State Transitions and the Continuum Limit for a 2D Interacting, Self-Propelled Particle System

Abstract

We study a class of swarming problems wherein particles evolve dynamically via pairwise interaction potentials and a velocity selection mechanism. We find that the swarming system undergoes various changes of state as a function of the self-propulsion and interaction potential parameters. In this paper, we utilize a procedure which, in a definitive way, connects a class of individual-based models to their continuum formulations and determine criteria for the validity of the latter. H-stability of the interaction potential plays a fundamental role in determining both the validity of the continuum approximation and the nature of the aggregation state transitions. We perform a linear stability analysis of the continuum model and compare the results to the simulations of the individual-based one.

References in corpus (4)

• Novel type of phase transition in a system of self-driven particles
• Noise-Induced Transition from Translational to Rotational Motion of Swarms
• New aspects of the continuous phase transition in the scalar noise model (SNM) of collective motion
• Nonequilibrium statistical mechanics of swarms of driven particles

Cited by in corpus (4)

• The Effect of Sensory Blind Zones on Milling Behavior in a Dynamic Self-Propelled Particle Model
• Predictive protocol of flocks with small-world connection pattern
• Numerical simulations of a non-conservative hyperbolic system with geometric constraints describing swarming behavior
• From particle to kinetic and hydrodynamic descriptions of flocking