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We study a system of Fokker-Planck equations recently introduced to describe the temporal evolution of statistical distributions of population densities with predator-prey interactions. At the macroscopic level, the system recovers a…

Analysis of PDEs · Mathematics 2026-03-11 Giuseppe Toscani , Mattia Zanella

We propose fully discrete, implicit-in-time finite-volume schemes for a general family of non-linear and non-local Fokker-Planck equations with a gradient-flow structure, usually known as aggregation-diffusion equations, in any dimension.…

Numerical Analysis · Mathematics 2020-09-29 Rafael Bailo , Jose A. Carrillo , Jingwei Hu

In this paper we study the problem of computing the effective diffusivity for a particle moving in chaotic and stochastic flows. In addition we numerically investigate the residual diffusion phenomenon in chaotic advection. The residual…

Numerical Analysis · Mathematics 2017-11-28 Zhongjian Wang , Jack Xin , Zhiwen Zhang

This paper derives the Fokker-Planck (FP) equation for a particle moving in potential by a randomly modulated dipole. The FP equation describes the anomalous diffusion observed in the companion paper [1] and breaks the conservation of the…

Mathematical Physics · Physics 2022-05-03 S. Katagiri , Y. Matsuo , Y. Matsuoka , A. Sugamoto

The present work analyzes stationary distributions of active Brownian particles in a harmonic trap. Generally, obtaining stationary distributions for this system is non-trivial, and up to date no exact expressions are available. In this…

Statistical Mechanics · Physics 2023-12-12 Derek Frydel

Diffusion processes have been applied with great success to model the dynamics of large populations throughout science, in particular biology. One advantage is that they bridge two different scales: the microscopic and the macroscopic one.…

Neurons and Cognition · Quantitative Biology 2013-09-11 Marc de Kamps

We develop a highly efficient method to numerically simulate thermal fluctuations and correlations in non-relativistic continuous bosonic one-dimensional systems. The method is suitable for arbitrary local interactions as long as the system…

Quantum Gases · Physics 2020-04-21 Stefan Beck , Igor E. Mazets , Thomas Schweigler

This work is devoted to studying complex dynamical systems under non-Gaussian fluctuations. We first estimate the Kantorovich-Rubinstein distance for solutions of non-local Fokker-Planck equations associated with stochastic differential…

Probability · Mathematics 2021-11-24 Ao Zhang , Jinqiao Duan

For quantum computers to become useful tools to physicists, engineers and computational scientists, quantum algorithms for solving nonlinear differential equations need to be developed. Despite recent advances, the quest for a solver that…

Quantum Physics · Physics 2024-01-25 Felix Tennie , Luca Magri

The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability of N stochastic variables with Lochner's generalized Dirichlet distribution (R.H. Lochner, A Generalized…

Mathematical Physics · Physics 2013-10-02 J. Bakosi , J. R. Ristorcelli

The Fokker-Planck (FP) equation has been derived for describing the temporal evolution of the particle size probability density function (PDF) for KJMA (Kolmogorov-Johnson-Mehl-Avrami) transformations. The classical case of transformations…

Materials Science · Physics 2023-03-22 M. Tomellini

This is the first paper of a series of our works on the self-similar orbit-averaged Fokker-Planck (OAFP) equation for distribution function of stars in dense isotropic star clusters. At the late stage of relaxation evolution of the…

Computational Physics · Physics 2020-08-26 Yuta Ito

The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability of N coupled stochastic variables with the Dirichlet distribution as its asymptotic solution. To ensure a bounded…

Mathematical Physics · Physics 2013-03-05 J. Bakosi , J. R. Ristorcelli

Fokker-Planck equations (forward Kolmogorov equations) evolve probability densities in time from an initial condition. For distributions over the real line, these evolution equations can sometimes be transformed into dynamics over the…

Analysis of PDEs · Mathematics 2025-09-26 David W. Cohen , Merek Johnson , Bruce M. Boghosian

The Fokker--Planck equation describes the evolution of a probability distribution towards equilibrium--the flow parameter is the equilibration time. Assuming the distribution remains normalizable for all times, it is equivalent to an open…

Statistical Mechanics · Physics 2016-09-14 Stam Nicolis , Julien Tranchida , Pascal Thibaudeau

An efficient method is presented as a means of an approximate, analytic time-dependent solution of the Fokker-Planck equation (FPE) for the Langevin model subjected to additive and multiplicative noise. We have assumed that the dynamical…

Statistical Mechanics · Physics 2008-10-19 Hideo Hasegawa

We propose a fixed-point-based numerical framework for computing stationary states of nonlocal Fokker-Planck-type equations. Instead of discretising the differential operators directly, we reformulate the stationary problem as a nonlinear…

Numerical Analysis · Mathematics 2026-02-06 José A. Carrillo , Yurij Salmaniw , Antonio León Villares

We propose a discrete lattice version of the Fokker-Planck kinetic equation along lines similar to the Lattice-Boltzmann scheme. Our work extends an earlier one-dimensional formulation to arbitrary spatial dimension $D$. A generalized…

Statistical Mechanics · Physics 2009-11-11 Daniele Moroni , Benjamin Rotenberg , Jean-Pierre Hansen , Sauro Succi , Simone Melchionna

The Diffusion Monte Carlo method is devoted to the computation of electronic ground-state energies of molecules. In this paper, we focus on implementations of this method which consist in exploring the configuration space with a {\bf fixed}…

Numerical Analysis · Mathematics 2007-05-23 Tony Lelievre , Mohamed El Makrini , Benjamin Jourdain

In this paper we present a direct perturbative method to solving certain Fokker-Planck equations, which have constant diffusion coefficients and some small parameters in the drift coefficients. The method makes use of the connection between…

Mathematical Physics · Physics 2009-11-13 Choon-Lin Ho , Yan-Min Dai