Generalized Diffusion

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dc.creatorLutsko, James F.
dc.creatorBoon, Jean Pierre
dc.date2007-11-28
dc.date.accessioned2026-07-07T09:57:12Z
dc.date.available2026-07-07T09:57:12Z
dc.descriptionThe Fokker-Planck equation for the probability $f(r,t)$ to find a random walker at position $r$ at time $t$ is derived for the case that the the probability to make jumps depends nonlinearly on $f(r,t)$. The result is a generalized form of the classical Fokker-Planck equation where the effects of drift, due to a violation of detailed balance, and of external fields are also considered. It is shown that in the absence of drift and external fields a scaling solution, describing anomalous diffusion, is only possible if the nonlinearity in the jump probability is of the power law type ($\sim f^{η}(r,t)$), in which case the generalized Fokker-Planck equation reduces to the well-known Porous Media equation. Monte-Carlo simulations are shown to confirm the theoretical results.
dc.description29 pages, 8 figures
dc.identifierhttps://arxiv.org/abs/0711.4487
dc.identifierhttp://arxiv.org/abs/0711.4487
dc.identifierPHYSICAL REVIEW E 77, 051103 2008
dc.identifierdoi:10.1103/PhysRevE.77.051103
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167255
dc.subjectStatistical Mechanics
dc.subjectMaterials Science
dc.subjectSoft Condensed Matter
dc.titleGeneralized Diffusion
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