Source-linked AI summary
Clearing out a maze: The hungry random walker and its anomalous diffusion
Tanja Schilling, Thomas Voigtmann
TL;DR
The paper models chemotaxis in a porous medium as a food-consuming random walk biased toward nearby food. Simulations on a percolating cluster show anomalous mean-squared-displacement dynamics with a propensity-dependent exponent and slower long-time growth than the unbiased walk.
Problem
The paper examines how food-directed motion interacts with anomalous diffusion in porous media.
Source: p. 1Method
It simulates a non-Markovian hungry walker on a two-dimensional percolating cluster that consumes encountered food and updates its movement bias.
Source: p. 2Results
The MSD follows a power law with a walk dimension larger than the unbiased random walk's, while food propensity produces continuously varying exponents and an initially faster but ultimately slower trajectory.
Source: p. 2Takeaways & Limitations
The model provides a simple example of continuously changing dynamical exponents and suggests that deep exploration of dangling ends reduces long-time area-exploration efficiency.
Source: p. 4The simulations cover a finite time window, so a much-later crossover to ordinary random-walk dynamics cannot be excluded.
Source: pp. 3–4
Abstract
from arXiv · showhide
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.