论文标题
异常环境中异常扩散的分析描述：fokker-Planck方程无分数衍生物
Analytic description of anomalous diffusion in heterogeneous environments: Fokker-Planck equation without fractional derivatives
论文作者
论文摘要
我们提出了一种在异质环境中扩散的模型，该模型在定性地反映了用碳纳米管的聚合物膜的传输特性。我们从随机方程系统中得出了Fokker-Planck方程，纳米管区域的聚合物和弹道制度的扩散状态。我们展示了在纳米管区域存在下如何更改概率密度函数。因此，观察到均方根位移的非线性时间依赖性，这表明异常扩散状态。因此，该模型解释了扩散球态异常扩散的外观机理。我们的方法没有假设任何类型的分布，并且使用分数区分设备。
We present a model of diffusion in heterogeneous environment, which qualitatively reflects the transport properties of a polymeric membrane with carbon nanotubes. We derived Fokker-Planck equation from system of stochastic equations, responding diffusion regime in polymer and ballistic regime in nanotube areas. We show how probability density function is changed in presence of nanotube areas. Hereupon nonlinear time dependence of mean square displacement is observed, that indicates anomalous diffusion regime. Thus, the model explains mechanism of appearance of anomalous diffusion for diffusion-ballistic regime. Our approach does not suppose any type of distributions and using fractional differentiate apparatus.
