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Original Research ARTICLE Provisionally accepted The full-text will be published soon. Notify me

Front. Phys. | doi: 10.3389/fphy.2019.00119

Transient Anomalous Diffusion in a Heterogeneous Environment

  • 1Stanford University, United States

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.

Keywords: Diffusion, heterogeneity, non-Gaussian statistics, soft materials, transport in living cells

Received: 30 May 2019; Accepted: 13 Aug 2019.

Copyright: © 2019 Spakowitz. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Prof. Andrew J. Spakowitz, Stanford University, Stanford, United States, ajspakow@stanford.edu