Microscopic field theory for structure formation in systems of self-propelled particles with generic torques

Abstract

We derive a dynamical field theory for self-propelled particles subjected to generic torques and forces by explicitly coarse-graining their microscopic dynamics, described by a many-body Fokker-Planck equation. The model includes both intrinsic torques inducing self-rotation, as well as interparticle torques leading to, for instance, the local alignment of particles' orientations. Within this approach, although the functional form of the pairwise interactions does not need to be specified, one can directly map the parameters of the field theory onto the parameters of particle-based models. We perform a linear stability analysis of the homogeneous solution of the field equations and find both long-wavelength and short-wavelength instabilities. The former signals the emergence of a macroscopic structure, which we associate with motility-induced phase separation, while the second one signals the growth of a finite structure with a characteristic size. Intrinsic torques hinder phase separation, pushing the onset of the long-wavelength instability to higher activities. Further, they generate finite-sized structures with a characteristic size proportional to both the self-propulsion velocity and the inverse of the self-rotation frequency. Our results show that a general mechanism might explain why chirality tends to suppress motility-induced phase separation but instead promotes the formation of non-equilibrium patterns.

arXiv comment12 pages, 5 figures

References in corpus (58)

• Novel type of phase transition in a system of self-driven particles
• Active Particles in Complex and Crowded Environments
• Collective motion
• The Mechanics and Statistics of Active Matter
• Motility-Induced Phase Separation
• Flocks, herds, and schools: A quantitative theory of flocking
• Dynamical clustering and phase separation in suspensions of self-propelled colloidal particles
• Athermal Phase Separation of Self-Propelled Particles with no Alignment
• Swimming in circles: Motion of bacteria near solid boundaries
• Emergence of macroscopic directed motion in populations of motile colloids
• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• Collective Motion of Vibrated Polar Disks
• Circular motion of asymmetric self-propelling particles
• Non-equilibrium clustering of self-propelled rods
• A continuum theory of phase separation kinetics for active Brownian particles
• Active Brownian Motion Tunable by Light
• Phase behaviour of active Brownian particles: The role of dimensionality
• Scalar ${\varphi }^4$ field theory for active-particle phase separation
• Computational models for active matter
• Full phase diagram of active Brownian disks: from melting to motility-induced phase separation
• Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis
• Microscopic theory for the phase separation of self-propelled repulsive disks
• Pattern formation in self-propelled particles with density-dependent motility
• Self-Propelled Rods: Insights and Perspectives for Active Matter
• Effective Interactions in Active Brownian Suspensions
• Effective Cahn-Hilliard equation for the phase separation of active Brownian particles
• Freezing and phase separation of self-propelled disks
• The Rotating Vicsek Model: Pattern Formation and Enhanced Flocking in Chiral Active Matter
• Nonequilibrium equation of state in suspensions of active colloids
• The Physics of the Vicsek Model
• Entropy production in field theories without time reversal symmetry: Quantifying the non-equilibrium character of active matter
• Non-Equilibrium Strongly Hyperuniform Fluids of Circle Active Particles with Large Local Density Fluctuations
• Generalized thermodynamics of Motility-Induced Phase Separation: Phase equilibria, Laplace pressure, and change of ensembles
• Kinetic Theory of Flocking: Derivation of Hydrodynamic Equations
• Interrupted Motility Induced Phase Separation in Aligning Active Colloids
• Light Activated Self-Propelled Colloids
• Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles
• Towards a statistical mechanical theory of active fluids
• Active phase separation by turning toward regions of higher density
• Boltzmann-Ginzburg-Landau approach for continuous descriptions of generic Vicsek-like models
• Collective behavior of penetrable self-propelled rods in two dimensions
• Activity induced synchronization: From Mutual Flocking to Chiral Self-Sorting
• A particle-field representation unifies paradigms in active matter
• Freezing a Flock: Motility-Induced Phase Separation in Polar Active Liquids
• Flowing crystal of self-propelled particles
• Clustering and phase separation of circle swimmers dispersed in a monolayer
• Velocity alignment promotes motility-induced phase separation
• Motility-induced phase separation of active particles in the presence of velocity alignment
• Dynamical Clustering Interrupts Motility Induced Phase Separation in Chiral Active Brownian Particles
• Simultaneous Phase Separation and Pattern Formation in Chiral Active Mixtures
• Interparticle torques suppress motility-induced phase separation for rodlike particles
• Dynamical self-assembly of dipolar active Brownian particles in two dimensions
• Micro-flock patterns and macro-clusters in chiral active Brownian disks
• Topology-driven ordering of flocking matter
• From scalar to polar active matter: Connecting simulations with mean-field theory
• Motility-Induced Clustering and Meso-Scale Turbulence in Active Polar Fluids
• Re-entrant phase separation in nematically aligning active polar particles
• Statistical Field Theory and Effective Action Method for scalar Active Matter

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• Experimental and numerical study of a second-order transition in the behavior of confined self-propelled particles
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