Myopic random walkers and exclusion processes: Single and multispecies

Abstract

A motility mechanism based on a simple exclusion process, where the probability of movement of an agent depends on the number of unoccupied nearest-neighbor sites is considered. Such interacting agents are termed myopic. This problem is an extension of the famous blind or myopic ant in a labyrinth problem. For the interacting agent models considered here, each agent plays the role of an ant in a labyrinth, where the paths of allowed sites though the labyrinth consist of sites not occupied by other agents. We derive a nonlinear diffusion equation for the average occupancy of the discrete agent-based model for myopic agents. In contrast, interacting blind agents have a constant probability of ..