Construction of the weakly‐relativistic Fokker‐Planck kinetic equation in the Darwin approximation

1996 ◽  
Vol 3 (6) ◽  
pp. 2255-2264 ◽  
Author(s):  
Monica Pozzo ◽  
Massimo Tessarotto
Keyword(s):  
Kinetic Equation ◽  
Darwin Approximation ◽  
Fokker Planck

The effects of ion-ion coffision on a ion-acoustic plasma pulse

1971 ◽  
Vol 5 (3) ◽  
pp. 343-355 ◽  
Author(s):  
Magne S. Espedal
Keyword(s):  
Kinetic Equation ◽  
Ion Collisions ◽  
Ion Acoustic ◽  
Plasma Pulse ◽  
Fokker Planck

The effects of ion-ion collisions, described by a Fokker-Planck operator in the kinetic equation, on an ion-acoustic plasma pulse, are studied. Our investigations show that the coffisions give a broadening of the pulse, and reduce the effect of interaction between the main plasma and the pulse.

The effect of velocity space diffusion on the universal instability in a plasma

1970 ◽  
Vol 4 (4) ◽  
pp. 729-738 ◽  
Author(s):  
R. S. B. Ong ◽  
M. Y. Yu
Keyword(s):  
Kinetic Equation ◽  
Temperature Gradient ◽  
Velocity Space ◽  
Homogeneous Plasma ◽  
Gradient Instability ◽  
Fokker Planck

The influence of collisions on the universal instability in a fully ionized in- homogeneous plasma is investigated by means of a simplified Fokker-Planck kinetic equation. For the Fokker-Planck model yields results qualitatively similar to the Bhatnagar-Gross-Krook model, but the two models give different collisional effects in the case where b ≥ 1. Further it is shown that collisions in general enhance the temperature gradient instability in a plasma when b ≪ 1 and reduce it when b ≥ 1.

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.

scholarly journals Solving the Fokker-Planck kinetic equation on a lattice

2006 ◽  
Vol 73 (6) ◽  
Author(s):  
Daniele Moroni ◽  
Benjamin Rotenberg ◽  
Jean-Pierre Hansen ◽  
Sauro Succi ◽  
Simone Melchionna
Keyword(s):  
Kinetic Equation ◽  
Fokker Planck

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 Monte Carlo implementation of a guiding-center Fokker-Planck kinetic equation

2013 ◽  
Vol 20 (9) ◽  
pp. 092505 ◽  
Author(s):  
E. Hirvijoki ◽  
A. Brizard ◽  
A. Snicker ◽  
T. Kurki-Suonio
Keyword(s):  
Monte Carlo ◽  
Kinetic Equation ◽  
Monte Carlo Implementation ◽  
Fokker Planck
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