Mean-field analysis of a dynamical phase transition in a cellular automaton model for collective motion

Abstract

A cellular automaton model is presented for random walkers with biologically motivated interactions favoring local alignment and leading to collective motion or swarming behavior. The degree of alignment is controlled by a sensitivity parameter, and a dynamical phase transition exhibiting spontaneous breaking of rotational symmetry occurs at a critical parameter value. The model is analyzed using nonequilibrium mean field theory: Dispersion relations for the critical modes are derived, and a phase diagram is constructed. Mean field predictions for the two critical exponents describing the phase transition as a function of sensitivity and density are obtained analytically.

4 pages, 4 figures, final version as published

References in corpus (2)

• Novel type of phase transition in a system of self-driven particles
• Lattice-gas model for collective biological motion

Cited by in corpus (24)

• Traffic and Related Self-Driven Many-Particle Systems
• Collective motion of self-propelled particles interacting without cohesion
• Freezing by Heating in a Driven Mesoscopic System
• Boltzmann and hydrodynamic description for self-propelled particles
• Collective motion and nonequilibrium cluster formation in colonies of gliding bacteria
• Gas-Kinetic-Based Traffic Model Explaining Observed Hysteretic Phase Transition
• Optimal Self-Organization
• Self-organized Vortex State in Two-dimensional Dictyostelium Dynamics
• Traffic jams, gliders, and bands in the quest for collective motion
• Alternating steady state in one-dimensional flocking
• Rippling patterns in aggregates of myxobacteria arise from cell-cell collisions
• Invasion-wave induced first-order phase transition in systems of active particles
• Motility-induced phase separation of active particles in the presence of velocity alignment
• Pattern formation mechanisms in motility mutants of Myxococcus xanthus
• Dynamic coordinated control laws in multiple agent models
• Flocking Regimes in a Simple Lattice Model
• Towards a quantitative kinetic theory of polar active matter
• Active matter beyond mean-field: Ring-kinetic theory for self-propelled particles
• Nucleation-induced transition to collective motion in active systems
• A Dynamically Diluted Alignment Model Reveals the Impact of Cell Turnover on the Plasticity of Tissue Polarity Patterns
• Vectorial active matter on the lattice: polar condensates and nematic filaments
• Cohesive motion in one-dimensional flocking
• Exploring the role of talent and luck in getting success
• Individual particle persistence antagonizes global ordering in populations of nematically-aligning self-propelled particles