Lattice Models of Nonequilibrium Bacterial Dynamics

Abstract

We study a model of self propelled particles exhibiting run and tumble dynamics on lattice. This non-Brownian diffusion is characterised by a random walk with a finite persistence length between changes of direction, and is inspired by the motion of bacteria such as E. coli. By defining a class of models with multiple species of particle and transmutation between species we can recreate such dynamics. These models admit exact analytical results whilst also forming a counterpart to previous continuum models of run and tumble dynamics. We solve the externally driven non-interacting and zero-range versions of the model exactly and utilise a field theoretic approach to derive the continuum fluctuating hydrodynamics for more general interactions. We make contact with prior approaches to run and tumble dynamics off lattice and determine the steady state and linear stability for a class of crowding interactions, where the jump rate decreases as density increases. In addition to its interest from the perspective of nonequilibrium statistical mechanics, this lattice model constitutes and efficient tool to simulate a class of interacting run and tumble models relevant to bacterial motion, so long as certain conditions (that we derive) are met.

33 pages, 12 figures

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Cited by in corpus (107)

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• Hydrodynamics determines collective motion and phase behavior of active colloids
• Active Brownian Particles and Run-and-Tumble Particles: a Comparative Study
• Microscopic theory for the phase separation of self-propelled repulsive disks
• Pattern formation in self-propelled particles with density-dependent motility
• Dynamics of Self-Propelled Particles Under Strong Confinement
• Spontaneous Segregation of Self-Propelled Particles with Different Motilities
• Generalized Thermodynamics of Phase Equilibria in Scalar Active Matter
• Entropy production in field theories without time reversal symmetry: Quantifying the non-equilibrium character of active matter
• Active particles with soft and curved walls: Equation of state, ratchets, and instabilities
• Revisiting the flocking transition using active spins
• Generalized thermodynamics of Motility-Induced Phase Separation: Phase equilibria, Laplace pressure, and change of ensembles
• Active colloidal suspensions: Clustering and phase behavior
• Tunable long range forces mediated by self-propelled colloidal hard spheres
• Entropy production of active particles and for particles in active baths
• Time-(ir)reversibility in active matter: from micro to macro
• Motility-induced phase separation and coarsening in active matter
• Clustering and heterogeneous dynamics in a kinetic Monte-Carlo model of self-propelled hard disks
• Run-and-tumble in a crowded environment: persistent exclusion process for swimmers
• Casimir Effect in Active Matter Systems
• Jamming and Attraction of Interacting Run-and-Tumble Random Walkers
• Exact Hydrodynamic Description of Active Lattice Gases
• Autonomous engines driven by active matter: Energetics and design principles
• Optimizing active work: Dynamical phase transitions, collective motion, and jamming
• Self-Organized Critical Coexistence Phase in Repulsive Active Particles
• Freezing a Flock: Motility-Induced Phase Separation in Polar Active Liquids
• Non-conservative forces and effective temperatures in active polymers
• Critical motility-induced phase separation belongs to the Ising universality class
• Exact stationary state of a run-and-tumble particle with three internal states in a harmonic trap
• Mechanical pressure and momentum conservation in dry active matter
• Phase Separation by Entanglement of Active Polymerlike Worms
• Phase separation and large deviations of lattice active matter
• Motility-induced phase separation of active particles in the presence of velocity alignment
• Kinetic theory for systems of self-propelled particles with metric-free interactions
• Hydrodynamic Limit For An Active Exclusion Process
• Active Microrheology in Active Matter Systems: Mobility, Intermittency and Avalanches
• Exact Solution of Two Interacting Run-and-Tumble Random Walkers with Finite Tumble Duration
• Exact spectral solution of two interacting run-and-tumble particles on a ring lattice
• Active Brownian particles driven by constant affinity
• Disorder-Induced Long-Ranged Correlations in Scalar Active Matter
• Phase diagram of two-lane driven diffusive systems
• Lamellar to micellar phases and beyond: when tactic active systems admit free-energy functionals
• Exact fluctuating hydrodynamics of active lattice gases -- Typical fluctuations
• Active Brownian Particles Escaping a Channel in Single File
• Disordered boundaries destroy bulk phase separation in scalar active matter
• Chemotaxis When Bacteria Remember: Drift versus Diffusion
• Coarsening and clustering in run-and-tumble dynamics with short-range exclusion
• Time-reversal symmetry violations and entropy production in field theories of polar active matter
• Tracer dynamics in one dimensional gases of active or passive particles
• Non-Gaussian noise without memory in active matter
• Disordered exclusion process revisited: some exact results in the low-current regime
• Collective Transport for Active Matter Run and Tumble Disk Systems on a Traveling Wave Substrate
• An Introduction to Motility-Induced Phase Separation
• Inclusions, Boundaries and Disorder in Scalar Active Matter
• Rheology of active fluids
• Activity-induced phase transition in a quantum many-body system
• Capillary action in scalar active matter
• Numerical treatment of the Boltzmann equation for self-propelled particle systems
• Bodies in an Interacting Active Fluid: Far-Field Influence of a Single Body and Interaction Between Two Bodies
• Universality of active wetting transitions
• Dewetting and Spreading Transitions for Active Matter on Random Pinning Substrates
• Non-Gaussian anomalous dynamics in systems of interacting run-and-tumble particles
• Nonexistence of motility induced phase separation transition in one dimension
• Universal properties of repulsive self-propelled particles and attractive driven particles
• Interacting, running and tumbling: the active Dyson Brownian motion
• Efficiency of one-dimensional active transport conditioned on motility
• A comparison of dynamical fluctuations of biased diffusion and run-and-tumble dynamics in one dimension
• Stochastic Kinetic Theory for Collective Behavior of Hydrodynamically Interacting Active Particles
• Kinetic Monte-Carlo Algorithms for Active-Matter systems
• Self-reinforcing directionality generates Lévy walks without the power-law assumption
• Sampling rare fluctuations of discrete-time Markov chains
• Modelling persistence of motion in a crowded environment: the diffusive limit of excluding velocity-jump processes
• Jamming of multiple persistent random walkers in arbitrary spatial dimension
• From a microscopic solution to a continuum description of active particles with a recoil interaction in one dimension
• Lane formation and critical coarsening in a model of bacterial competition
• Superdiffusion in self-reinforcing run-and-tumble model with rests
• Quantifying dissipation in flocking dynamics: When tracking internal states matters
• How motility affects Ising transitions
• Perpendicular and Parallel Phase Separation in Two Species Driven Diffusive Lattice Gases
• Field theories and quantum methods for stochastic reaction-diffusion systems
• Stationary particle currents in sedimenting active matter wetting a wall
• Reentrant condensation transition in a model of driven scalar active matter with diffusivity edge
• Diffusive oscillators capture the pulsating states of deformable particles
• Interfacial and density fluctuations in a lattice model of motility-induced phase separation
• Power-law correlation in the homogeneous disordered state of anisotropically self-propelled systems
• Geometric and Nonequilibrium Criticality in Run-and-Tumble Particles with Competing Motility and Attraction
• Dynamical phase transitions for the activity biased Ising model in a magnetic field
• Localization due to topological stochastic disorder in active networks
• Active velocity processes with suprathermal stationary distributions and long-time tails
• Competition between lanes and transient jammed clusters in driven binary mixtures
• Synthetic Quorum Sensing and Absorbing Phase Transitions in Colloidal Active Matter
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• Counter-flow induced clustering: Exact results
• Geometric view of stochastic thermodynamics for non-equilibrium steady states
• Crystal to liquid cross-over for active particles with inverse-square power-law interaction
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• Bubble formation in active binary mixture model
• Non-additive large deviations function for the particle densities of driven systems in contact
• A regularised Dean-Kawasaki model: derivation and analysis
• An Infinite Set of Integral Formulae for Polar, Nematic, and Higher Order Structures at the Interface of Motility-Induced Phase Separation
• Run-and-tumble particles on a line with a fertile site
• Jamming of active particles in narrow pores: Implications for ratchet effect and diffusion coefficient
• Defect-Mediated Aggregation and Motility-Induced Phase Separation in Self-Propelled Lattice-Gas Active XY Model
• Emergent centrality in rank-based supplanting process