scholarly journals Invariance principle and model reduction for the Fokker–Planck equation

2016 ◽  
Vol 374 (2080) ◽  
pp. 20160142 ◽  
Author(s):  
I. V. Karlin
Keyword(s):  
Kinetic Equation ◽  
Model Reduction ◽  
Invariance Principle ◽  
Planck Equation ◽  
Multiscale Modelling ◽  
Moment Equations ◽  
Fokker Planck Equation ◽  
Explicit Formulae ◽  
Lowest Eigenvalue ◽  
Fokker Planck

The principle of dynamic invariance is applied to obtain closed moment equations from the Fokker–Planck kinetic equation. The analysis is carried out to explicit formulae for computation of the lowest eigenvalue and of the corresponding eigenfunction for arbitrary potentials. This article is part of the themed issue ‘Multiscale modelling at the physics–chemistry–biology interface’.

scholarly journals Allgemeine 13-Momenten-Näherung zur Fokker-Planck-Gleichung eines Plasmas

1965 ◽  
Vol 20 (10) ◽  
pp. 1243-1255
Author(s):  
Friedrich Hertweck
Keyword(s):  
Heat Flux ◽  
Lower Order ◽  
Planck Equation ◽  
Electrical Current ◽  
Moment Equations ◽  
Fokker Planck Equation ◽  
Electrons And Ions ◽  
The Difference ◽  
Fokker Planck

For the Fokker-Planck-equation for a plasma the system of moment equations is derived. The highest order moments considered are the components of the heat flux. For these the condition must be satisfied that they are small compared with (5/2) p √p/ϱe. All moments of lower order, especially the difference velocity of electrons and ions (i.e. the electrical current) and the anisotropy of pressure are arbitrary in this approximation.

scholarly journals An interplay between attraction and repulsion in infinite populations

2021 ◽  
Vol 11 (4) ◽  
Author(s):  
Yuri Kozitsky
Keyword(s):  
Kinetic Equation ◽  
Short Range ◽  
Numerical Solutions ◽  
Planck Equation ◽  
Infinite Population ◽  
Poisson Law ◽  
Fokker Planck Equation ◽  
Proposed Model ◽  
Fokker Planck

AbstractWe propose and study a model describing an infinite population of point entities arriving in and departing from $$X=\mathbb {R}^d$$ X = R d , $$d\ge 1$$ d ≥ 1 . The already existing entities force each other to leave the population (repulsion) and attract the newcomers. The evolution of the population states is obtained by solving the corresponding Fokker-Planck equation. Without interactions, the evolution preserves states in which the probability $$p(n,\Lambda )$$ p ( n , Λ ) of finding n points in a compact vessel $$\Lambda \subset X$$ Λ ⊂ X obeys the Poisson law. As we show, for pure attraction the decay of $$p(n,\Lambda )$$ p ( n , Λ ) with $$n\rightarrow +\infty $$ n → + ∞ may be essentially slower. The main result is the statement that in the presence of repulsion—even of an arbitrary short range—the evolution preserves states in which the decay of $$p(n,\Lambda )$$ p ( n , Λ ) is at most Poissonian. We also derive the corresponding kinetic equation, the numerical solutions of which can provide more detailed information on the interplay between attraction and repulsion. Further possibilities in studying the proposed model are also discussed.

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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