Self-propelled Vicsek particles at low speed and low density

Abstract

We study through numerical simulation the Vicsek model for very low speeds and densities. We consider scalar noise in 2-d and 3-d, and vector noise in 3-d. We focus on the behavior of the critical noise with density and speed, trying to clarify seemingly contradictory earlier results. We find that, for scalar noise, the critical noise is a power law both in density and speed, but although we confirm the density exponent in 2-d, we find a speed exponent different from earlier reports (we consider lower speeds than previous studies). On the other hand, for the vector noise case we find that the dependence of the critical noise cannot be separated as a product of power laws in speed and density. Finally, we study the dependence of the relaxation time with speed and find the same power law in 2-d and 3-d, with and exponent that depends on whether the noise is above or below the critical value.

7 pages, 11 figures

References in corpus (5)

• Novel type of phase transition in a system of self-driven particles
• Collective motion of self-propelled particles interacting without cohesion
• Spontaneously ordered motion of self-propelled particles
• From Phase to Micro-Phase Separation in Flocking Models: The Essential Role of Non-Equilibrium Fluctuations
• The Physics of the Vicsek Model

Cited by in corpus (2)

• Short-time dynamics in active systems: the Vicsek model
• Noisy multistate voter model for flocking in finite dimensions