Predictive local field theory for interacting active Brownian spheres in two spatial dimensions

Abstract

We present a predictive local field theory for the nonequilibrium dynamics of interacting active Brownian particles with a spherical shape in two spatial dimensions. The theory is derived by a rigorous coarse-graining starting from the Langevin equations that describe the trajectories of the individual particles. For maximal accuracy and generality of the theory, it includes configurational order parameters and derivatives up to infinite order. In addition, we discuss possible approximations of the theory and present reduced models that are easier to apply. We show that our theory contains popular models such as Active Model B + as special cases and that it provides explicit expressions for the coefficients occurring in these and other, often phenomenological, models. As a further outcome, the theory yields an analytical expression for the density-dependent mean swimming speed of the particles. To demonstrate an application of the new theory, we analyze a simple reduced model of the lowest nontrivial order in derivatives, which is able to predict the onset of motility-induced phase separation of the particles. By a linear stability analysis, an analytical expression for the spinodal corresponding to motility-induced phase separation is obtained. This expression is evaluated for the case of particles interacting repulsively by a Weeks-Chandler-Anderson potential. The analytical predictions for the spinodal associated with these particles are found to be in very good agreement with the results of Brownian dynamics simulations that are based on the same Langevin equations as our theory. Furthermore, the critical point predicted by our analytical results agrees excellently with recent computational results from the literature.

arXiv comment15 pages, 2 figures, 2 tables

References in corpus (58)

• Active Particles in Complex and Crowded Environments
• Motility-Induced Phase Separation
• Physics of Microswimmers - Single Particle Motion and Collective Behavior
• Dynamical clustering and phase separation in suspensions of self-propelled colloidal particles
• Athermal Phase Separation of Self-Propelled Particles with no Alignment
• Active Brownian Particles. From Individual to Collective Stochastic Dynamics
• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• How far from equilibrium is active matter?
• When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation
• Pressure is not a state function for generic active fluids
• Emergent behavior in active colloids
• A continuum theory of phase separation kinetics for active Brownian particles
• Phase behaviour of active Brownian particles: The role of dimensionality
• Scalar ${\varphi }^4$ field theory for active-particle phase separation
• Hydrodynamics determines collective motion and phase behavior of active colloids
• Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview
• Pressure and Phase Equilibria in Interacting Active Brownian Spheres
• Full phase diagram of active Brownian disks: from melting to motility-induced phase separation
• Activity-induced phase separation and self-assembly in mixtures of active and passive particles
• Orientational order of motile defects in active nematics
• Arrested phase separation in reproducing bacteria: a generic route to pattern formation?
• Microscopic theory for the phase separation of self-propelled repulsive disks
• Effective Cahn-Hilliard equation for the phase separation of active Brownian particles
• Cooperative Motion of Active Brownian Spheres in Three-Dimensional Dense Suspensions
• Negative interfacial tension in phase-separated active suspensions
• Cluster phases and bubbly phase separation in active fluids: Reversal of the Ostwald process
• Generalized thermodynamics of Motility-Induced Phase Separation: Phase equilibria, Laplace pressure, and change of ensembles
• Tunable long range forces mediated by self-propelled colloidal hard spheres
• Theories of Binary Fluid Mixtures: From Phase-Separation Kinetics to Active Emulsions
• An active approach to colloidal self-assembly
• Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles
• Traveling and resting crystals in active systems
• Critical behavior of active Brownian particles
• A self-driven phase transition drives Myxococcus xanthus fruiting body formation
• A classical nucleation theory description of active colloid assembly
• A particle-field representation unifies paradigms in active matter
• Dynamical Density Functional Theory For Microswimmers
• The self-propelled Brownian spinning top: dynamics of a biaxial swimmer at low Reynolds numbers
• Heat, temperature and Clausius inequality in a model for active brownian particles
• Nonequilibrium dynamics of mixtures of active and passive colloidal particles
• Statistical Properties of Autonomous Flows in 2D Active Nematics
• Active crystals and their stability
• Chemical potential in active systems: predicting phase equilibrium from bulk equations of state?
• Dynamical density functional theory for colloidal particles with arbitrary shape
• Phase separation and large deviations of lattice active matter
• Active Brownian particles near straight or curved walls: Pressure and boundary layers
• Active crystals on a sphere
• Modeling multiple time scales during glass formation with phase-field crystals
• Resting and Traveling Localized States in an Active Phase-Field-Crystal Model
• Local stress and pressure in an inhomogeneous system of spherical active Brownian particles
• Modelling fluids and crystals using a two-component modified phase field crystal model
• A mesoscopic field theoretical approach for active systems
• Differently Shaped Hard Body Colloids in Confinement: From passive to active particles
• Microscopic derivation of the hydrodynamics of active-Brownian-particle suspensions
• Green-Kubo approach to the average swim speed in active Brownian systems
• Pair-distribution function of active Brownian spheres in two spatial dimensions: simulation results and analytic representation
• A microscopic field theoretical approach for binary mixtures of active and passive particles
• Effective run-and-tumble dynamics of bacteria baths

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