Anomalous diffusion in the strong scattering limit: A Lévy walk approach

摘要: The continuous time random walk (CTRW) is a powerful stochastic theory developed and used to analyze regular anomalous diffusion. In particular this framework has been applied sublinear, dispersive, transport enhanced Levy walks. its earlier version the CTRW does not include velocities of walker explicitly, therefore it suited situations with randomly distributed velocities. Experiments have recently considered systems which exhibit diffusion are characterized by an inherent distribution Here we develop modified formalism, based on velocity picture in strong scattering limit, emphasis limit. We consider particle collides unspecified objects changing velocity. intervals between collision events moves freely. Two probability density functions (PDF) describe such process: (a) q(τ), PDF times events, (b) F(v), particle. renewal process both independent, identically distributed, variables. When either q(τ) or F(v) long-tailed may become non-Gaussian. find at r t, ρ(r, t), found Fourier-Laplace space. discuss role initial conditions especially way P(v, probabilty that v decays equilibrium. phase diagram regimes enhanced, sublinear normal types presented. differences similarities here for jump processes.