  Density-dependent diffusion is a widespread phenomenon in nature. We have
examined the density-dependent diffusion behavior of some biological processes
such as tumor growth and invasion [23]. Here, we extend our previous work by
developing computational techniques to analyze the density-dependent diffusion
behavior of one-dimensional interacting particle systems, which have been used
to model numerous microscopic processes [17-19], and we apply our techniques to
an interacting system of Brownian particles, with hard-core interactions and
nearest-neighbor adhesion, known as single-file dynamics. Through large-scale
numerical simulations that exploit Monte-Carlo techniques and high-performance
computing resources, we show that the diffusion rate in such systems depends on
the average particle density. Extensions to the techniques we present here
enable researchers to examine the density-dependent diffusion behavior of many
physical systems in nature that undergo one-dimensional diffusion associated
with a change in the particle density; such as ion transport processes,
channeling in zeolites, etc.
