Abstract
In this work, we explore how the emergence of collective motion in a system of particles is influenced by the structure of their domain. Using the Vicsek model to generate flocking, we simulate two-dimensional systems that are confined based on varying obstacle arrangements. The presence of obstacles alters the topological structure of the domain where collective motion occurs, which, in turn, alters the scaling behavior. We evaluate these trends by considering the scaling exponent and critical noise threshold for the Vicsek model, as well as the associated diffusion properties of the system. We show that obstacles tend to inhibit collective motion by forcing particles to traverse the system based on curved trajectories that reflect the domain topology. Our results highlight key challenges related to the development of a more comprehensive understanding of geometric structure's influence on collective behavior.
Highlights
Collective behavior associated with living in groups is documented across the animal kingdom [1]
We consider the extent to which critical phenomena are influenced by geometric structure in the context of the Vicsek model
We simulate dynamics of the Vicsek model on 2D surfaces with varying topology, and we study the ramifications for scaling behavior and the critical phase transition
Summary
Collective behavior associated with living in groups is documented across the animal kingdom [1]. Geometric barriers have a natural tendency to inhibit information exchange within a system Since these effects are antagonistic in comparison to the super-diffusive tendencies associated with collective motion, it is interesting to consider their interaction. Within this context, the influence of geometry is of interest due to the possibility that confinement may frustrate a superdiffusive process. Introducing obstacles changes the domain topology and forces particles to travel along curved trajectories; based on the fact that geodesic curves cannot intersect with the obstacles, particles cannot travel long distances along straightline trajectories when obstacles are present This geometric effect leads to fundamental changes to the scaling behavior. In the sections that follow, we provide a straightforward demonstration of these effects and consider their consequences for collective motion
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