Collective motion

Abstract

We review the observations and the basic laws describing the essential aspects of collective motion -- being one of the most common and spectacular manifestation of coordinated behavior. Our aim is to provide a balanced discussion of the various facets of this highly multidisciplinary field, including experiments, mathematical methods and models for simulations, so that readers with a variety of background could get both the basics and a broader, more detailed picture of the field. The observations we report on include systems consisting of units ranging from macromolecules through metallic rods and robots to groups of animals and people. Some emphasis is put on models that are simple and realistic enough to reproduce the numerous related observations and are useful for developing concepts for a better understanding of the complexity of systems consisting of many simultaneously moving entities. As such, these models allow the establishing of a few fundamental principles of flocking. In particular, it is demonstrated, that in spite of considerable differences, a number of deep analogies exist between equilibrium statistical physics systems and those made of self-propelled (in most cases living) units. In both cases only a few well defined macroscopic/collective states occur and the transitions between these states follow a similar scenario, involving discontinuity and algebraic divergences.

Submitted to Physics Reports, Jan, 2012

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• A question of scale
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Cited by in corpus (758)

• Active Particles in Complex and Crowded Environments
• Non-Hermitian Physics
• Physics of Microswimmers - Single Particle Motion and Collective Behavior
• Dynamical clustering and phase separation in suspensions of self-propelled colloidal particles
• Human Mobility: Models and Applications
• Emergence of macroscopic directed motion in populations of motile colloids
• Quantifying Long-Term Scientific Impact
• Control Principles of Complex Networks
• How far from equilibrium is active matter?
• Fluid dynamics of bacterial turbulence
• Colloquium: Criticality and dynamical scaling in living systems
• Emergent behavior in active colloids
• Living Liquid Crystals
• Universal power law governing pedestrian interactions
• Active matter
• Computational models for active matter
• Orientational order of motile defects in active nematics
• Flocking at a distance in active granular matter
• Microscopic theory for the phase separation of self-propelled repulsive disks
• Clusters, asters and collective oscillations in chemotactic colloids
• Emergent vortices in populations of colloidal rollers
• Self-Propelled Rods: Insights and Perspectives for Active Matter
• Effective Interactions in Active Brownian Suspensions
• Hierarchy measure for complex networks
• Predator-Prey Interactions between Droplets Driven by Nonreciprocal Oil Exchange
• Unstable fronts and stable "critters" formed by microrollers
• Nonreciprocity as a generic route to traveling states
• Diffusion, subdiffusion, and trapping of active particles in heterogeneous media
• Cooperative Motion of Active Brownian Spheres in Three-Dimensional Dense Suspensions
• From Phase to Micro-Phase Separation in Flocking Models: The Essential Role of Non-Equilibrium Fluctuations
• Spontaneous velocity alignment in Motility-induced Phase Separation
• The Rotating Vicsek Model: Pattern Formation and Enhanced Flocking in Chiral Active Matter
• Emergent collective phenomena in a mixture of hard shapes through active rotation
• Collective Motion of Moshers at Heavy Metal Concerts
• Traffic Instabilities in Self-Organized Pedestrian Crowds
• Dynamic clustering and chemotactic collapse of self-phoretic active particles
• Flocking algorithm for autonomous flying robots
• Ferromagnetic and antiferromagnetic order in bacterial vortex lattices
• Flocking and turning: a new model for self-organized collective motion
• Topological Data Analysis of Biological Aggregation Models
• Reentrant Phase Behavior in Active Colloids with Attraction
• Cluster mean-field approach to the steady-state phase diagram of dissipative spin systems
• Large-scales patterns in a minimal cognitive flocking model: incidental leaders, nematic patterns, and aggregates
• Distortion and destruction of colloidal flocks in disordered environments
• The physics of active polymers and filaments
• Emergent oscillations assist obstacle negotiation during ant cooperative transport
• Stabilization of active matter by flow-vortex lattices and defect ordering
• Facets of glass physics
• Nonequilibrium glassy dynamics of self-propelled hard disks
• Revisiting the flocking transition using active spins
• Collective behavior and evolutionary games - An introduction
• Dense active matter model of motion patterns in confluent cell monolayers
• Spatiotemporal order and emergent edge currents in active spinner materials
• Active colloidal suspensions: Clustering and phase behavior
• Entropy production and fluctuation theorems for active matter
• Virial pressure in systems of active Brownian particles
• Model of collective fish behavior with hydrodynamic interactions
• Optimal noise maximizes collective motion in heterogeneous media
• Crowd Behavior Analysis: A Review where Physics meets Biology
• Long-range nematic order and anomalous fluctuations in suspensions of swimming filamentous bacteria
• Data-driven quantitative modeling of bacterial active nematics
• Perspective: Nonequilibrium glassy dynamics in dense systems of active particles
• Long-range Ordering of Vibrated Polar Disks
• Mean-Field Optimal Control
• Critical thresholds in flocking hydrodynamics\\with nonlocal alignment
• Selective and Collective Actuation in Active Solids
• Hydrodynamics of confined active fluids
• Initiation and spread of escape waves within animal groups
• Conformational properties of active semiflexible polymers
• Predator confusion is sufficient to evolve swarming behavior
• Non-Gaussian statistics for the motion of self-propelled Janus particles: experiment versus theory
• Consensus Seeking in Multi-Agent Systems with Multiplicative Measurement Noises
• Time-(ir)reversibility in active matter: from micro to macro
• Active colloids in complex fluids
• Motility-induced phase separation and coarsening in active matter
• Stochastic thermodynamics for active matter
• Emergence and Persistence of Collective Cell Migration on Small Circular Micropatterns
• Clustering and heterogeneous dynamics in a kinetic Monte-Carlo model of self-propelled hard disks
• Circular swimming motility and disordered hyperuniform state in an algae system
• Collective behavior of penetrable self-propelled rods in two dimensions
• Unusual swelling of a polymer in a bacterial bath
• Local equilibrium in bird flocks
• Active colloids in liquid crystals
• Swarming, swirling and stasis in sequestered bristle-bots
• Intracellular transport driven by cytoskeletal motors: General mechanisms and defects
• Modeling a spheroidal microswimmer and cooperative swimming in thin films
• Activity induced synchronization: From Mutual Flocking to Chiral Self-Sorting
• Nonparametric inference of interaction laws in systems of agents from trajectory data
• Emergent comet-like swarming of optically driven thermally active colloids
• Universal survival probability for a $d$-dimensional run-and-tumble particle
• Probing the spatiotemporal dynamics of catalytic Janus particles with single-particle tracking and differential dynamic microscopy
• Exact Hydrodynamic Description of Active Lattice Gases
• Locating the source of diffusion in complex networks by time-reversal backward spreading
• Intermediate scattering function of an anisotropic active Brownian particle
• Invisible control of self-organizing agents leaving unknown environments
• Minimal continuum theories of structure formation in dense active fluids
• First-passage time of run-and-tumble particles
• Properties of pedestrians walking in line: Stepping behavior
• Polarization of active Janus particles
• Optimizing active work: Dynamical phase transitions, collective motion, and jamming
• Emergent spatial structures in flocking models: a dynamical system insight
• Continuous versus Discontinuous Transitions in the $D$-Dimensional Generalized Kuramoto Model: Odd $D$ is Different
• Shape and Displacement Fluctuations in Soft Vesicles Filled by Active Particles
• Freezing a Flock: Motility-Induced Phase Separation in Polar Active Liquids
• Giant Negative Mobility of Janus Particles in a Corrugated Channel
• Engineering sensorial delay to control phototaxis and emergent collective behaviors
• Generic long-range interactions between passive bodies in an active fluid
• Active swarms on a sphere
• Active Brownian motion in a narrow channel
• Structure and dynamics of a self-propelled semiflexible filament
• Active turbulence in microswimmer suspensions -- the role of active hydrodynamic stress and volume exclusion
• From single-particle to collective effective temperatures in an active fluid of self-propelled particles
• Nonmutual torques and the unimportance of motility for long-range order in two-dimensional flocks
• Capturing self-propelled particles in a moving microwedge
• Asymmetric exchange in flocks
• Group chasing tactics: how to catch a faster prey?
• Flocking without alignment interactions in attractive active Brownian particles
• Phase co-existence in bidimensional passive and active dumbbell systems
• Magnetotactic bacteria in a droplet self-assemble into a rotary motor
• Clustering and flocking of repulsive chiral active particles with non-reciprocal couplings
• Contrarians synchronize beyond the limit of pairwise interactions
• Flocking dynamics and mean-field limit in the Cucker-Smale-type model with topological interactions
• From the origin of life to pandemics: Emergent phenomena in complex systems
• Invasion-wave induced first-order phase transition in systems of active particles
• Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics
• Phase diagram of incoherently driven strongly correlated photonic lattices
• Active Brownian particles: Entropy production and fluctuation-response
• Velocity alignment promotes motility-induced phase separation
• Propagation of chaos: a review of models, methods and applications. II. Applications
• Opinion formation and distribution in a bounded confidence model on various networks
• Diffusion of Chiral Janus Particles in a Sinusoidal Channel
• Morphology of clusters of attractive dry and wet self-propelled spherical particle suspensions
• Hyperuniform Active Chiral Fluids with Tunable Internal Structure
• Morphological computation and decentralized learning in a swarm of sterically interacting robots
• Disordered collective motion in dense assemblies of persistent particles
• Motility-sorting of self-propelled particles in micro-channels
• Applicability of Effective Pair Potentials for Active Brownian Particles
• Global regularity for the fractional Euler alignment system
• Quantitative Assessment of the Toner and Tu Theory of Polar Flocks
• Swarm-Enabling Technology for Multi-Robot Systems
• Optimal Network Topology for Effective Collective Response
• Self-Aligning Polar Active Matter
• Conformation and dynamics of a self-avoiding active flexible polymer
• A kinetic model and scaling properties for non-equilibrium clustering of self-propelled particles
• Perspectives on adaptive dynamical systems
• Spontaneous motion and deformation of a self-propelled droplet
• A review of active matter reviews
• Swimming in Complex Fluids
• Self propelled particle transport in regular arrays of rigid asymmetric obstacles
• Kinetic theory for systems of self-propelled particles with metric-free interactions
• Collective Motion with Anticipation: Flocking, Spinning, and Swarming
• Flocking in complex environments -- attention trade-offs in collective information processing
• Anomalous Topological Active Matter
• Learning to flock through reinforcement
• Mixing and demixing of binary mixtures of polar chiral active particles
• Effective temperatures in inhomogeneous passive and active bidimensional Brownian particle systems
• \textit{C. elegans} collectively forms dynamical networks
• Design of nematic liquid crystals to control microscale dynamics
• Simultaneous Phase Separation and Pattern Formation in Chiral Active Mixtures
• Condensation transition in the late-time position of a Run-and-Tumble particle
• Emergent Structural Mechanisms for High-Density Collective Motion Inspired by Human Crowds
• D-dimensional oscillators in simplicial structures: odd and even dimensions display different synchronization scenarios
• Antipolar ordering of topological defects in active liquid crystals
• Chirality separation of mixed chiral microswimmers in a periodic channel
• Collective forces in scalar active matter
• Pattern-induced local symmetry breaking in active matter systems
• Universal Properties of a Run-and-Tumble Particle in Arbitrary Dimension
• Mesoscale pattern formation of self-propelled rods with velocity reversal
• Self-Organization and Artificial Life
• Order and Information in the Patterns of Spinning Magnetic Micro-disks at the Air-water Interface
• Understanding Collective Dynamics of Soft Active Colloids by Binary Scattering
• Autonomous waves and global motion modes in living active solids
• Dynamics of a homogeneous active dumbbell system
• Fishing out collective memory of migratory schools
• Intermediate scattering function of an anisotropic Brownian circle swimmer
• Nutrient transport driven by microbial active carpets
• Giant fluctuations and structural effects in a flocking epithelium
• Discontinuous fluidisation transition in assemblies of actively-deforming particles: A new paradigm for collective motion in dense active materials
• Light Sailboats: Laser driven autonomous microrobots
• Collective motion of groups of self-propelled particles following interacting leaders
• Silent Flocks
• Dynamic Clustering in Suspension of Motile Bacteria
• Resilience and Controllability of Dynamic Collective Behaviors
• Self-organization of swimmers drives long-range fluid transport in bacterial colonies
• Light, Matter, Action: Shining light on active matter
• Dynamics of social contagions with limited contact capacity
• Phase behaviour and dynamical features of a two-dimensional binary mixture of active/passive spherical particles
• Robustness of flight leadership relations in pigeons
• Spontaneous vortex formation by microswimmers with retarded attractions
• A Critical-like Collective State Leads to Long-range Cell Communication in Dictyostelium discoideum Aggregation
• Analyzing Collective Motion with Machine Learning and Topology
• Phase transition and diffusion among socially interacting self-propelled agents
• Traveling Bands, Clouds, and Vortices of Chiral Active Matter
• Effects of heterogeneous social interactions on flocking dynamics
• Active dumbbells: dynamics and morphology in the coexisting region
• First order phase transition in a self-propelled particles model with variable angular range of interaction
• Synchronization in dynamical networks of locally coupled self-propelled oscillators
• Giant Kovacs-Like Memory Effect for Active Particles
• Effective diffusion coefficient including the Marangoni effect
• Thermodynamics of emergent structure in active matter
• Active particles in heterogeneous media display new physics: existence of optimal noise and absence of bands and long-range order
• Effect of polydispersity on the dynamics of active Brownian particles
• Biological Modelling with Nonlocal Advection Diffusion Equations
• Small noise may diversify collective motion in Vicsek model
• Oscillatory chiral flows in confined active fluids with obstacles
• Dry Active Matter exhibits a self-organized 'Cross Sea' Phase
• Ratchet transport powered by chiral active particles
• Nonequilibrium Brownian motion beyond the effective temperature
• Wetting Transitions Displayed by Persistent Active Particles
• Asymptotic flocking in the Cucker-Smale model with reaction-type delays in the non-oscillatory regime
• Marginal speed confinement resolves the conflict between correlation and control in natural flocks of birds
• Interpretable machine learning for inferring the phase boundaries in a nonequilibrium system
• Polar state memory in active fluids
• Phase Separation and Emergent Structures in an Active Nematic
• Characterization of MIPS in a suspension of repulsive Active Brownian Particles through dynamical features
• Active motion on curved surfaces
• Statistical properties of swarms of self-propelled particles with repulsions across the order-disorder transition
• Active Matter Class with Second-Order Transition to Quasi-Long-Range Polar Order
• Group performance is maximized by hierarchical competence distribution
• Dynamical renormalization group approach to the collective behaviour of swarms
• Non-equilibrium fluctuations and nonlinear response of an active bath
• Self-propelled chimeras
• Active Brownian particle in harmonic trap: exact computation of moments, and re-entrant transition
• Short-range interaction vs long-range correlation in bird flocks
• Collective behavior of self-steering active particles with velocity alignment and visual perception
• Anatomy of Leadership in Collective Behaviour
• Critical Phenomena in Active Matter
• Selective social interactions and speed-induced leadership in schooling fish
• Modelling collective motion based on the principle of agency
• Model of human collective decision-making in complex environments
• Pattern formation in active particle systems due to competing alignment interactions
• Oscillatory Motion of a Camphor Grain in a One-Dimensional Finite Region
• Vortex dynamics and Lagrangian statistics in a model for active turbulence
• Emergent probability fluxes in confined microbial navigation
• Active Brownian Particles Escaping a Channel in Single File
• Multi-stable free states of an active particle from a coherent memory dynamics
• Consensus reaching in swarms ruled by a hybrid metric-topological distance
• Emergence of Lévy Walks in Systems of Interacting Individuals
• The Brownian Mean Field model
• Disordered boundaries destroy bulk phase separation in scalar active matter
• Solute Induced Jittery Motion of Self-Propelled Droplets
• Superdiffusion, large-scale synchronization and topological defects
• Influence of Sensorial Delay on Clustering and Swarming
• The entropic basis of collective behaviour
• Active Brownian Rods
• Polar flock in the presence of random quenched rotators
• Solvable Dynamics of Coupled High-Dimensional Generalized Limit-Cycle Oscillators
• Inverse Reinforcement Learning in Swarm Systems
• Hydrodynamic Swarming of Thermally Active Dimeric Colloids
• Global existence and stability of nearly aligned flocks
• A Critical Assessment of the Boltzmann Approach for Active Systems
• Coarsening and clustering in run-and-tumble dynamics with short-range exclusion
• Chapman-Enskog expansion for the Vicsek model of self-propelled particles
• Gliding filament system giving both orientational order and clusters in collective motion
• Micro-flock patterns and macro-clusters in chiral active Brownian disks
• Thermal and Athermal Swarms of Self-Propelled Particles
• Simflowny 2: An upgraded platform for scientific modeling and simulation
• Energy transfer between colloids via critical interactions
• Transient dispersion process of active particles
• Collective dynamics in systems of active Brownian particles with dissipative interactions
• Active Brownian particles: mapping to equilibrium polymers and exact computation of moments
• Scale-free behavioral cascades and effective leadership in schooling fish
• From scalar to polar active matter: Connecting simulations with mean-field theory
• Self-Organized Vortices of Circling Self-Propelled Particles and Curved Active Flagella
• Active particles powered by Quincke rotation in a bulk fluid
• Tracking collective cell motion by topological data analysis
• Motion of two micro-wedges in a turbulent bacterial bath
• Stochastic cycle selection in active flow networks
• Sorting of chiral active particles driven by rotary obstacles
• Body size affects the strength of social interactions and spatial organisation of a schooling fish (Pseudomugil signifer)
• Glassy dynamics of a model of bacterial cytoplasm with metabolic activities
• Universal phenomenology at critical exceptional points of nonequilibrium $O(N)$ models
• Diffusive regimes in a two-dimensional chiral fluid
• When costly migration helps to improve cooperation
• Active matter invasion of a viscous fluid: unstable sheets and a no-flow theorem
• Thermodynamics and computation during collective motion near criticality
• Effect of Vision Angle on the Phase Transition in a Flocking Behavior of Animal Groups
• Macroscopic Time-Reversal Symmetry Breaking at Nonequilibrium Phase Transition
• Collective mechano-response dynamically tunes cell-size distributions in growing bacterial colonies
• Markovian robots: minimal navigation strategies for active particles
• Fundamental ingredients for the emergence of discontinuous phase transitions in the majority vote model
• Semiflexible polymer in a gliding assay: reentrant transition, role of turnover and activity
• Morphological transitions of active Brownian particle aggregates on porous walls
• Activity-induced phase transition in a quantum many-body system
• Collective dynamics of soft active particles
• Numerical treatment of the Boltzmann equation for self-propelled particle systems
• Threefold way to the dimension reduction of dynamics on networks: an application to synchronization
• Emergence of collective motion in a model of interacting Brownian particles
• A note on the duality between interaction responses and mutual positions in flocking and schooling
• Towards a quantitative kinetic theory of polar active matter
• Polarization-Density Patterns of Active Particles in Motility Gradients
• Collective behavior of Vicsek particles without and with obstacles
• Systematic extension of the Cahn-Hilliard model for motility-induced phase separation
• Existence and stability of unidirectional flocks in hydrodynamic Euler Alignment systems
• Blood crystal: emergent order of red blood cells under wall-confined shear flow
• Influence of interaction softness in phase separation of active particles
• Active matter beyond mean-field: Ring-kinetic theory for self-propelled particles
• Optimal navigation strategy of active Brownian particles in target-search problems
• An agent-based framework of active matter with applications in biological and social systems
• Bodies in an Interacting Active Fluid: Far-Field Influence of a Single Body and Interaction Between Two Bodies
• Active particles with polar alignment in ring-shaped confinement
• Flowing active liquids in a pipe: Hysteretic response of polar flocks to external fields
• Collective behavior of self-propelled rods with quorum sensing
• Rheology of active polar emulsions: from linear to unidirectional and unviscid flow, and intermittent viscosity
• Motility-Induced Clustering and Meso-Scale Turbulence in Active Polar Fluids
• A Boltzmann model for rod alignment and schooling fish
• Aspects of the density field in an active nematic
• Scale free chaos in the confined Vicsek flocking model
• Active matter, microreversibility, and thermodynamics
• Particle-scale statistical theory for hydrodynamically induced polar ordering in microswimmer suspensions
• Configuration Dynamics of a Flexible Polymer Chain in a Bath of Chiral Active Particles
• Speed-Dispersion Induced Alignment : a 1D model inspired by swimming droplets experiments
• Single particle motion and collective dynamics in Janus motor systems
• Brownian Molecules Formed by Delayed Harmonic Interactions
• Guiding self-assembly of active colloids by temporal modulation of activity
• From Clarkia to Escherichia and Janus: the physics of natural and synthetic active colloids
• Exact coherent structures and phase space geometry of pre-turbulent 2D active nematic channel flow
• Hybrid dynamics in delay-coupled swarms with "mothership" networks
• Universality of active wetting transitions
• Microscopic theory for the diffusion of an active particle in a crowded environment
• Scaling of cluster growth for coagulating active particles
• Development of swarm behavior in artificial learning agents that adapt to different foraging environments
• Learning Anisotropic Interaction Rules from Individual Trajectories in a Heterogeneous Cellular Population
• Emergent behaviors in group ring flocks
• Asynchrony promotes polarized collective motion in attraction based models
• Noisy Pursuit and Pattern Formation of Self-Steering Active Particles
• Formation and collision of traveling bands in interacting deformable self-propelled particles
• A simple cognitive model explains movement decisions during schooling in zebrafish
• Contrarian compulsions produce time dependent flocking of active particles
• Hydrodynamic effects on the liquid-hexatic transition of active colloids
• Kuramoto dilemma alleviated by optimizing connectivity and rationality
• Sufficient conditions for wave instability in three-component reaction-diffusion systems
• Interpretable Conservation Law Estimation by Deriving the Symmetries of Dynamics from Trained Deep Neural Networks
• Emerging mesoscale flows and chaotic advection in dense active matter
• Phase Coexistence Implications of Violating Newton's Third Law
• Global Thermodynamics for Heat Conduction Systems
• Complex Network Structure of Flocks in the Standard Vicsek Model
• Non-symmetric interactions trigger collective swings in globally ordered systems
• Coherent motion of monolayer sheets under confinement and its pathological implications
• Strong collective currents of gold nanoparticles in an optical vortex lattice
• Guiding the Self-organization of Cyber-Physical Systems
• Anomalous segregation dynamics of self-propelled particles
• Impact of chirality on active Brownian particle: Exact moments in two and three dimensions
• Velocity and Speed Correlations in Hamiltonian Flocks
• Majority vote model with ancillary noise in complex networks
• Competing Active and Passive Interactions Drive Amoeba-like Living Crystallites and Ordered Bands
• Intermittent relaxation and avalanches in extremely persistent active matter
• Brownian particle in a Poisson-shot-noise active bath: exact statistics, effective temperature, and inference
• Promoting collective motion of self-propelled agents by distance-based influence
• Curvature-controlled defect dynamics in active systems
• Dispersion of activity at an active-passive nematic interface
• Synchronization on the circle
• A multi-layer model for self-propelled disks interacting through alignment and volume exclusion
• Attractor-driven matter
• Flocking: Influence of Metric Versus Topological Interactions
• Spatial organization and cyclic dominance in asymmetric predator-prey spatial games
• Pattern Formation in Populations with Density-Dependent Movement and Two Interaction Scales
• A geometric approach to self-propelled motion in isotropic and anisotropic environments
• Effects of shady environments on fish collective behavior
• Coarsening Dynamics in the Vicsek Model of Active Matter
• Testing a thermodynamic approach to collective animal behavior in laboratory fish schools
• Agent-Based Models in Social Physics
• Adaptive network models of collective decision making in swarming systems
• Hohenberg-Mermin-Wagner type theorems for equilibrium models of flocking
• Reaction processes among self-propelled particles
• Vortex phase matching of a self-propelled model of fish with autonomous fin motion
• Extended Poisson-Kac theory: A unifying framework for stochastic processes with finite propagation velocity
• The structure and dynamics of self-assembling colloidal monolayers in oscillating magnetic fields
• Swimming suppresses correlations in dilute suspensions of pusher microorganisms
• Mixing and de-mixing of model microswimmers in bi-motility mixtures
• Milling and meandering: Flocking dynamics of stochastically interacting agents with a field of view
• The role of neighbours selection on cohesion and order of swarms
• Self-propelled Vicsek particles at low speed and low density
• Linear response to leadership, effective temperature and decision making in flocks
• Emergence in artificial life
• Diffusion of chiral active particles in a Poiseuille flow
• Optimal strategies for driving a mobile agent in a guidance by repulsion model
• Discovering dynamic laws from observations: the case of self-propelled, interacting colloids
• Collective Flows Drive Cavitation in Spinner Monolayers
• Heating leads to liquid-crystal and crystalline order in a two-temperature active fluid of rods
• Spatio-temporal correlations in models of collective motion ruled by different dynamical laws
• Controlled pattern formation of stochastic Cucker-Smale systems with network structures
• Efficiency of one-dimensional active transport conditioned on motility
• Environmental Memory Boosts Group Formation of Clueless Individuals
• Stable Swarming Using Adaptive Long-range Interactions
• Effective Entropy Production and Thermodynamic Uncertainty Relation of Active Brownian Particles
• Metastable Clusters and Channels Formed by Active Particles with Aligning Interactions
• Ordering dynamics of self-propelled particles in an inhomogeneous medium
• Unstable oscillations and bistability in delay-coupled swarms
• Dynamic Clustering of Active Rings
• Polar active liquids: a universal classification rooted in nonconservation of momentum
• Re-entrant phase separation in nematically aligning active polar particles
• Hunting active Brownian particles: Learning optimal behavior
• Clustering determines the survivor for competing Brownian and Lévy walkers
• Stokesian swimmers and active particles
• Signatures of criticality in turning avalanches of schooling fish
• Dressed Active Particles in Spherical Crystals
• Entropy production by active particles: Coupling of odd and even functions of velocity
• Focusing of Active Particles in a Converging Flow
• Topological sound in active-liquid metamaterials
• Solitary states in the mean-field limit
• Power law observed in the motion of an asymmetric camphor boat under viscous conditions
• Microscopic field theory for structure formation in systems of self-propelled particles with generic torques
• Hydrodynamically-bound states of a pair of microrollers: a dynamical system insight
• An all-leader agent-based model for turning and flocking birds
• Emergence of a giant rotating cluster of fish in three dimensions by local interactions
• A Quantitative Kinetic Theory of Flocking with Three-Particle-Closure
• Inter-particle adhesion regulates the surface roughness of growing dense three-dimensional active particle aggregates
• Active dry granular flows: rheology and rigidity transitions
• Individual and collective dynamics of self-propelled soft particles
• Linear stability of an active fluid interface
• Effective equilibrium picture in $xy-$model with exponentially correlated noise
• Command of Collective Dynamics by Topological Defects in Spherical Crystals
• Identifying manifolds underlying group motion in Vicsek agents
• Two-temperature activity induces liquid-crystal phases inaccessible in equilibrium
• Active spheroids in viscosity gradients
• Leveraging Memory Effects and Gradient Information in Consensus-Based Optimization: On Global Convergence in Mean-Field Law
• Mechanisms of carrier transport induced by a microswimmer bath
• Do hydrodynamically assisted binary collisions lead to orientational ordering of microswimmers?
• Energy cost study for controlling complex social networks with conformity behavior
• Swarming transitions in hierarchical societies
• Fluctuations of rotational and translational degrees of freedom in an interacting active dumbbell system
• Nucleation-induced transition to collective motion in active systems
• The Hurst exponents of Nitzschia sp. diatom trajectories observed by light microscopy
• Emergent pattern formation in an interstitial biofilm
• Lane formation dynamics of oppositely self-driven binary particles: Effects of density and finite system size
• Simulation of microswimmer hydrodynamics with multiparticle collision dynamics
• Relaxation in a Phase-separating Two-dimensional Active Matter System with Alignment Interaction
• Alignment interactions drive structural transitions in biological tissues
• Active polar flock with birth and death
• Hydrodynamic pursuit by cognitive self-steering microswimmers
• Diffusion of a tracer in a dense mixture of soft particles connected to different thermostats
• Heterogeneity extends criticality
• Evidence of fluctuation-induced first-order phase transition in active matter
• Kinetic Monte-Carlo Algorithms for Active-Matter systems
• Free utility model for explaining the social gravity law
• Molecular theory of Langevin dynamics for active self-diffusiophoretic colloids
• Renormalization group crossover in the critical dynamics of field theories with mode coupling terms
• Phase transitions in a multistate majority-vote model on complex networks
• Self-generated gradients stabilize the hydrodynamic instabilities in active suspensions
• Explosive Phase Transition in a Majority-Vote Model with Inertia
• Calculation of displacement correlation tensor indicating vortical cooperative motion in two-dimensional colloidal liquids
• Gregarious vs Individualistic Behavior in Vicsek Swarms and the Onset of First-Order Phase Transitions
• Swirling due to misaligned perception-dependent motility
• Large density expansion of a hydrodynamic theory for self-propelled particles
• Collective olfactory search in a turbulent environment
• Gravity induced formation of spinners and polar order of spherical microswimmers on a surface
• Dynamic ordering transitions in charged solid
• Percolation transition in phase separating active fluid
• Density distributions and depth in flocks
• Spontaneous wave formation in stochastic self-driven particle systems
• Overlapping modularity at the critical point of k-clique percolation
• Hydrodynamic Equations for Flocking Models without Velocity Alignment
• Controlling the transport of active matter in disorderd lattices of asymmetrical obstacles
• Selective decision-making and collective behavior of fish by the motion of visual attention
• From single to collective motion of social amoebae: a computational study of interacting cells
• Emergence of a single cluster in Vicsek's model at very low noise
• Polymer translocation through nanopore assisted by an environment of active rods
• Self-propulsion with speed and orientation fluctuation: exact computation of moments and dynamical bistabilities in displacement
• Intermittent direction reversals of moving spatially-localized turbulence observed in two-dimensional Kolmogorov flow
• Two floating camphor particles interacting through lateral capillary force
• Self-Elongation with Sequential Folding of a Filament of Bacterial Cells
• Flocking of Active Particles in a Turbulent Flow
• Emergent pattern formation of active magnetic suspensions in an external field
• A qualitative mathematical model of the immune response under the effect of stress
• Minimal stochastic field equations for one-dimensional flocking
• Dynamical anomalies and structural features of Active Brownian Particles characterised by two repulsive length scales
• Novel Stability Conditions for Nonlinear Monotone Systems and Consensus in Multi-Agent Networks
• Mobility driven coexistence of living organisms
• The microscopic phase density functional approach to the construction of the kinetic and hydrodynamic description for the system of self-propelled particles
• Critical transition for colliding swarms
• Meta-Structures: The Search of Coherence in Collective Behaviours (without Physics)
• GPU parallel simulation algorithm of Brownian particles with excluded volume using Delaunay triangulations
• Polar swimmers induce several phases in active nematics
• Order-disorder transition in active nematic: A lattice model study
• Swinging Motion of Active Deformable Particles in Poiseuille Flow
• Pattern formation and phase transition in the collective dynamics of a binary mixture of polar self-propelled particles
• Environmental path-entropy and collective motion
• Optimal forwarding ratio on dynamical networks with heterogeneous mobility
• A discrete in continuous mathematical model of cardiac progenitor cells formation and growth as spheroid clusters (Cardiospheres)
• Controlling Inter-Particle Distances in Crowds of Motile, Cognitive, Active Particles
• Collective behavior of squirmers in thin films
• Collective Hall current in chiral active fluids: Coupling of phase and mass transport through traveling bands
• Predicting the long-term collective behaviour of fish pairs with deep learning
• Absence of jamming in ant trails: Feedback control of self propulsion and noise
• Tuning attraction and repulsion between active particles through persistence
• Order-disorder transition in repulsive self-propelled particle systems
• Emergent Synchronization and Flocking in Purely Repulsive Self-Navigating Particles
• Crossover between parabolic and hyperbolic scaling, oscillatory modes and resonances near flocking
• From a microscopic solution to a continuum description of active particles with a recoil interaction in one dimension
• Density-Independent Model of Self-Propelled Particles
• Turbulence-induced clustering in compressible active fluids
• Deriving hydrodynamic equations from dry active matter models in three dimensions
• Traveling pulse emerges from individuals coordinating their stop-and-go motion: a case study in sheep
• Collective Motion of Quincke Rollers with Fully Resolved Hydrodynamics
• Aging or DEAD: origin of the non-monotonic response to weak self-propulsion in active glasses
• Oscillation and collective conveyor of water-in-oil droplets by microfluidic bolus flow
• Optimal collision avoidance in swarms of active Brownian particles
• A continuum model for nematic alignment of self-propelled particles
• Magnetized granular particles running and tumbling on $S^1$
• Stability of milling patterns in self-propelled swarms on surfaces
• Superposition principle and schemes for Measure Differential Equations
• Collective orientation of an immobile fish school, effect on rheotaxis
• Bulk condensation by an active interface
• Drift induced by dissipation
• Exact hydrodynamics and onset of phase separation for an active exclusion process
• Mean field theory of chaotic insect swarms
• Noise-induced vortex reversal of self-propelled particles
• Learning phase transitions from regression uncertainty: A new regression-based machine learning approach for automated detection of phases of matter
• Sociohydrodynamics: data-driven modelling of social behavior
• Consensus and Information Cascades in Game-Theoretic Imitation Dynamics with Static and Dynamic Network Topologies
• Toward Task Capable Active Matter: Learning to Avoid Clogging in Confined Collectives via Collisions
• Synchronization in leader-follower switching dynamics
• Heterophilious dynamics enhances consensus
• Trapping of an active Brownian particle at a partially absorbing wall
• Flocking dynamics with voter-like interactions
• Generalized persistence dynamics for active motion
• Theoretical constraints imposed by gradient detection and dispersal on microbial size in astrobiological environments
• Tagged active particle: probability distribution in a slowly varying external potential is determined by effective temperature obtained from the Einstein relation
• Designing circle Swimmers: Principles and strategies
• Alignment Destabilizes Crystal Orders in Active Systems
• Pairing-induced motion of source and inert particles driven by surface tension
• Biohybrid active matter -- the emergent properties of cell-mediated microtransport
• Propagation of chaos: a review of models, methods and applications. I. Models and methods
• Data-driven discovery of stochastic dynamical equations of collective motion
• Emergence of collective propulsion through cell-cell adhesion
• Fighting the flow: the stability of model flocks in a vortical flow
• Capturing pattern bi-stability dynamics in delay-coupled swarms
• Braiding a flock: winding statistics of interacting flying spins
• Non-ideal rheology of semidilute bacterial suspensions
• Transport coefficients of self-propelled particles. II. Numerics for vorticity fluctuations and the reverse perturbation method
• Detecting and characterizing phase transitions in active matter using entropy
• Stability of flocking in the reciprocal two-species Vicsek model: Effects of relative population, motility, and noise
• Transport coefficients of self-propelled particles: Reverse perturbations and transverse current correlations
• Phase transitions on a class of generalized Vicsek-like models of collective motion
• Long-wavelength instabilities in a system of interacting active particles
• Emergent dynamics of the Lohe Hermitian sphere model with frustration
• Statistical complexity measures as telltale of relevant scales in emergent dynamics of spatial systems
• Diffusive oscillators capture the pulsating states of deformable particles
• Rototaxis: localization of active motion under rotation
• Role of interfacial friction for flow instabilities in a thin polar ordered active fluid layer
• Bulk topological states in a new collective dynamics model
• Scalar model of flocking dynamics on complex social networks
• Dynamics of Deformable Active Particles under External Flow Field
• Pattern formation and the mechanics of a motor-driven filamentous system confined by rigid membranes
• The politics of physicists social models
• Kinetic description and macroscopic limit of swarming dynamics with continuous leader-follower transitions
• Short-time dynamics in active systems: the Vicsek model
• Collective response to local perturbations: how to evade threats without losing coherence
• Flock2: A model for orientation-based social flocking
• Measurements and modelling of induced flow in collective vertical migration
• Complete aggregation of the Lohe tensor model with the same free flow
• The collective motion of self-propelled particles affected by the spatial-dependent noise
• Flocking at the edge of chaos
• Social Phases in Human Movement
• Cell Motion Alignment as Polarity Memory Effect
• Collision-induced torque mediates transition of chiral dynamic patterns formed by active particles
• Nonquenched rotators ease flocking and memorise it
• Mean Field Model for Collective Motion Bistability
• On Kinetic Equations Modeling Evolution of Systems in Mathematical Biology
• Keeping speed and distance for aligned motion
• Vectorial active matter on the lattice: polar condensates and nematic filaments
• Formation of Spiral-Coils among Self-Propelled Chains
• From Flocking to Condensation: Collective Dynamics in Binary Chiral Active Matter
• Boundary induced convection in a collection of polar self-propelled particles
• Active Phases for Particles on Resource Landscapes
• Flip motion of solitary wave in an Ising-type Vicsek model
• Influence of distinct kinds of temporal disorder in discontinuous phase transitions
• On the Schrödinger-Lohe hierarchy for aggregation and its emergent dynamics
• Spontaneous Spatiotemporal Ordering of Shape Oscillations Enhances Cell Migration
• Low-temperature marginal ferromagnetism explains anomalous scale-free correlations in natural flocks
• Active-passive mixtures with bulk loading: a minimal active engine in one dimension
• Topological transition in filamentous cyanobacteria: from motion to structure
• How reciprocity impacts ordering and phase separation in active nematics?
• Emergent clustering due to quorum sensing interactions in active matter
• Aversion of face-to-face situation of pedestrians eases crowding condition
• Propagating wave in the flock of self-propelled particles
• Tunable Memory and Activity of Quincke Particles in Micellar Fluid
• Effect of anisotropy on the formation of active particle films
• Fluctuation Theorems for Heat exchanges between passive and active baths
• Vortex with four-fold defect lines in a simple model of self-propelled particles
• An Alignment-Free Explanation for Collective Predator Evasion in Moving Animal Groups
• Geometry for a `penguin-albatross' rookery
• Micellization in active matter of asymmetric self-propelled particles: Experiments
• Gaussian theory for spatially distributed self-propelled particles
• The precursor of the critical transitions in majority vote model with the noise feedback from the vote layer
• Free energy of a chemotactic model with nonlinear diffusion
• How zealots affect the energy cost for controlling complex social networks
• A generic coupling between internal states and activity leads to activation fronts and criticality in active systems
• Active particle dynamics beyond the jamming density
• Ordering kinetics in the active Ising model
• Phase Transitions in Models of Bird Flocking
• On the identifiability of interaction functions in systems of interacting particles
• Self-Aligning Active Agents with Inertia and Active Torque
• Identifiability of interaction kernels in mean-field equations of interacting particles
• Convergence of a first-order consensus-based global optimization algorithm
• Active matter clusters at interfaces
• Simple mathematical model for a pairing-induced motion of active and passive particles
• On the detection and identification of edge disconnections in a multi-agent consensus network
• Unravelling the puzzling intermediate states in the Biham-Middleton-Levine traffic mode
• Minimal mechanism for flocking in phoretically interacting active particles
• Lateral contact yields longitudinal cohesion in active undulatory systems
• Hydrodynamics of Active Lévy Matter
• Active Matter Flocking via Predictive Alignment
• Percolation transitions in the binary mixture of active Brownian particles with different softness
• Spatial flocking: Control by speed, distance, noise and delay
• Exploring the onset of collective motion in self-organised trails of social organisms
• Meanfield games and model predictive control
• Propagating speed waves in flocks: a mathematical model
• Symmetry and stability of orientationally ordered collective motions of self-propelled, semiflexible filaments
• A note on Spontaneous Symmetry Breaking in flocks of birds
• Birds on a Wire
• Hermitian and non-Hermitian topology in active matter
• Discrete Laplacian Thermostat for Spin Systems with Conserved Dynamics
• Visual collective behaviors on spherical robots
• Mixed-Symmetry Shell-Model Calculations
• Modeling of chemically active particles at an air-liquid interface
• Synchronized Rotations of Active Particles on Chemical Substrates
• Noisy pursuit by a self-steering active particle in confinement
• Collective excitations in active solids featuring alignment interactions
• Cucker-Smale flocking with alternating leaders
• Emergent States in Systems of Chiral Self-Propelled Rods
• Quaternions in collective dynamics
• Scale-free chaos in the 2D harmonically confined Vicsek model
• One- and Two-dimensional Solitary Wave States in the Nonlinear Kramers Equation with Movement Direction as a Variable
• Robust Design from Systems Physics
• Noisy multistate voter model for flocking in finite dimensions
• Emergent short-range repulsion for attractively coupled active particles
• Self-Propelled Collective Motion with Multiplicative Scalar Noise
• Convergence speed of unsteady distributed consensus: decay estimate along the settling spanning-trees
• Solitary wave state in the nonlinear Kramers equation for self-propelled particles
• Effect of gravitational field on collective motion of fish
• Power laws of natural swarms are fingerprints of an extended critical region
• Aster Swarming by Collective Mechanics of Dyneins and Kinesins
• Convergence and error estimates for time-discrete consensus-based optimization algorithms
• Pattern Formation and Flocking for Particles Near the Jamming Transition on Resource Gradient Substrates
• The Emergence of Lines of Hierarchy in Collective Motion of Biological Systems
• On Kinetic Equations for Collisional Dynamics of Active Soft Condensed Matter
• Nonlinear dynamics and emergent statistical regularity in classical Lennard-Jones three-body system upon disturbance
• Critical assessment of von Mises distribution and an infinite series ansatz for self-propelled particles
• Asymmetric Nucleation Processes in Spontaneous Mode Switch of Active Matter
• Global well-posedness for the Euler alignment system with mildly singular interactions
• Patterns of active dipolar particles in external magnetic fields
• Strain rate controls alignment in growing bacterial monolayers
• Collective dynamics of densely confined active polar disks with self- and mutual alignment
• Asymptotic behavior of the linear consensus model with delay and anticipation
• Active Lévy Matter: Anomalous Diffusion, Hydrodynamics and Linear Stability
• Ergostatting and Thermostatting at a Fixed Point
• Chirality, confinement and dimensionality govern re-entrant transitions in active matter
• Anti-hyperuniform Critical States of Active Topological Defects
• Active particles in reactive disordered media: how does adsorption affects diffusion?
• Most probable paths for active Ornstein-Uhlenbeck particles
• Sparse Stabilization and Control of Alignment Models
• Learning interaction rules from multi-animal trajectories via augmented behavioral models
• Nematic alignment of self-propelled particles in the macroscopic regime
• Distributed Alignment Processes with Samples of Group Average
• Band structure in collective motion with quenched range of interaction
• Complexity, Development, and Evolution in Morphogenetic Collective Systems
• Cluster Prediction for Opinion Dynamics from Partial Observations
• Transient phases in the Vicsek model of flocking
• Persistent exclusion process with time-periodic drive
• Entropy production in active Rouse polymers
• Flocking transition in phoretically interacting active particles with pinning disorder
• American coot collective on-water dynamics
• Active chain spirograph: Dynamic patterns formed in extensible chains due to follower activity
• Traveling Fronts and the Smoothing of the Collective-Motion Phase Transition in Vibrated Polar Disks
• Soliton approximation in continuum models of leader-follower behavior
• Flocking dynamics mediated by weighted social networks
• Zoology of collective patterns modulated by non-reciprocal, long-range interactions
• Universality in Incompressible Active Fluid: Effect of Non-local Shear Stress
• Swarming collapse under limited information flow between individuals
• Modeling of pedestrians
• Outdoor flocking and formation flight with autonomous aerial robots
• A Data-Driven Statistical Description for the Hydrodynamics of Active Matter
• Dynamics in an emergent quantum-like state space generated by a nonlinear classical network
• An efficient method for sorting and selecting for social behaviour
• Decentralized Circle Formation Control for Fish-like Robots in the Real-world via Reinforcement Learning
• Defect-mediated dynamics of coherent structures in active nematics
• Collective motion from quantum-inspired dynamics in visual perception
• Boltzmann approach to collective motion via nonlocal visual interaction
• On the stochastic flocking of the Cucker-Smale flock with randomly switching topologies
• Models of Animal Behavior as Active Particle Systems with Nonreciprocal Interactions
• Emergence of stochastic flocking for the discrete Cucker-Smale model with randomly switching topologies
• The $\mathbf{Q}$-tensor Model with Uniaxial Constraint
• Jamming in a lattice model of stochastically interacting agents with a field of view
• Distributed Neighbor Selection in Multi-agent Networks
• Analysis of aligning active local searchers orbiting around their common home position
• Energy-efficient flocking with nonlinear navigational feedback
• Phototactic cyanobacteria as an active matter system
• Coupled Self-Organized Hydrodynamics and Stokes models for suspensions of active particles
• Leader formation with mean-field birth and death models
• Macroscopic limit of a Fokker-Planck model of swarming rigid bodies
• Asymptotic theory of hydrodynamic interactions between slender filaments
• Intrinsic statistical separation of subpopulations in heterogeneous collective motion via dimensionality reduction
• Aspect-ratio-dependent void formation in active rhomboidal and elliptical particle systems
• Quantification of collective behaviour via causality analysis
• Run-and-tumble particles on a line with a fertile site
• Network community detection via iterative edge removal in a flocking-like system
• Phenomenological modeling of the motility of self-propelled microorganisms
• Active osmotic-like pressure on permeable inclusions
• Collective motion of oscillatory walkers
• On Cucker-Smale model with noise and delay
• Scaling behavior of transient dynamics of vortex-like states in self-propelled particles
• Queuing models for abstracting interactions in Bacterial communities
• Bugs with Features: Vision-Based Fault-Tolerant Collective Motion Inspired by Nature
• Transverse Self-Propulsion Enhances the Aggregation of Active Dumbbells
• Reduced description method in the kinetic theory of Brownian motion with active fluctuations
• Cellular geometry controls the efficiency of motile sperm aggregates
• Dynamical phase transitions in two-dimensional Brownian Matter
• Generating consensus and dissent on massive discussion platforms with a semantic-vector model
• Local disalignment can promote coherent collective motion through rapid information transfer
• Confinement-induced collective motion in suspensions of run-and-tumble particles
• Topological Flux on a Context Manifold Generates Nonreciprocal Collective Dynamics
• Continuum model for linked fibers with alignment interactions
• Automatic trajectory measurement of large numbers of crowded objects
• Field-controlled interfacial transport and pinning in an active spin system
• The Inertial Spin Model of flocking with position-dependent forces
• Hydrodynamics of simple active liquids: the emergence of velocity correlations
• Kinetic Event-Chain Algorithm for Active Matter
• Individual particle persistence antagonizes global ordering in populations of nematically-aligning self-propelled particles
• The dynamics of sperm cooperation in a competitive environment
• Morphology, Polarization Patterns, Compression, and Entropy Production in Phase-Separating Active Dumbbell Systems
• Snowdrift game induces pattern formation in systems of self-propelled particles
• Energetics-based model for a diffusiophoretic motion of a deformable droplet
• Hydrodynamic bend instability of motile particles on a substrate
• Self-organized Collective Motion with a Simulated Real Robot Swarm
• Target-density formation in swarms with stochastic sensing and dynamics
• Modelling Hierarchical Flocking
• Automated Guidance of Collective Movement in a Multi-Agent Model of Physarum polycephalum
• Phases and homogeneous ordered states in alignment-based self-propelled particle models
• Quantifying Influence and Information Transfer in a Modified Vicsek Model with Non-reciprocal Interactions
• Modelling pattern formation through differential repulsion
• Thermodynamic efficiency of self-organisation in nonequilibrium steady states
• Agent-Based Simulation of the Two-Dimensional Patlak-Keller-Segel Model
• Work to insert a particle into an active fluid
• First-order condensation transition in the position distribution of a run-and-tumble particle in one dimension
• Long-ranged velocity correlations in dense systems of self-propelled particles
• Noncentral forces mediated between inclusions in a bath of active Brownian rods
• Active matter in infinite dimensions: Fokker-Planck equation and dynamical mean-field theory at low density
• Invariance of velocity angles and flocking in the Inertial Spin model
• Collective Movement with Signaling
• An age-structured continuum model for myxobacteria
• Switching particle systems for foraging ants showing phase transitions in path selections
• Collective behaviors of self-propelled particles with tunable alignment angles
• Collective treadmilling in fire ant rafts permits sustained protrusion growth
• Optimizing collective fieldtaxis of swarming agents through reinforcement learning
• Towards Swarm Calculus: Urn Models of Collective Decisions and Universal Properties of Swarm Performance
• Beyond the Markovian limit: Exact solutions for active motion in a power-law viscoelastic bath
• Cell$-$cell and Cell$-$noise Interactions of Bacterial Cells in a Shallow Circular Pool and Transitions of Collective Motions
• On the Optimal Interaction Range for Multi-Agent Systems Under Adversarial Attack
• Tentative guidelines for the implementation of meta-structural and network software models of collective behaviours
• Interaction Mechanisms Quantified from Dynamical Features of Frog Choruses
• A Likelihood Approach for Inference of Population Heterogeneity in Particle Ensembles with Second-Order Langevin Dynamics
• Modelling Crowd Dynamics: a Multiscale, Measure-theoretical Approach
• A non-linear kinetic model of self-propelled particles with multiple equilibria
• Community Integration Algorithms (CIAs) for Dynamical Systems on Networks
• Information conduction and convection in noiseless Vicsek flocks
• A phase diagram for bacterial swarming