title: Characterizing transport through a crowded environment with different obstacle sizes.
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.
authors: School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia.
authors: Adam J
authors: AJ
authors: Ellery
authors: School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia.
authors: Matthew J
authors: MJ
authors: Simpson
authors: School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia.
authors: Scott W
authors: SW
authors: McCue
authors: Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford, United Kingdom.
authors: Ruth E
authors: RE
authors: Baker
mesh_terms: D001692:Biological Transport; D008954:Models, Biological; D010316:Particle Size