Communication: Distinguishing between short-time non-Fickian diffusion and long-time Fickian diffusion for a random walk on a crowded lattice

Journal Article · Sat May 07 04:00:00 EDT 2016 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4948782· OSTI ID:22657950

Ellery, Adam J.; Simpson, Matthew J. ^[1]; Baker, Ruth E. ^[2]

---

1. School of Mathematical Sciences, Queensland University of Technology (QUT), Brisbane (Australia)
2. Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford (United Kingdom)

The motion of cells and molecules through biological environments is often hindered by the presence of other cells and molecules. A common approach to modeling this kind of hindered transport is to examine the mean squared displacement (MSD) of a motile tracer particle in a lattice-based stochastic random walk in which some lattice sites are occupied by obstacles. Unfortunately, stochastic models can be computationally expensive to analyze because we must average over a large ensemble of identically prepared realizations to obtain meaningful results. To overcome this limitation we describe an exact method for analyzing a lattice-based model of the motion of an agent moving through a crowded environment. Using our approach we calculate the exact MSD of the motile agent. Our analysis confirms the existence of a transition period where, at first, the MSD does not follow a power law with time. However, after a sufficiently long period of time, the MSD increases in proportion to time. This latter phase corresponds to Fickian diffusion with a reduced diffusivity owing to the presence of the obstacles. Our main result is to provide a mathematically motivated, reproducible, and objective estimate of the amount of time required for the transport to become Fickian. Our new method to calculate this crossover time does not rely on stochastic simulations.

• OSTI ID: 22657950
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 17 Vol. 144; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
DIFFUSION
EXPERIMENTAL DATA
GRAPH THEORY
RANDOMNESS
SIMULATION
STOCHASTIC PROCESSES