Emergence of Collective Motion in a Model of Interacting Brownian Particles

Abstract

By studying a system of Brownian particles, interacting only through a local social-like force (velocity alignment), we show that self-propulsion is not a necessary feature for the flocking transition to take place as long as underdamped particle dynamics can be guaranteed. Moreover, the system transits from stationary phases close to thermal equilibrium, with no net flux of particles, to farfrom-equilibrium ones exhibiting collective motion, long-range order and giant number fluctuations, features typically associated to ordered phases of models where self-propulsion is considered.PACS numbers: 05.70.Fh, 05.70.Ln Collective motion is an ubiquitous phenomenon in biological groups such as flocks of birds, schools of fishes, swarms of insects, etc. The study of these far-fromequilibrium systems has attracted great interest over the last few decades, as the spontaneous emergence of such ordered phases and coordinated behavior, arising from local interactions, cannot be accounted for by the standard theorems of statistical mechanics [1].Introduced almost twenty years ago, the seminal model by Vicsek et al.[2] provided a simple tool to study the transition to collective motion, in a non-equilibrium situation, taking into account two basic ingredients: the selfpropulsive character of the particles and a local velocityalignment interaction among them. Due to the discrete nature of the model, a given particle instantaneously orients its direction of motion along the average direction of motion of its neighbors within a radius R, while stochastic perturbations are considered by adding a random angle ("noise") to this direction. In two dimensions, the system displays an ordered phase characterized by collective motion with long-range order and giant number fluctuations [3], just below a critical value of the noise intensity that depends on the particle density. It is in this respect that this model can be considered as a paradigm of non-equilibrium phase transitions, since such ordered phases are forbidden in equilibrium (for Heisenberg-like models) by the Mermin-Wagner-Hohenberg theorem [4]. Above this value, the ordered phase breaks down into a stationary, disordered and out-of-equilibrium one.Over the years, many generalizations of the model have been developed, keeping self-propulsion as an essential ingredient for the phase transition to take place, in combination with interactions of the "social" type among the particles such as velocity-alignment [5,6]. This has led to the development of sophisticated nonlinear friction terms [7,8], a bias that may be justified arguing, on the one hand, that the concept of self-propelled (or active Brownian) particles captures the natural ability (seen in many biological systems) for the agents to develop motion by themselves [9,10] and, on the other, that it is an important ingredient for pattern formation in models of collective motion [11].In this Letter, we study the emergence of collective motion in a two-dimensional system of N passive Brownian (not-self-propelled) partic...

Statistical Mechanics of Active Ornstein Uhlenbeck Particles

“…A similar phaseseparation scenario has been reported for AOUPs interacting via pairwise repulsive forces [41,93], as well as for resembling kinetic Monte Carlo dynamics [94,95]. This further highlights that, despite their simplicity, AOUPs retain the qualitative features of self-propelled particles at the level of collective dynamics, as was established, for instance, for the transition to collective motion [96]. In this section, we bring our knowledge on MIPS in AOUPs up to par with their non-Gaussian counterparts.…”

Thermodynamic uncertainty relation for underdamped Langevin systems driven by a velocity-dependent force

“…To account for the effect of a Lorentz force on the TUR, a more generalized TUR is required, taking into consideration a velocitydependent force in the underdamped dynamics. Velocitydependent force plays a key role in many important contexts, such as molecular refrigerators (cold damping) [27][28][29][30][31][32], collective motions of active/passive Brownian particles with velocity-dependent interactions [33][34][35][36][37][38][39], and certain active matter dynamics [40][41][42][43][44][45].…”

Diffusion of active chiral particles

“…Last equation is supplemented by additional stochastic differential equations for the swimming velocity v swim (t) = v s (t)v swim (t), from which the explicit time dependence of the swimming speed v s (t) and the swimming directionv swim (t), are determined [9,65]. In the overdamped-speed limit, i.e.…”

“…[9] for instance). This approximation is well supported by experimental studies in many real biological systems [10][11][12][13][14][15] where fluctuations around the average value are small.…”