Keeping speed and distance for aligned motion

Abstract

The cohesive collective motion (flocking, swarming) of autonomous agents is ubiquitously observed and exploited in both natural and man-made settings, thus, minimal models for its description are essential. In a model with continuous space and time we find that if two particles arrive symmetrically in a plane at a large angle, then (i) radial repulsion and (ii) linear self-propelling toward a fixed preferred speed are sufficient for them to depart at a smaller angle. For this local gain of momentum explicit velocity alignment is not necessary, nor are adhesion/attraction, inelasticity or anisotropy of the particles, or nonlinear drag. With many particles obeying these microscopic rules of motion we find that their spatial confinement to a square with periodic boundaries (which is an indirect form of attraction) leads to stable macroscopic ordering. After varying the density of particles at constant system size and varying the size of the system with constant particle density we predict that in the infinite system size (or density) limit the hysteresis loop disappears and the transition becomes continuous. We note that animals, humans, drones, etc. tend to move asynchronously and are often more responsive to motion than positions. Thus, for them velocity-based continuous models can provide higher precision than coordinate-based models. An additional characteristic and realistic feature of the model is that convergence to the ordered state is fastest at a finite density, which is in contrast to models applying (discontinuous) explicit velocity alignments and discretized time. In summary, we find that the investigated model can provide a minimal description of flocking.

8 pages, 7 color figures

References in corpus (11)

• Novel type of phase transition in a system of self-driven particles
• Understanding individual human mobility patterns
• Statistical physics of social dynamics
• Hierarchical group dynamics in pigeon flocks
• Phase transition in the collective migration of tissue cells: experiment and model
• Non-equilibrium clustering of self-propelled rods
• Collective motion and nonequilibrium cluster formation in colonies of gliding bacteria
• New aspects of the continuous phase transition in the scalar noise model (SNM) of collective motion
• Phase transitions in swarming systems: A recent debate
• Turning with the others: novel transitions in an SPP model with coupling of accelerations
• Patterns, transitions and the role of leaders in the collective dynamics of a simple robotic flock