Phase separation and emergence of collective motion in a one-dimensional system of active particles

Abstract

We study numerically a one-dimensional systems of self-propelled particles, where the state of the particles is given by their moving direction (left or right), which is encoded by a spin-like variable, and their position. Particles interact by short-ranged, spring-like attractive forces and do not possess spin-spin interactions (i.e. velocity alignment). Newton's third law is broken in this model by assuming an asymmetric interaction range that is larger in the direction of the moving direction of the particle. We show that in this nonequilibrium system, due to the absence of the action-reaction symmetry, there exists an intimate link between phase separation and the formation of highly-coherent, spatially localized, moving flocks (i.e. collective motion). More specifically, we prove the existence of two fundamentally different types of active phase separation, which we refer to as neutral (NPS) and polar (PPS) phase separation. Furthermore, we indicate that NPS is subdivided in two classes with distinct critical exponents. These results are of key importance to understand that in Active Matter there exist several phase-separation classes and that the emergence of polar, self-organized patterns (i.e. flocks) does not require the presence of a velocity alignment.

Time-dependent properties of interacting active matter: dynamical behavior of one-dimensional systems of self-propelled particles

“…Such a regime guarantees that boundary conditions do not play a significant role and that the one-dimensional version of traveling crystals does not occur [67,68]. At variance with previous studies [69][70][71][72][73], we consider high-density regimes, in such a way that the one-dimensional system of active particles is compact enough and neither defects in the periodic arrangement of the particles nor clusters can easily form: the system attains homogeneous configurations for the whole set of parameters numerically explored in this work.…”

Time-dependent properties of interacting active matter: Dynamical behavior of one-dimensional systems of self-propelled particles

“…These traveling states, corresponding to the formation of a single velocity domain, occur for L v 0 τ and are not discussed in this paper. At variance with previous studies [43,[75][76][77][78], we consider high-density regimes, in such a way that the one-dimensional system of active particles is compact enough and neither defects in the periodic arrangement of the particles nor clusters can easily form: the system attains homogeneous configurations for the whole set of parameters numerically explored in this work.…”

“…Instead, explicit alignment interactions (coupling the self-propulsions of the particles) are needed to induce flocking states, such as band formation [39][40][41][42]. We remark that other complex dynamics involving, for instance, spin variables but no Vicsek-type interactions [43], could produce local velocity alignment and even flocking phenomena [44,45]. At present, notwithstanding the existing detailed information about the velocity domains, obtained by measuring the equal-time spatial velocity correlations, very little is known about their dynamical properties.…”

Collective motion of run-and-tumble repulsive and attractive particles in one-dimensional systems

“…Following a similar idea, there exists a number of studies on pattern emergence and self-organization in active systems resulting from the competition between selfpropulsion and excluded volume interactions reporting the effects of alignment interactions [28] or attractive forces [8,[29][30][31] both in 1D and 2D. In particular, Ref.…”