Srokowski Tomasz
Institute of Nuclear Physics, Polish Academy of Sciences, PL-31-342 Kraków, Poland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Mar;89(3):030102. doi: 10.1103/PhysRevE.89.030102. Epub 2014 Mar 31.
Diffusion in nonhomogeneous media is described by a dynamical process driven by a general Lévy noise and subordinated to a random time; the subordinator depends on the position. This problem is approximated by a multiplicative process subordinated to a random time: it separately takes into account effects related to the medium structure and the memory. Density distributions and moments are derived from the solutions of the corresponding Langevin equation and compared with the numerical calculations for the exact problem. Both subdiffusion and enhanced diffusion are predicted. Distribution of the process satisfies the fractional Fokker-Planck equation.
非均匀介质中的扩散由一个由一般 Lévy 噪声驱动并从属于随机时间的动力学过程描述；从属过程取决于位置。该问题通过从属于随机时间的乘法过程进行近似：它分别考虑了与介质结构和记忆相关的效应。密度分布和矩从相应的朗之万方程的解中导出，并与精确问题的数值计算进行比较。预测了亚扩散和增强扩散。该过程的分布满足分数阶福克-普朗克方程。
