Effect of the orientational relaxation on the collective motion of patterns formed by self-propelled particles

Abstract

We investigate the collective behavior of self-propelled particles (SPPs) undergoing competitive processes of pattern formation and rotational relaxation of their self-propulsion velocities. In full accordance with previous work, we observe transitions between different steady states of the SPPs caused by the intricate interplay among the involved effects of pattern formation, orientational order, and coupling between the SPP density and orientation fields. Based on rigorous analytical and numerical calculations, we prove that the rate of the orientational relaxation of the SPP velocity field is the main factor determining the steady states of the SPP system. Further, we determine the boundaries between domains in the parameter plane that delineate qualitatively different resting and moving states. In addition, we analytically calculate the collective velocity $\vec{v}$ of the SPPs and show that it perfectly agrees with our numerical results. We quantitatively demonstrate that $\vec{v}$ does not vanish upon approaching the transition boundary between the moving pattern and homogeneous steady states.

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References in corpus (9)

• Interaction Ruling Animal Collective Behaviour Depends on Topological rather than Metric Distance: Evidence from a Field Study
• Dynamical clustering and phase separation in suspensions of self-propelled colloidal particles
• Athermal Phase Separation of Self-Propelled Particles with no Alignment
• Modeling Elastic and Plastic Deformations in Non-Equilibrium Processing Using Phase Field Crystals
• Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview
• Effective Cahn-Hilliard equation for the phase separation of active Brownian particles
• Traveling and resting crystals in active systems
• Localized states in the conserved Swift-Hohenberg equation with cubic nonlinearity
• Active crystals and their stability

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