Clearing out a maze: The hungry random walker and its anomalous diffusion

Tanja Schilling; Thomas Voigtmann

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arXiv · 1607.01123

Clearing out a maze: The hungry random walker and its anomalous diffusion

Tanja Schilling·Thomas Voigtmann

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Abstract

We study chemotaxis in a porous medium using as a model a biased ("hungry") random walk on a percolating cluster. In close resemblance to the 1980s arcade game Pac-Man, the hungry random walker consumes food, which is initially distributed in the maze, and biases its movement towards food-filled sites. We observe that, on the percolating cluster, the mean-squared displacement of the pacman process shows anomalous dynamics, which follow a power law with a dynamical exponent different from both that of a self avoiding random walk as well as that of an unbiased random walk. The change in dynamics with the propensity to move towards food is well described by a dynamical exponent that depends continuously on this propensity, and results in slower differential growth when compared to the unbiased random walk.

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Tanja Schilling, Thomas Voigtmann. 2016-07-25. Clearing out a maze: The hungry random walker and its anomalous diffusion. https://arxiv.org/abs/1607.01123

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