Mean-field approach for diffusion of interacting particles

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
G SuárezH Mártin

Abstract

A nonlinear Fokker-Planck equation is obtained in the continuous limit of a one-dimensional lattice with an energy landscape of wells and barriers. Interaction is possible among particles in the same energy well. A parameter γ, related to the barrier's heights, is introduced. Its value is determinant for the functional dependence of the mobility and diffusion coefficient on particle concentration, but has no influence on the equilibrium solution. A relation between the mean-field potential and the microscopic interaction energy is derived. The results are illustrated with classical particles with interactions that reproduce fermion and boson statistics.

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Feb 14, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·G P SuárezH O Mártin

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Citations

May 16, 2018·Physical Review. E·Jianping Xu, Guancheng Jiang
Jun 17, 2018·Physical Review. E·Jianping Xu, Guancheng Jiang
Sep 27, 2018·Physical Review. E·M Di Pietro Martínez, M Hoyuelos
Oct 3, 2019·Physical Review. E·M Di Pietro Martínez, M Hoyuelos
Jan 21, 2021·Physical Review. E·M Di Pietro MartínezM Hoyuelos

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