Transient Anomalous Diffusion in a Heterogeneous Environment
Transient Anomalous Diffusion in a Heterogeneous Environment
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DOI：
10.3389/fphy.2019.00119
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发表时间：
2019-09
影响因子：
3.1
通讯作者：
A. Spakowitz
中科院分区：
文献类型：
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作者：
A. Spakowitz
这项工作提供了一个分析模型的扩散率随位置而变化的非均匀环境中的颗粒的扩散运动。扩散率模型描述的环境是均匀的随机定位的口袋较大的扩散。这种异质性的一般框架是服从系统的扩展的绿色的功能，我们采用图解的方法来确定这种扩展中的共同条款。在收集这些图的一个共同的家庭，我们到达的粒子绿色的功能，捕捉空间变化的扩散率的分析表达式。由此产生的绿色的功能是用来分析异常扩散和峰度不同程度的异质性，我们比较这些结果与数值模拟，以确认其有效性。这些结果作为分析非均质材料和活细胞中一系列扩散现象的基础。
This work provides an analytical model for the diffusive motion of particles in a heterogeneous environment where the diffusivity varies with position. The model for diffusivity describes the environment as being homogeneous with randomly positioned pockets of larger diffusivity. This general framework for heterogeneity is amenable to a systematic expansion of the Green's function, and we employ a diagrammatic approach to identify common terms in this expansion. Upon collecting a common family of these diagrams, we arrive at an analytical expression for the particle Green's function that captures the spatially varying diffusivity. The resulting Green's function is used to analyze anomalous diffusion and kurtosis for varying levels of heterogeneity, and we compare these results with numerical simulations to confirm their validity. These results act as a basis for analysis of a range of diffusive phenomena in heterogeneous materials and living cells.