Random walk's models for fractional diffusion equation
| Autor: | Ali Abdennadher, Wafa Hamrouni |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Physics
Diffusion equation Heterogeneous random walk in one dimension Partial differential equation Anomalous diffusion Applied Mathematics 010102 general mathematics Space (mathematics) Random walk 01 natural sciences Fractional calculus 010101 applied mathematics Discrete Mathematics and Combinatorics Statistical physics 0101 mathematics Diffusion (business) |
| Zdroj: | Discrete and Continuous Dynamical Systems - Series B. 21:2509-2530 |
| ISSN: | 1531-3492 |
| DOI: | 10.3934/dcdsb.2016058 |
| Popis: | Fractional diffusion equations are used for mass spreading in inhomogeneous media. They are applied to model anomalous diffusion, where a cloud of particles spreads in a different manner than the classical diffusion equation predicts. Thus, they involve fractional derivatives. Here we present a continuous variant of Grunwald-Letnikov's formula, which is useful to compute the flux of particles performing random walks, allowing for heavy-tailed jump distributions. In fact, we set a definition of fractional derivatives yielding the operators which enable us to retrieve the space fractional variant of Fick's law, for enhanced diffusion in disordered media, without passing through any partial differential equation for the space and time evolution of the concentration. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|