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Anomalous diffusion in semi-crystalline polymer structures | | E G Kostadinova
; J L Padgett
; C D Liaw
; L S Matthews
; T W Hyde
; | | Date: |
1 Jun 2020 | | 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 an analytical method for studying anomalous diffusion which combines
concepts from fractional calculus and spectral theory in a model where
transport is guided by non-local interactions and random disorder. The proposed
technique determines transport properties from the spectrum of an Anderson-type
Hamiltonian with a discrete fractional Laplacian operator (-{Delta})^s, 0<s<2
and a random distribution of disorder. We present a physical interpretation of
the model in the context of light diffusion through semi-crystalline polymer
structures. In this formulation, transport is numerically studied as a function
of disorder concentration, characteristics of nonlocal interactions, and vector
scales in the Hilbert space. 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 correlation lengths in the sub-diffusive case, where all
states are normally expected to be localized for a disordered system. | | Source: | arXiv, 2006.1068 | | Services: | Forum | Review | PDF | Favorites | |
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