2007/11/28 by James F. Lutsko, Jean Pierre Boon · 4 citations
Decision Sciences · Mathematics · Physics and Astronomy · #Fractional Differential Equations Solutions #Probabilistic and Robust Engineering Design #Statistical Mechanics and Entropy #cond-mat.mtrl-sci #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.77.051103
published as PHYSICAL REVIEW E 77, 051103 2008 · 29 pages, 8 figures
arxiv created 2007/11/28 · openalex publication_date 2008/05/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
The 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 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 possible only if the nonlinearity in the jump probability is of the power law type [ approximately f;eta(r,t)] , in which case the generalized Fokker-Planck equation reduces to the porous media equation. Monte Carlo simulations are shown to confirm the theoretical results.