Scaling behavior of non-equilibrium phase transitions in spontaneously ordered motion of self-propelled particles

Abstract

Many animal groups, such as bird flocks, clearly present structural order and appear to move as a single coherent entity. In interest to understand the complex behavior of these systems, many models have been proposed and tested so far. The aim of this work is to study and discuss numerically the scaling behavior in the 2D non-equilibrium phase transitions in spontaneously ordered motion of self-propelled particles in the framework of Vicsek model. This model is an important tool to study the behavior of collective motion of live biological and physical organisms. The calculation of the scaling exponents is effected by using the scaling dynamic method. However, the time evolution of the particles velocity present two different regimes separated by a cross-over time which increases linearly with both applied noise and radius of repulsive zone, but it decreases exponentially with the radius of orientation zone. The results show that the obtained exponents are similar to the growth and roughness ones used in the interfaces growth and to the submonolayer deposition process. The obtained values of these exponents are not dependent on the noises value, which proves their universality characters. Hence the kinetic evolution of the spontaneously ordered motion of self-propelled particles is self-similar. Implications of these findings are discussed.