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Deterministic diffusion of particles
Author(s) -
Russo Giovanni
Publication year - 1990
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160430602
Subject(s) - voronoi diagram , mathematics , convergence (economics) , diffusion , diffusion process , grid , fokker–planck equation , distribution (mathematics) , finite element method , statistical physics , mathematical analysis , geometry , partial differential equation , physics , computer science , knowledge management , innovation diffusion , economics , economic growth , thermodynamics
The diffusion of the particles is described in terms of a mean motion with a speed equal to the osmotic velocity associated with the diffusion process. Three numerical schemes are presented. The first two are based on the approximation of the gradient on an irregular mesh. The third is derived from a finite‐element approach. Voronoi diagrams are used to handle the irregular grid of the particles. The convergence of the schemes is studied numerically, by comparing the results with the exact solution. Applications to the Fokker‐Planck equation and to the problem of disposing particles according to a given probability distribution are presented.