Fokker−Planck Equation and Langevin Equation for One Brownian Particle in a Nonequilibrium Bath

1996 ◽  
Vol 100 (49) ◽  
pp. 19035-19042 ◽  
Author(s):  
Joan-Emma Shea ◽  
Irwin Oppenheim
Keyword(s):  
Langevin Equation ◽  
Brownian Particle ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck

Brownian Motion of Rotating Particles

1968 ◽  
Vol 23 (4) ◽  
pp. 597-609 ◽  
Author(s):  
Siegfried Hess
Keyword(s):  
Brownian Motion ◽  
Angular Velocity ◽  
Brownian Particle ◽  
Planck Equation ◽  
Transverse Force ◽  
Particle Collision ◽  
Fokker Planck Equation ◽  
Rotational Motions ◽  
Transport Relaxation ◽  
Fokker Planck

A kinetic theory for the Brownian motion of spherical rotating particles is given starting from a generalized Fokker-Planck equation. The generalized Fokker-Planck collision operator is a sum of two ordinary Fokker-Planck differential operators in velocity and angular velocity space respectively plus a third term which provides a coupling of translational and rotational motions. This term stems from a transverse force proportional to the cross product of velocity and angular velocity of a Brownian particle. Collision brackets pertaining to the generalized Fokker-Planck operator are defined and their general properties are discussed. Application of WALDMANN'S moment method to the Fokker-Planck equation yields a set of coupled linear differential equations (transport-relaxation equations) for certain local mean values. The constitutive laws for diffusion, heat conduction by Brownian particles and spin diffusion are deduced from the transport-relaxation equations. The transport-relaxations coefficients appearing in them are given in terms of the two friction coefficients for the damping of translational and rotational motions and a third coefficient which is a measure of the transverse force. By the coupling of translational and rotational motions a diffusion flow gives rise to a correlation of linear and angular velocities.

scholarly journals Numerical Solution of Two Dimensional Time-Space Fractional Fokker Planck Equation With Variable Coefficients

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1260
Author(s):  
Elsayed I. Mahmoud ◽  
Viktor N. Orlov
Keyword(s):  
Brownian Particle ◽  
Planck Equation ◽  
Variable Coefficients ◽  
Stability And Convergence ◽  
Two Dimensional ◽  
Fokker Planck Equation ◽  
Time Space ◽  
Liouville Derivative ◽  
The Stability ◽  
Fokker Planck

This paper presents a practical numerical method, an implicit finite-difference scheme for solving a two-dimensional time-space fractional Fokker–Planck equation with space–time depending on variable coefficients and source term, which represents a model of a Brownian particle in a periodic potential. The Caputo derivative and the Riemann–Liouville derivative are considered in the temporal and spatial directions, respectively. The Riemann–Liouville derivative is approximated by the standard Grünwald approximation and the shifted Grünwald approximation. The stability and convergence of the numerical scheme are discussed. Finally, we provide a numerical example to test the theoretical analysis.

scholarly journals Deterministic and Stochastic Research of Cubic Population Model with Harvesting

2021 ◽  
pp. 2150023
Author(s):  
Özgür Gültekin ◽  
Çağatay Eskin ◽  
Esra Yazicioğlu
Keyword(s):  
Langevin Equation ◽  
Allee Effect ◽  
Deterministic Model ◽  
Probability Distributions ◽  
Gaussian White Noise ◽  
Quadratic Function ◽  
Planck Equation ◽  
Detailed Examination ◽  
Fokker Planck Equation ◽  
Fokker Planck

A detailed examination of the effect of harvesting on a population has been carried out by extending the standard cubic deterministic model by considering a population under Allee effect with a quadratic function representing harvesting. Weak and strong Allee effect transitions, carrying capacity, and Allee threshold change according to harvesting are first discussed in the deterministic model. A Fokker–Planck equation has been obtained starting from a Langevin equation subject to correlated Gaussian white noise with zero mean, and an Approximate Fokker–Planck Equation has been obtained from a Langevin equation subject to correlated Gaussian colored noise with zero mean. This allowed to calculate the stationary probability distributions of populations, and thus to discuss the effects of linear and nonlinear (Holling type-II) harvesting for populations under Allee effect and subject to white and colored noises, respectively.

PARITY-VIOLATING ANOMALY FROM THE FOKKER-PLANCK EQUATION

1991 ◽  
Vol 06 (02) ◽  
pp. 123-128
Author(s):  
G. NARDULLI ◽  
L. TEDESCO
Keyword(s):  
Langevin Equation ◽  
Gauge Theories ◽  
Planck Equation ◽  
Quantization Scheme ◽  
Stochastic Quantization ◽  
Fokker Planck Equation ◽  
Fokker Planck

We compute parity-violating anomaly in gauge theories with odd number of dimensions using an approach based on the effective Fokker-Planck equation in the stochastic quantization scheme. We find results that agree with those obtained by the Langevin equation.

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