hand, the entropy nonextensivity concept appears to provide a useful framework to describe the fractal nature of the Fermi surface in the nondegenerate case. Analytical calculations are given for some atomic properties, such as the total binding energy of the electrons in the atom. The nonextensivity of entropy is indicated to have the potential to provide a means to remedy one of the well-known weaknesses in the Thomas-Fermi Model---the boundary effect. The virial theorem has been shown to be a robust result that holds also in the nonextensive entropy regime.
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Thomas-Fermi Model for an atom in a very strong magnetic field: thermal effects
Physica A: Statistical Mechanics and its Applications, 1995Co-Authors: Bhimsen K. Shivamoggi, Ppjm Piet SchramAbstract:Thermal effects on the Thomas-Fermi Model for atoms in a very strong magnetic field are considered. The binding energy of the atom is calculated with the thermal effects taken into account.
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Relativistic Thomas-Fermi Model for Atoms in a Very Strong Magnetic Field
Europhysics Letters (EPL), 1993Co-Authors: Bhimsen K. Shivamoggi, P. MulserAbstract:Relativistic effects on the Thomas-Fermi Model for atoms in a very strong magnetic field are considered. A general calculation of the binding energy is given which does not refer to any specific solution of the equation governing the self-consistent electrostatic potential.
Pavel Levashov - One of the best experts on this subject based on the ideXlab platform.
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TFmix: A high-precision implementation of the finite-temperature Thomas–Fermi Model for a mixture of atoms
Computer Physics Communications, 2019Co-Authors: O P Shemyakin, Pavel Levashov, P.a. KrasnovaAbstract:Abstract In this work we present a TFmix code intended for numerical calculation of the thermal part of electronic thermodynamic properties of a mixture of elements by the finite-temperature Thomas–Fermi Model. The code is based on analytical Models for both first and second derivatives of Helmholtz thermodynamic potential. All numerical calculations are made within a controlled high accuracy: tests for thermodynamic consistency give at least 11 coinciding decimal digits. The code calculates thermodynamic functions on a regular grid of isotherms and isochores; at each grid point some extensive parameters and the number of free electrons are output both for the whole mixture and for each component. Other extensive or intensive thermodynamic properties, including pressure, entropy, isochoric and isobaric heat capacities, isothermal and adiabatic sound velocities can be easily calculated from the information available at each grid point. Several unit systems are provided for convenience. A cross-platform graphical user interface is developed to simplify the use of the code. Program summary Program Title: TFmix, version 1.0 Program Files doi: http://dx.doi.org/10.17632/mc3vj77jfn.1 Licensing provisions: GPLv3 Programming language: C, Python Nature of problem: Any substance consists of elements so its equation of state contains a contribution of electronic gas. Thermodynamics of the electronic gas in a mixture of ions and electrons has been studied in many approaches. Thermodynamic properties of a uniform ideal electron gas can be calculated using the well-known analytical Model of Fermi-gas. On the other hand, Models of electron gas which take into account interaction effects are quite complicated and require sophisticated computational techniques. Even a simplified semiclassical Thomas–Fermi Model is based upon the numerical solution of a non-linear boundary problem. Two main issues of the Thomas–Fermi Model restrict its usage: uncontrolled accuracy of calculated thermodynamic functions (especially second derivatives of a thermodynamic potential), and unphysical behavior of the Model at relatively low temperatures. Solution method: Each atom in the mixture is surrounded by a spherical cell. The radii of the cells are fitted to equalize the chemical potentials of all atoms. A guaranteed accuracy of first derivatives of the thermodynamic potential is provided by a transformation of integrals over the Thomas–Fermi potential to a system of differential equations. One of equations in the system is the Thomas–Fermi equation. Second derivatives of the thermodynamic potential are calculated similarly with the only difference that a corresponding derivative of the Thomas–Fermi equation is used in the system of differential equation. To avoid the unphysical behavior of the Thomas–Fermi Model at low temperatures we extract a thermal contribution to thermodynamic properties which vanishes at zero temperature. To eliminate the error which appears from the subtraction of the cold part at low temperatures we use asymptotic expressions for thermodynamic functions and the Thomas–Fermi equation. The code calculates regular tables of thermodynamic functions on a grid of isotherms and isochores including second derivatives of a thermodynamic potential. This information is necessary for astrophysical applications, for continuum mechanics simulation of processes in plasma and for the creation of wide-range equations of state. A graphical user interface is provided with the code and allows to specify input parameters, to perform calculations and to plot the results. Additional comments including restrictions and unusual features: GSL library version 1.16 or 2.x is required for compilation; matplotlib Python library is required to run the graphical user interface.
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Region of validity of the Thomas–Fermi Model with corrections
Physics of Plasmas, 2016Co-Authors: Sergey Dyachkov, Pavel Levashov, Dmitry MinakovAbstract:A new method to calculate thermodynamically consistent shell corrections in a wide range of parameters is used to predict the region of validity of the Thomas-Fermi approach. The method is applicable both at low and high density. Thermodynamic functions of electrons calculated by the Thomas–Fermi Model are compared with quantum, exchange, and shell corrections. The corrections become quite big at moderate and low densities and low temperatures in the region of strongly coupled plasma.
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Region of validity of the finite–temperature Thomas–Fermi Model with respect to quantum and exchange corrections
Physics of Plasmas, 2014Co-Authors: Sergey Dyachkov, Pavel LevashovAbstract:We determine the region of applicability of the finite–temperature Thomas–Fermi Model and its thermal part with respect to quantum and exchange corrections. Very high accuracy of computations has been achieved by using a special approach for the solution of the boundary problem and numerical integration. We show that the thermal part of the Model can be applied at lower temperatures than the full Model. Also we offer simple approximations of the boundaries of validity for practical applications.
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Thermal contribution to thermodynamic functions in the Thomas–Fermi Model
Journal of Physics A: Mathematical and Theoretical, 2010Co-Authors: O P Shemyakin, Pavel Levashov, L R Obruchkova, Konstantin V. KhishchenkoAbstract:We propose a method of calculation of thermodynamic functions in the Thomas–Fermi Model at finite temperature θ. Expressions for first and second derivatives of the free energy are analytically obtained in the framework of the Model. A special treatment of thermodynamic functions at low temperatures is provided by asymptotic series expansion at θ → 0. A special algorithm is used to ensure required accuracy for all values in a wide range of volumes and temperatures. We compare the results of our computations with ideal Boltzmann and Fermi gas Models.
P. Mulser - One of the best experts on this subject based on the ideXlab platform.
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Relativistic Thomas-Fermi Model for Atoms in a Very Strong Magnetic Field
Europhysics Letters (EPL), 1993Co-Authors: Bhimsen K. Shivamoggi, P. MulserAbstract:Relativistic effects on the Thomas-Fermi Model for atoms in a very strong magnetic field are considered. A general calculation of the binding energy is given which does not refer to any specific solution of the equation governing the self-consistent electrostatic potential.
Mathieu Salanne - One of the best experts on this subject based on the ideXlab platform.
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A semiclassical Thomas-Fermi Model to tune the metallicity of electrodes in molecular simulations.
The Journal of chemical physics, 2020Co-Authors: Laura Scalfi, Thomas Dufils, Kyle G. Reeves, Benjamin Rotenberg, Mathieu SalanneAbstract:Spurred by the increasing needs in electrochemical energy storage devices, the electrode/electrolyte interface has received a lot of interest in recent years. Molecular dynamics simulations play a prominent role in this field since they provide a microscopic picture of the mechanisms involved. The current state-of-the-art consists of treating the electrode as a perfect conductor, precluding the possibility to analyze the effect of its metallicity on the interfacial properties. Here, we show that the Thomas–Fermi Model provides a very convenient framework to account for the screening of the electric field at the interface and differentiating good metals such as gold from imperfect conductors such as graphite. All the interfacial properties are modified by screening within the metal: the capacitance decreases significantly and both the structure and dynamics of the adsorbed electrolyte are affected. The proposed Model opens the door for quantitative predictions of the capacitive properties of materials for energy storage.
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A semiclassical Thomas-Fermi Model to tune the metallicity of electrodes in molecular simulations
Journal of Chemical Physics, 2020Co-Authors: Laura Scalfi, Thomas Dufils, Benjamin Rotenberg, Kyle Reeves, Mathieu SalanneAbstract:Spurred by the increasing needs in electrochemical energy storage devices, the electrode/electrolyte interface has received a lot of interest in recent years. Molecular dynamics simulations play a prominent role in this field since they provide a microscopic picture of the mechanisms involved. The current state-of-the-art consists of treating the electrode as a perfect conductor, precluding the possibility to analyze the effect of its metallicity on the interfacial properties. Here, we show that the Thomas-Fermi Model provides a very convenient framework to account for the screening of the electric field at the interface and differentiating good metals such as gold from imperfect conductors such as graphite. All the interfacial properties are modified by screening within the metal: the capacitance decreases significantly and both the structure and dynamics of the adsorbed electrolyte are affected. The proposed Model opens the door for quantitative predictions of the capacitive properties of materials for energy storage. Published under license by AIP Publishing. https://doi.org/10.1063/5.0028232 ., s
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A semiclassical Thomas-Fermi Model to tune the metallicity of electrodes in molecular simulations
arXiv: Materials Science, 2019Co-Authors: Laura Scalfi, Thomas Dufils, Kyle G. Reeves, Benjamin Rotenberg, Mathieu SalanneAbstract:Spurred by the increasing needs in electrochemical energy storage devices, the electrode/electrolyte interface has received a lot of interest in recent years. Molecular dynamics simulations play a proeminent role in this field since they provide a microscopic picture of the mechanisms involved. The current state-of-the-art consists in treating the electrode as a perfect conductor, precluding the possibility to analyze the effect of its metallicity on the interfacial properties. Here we show that the Thomas-Fermi Model provides a very convenient framework to account for the screening of the electric field at the interface and differenciating good metals such as gold from imperfect conductors such as graphite. All the interfacial properties are modified by screening within the metal: the capacitance decreases significantly and both the structure and dynamics of the adsorbed electrolyte are affected. The proposed Model opens the door for quantitative predictions of the capacitive properties of materials for energy storage.
B A Zon - One of the best experts on this subject based on the ideXlab platform.
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Rydberg spectra of atoms and positive ions in the Thomas–Fermi Model
Journal of Physics B: Atomic Molecular and Optical Physics, 2003Co-Authors: A S Kornev, B A ZonAbstract:The introduction of polarization interaction of an electron with a core in the Thomas–Fermi Model with Patil modification gives theoretical values of the quantum defects coinciding with experiment within several per cent. As a result of calculations it is possible to determine the parameter r0 in phenomenological dependence of polarization interaction of an electron with the ionic core (α/2)(r2+r02)−2. In some cases the parameter r0 strongly depends on the orbital momentum of an electron.
