Magnetized Fokker–Planck equation with quasilinear diffusion for nonaxially symmetric velocity distribution functions

1986 ◽  
Vol 29 (9) ◽  
pp. 3027-3030
Author(s):  
Mohamed H. A. Hassan
Keyword(s):  
Velocity Distribution ◽  
Planck Equation ◽  
Distribution Functions ◽  
Fokker Planck Equation ◽  
Velocity Distribution Functions ◽  
Quasilinear Diffusion ◽  
Fokker Planck

Comparison Between Theoretical Values and Simulation Results of Transport Coefficients for the Dissipative Particle Dynamics Method

2004 ◽  
Author(s):  
Akira Satoh
Keyword(s):  
Transport Coefficients ◽  
Dissipative Particle Dynamics ◽  
Planck Equation ◽  
Equation Of Motion ◽  
Particle Dynamics ◽  
Momentum Conservation ◽  
Distribution Functions ◽  
Fokker Planck Equation ◽  
Dynamics Method ◽  
Fokker Planck

In the present study, we have derived an expression for transport coefficients such as viscosity, from the equation of motion of dissipative particles. In the concrete, we have shown the Fokker-Planck equation in phase space, and macroscopic conservation equations such as the equation of continuity and the equation of momentum conservation. The basic equations of the single-particle and pair distribution functions have been derived using the Fokker-Planck equation. The solutions of these distribution functions have approximately been solved by the perturbation method under the assumption of molecular chaos. The expression of the viscosity due to dissipative forces has been obtained using the approximate solutions of the distribution functions. Also, we have conducted non-equilibrium dynamics simulations to investigate the influence of the parameters, which have appeared in defining the equation of motion in the dissipative particle dynamics method.

scholarly journals FOKKER–PLANCK EQUATION FOR FRACTIONAL SYSTEMS

2007 ◽  
Vol 21 (06) ◽  
pp. 955-967 ◽  
Author(s):  
VASILY E. TARASOV
Keyword(s):  
Phase Space ◽  
Power Systems ◽  
Fractional Power ◽  
Planck Equation ◽  
Distribution Functions ◽  
Fractional Integrals ◽  
Fractional Systems ◽  
Fokker Planck Equation ◽  
Bogoliubov Equations ◽  
Fokker Planck

The normalization condition, average values, and reduced distribution functions can be generalized by fractional integrals. The interpretation of the fractional analog of phase space as a space with noninteger dimension is discussed. A fractional (power) system is described by the fractional powers of coordinates and momenta. These systems can be considered as non-Hamiltonian systems in the usual phase space. The generalizations of the Bogoliubov equations are derived from the Liouville equation for fractional (power) systems. Using these equations, the corresponding Fokker–Planck equation is obtained.

scholarly journals Weak Turbulence and Quasilinear Diffusion for Relativistic Wave-Particle Interactions Via a Markov Approach

2022 ◽  
Vol 8 ◽  
Author(s):  
Oliver Allanson ◽  
Thomas Elsden ◽  
Clare Watt ◽  
Thomas Neukirch
Keyword(s):  
Planck Equation ◽  
Turbulence Theory ◽  
General Nature ◽  
Weak Turbulence ◽  
Quasilinear Theory ◽  
Fokker Planck Equation ◽  
Background Magnetic Field ◽  
Quasilinear Diffusion ◽  
Markovian Approach ◽  
Fokker Planck

We derive weak turbulence and quasilinear models for relativistic charged particle dynamics in pitch-angle and energy space, due to interactions with electromagnetic waves propagating (anti-)parallel to a uniform background magnetic field. We use a Markovian approach that starts from the consideration of single particle motion in a prescribed electromagnetic field. This Markovian approach has a number of benefits, including: 1) the evident self-consistent relationship between a more general weak turbulence theory and the standard resonant diffusion quasilinear theory (as is commonly used in e.g. radiation belt and solar wind modeling); 2) the general nature of the Fokker-Planck equation that can be derived without any prior assumptions regarding its form; 3) the clear dependence of the form of the Fokker-Planck equation and the transport coefficients on given specific timescales. The quasilinear diffusion coefficients that we derive are not new in and of themselves, but this concise derivation and discussion of the weak turbulence and quasilinear theories using the Markovian framework is physically very instructive. The results presented herein form fundamental groundwork for future studies that consider phenomena for which some of the assumptions made in this manuscript may be relaxed.

THE ASYMPTOTICS OF COLLISION OPERATORS FOR TWO SPECIES OF PARTICLES OF DISPARATE MASSES

1996 ◽  
Vol 06 (03) ◽  
pp. 405-436 ◽  
Author(s):  
PIERRE DEGOND ◽  
BRIGITTE LUCQUIN-DESREUX
Keyword(s):  
Time Scales ◽  
Planck Equation ◽  
Distribution Functions ◽  
Relaxation Phenomenon ◽  
Mass Ratio ◽  
Homogeneous Case ◽  
Fokker Planck Equation ◽  
Disparate Mass ◽  
Fokker Planck

We analyze the dynamics of a disparate mass binary gas or of a plasma in the homogeneous case, at various time scales, in the framework of the Boltzmann or Fokker–Planck equation. We intend to provide a rigorous foundation to the epochal relaxation phenomenon first pointed out by Grad. From general basic physical hypotheses, we derive the scaling of the equations as a function of the mass ratio of the particles, and we expand the collision operators in powers of this mass ratio. Then, Hilbert or Chapman–Enskog type expansions of the distribution functions allow us to investigate the dynamics of the mixture at various time scales, and we verify that the behavior of the obtained models is coherent with Grad's hypothesis.

AN APPLICATION OF FOKKER–PLANCK EQUATION TO JOSEPHSON JUNCTION

1989 ◽  
Vol 9 (1) ◽  
pp. 109-120
Author(s):  
G. Liao ◽  
A.F. Lawrence ◽  
A.T. Abawi
Keyword(s):  
Josephson Junction ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck
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