par Lutsko, James 
;Boon, Jean-Pierre
Référence Physical review. E, Statistical, nonlinear, and soft matter physics, 88, 2, 022108
Publication Publié, 2013-08
;Boon, Jean-Pierre Référence Physical review. E, Statistical, nonlinear, and soft matter physics, 88, 2, 022108
Publication Publié, 2013-08
Article révisé par les pairs
| Résumé : | 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 [r2(t)∼tγ with 0<γ≤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 γ. 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. © 2013 American Physical Society. |
