Clearing out a maze: A model of chemotactic motion in porous media

Abstract

We study the anomalous dynamics of a biased hungry (or greedy) random walk on a percolating cluster. The model mimics chemotaxis in a porous medium: In close resemblance to the 1980s arcade game PAC-MAN(R) , the hungry random walker consumes food, which is initially distributed in the maze, and biases its movement towards food-filled sites. We observe that the mean-squared displacement of the process follows a power law with an exponent that is different from previously known exponents describing passive or active microswimmer dynamics. The change in dynamics is well described by a dynamical exponent that depends continuously on the propensity to move towards food. It results in slower differential growth when compared to the unbiased random walk.