Novel type of phase transition in a system of self-driven particles.

By Tamás Vicsek, András Czirók, E. Ben-Jacob, I. Cohen, Ofer Sochet. 1995

A simple model with a novel type of dynamics is introduced in order to investigate the emergence of self-ordered motion in systems of particles with biologically motivated interaction. In our model particles are driven with a constant absolute velocity and at each time step assume the average direction of motion of the particles in their neighborhood with some random perturbation $(\ensuremath{\eta})$ added. We present numerical evidence that this model results in a kinetic phase transition from no transport (zero average velocity, $|{\mathbf{v}}_{a}|\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$) to finite net transport through spontaneous symmetry breaking of the rotational symmetry. The transition is continuous, since $|{\mathbf{v}}_{a}|$ is found to scale as $({\ensuremath{\eta}}_{c}\ensuremath{-}\ensuremath{\eta}{)}^{\ensuremath{\beta}}$ with $\ensuremath{\beta}\ensuremath{\simeq}0.45$.

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Citations in the corpus

An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination (2012, background): “The study of distributed control of multiple vehicles was perhaps first motivated by the work in distributed computing [1], management science [ 2], [3], and statistical physics [4].”
Distributed subgradient methods and quantization effects (2008, neutral): “, [26], [9], [4], [16], [5], and [17], [18]).”
Inverse Reinforcement Learning in Swarm Systems (2016, methodology): “In our first experiment, we tested a modified version of the so-called Vicsek or self-propelled particles model [30].”
Consensus of fractional-order multi-agent systems with input time delay (2017, background): “The consensus problem inspired by the field of management science [10] and statistical physics [26] has a long history in”
Distributed Control of Robotic Networks: A Mathematical Approach to Motion Coordination Algorithms (2009, methodology): “Adjacency-based averaging algorithms arising from unweighted (undirected) graphs without self-loops are also known as the equal-neighbor averaging rule or the Vicsek’s model ; see [Vicsek et al., 1995].”
Fluid dynamics of self-propelled microorganisms, from individuals to concentrated populations (2007, background): “Models of various types have been proposed to address these phenomena, from very simple discrete-particle dynamics not involving hydrodynamics (Vicsek et al. 1995) to continuum models based on”
Temperature in and out of equilibrium: A review of concepts, tools and attempts (2017, background): “The ancestor of aligning self-propelled particles is the Vicsek model, where the aligning mechanism is collective: at each time-step all particles in a given radius take as new orientation (which determine the direction of motion) their average orientation plus a small amount of noise [298].”
Broadcast Gossip Algorithms for Consensus (2009, background): “all nodes to eventually agree on a parameter [ 6 ].”
Emergent dynamics of the Cucker-Smale flocking model and its variants (2016, methodology): “[6, 64], and they have been extensively studied recently because of their possible applications to sensor networks, controls of robots and unmanned aerial vehicles [49, 55, 57], and opinion formation of social networks.”