Coarsening Dynamics in the Vicsek Model of Active Matter

Abstract

We study the flocking model introduced by Vicsek in the "coarsening" regime. At standard self-propulsion speeds, we find two distinct growth laws for the coupled density and velocity fields. The characteristic length scale of the density domains grows as $L_{\rho }(t)\sim t^{{\theta }_{\rho }}$ (with ${\theta }_{\rho }\simeq 0.25$), while the velocity length scale grows much faster, $viz.$, $L_v(t)\sim t^{{\theta }_v}$ (with ${\theta }_v\simeq 0.83$). The spatial fluctuations in the density and velocity fields are studied by calculating the two-point correlation function and the structure factor, which show deviations from the well-known Porod's law. This is a natural consequence of scattering from irregular morphologies that dynamically arise in the system. At large values of the scaled wave-vector, the scaled structure factors for the density and velocity fields decay with powers $-2.6$ and $-1.52$, respectively.

15 pages, 4 figures

References in corpus (8)

• Novel type of phase transition in a system of self-driven particles
• Collective motion of self-propelled particles interacting without cohesion
• From Phase to Micro-Phase Separation in Flocking Models: The Essential Role of Non-Equilibrium Fluctuations
• New aspects of the continuous phase transition in the scalar noise model (SNM) of collective motion
• Active nematics are intrinsically phase-separated
• Criticality and the Onset of Ordering in the Standard Vicsek Model
• Violation of Porod law in a freely cooling granular gas in one dimension
• Aspects of the density field in an active nematic

Cited by in corpus (7)

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• Time-dependent properties of run-and-tumble particles. II.: Current fluctuations
• Equilibrium to off-equilibrium crossover in homogeneous active matter
• Diffusion dynamics of an overdamped active ellipsoidal particle in two dimensions
• Ordering kinetics in the active Ising model
• Coarsening, condensates and extremes in aggregation-fragmentation models
• Three-state active lattice gas: a discrete Vicseklike model with excluded volume