Self-organized pattern formation in a diverse attractive-repulsive swarm

A diverse, asynchronous swarm consisting of N mobile, attractive-repulsive particles evolves inside a two-dimensional confinement. Each particle k is characterized by a preferred neighboring distance rho(k) determined from a truncated normal distribution of mean (rho) over bar and standard deviation sigma(rho), for 0 <= rho < infinity. Pairwise particle interaction is either attractive or repulsive depending on whether the distance between two particles is greater or less than rho(k). The swarm forms self-organized metastable patterns as particles adjust their positions via random asynchronous evolution. An order parameter U is defined as a measure for pattern metastability, which is found to exhibit a first-order phase transition at sigma(rho c) = 0.606. For sigma(rho) < sigma(rho c) tetrapolar patterns are formed, whereas for sigma(rho) > sigma(rho c) stellate patterns are formed. This work explores the role of diversity in self-organized pattern formation in an attractive-repulsive swarm system. Copyright (C) EPLA, 2009