Examples of two point kinetic equations obeying the entropy principle

1981 ◽  
Vol 59 (9) ◽  
pp. 1241-1250 ◽  
Author(s):  
Miroslav Grmela ◽  
Jean Salmon
Keyword(s):  
Kinetic Equation ◽  
Large Time ◽  
Transport Coefficients ◽  
Kinetic Equations ◽  
Boltzmann Kinetic Equation ◽  
Qualitative Properties ◽  
Long Time Behaviour ◽  
Long Time ◽  
Entropy Principle ◽  
Qualitative Properties Of Solutions

Qualitative properties of solutions of a two point extension of the Boltzmann kinetic equation and of solutions of the Frey–Salmon two point kinetic equation are investigated. Our attention is focussed on: (i) compatibility of the long time behaviour of solutions with equilibrium thermodynamics, (ii) the thermodynamic equation of state implied by the two point kinetic equations, (iii) one point kinetic equations whose solutions approximate well the solutions to the two point kinetic equations for large time, and (iv) transport coefficients implied by the two point kinetic equations.

Collisional transport for a superthermal ion species in magnetized plasma

1986 ◽  
Vol 36 (3) ◽  
pp. 313-328 ◽  
Author(s):  
F. Cozzani ◽  
W. Horton
Keyword(s):  
Kinetic Equation ◽  
Transport Theory ◽  
A Priori ◽  
Transport Coefficients ◽  
Kinetic Equations ◽  
High Energy ◽  
Magnetized Plasma ◽  
Fractional Density ◽  
Background Ions ◽  
Ion Species

The transport theory of a high-energy ion species injected isotropically in a magnetized plasma is considered for arbitrary ratios of the high-energy ion cyclotron frequency to the collisional slowing down time. The assumptions of (i) low fractional density of the high-energy species and (ii) average ion speed faster than the thermal ions and slower than the electrons are used to decouple the kinetic equation for the high-energy species from the kinetic equations for background ions and electrons. The kinetic equation is solved by a Chapman–Enskog expansion in the strength of the gradients; an equation for the first correction to the lowest-order distribution function is obtained without scaling a priori the collision frequency with respect to the gyrofrequency. Various transport coefficients are explicitly calculated for the two cases of a weakly and a strongly magnetized plasma.

Numerical Study of Nonequilibrium Diagram Theory

1972 ◽  
Vol 50 (4) ◽  
pp. 317-335 ◽  
Author(s):  
Gary R. Dowling ◽  
H. Ted Davis
Keyword(s):  
Distribution Function ◽  
Correlation Function ◽  
Kinetic Equation ◽  
Numerical Study ◽  
Pair Correlation ◽  
Transport Coefficients ◽  
Kinetic Equations ◽  
Collision Operator ◽  
Dense Fluid ◽  
Equilibrium Pair

In this paper we numerically analyze the first few diagrams in a Boltzmann-like collision operator that occurs in Severne's exact kinetic equation for the singlet distribution function. A similar analysis was used by Allen and Cole in deriving their singlet and doublet kinetic equations. Our analysis shows that the diagrams neglected by Allen and Cole in their kinetic equations are not negligible and these should be incorporated into dense fluid theories. The Allen–Cole kinetic transport coefficients and equilibrium pair correlation function are presented and calculated for dense argon. These results are not promising.

scholarly journals Tracing X-ray-induced formation of warm dense gold with Boltzmann kinetic equations

2021 ◽  
Vol 75 (8) ◽  
Author(s):  
Beata Ziaja ◽  
John Jasper Bekx ◽  
Martin Masek ◽  
Nikita Medvedev ◽  
Przemyslaw Piekarz ◽  
...  
Keyword(s):  
Kinetic Equation ◽  
Kinetic Equations ◽  
Dense Matter ◽  
High Energy ◽  
Boltzmann Kinetic Equation ◽  
High Energy Density ◽  
X Rays ◽  
Equation Approach ◽  
Warm Dense Matter ◽  
X Ray

Abstract In this paper, we report on the Boltzmann kinetic equation approach adapted for simulations of warm dense matter created by irradiation of bulk gold with intense ultrashort X-ray pulses. X-rays can excite inner-shell electrons, which triggers creation of deep-lying core holes. Their relaxation, especially in heavier elements such as gold (atomic number $$Z= 79$$ Z = 79 ) takes complicated pathways, involving collisional processes, and leading through a large number of active configurations. This number can be so high that solving a set of evolution equations for each configuration becomes computationally inefficient, and another modeling approach should be used instead. Here, we use the earlier introduced ’predominant excitation and relaxation path’ approach. It still uses true atomic configurations but limits their number by restricting material relaxation to a selected set of predominant pathways for material excitation and relaxation. With that, we obtain time-resolved predictions for excitation and relaxation in X-ray irradiated bulk of gold, including the respective change of gold optical properties. We compare the predictions with the available data from high-energy-density experiments. Their good agreement indicates ability of the Boltzmann kinetic equation approach to describe warm dense matter created from high-Z materials after their irradiation with X rays, which can be validated in future experiments. Graphic Abstract

scholarly journals A hierarchy of hydrodynamic models for silicon carbide semiconductors

2017 ◽  
Vol 8 (1) ◽  
pp. 251-264
Author(s):  
Orazio Muscato ◽  
Vincenza Di Stefano
Keyword(s):  
Silicon Carbide ◽  
Hydrodynamic Model ◽  
Energy Transport ◽  
Transport Coefficients ◽  
Kinetic Equations ◽  
Maximum Entropy Principle ◽  
Hydrodynamic Models ◽  
Drift Diffusion ◽  
Transport Models ◽  
Entropy Principle

Abstract The electro-thermal transport in silicon carbide semiconductors can be described by an extended hydrodynamic model, obtained by taking moments from kinetic equations, and using the Maximum Entropy Principle. By performing appropriate scaling, one can obtain reduced transport models such as the Energy transport and the drift-diffusion ones, where the transport coefficients are explicitly determined.

Qualitative properties of solutions to set optimization problems

2021 ◽  
Vol 40 (2) ◽  
Author(s):  
Lam Quoc Anh ◽  
Nguyen Huu Danh ◽  
Pham Thanh Duoc ◽  
Tran Ngoc Tam
Keyword(s):  
Optimization Problems ◽  
Set Optimization ◽  
Qualitative Properties ◽  
Qualitative Properties Of Solutions

Old and New Results for First Order Periodic ODEs without Uniqueness: a Comprehensive Study by Lower and Upper Solutions

2004 ◽  
Vol 4 (3) ◽  
Author(s):  
Franco Obersnel ◽  
Pierpaolo Omari
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Lower And Upper Solutions ◽  
Elementary Approach ◽  
Qualitative Properties ◽  
First Order ◽  
The Past ◽  
The Cauchy Problem ◽  
Qualitative Properties Of Solutions ◽  
Comprehensive Study

AbstractAn elementary approach, based on a systematic use of lower and upper solutions, is employed to detect the qualitative properties of solutions of first order scalar periodic ordinary differential equations. This study is carried out in the Carathéodory setting, avoiding any uniqueness assumption, in the future or in the past, for the Cauchy problem. Various classical and recent results are recovered and generalized.

scholarly journals Radially symmetric solutions to the Hénon–Lane–Emden system on the critical hyperbola

2014 ◽  
Vol 16 (03) ◽  
pp. 1350030 ◽  
Author(s):  
Roberta Musina ◽  
K. Sreenadh
Keyword(s):  
Variational Methods ◽  
Existence Results ◽  
Qualitative Properties ◽  
Radially Symmetric Solutions ◽  
Qualitative Properties Of Solutions

We use variational methods to study the existence of non-trivial and radially symmetric solutions to the Hénon–Lane–Emden system with weights, when the exponents involved lie on the "critical hyperbola". We also discuss qualitative properties of solutions and non-existence results.

Kinetic equations for plasmas subjected to a strong time-dependent extenal field. Part 2. The weak-interaction approximation

1974 ◽  
Vol 11 (3) ◽  
pp. 377-387 ◽  
Author(s):  
R. Balescu ◽  
J. H. Misguich
Keyword(s):  
Kinetic Equation ◽  
General Theory ◽  
Weak Interaction ◽  
Weak Coupling ◽  
Kinetic Equations ◽  
Time Dependent ◽  
External Fields ◽  
Interaction Approximation

The general theory developed in part 1 is illustrated for a plasma described by the weak-coupling (Landau) approximation. The kinetic equation, valid for arbitrarily strong external fields, is written out explicitly.

scholarly journals Long-time behaviour of a thermomechanical model for adhesive contact

2011 ◽  
Vol 4 (2) ◽  
pp. 273-309 ◽  
Author(s):  
Elena Bonetti ◽  
◽  
Giovanna Bonfanti ◽  
Riccarda Rossi ◽  
◽  
...  
Keyword(s):  
Adhesive Contact ◽  
Time Behaviour ◽  
Thermomechanical Model ◽  
Long Time Behaviour ◽  
Long Time
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