Approximation of the Linear Boltzmann Equation by the Fokker-Planck Equation

1967 ◽  
Vol 162 (1) ◽  
pp. 186-188 ◽  
Author(s):  
R. F. Pawula
Keyword(s):  
Boltzmann Equation ◽  
Planck Equation ◽  
Linear Boltzmann Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck

Grad–Fokker–Planck plasma equations. Part 1. Coffision moments

1982 ◽  
Vol 27 (3) ◽  
pp. 437-452 ◽  
Author(s):  
K. A. Broughan
Keyword(s):  
Boltzmann Equation ◽  
Planck Equation ◽  
Computer Language ◽  
Collision Term ◽  
Moment Equations ◽  
Species Pair ◽  
Collision Integrals ◽  
Fokker Planck Equation ◽  
Hot Plasma ◽  
Fokker Planck

Thirteen moments are taken of the collision term in the Boltzmann–Fokker– Planck equation for a multi-species, multi-temperature, hot plasma, following the method first developed by Grad for neutral gases. The collision integrals are evaluated for each colliding species pair. These integrals give, in particular, the rate of exchange of momentum and energy produced by collisions. The set of integrals may be combined with moments of the remaining terms in the Boltzmann equation to give thirteen moment equations for each species of particle. To complete the calculation, extensive use was made of the symbolic computer language REDUCE.

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

scholarly journals Time-changed fractional Ornstein-Uhlenbeck process

2020 ◽  
Vol 23 (2) ◽  
pp. 450-483 ◽  
Author(s):  
Giacomo Ascione ◽  
Yuliya Mishura ◽  
Enrica Pirozzi
Keyword(s):  
Planck Equation ◽  
Uhlenbeck Process ◽  
Fokker Planck Equation ◽  
Ornstein Uhlenbeck Process ◽  
Fokker Planck

AbstractWe define a time-changed fractional Ornstein-Uhlenbeck process by composing a fractional Ornstein-Uhlenbeck process with the inverse of a subordinator. Properties of the moments of such process are investigated and the existence of the density is shown. We also provide a generalized Fokker-Planck equation for the density of the process.

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