# Fokker-Planck equation

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## Fokker-Planck equation

[¦fō·kər ¦pläŋk i′kwā·zhən]
(statistical mechanics)
An equation for the distribution function of a gas, analogous to the Boltzmann equation but applying where the forces are long-range and the collisions are not binary.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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Analysis of splitting methods for solving a partial integro-differential Fokker-Planck equation. Applied Mathematics and Computation, 294:1-17, 2017.
For the stochastic system (42) the Fokker-Planck equation reads
The Fokker-Planck equation in image space {[??]} is then given by
Stohny, "Symmetry properties and exact solutions of the fokker-planck equation," Journal of Nonlinear Mathematical Physics, vol.
In the Fokker-Planck equation, the so called Kramers-Moyal coefficients [D.sub.I]([alpha], t) and [D.sub.2]([alpha], t) describe drift ([D.sub.I]) and diffusion ([D.sub.2]) of the probability distribution.
The most difficult part of the code is the solution of the Fokker-Planck equation. There are three parameters.
(i) The square-root of [B.sub.[alpha][beta]] (e.g., the Cholesky-decomposition, [b.sub.[alpha][beta]]) exists, required by the correspondence of the SDE (5) and the Fokker-Planck equation (6).
as can be seen from inserting the rates (28) and (29) into the Fokker-Planck equation (22).
A probability distribution function of fiber orientation (or Fokker-Planck equation) is introduced by statistical method in concentrated suspensions.
By expanding the functions g, d, f, which depend smoothly on n, into a Taylor series to the second order inclusive, the system of the discrete equations is represented by the continual differential equation in the partial derivatives (Fokker-Planck equation) :
In 17 concise chapters and a remarkable collection of appendices be describes the Langevin equation, the fluctuation-dissipation relation, auto-correlation of velocity, Markov processes, the Fokker-Planck equation, the diffusion equation, diffusion in a finite region, Brownian motion, first-passage time, displacement phase-space Fokker-Planck equations, diffusion as a potential, diffusion in a magnetic field, Kubo-Green formulas, dynamic mobility, and the generalized Langevin equation.

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