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.

Dynamical properties and scaling behavior of self-propelled particles: Langevin dynamics

“…The mean velocity system is calculated as va=1/N∑i=1i=Nvi .The corresponding results calculated for system density ρ=0.5 , for radius value R=5 and for several noise values are plotted in Figure 2. The obtained profile is more consistent with the one obtained by the Vicsek model (Bakir et al , 2016). This system’s velocity profile presents two different regimes and can be fitted by the exponential growth function: vafalse(tfalse)=vltrue(1−e−t/truetctrue), where vl and tc represent, respectively, the mean velocity of system at the equilibrium phase and the characteristic time.…”

“…The results indicate that tc decreases exponentially with the noise as tc=Ae−η/trueηc , where A and ηc=0.65 are, respectively, a constant and the characteristic noise value which depend on the system’s density ρ. This profile of tc is more consistent with the investigations by Bakir et al (2016).…”

“…Therefore, some investigations show that individuals move together in time and they interact with their neighbors to maintain the alignment of the group in the same direction, where the system evolves coordinated and synchronized with a self-organized dynamic. In this dynamic, the individuals attempt to be closest to their neighbors in order to keep coherence of the group (Bakir et al , 2016).…”

“…Generally, this does not hold the real motion of biological organisms (Bazazi et al , 2011). Furthermore, recent experimental realizations of swarming in nonliving systems are based on rectification of fluctuation due to asymmetric friction and therefore imply a non-negligible role of speed fluctuation (Bakir et al , 2016, 2017).…”

“…Hence, the aim of the present paper, which is continuation of our study (Bakir et al , 2016) of flocking behavior, is to investigate the behavior of collective motion of living biological organisms in the 2D plane by adopting a new approach based on the use of Langevin dynamics. Langevin dynamics is a powerful tool to study these systems because they present a stochastic process due to collisions between their constituents.…”