Lattice formulation of the Fokker-Planck equation
S. Melchionna, S. Succi, J.-P. Hansen
TL;DR
This paper introduces a lattice-based formulation of the Fokker-Planck equation that models dissipative interactions and applies it to electrorheological transport, achieving accurate results and outlining future extensions.
Contribution
A novel lattice formulation of the Fokker-Planck equation that incorporates dissipative effects and is validated against analytical solutions.
Findings
Quantitative agreement with analytical solutions for electrorheological transport
Effective modeling of dissipative interactions on a lattice
Framework for future inclusion of inelastic collisions
Abstract
A lattice version of the Fokker-Planck equation (FPE), accounting for dissipative interactions, not resolved on the molecular scale, is introduced. The lattice FPE is applied to the study of electrorheological transport of a one-dimensional charged fluid, and found to yield quantitative agreement with a recent analytical solution. Future extensions, including inelastic ion-ion collisions, are also outlined.
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