Abstract
From the spread of pollutants in the atmosphere to the transmission of nutrients across cell membranes, anomalous diffusion processes are ubiquitous in natural systems. The ability to understand and control the mechanisms guiding such processes across various scales has important application to research in materials science, finance, medicine, and energetics. Here we present a numerical study of anomalous diffusion of light through a semi-crystalline polymer structure where transport is guided by random disorder and nonlocal interactions. The numerical technique examines diffusion properties in one-dimensional (1D) space via the spectrum of an Anderson-type Hamiltonian with a discrete fractional Laplacian operator (-{\Delta})^s, 0<s<2 and a random distribution of disorder. The results show enhanced transport for s<1 (super-diffusion) and enhanced localization for s>1 (sub-diffusion) for most examined cases. An important finding of the present study is that transport can be enhanced at key spatial scales in the sub-diffusive case, where all states are normally expected to be localized for a (1D) disordered system.
Highlights
The ubiquity of anomalous diffusion processes observed in laboratory experiments and in nature is well captured by the words of Klafter and Sokolov [1]: “ these phenomena are called anomalous, they are abundant in everyday life: anomalous is normal.”
In this paper we study, numerically, anomalous diffusion using the fractional Laplacian spectral (FLS) method [15], which is suitable for modeling transport guided by nonlocal interactions and random disorder
We presented a numerical study of transport in disordered media, where nonlocal interactions can arise due to positive or negative correlations
Summary
The ubiquity of anomalous diffusion processes observed in laboratory experiments and in nature is well captured by the words of Klafter and Sokolov [1]: “ these phenomena are called anomalous, they are abundant in everyday life: anomalous is normal.” Superdiffusion has been observed in the search patterns of animals [2,3,4], the spread of pollutants in the ocean and the atmosphere [5,6], and particle transport in turbulent plasmas [7,8,9]. Superdiffusion has been observed in the search patterns of animals [2,3,4], the spread of pollutants in the ocean and the atmosphere [5,6], and particle transport in turbulent plasmas [7,8,9]. In this paper we study, numerically, anomalous diffusion using the fractional Laplacian spectral (FLS) method [15], which is suitable for modeling transport guided by nonlocal interactions and random disorder.
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