Characterizing transport through a crowded environment with different obstacle sizes
Ellery, Adam, Simpson, Matthew, McCue, Scott W., & Baker, Ruth (2014) Characterizing transport through a crowded environment with different obstacle sizes. Journal of Chemical Physics, 140(5), 054108.

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Abstract
Transport through crowded environments is often classified as anomalous, rather than classical, Fickian diffusion. Several studies have sought to describe such transport processes using either a continuous time random walk or fractional order differential equation. For both these models the transport is characterized by a parameter α, where α = 1 is associated with Fickian diffusion and α < 1 is associated with anomalous subdiffusion. Here, we simulate a single agent migrating through a crowded environment populated by impenetrable, immobile obstacles and estimate α from mean squared displacement data. We also simulate the transport of a population of such agents through a similar crowded environment and match averaged agent density profiles to the solution of a related fractional order differential equation to obtain an alternative estimate of α. We examine the relationship between our estimate of α and the properties of the obstacle field for both a single agent and a population of agents; we show that in both cases, α decreases as the obstacle density increases, and that the rate of decrease is greater for smaller obstacles. Our work suggests that it may be inappropriate to model transport through a crowded environment using widely reported approaches including power laws to describe the mean squared displacement and fractional order differential equations to represent the averaged agent density profiles.
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ID Code:  66517 

Item Type:  Journal Article 
Refereed:  Yes 
Keywords:  diffusion, random walk, fractional differential equation, microenvironment, cancer, wound healing 
DOI:  10.1063/1.4864000 
ISSN:  10897690 
Subjects:  Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Biological Mathematics (010202) 
Divisions:  Current > Institutes > Institute of Health and Biomedical Innovation Current > Schools > School of Mathematical Sciences Current > QUT Faculties and Divisions > Science & Engineering Faculty 
Funding:  
Copyright Owner:  Copyright 2014 AIP Publishing LLC 
Deposited On:  22 Jan 2014 22:48 
Last Modified:  15 Apr 2014 14:15 
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