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- W2234190772 abstract "We present a master equation formulation based on a Markovian random walk model that exhibits subdiffusion, classical diffusion, and superdiffusion as a function of a single parameter. The nonclassical diffusive behavior is generated by allowing for interactions between a population of walkers. At the macroscopic level, this gives rise to a nonlinear Fokker-Planck equation. The diffusive behavior is reflected not only in the mean squared displacement [$ensuremath{langle}{r}^{2}(t)ensuremath{rangle}ensuremath{sim}{t}^{ensuremath{gamma}}$ with $0<ensuremath{gamma}ensuremath{le}1.5$] but also in the existence of self-similar scaling solutions of the Fokker-Planck equation. We give a physical interpretation of sub- and superdiffusion in terms of the attractive and repulsive interactions between the diffusing particles and we discuss analytically the limiting values of the exponent $ensuremath{gamma}$. Simulations based on the master equation are shown to be in agreement with the analytical solutions of the nonlinear Fokker-Planck equation in all three diffusion regimes." @default.
- W2234190772 created "2016-06-24" @default.
- W2234190772 creator A5007628055 @default.
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- W2234190772 date "2013-08-07" @default.
- W2234190772 modified "2023-10-16" @default.
- W2234190772 title "Microscopic theory of anomalous diffusion based on particle interactions" @default.
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- W2234190772 doi "https://doi.org/10.1103/physreve.88.022108" @default.
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