Optimal noise maximizes collective motion in heterogeneous media

Collective dynamics of coherent motile cells on curved surfaces

Cellular dynamic behaviors in organ morphogenesis and embryogenesis are affected by geometrical constraints. In this paper, we investigate how the surface topology and curvature of the underlying substrate tailor collective cell migration. An active vertex model is developed to explore the collective dynamics of coherent cells crawling on curved surfaces. We show that cells can self-organize into rich dynamic patterns including local swirling, global rotation, spiral crawling, serpentine crawling, and directed migration, depending on the interplay between cell-cell interactions and geometric constraints. Increasing substrate curvature results in higher cell-cell bending energy and thus tends to suppress local swirling and enhance density fluctuations. Substrate topology is revealed to regulate both the collective migration modes and density fluctuations of cell populations. In addition, upon increasing noise intensity, a Kosterlitz-Thouless-like ordering transition can emerge on both undevelopable and developable surfaces. This study paves the way to investigate various in vivo morphomechanics that involve surface curvature and topology.

Active uniaxially ordered suspensions on disordered substrates

Multiple experiments on active systems consider oriented active suspensions on substrates or in chambers tightly confined along one direction. The theories of polar and apolar phases in such geometries were considered in A. Maitra et al. [Phys. Rev. Lett. 124, 028002 (2020)10.1103/PhysRevLett.124.028002] and A. Maitra et al. [Proc. Natl. Acad. Sci. USA 115, 6934 (2018)10.1073/pnas.1720607115], respectively. However, the presence of quenched random disorder due to the substrate cannot be completely eliminated in many experimental contexts possibly masking the predictions from those theories. In this paper, I consider the effect of quenched orientational disorder on the phase behavior of both polar and apolar suspensions on substrates. I show that polar suspensions have long-range order in two dimensions with anomalous number fluctuations, while their apolar counterparts have only short-range order, albeit with a correlation length that can increase with activity, and even more violent number fluctuations than active nematics without quenched disorder. These results should be of value in interpreting experiments on active suspensions on substrates with random disorder.

Controlling the transport of active matter in disordered lattices of asymmetrical obstacles

We investigate the transport of active matter in the presence of a disordered square lattice of asymmetric obstacles, which is built by removing a fraction of them from the initial full lattice. We obtain a spontaneous inversion of the net particle current, compared to the usual sense of such a current as a function of the fraction of removed obstacles and particle density. We observed that the negative current regime is the consequence of trapping of particles among the obstacles which favors that more particles move in the negative current direction. The same reasoning applies to the positive current regime as well. We show a calculation that partially reproduces our numerical results, based on the argument that the mean current is given by the product of the mean speed and the mean number of travelers in each direction; the breakdown of this assumption is responsible for the failure of our calculation to reproduce the initial negative current regime.

Capillary Action in Scalar Active Matter

We study the capacity of active matter to rise in thin tubes against gravity and other related phenomena like wetting of vertical plates and spontaneous imbibition, where a wetting liquid is drawn into a porous medium. This capillary action or capillarity is well known in classical fluids and originates from attractive interactions between the liquid molecules and the container walls, and from the attraction of the liquid molecules among each other. We observe capillarity in a minimal model for scalar active matter with purely repulsive interactions, where an effective attraction emerges due to slowdown during collisions between active particles and between active particles and walls. Simulations indicate that the capillary rise in thin tubes is approximately proportional to the active sedimentation length λ and that the wetting height of a vertical plate grows superlinear with λ. In a disordered porous medium the imbibition height scales as ⟨h⟩∝λϕ_{m}, where ϕ_{m} is its packing fraction. These predictions are highly relevant for suspensions of sedimenting active colloids or motile bacteria in a porous medium under the influence of a constant force field.

Nonquenched rotators ease flocking and memorize it

We introduce a minimal model for a two-dimensional polar flock with nonquenched rotators and show that the rotators make the usual macroscopic long-range order of the flock more robust than the clean system. The rotators memorize the flock-information which helps in establishing the robustness. Moreover, the memory of the rotators assists in probing the moving flock. We also formulate a hydrodynamic framework for the microscopic model that makes our study comprehensive. Using linearized hydrodynamics, it is shown that the presence of such nonquenched heterogeneities increases the sound speeds of the flock. The enhanced sound speeds lead to faster convection of information and consequently the robust ordering in the system. We argue that similar nonquenched heterogeneities may be useful in monitoring and controlling large crowds.

Ramifications of disorder on active particles in one dimension

The effects of quenched disorder on a single and many active run-and-tumble particles are studied in one dimension. For a single particle, we consider both the steady-state distribution and the particle's dynamics subject to disorder in three parameters: a bounded external potential, the particle's speed, and its tumbling rate. We show that in the case of a disordered potential, the behavior is like an equilibrium particle diffusing on a random force landscape, implying a dynamics that is logarithmically slow in time. In the situations of disorder in the speed or tumbling rate, we find that the particle generically exhibits diffusive motion, although particular choices of the disorder may lead to anomalous diffusion. Based on the single-particle results, we find that in a system with many interacting particles, disorder in the potential leads to strong clustering. We characterize the clustering in two different regimes depending on the system size and show that the mean cluster size scales with the system size, in contrast to nondisordered systems.

Enhanced dynamics of active Brownian particles in periodic obstacle arrays and corrugated channels

We study the motion of an active Brownian particle (ABP) using the overdamped Langevin dynamics on a two-dimensional substrate with periodic array of obstacles and in a quasi-one-dimensional corrugated channel comprised of periodically arrayed obstacles. The periodic arrangement of the obstacles enhances the persistent motion of the ABP in comparison to its motion in the free space. Persistent motion increases with the activity of the ABP. We note that the periodic arrangement induces directionality in ABP motion at late time, and it increases with the size of the obstacles. We also note that the ABP exhibits a super-diffusive dynamics in the corrugated channel. The transport property is independent of the shape of the channel; rather it depends on the packing fraction of the obstacles in the system. However, the ABP shows the usual diffusive dynamics in the quasi-one-dimensional channel with flat boundary.

Flow and clogging of particles in shaking random obstacles

Transport of three types of particles (passive particles, active particles, and polar particles) is investigated in a random obstacle array in the presence of a dc drift force. The obstacles are static or synchronously shake along the given direction. When the obstacles are static, the average velocity is a peaked function of the dc drift force (negative differential mobility) for low particle density, while the average velocity monotonically increases with the dc drift force (positive differential mobility) for high particle density. Under the same conditions, passive particles are most likely to pass through the obstacles, while polar particles are easily trapped by the obstacles. The polar alignment can strongly reduce the overall mobility of particles. When the obstacles shake along the given direction, the optimal shaking frequency or amplitude can maximize the average velocity. It is more effective to reduce clogging for the transverse shaking than that for the longitudinal shaking.

Contrarian compulsions produce exotic time-dependent flocking of active particles

Animals having a tendency to align their velocities to an average of those of their neighbors may flock as illustrated by the Vicsek model and its variants. If, in addition, they feel a systematic contrarian trend, the result may be a time periodic adjustment of the flock or period doubling in time. These exotic phases are predicted from kinetic theory and numerically found in a modified two-dimensional Vicsek model of self-propelled particles. Numerical simulations demonstrate striking effects of alignment noise on the polarization order parameter measuring particle flocking: maximum polarization length is achieved at an optimal nonzero noise level. When contrarian compulsions are more likely than conformist ones, nonuniform polarized phases appear as the noise surpasses threshold.

Swarming in the Dirt: Ordered Flocks with Quenched Disorder

The effect of quenched (frozen) disorder on the collective motion of active particles is analyzed. We find that active polar systems are far more robust against quenched disorder than equilibrium ferromagnets. Long-ranged order (a nonzero average velocity ⟨v⟩) persists in the presence of quenched disorder even in spatial dimensions d=3; in d=2, quasi-long-ranged order (i.e., spatial velocity correlations that decay as a power law with distance) occurs. In equilibrium systems, only quasi-long-ranged order in d=3 and short-ranged order in d=2 are possible. Our theoretical predictions for two dimensions are borne out by simulations.

Controlled Fluidization, Mobility, and Clogging in Obstacle Arrays Using Periodic Perturbations

We show that the clogging susceptibility and flow of particles moving through a random obstacle array can be controlled with a transverse or longitudinal ac drive. The flow rate can vary over several orders of magnitude, and we find both an optimal frequency and an optimal amplitude of driving that maximizes the flow. For dense arrays, at low ac frequencies, a heterogeneous creeping clogged phase appears in which rearrangements between different clogged configurations occur. At intermediate frequencies, a high-mobility fluidized state forms, and, at high frequencies, the system reenters a heterogeneous frozen clogged state. These results provide a technique for optimizing flow through heterogeneous media that could also serve as the basis for a particle separation method.

Laning and clustering transitions in driven binary active matter systems

It is well known that a binary system of nonactive disks that experience driving in opposite directions exhibits jammed, phase separated, disordered, and laning states. In active matter systems, such as a crowd of pedestrians, driving in opposite directions is common and relevant, especially in conditions which are characterized by high pedestrian density and emergency. In such cases, the transition from laning to disordered states may be associated with the onset of a panic state. We simulate a laning system containing active disks that obey run-and-tumble dynamics, and we measure the drift mobility and structure as a function of run length, disk density, and drift force. The activity of each disk can be quantified based on the correlation timescale of the velocity vector. We find that in some cases, increasing the activity can increase the system mobility by breaking up jammed configurations; however, an activity level that is too high can reduce the mobility by increasing the probability of disk-disk collisions. In the laning state, the increase of activity induces a sharp transition to a disordered strongly fluctuating state with reduced mobility. We identify a novel drive-induced clustered laning state that remains stable even at densities below the activity-induced clustering transition of the undriven system. We map out the dynamic phase diagrams highlighting transitions between the different phases as a function of activity, drive, and density.

Clearing out a maze: A model of chemotactic motion in porous media

We study the anomalous dynamics of a biased "hungry" (or "greedy") random walk on a percolating cluster. The model mimics chemotaxis in a porous medium: In close resemblance to the 1980s arcade game PAC-MAN^®, the hungry random walker consumes food, which is initially distributed in the maze, and biases its movement towards food-filled sites. We observe that the mean-squared displacement of the process follows a power law with an exponent that is different from previously known exponents describing passive or active microswimmer dynamics. The change in dynamics is well described by a dynamical exponent that depends continuously on the propensity to move towards food. It results in slower differential growth when compared to the unbiased random walk.

Cold Active Motion: How Time-Independent Disorder Affects the Motion of Self-Propelled Agents

Assemblages of self-propelled particles, often termed active matter, exhibit collective behavior due to competition between neighbor alignment and noise-induced decoherence. However, very little is known of how the quenched (i.e., time-independent) disorder impacts active motion. Here we report on the effects of quenched disorder on the dynamics of self-propelled point particles. We identified three major types of quenched disorder relevant in the context of active matter: random torque, force, and stress. We demonstrate that even in the absence of external fluctuations ("cold active matter"), quenched disorder results in nontrivial dynamic phases not present in their "hot" counterpart. In particular, by analyzing when the equations of motion exhibit a Hamiltonian structure and when attractors may be present, we identify in which scenarios particle trapping, i.e., the asymptotic convergence of particle trajectories to bounded areas in space ("traps"), can and cannot occur. Our study provides new fundamental insights into active systems realized by self-propelled particles on natural and synthetic disordered substrates.

Clogging and depinning of ballistic active matter systems in disordered media

We numerically examine ballistic active disks driven through a random obstacle array. Formation of a pinned or clogged state occurs at much lower obstacle densities for the active disks than for passive disks. As a function of obstacle density, we identify several distinct phases including a depinned fluctuating cluster state, a pinned single-cluster or jammed state, a pinned multicluster state, a pinned gel state, and a pinned disordered state. At lower active disk densities, a drifting uniform liquid forms in the absence of obstacles, but when even a small number of obstacles are introduced, the disks organize into a pinned phase-separated cluster state in which clusters nucleate around the obstacles, similar to a wetting phenomenon. We examine how the depinning threshold changes as a function of disk or obstacle density and find a crossover from a collectively pinned cluster state to a disordered plastic depinning transition as a function of increasing obstacle density. We compare this to the behavior of nonballistic active particles and show that as we vary the activity from completely passive to completely ballistic, a clogged phase-separated state appears in both the active and passive limits, while for intermediate activity, a readily flowing liquid state appears and there is an optimal activity level that maximizes the flux through the sample.

Active particle condensation by non-reciprocal and time-delayed interactions

We consider the flocking of self-propelling agents in two dimensions, each of which communicates with its neighbors within a limited vision-cone. Also, the communication occurs with some time-delay. The communication among the agents are modeled by Vicsek rules. In this study we explore the combined effect of non-reciprocal interaction (induced by limited vision-cone) among the agents and the presence of delay in the interactions on the dynamical pattern formation within the flock. We find that under these two influences, without any position-based attractive interactions or confining boundaries, the agents can spontaneously condense into "drops". Though the agents are in motion within the drop, the drop as a whole is pinned in space. We find that this novel state of the flock has a well-defined order and it is stabilized by the noise present in the system.

Collective motion of active Brownian particles with polar alignment

We present a comprehensive computational study of the collective behavior emerging from the competition between self-propulsion, excluded volume interactions and velocity-alignment in a two-dimensional model of active particles. We consider an extension of the active brownian particles model where the self-propulsion direction of the particles aligns with the one of their neighbors. We analyze the onset of collective motion (flocking) in a low-density regime (10% surface area) and show that it is mainly controlled by the strength of velocity-alignment interactions: the competition between self-propulsion and crowding effects plays a minor role in the emergence of flocking. However, above the flocking threshold, the system presents a richer pattern formation scenario than analogous models without alignment interactions (active brownian particles) or excluded volume effects (Vicsek-like models). Depending on the parameter regime, the structure of the system is characterized by either a broad distribution of finite-sized polar clusters or the presence of an amorphous, highly fluctuating, large-scale traveling structure which can take a lane-like or band-like form (and usually a hybrid structure which is halfway in between both). We establish a phase diagram that summarizes collective behavior of polar active brownian particles and propose a generic mechanism to describe the complexity of the large-scale structures observed in systems of repulsive self-propelled particles.

Negative differential mobility and trapping in active matter systems

Using simulations, we examine the average velocity as a function of applied drift force for active matter particles moving through a random obstacle array. We find that for low drift force, there is an initial flow regime where the mobility increases linearly with drive, while for higher drift forces a regime of negative differential mobility appears in which the velocity decreases with increasing drive due to the trapping of active particles behind obstacles. A fully clogged regime exists at very high drift forces when all the particles are permanently trapped behind obstacles. We find for increasing activity that the overall mobility is nonmonotonic, with an enhancement of the mobility for small levels of activity and a decrease in mobility for large activity levels. We show how these effects evolve as a function of disk and obstacle density, active run length, drift force, and motor force.

The topography of the environment alters the optimal search strategy for active particles

In environments with scarce resources, adopting the right search strategy can make the difference between succeeding and failing, even between life and death. At different scales, this applies to molecular encounters in the cell cytoplasm, to animals looking for food or mates in natural landscapes, to rescuers during search and rescue operations in disaster zones, and to genetic computer algorithms exploring parameter spaces. When looking for sparse targets in a homogeneous environment, a combination of ballistic and diffusive steps is considered optimal; in particular, more ballistic Lévy flights with exponent [Formula: see text] are generally believed to optimize the search process. However, most search spaces present complex topographies. What is the best search strategy in these more realistic scenarios? Here, we show that the topography of the environment significantly alters the optimal search strategy toward less ballistic and more Brownian strategies. We consider an active particle performing a blind cruise search for nonregenerating sparse targets in a 2D space with steps drawn from a Lévy distribution with the exponent varying from [Formula: see text] to [Formula: see text] (Brownian). We show that, when boundaries, barriers, and obstacles are present, the optimal search strategy depends on the topography of the environment, with [Formula: see text] assuming intermediate values in the whole range under consideration. We interpret these findings using simple scaling arguments and discuss their robustness to varying searcher's size. Our results are relevant for search problems at different length scales from animal and human foraging to microswimmers' taxis to biochemical rates of reaction.

Multi-fractal characterization of bacterial swimming dynamics: a case study on real and simulated Serratia marcescens

To add to the current state of knowledge about bacterial swimming dynamics, in this paper, we study the fractal swimming dynamics of populations of Serratia marcescens bacteria both in vitro and in silico, while accounting for realistic conditions like volume exclusion, chemical interactions, obstacles and distribution of chemoattractant in the environment. While previous research has shown that bacterial motion is non-ergodic, we demonstrate that, besides the non-ergodicity, the bacterial swimming dynamics is multi-fractal in nature. Finally, we demonstrate that the multi-fractal characteristic of bacterial dynamics is strongly affected by bacterial density and chemoattractant concentration.

Dewetting and spreading transitions for active matter on random pinning substrates

We show that sterically interacting self-propelled disks in the presence of random pinning substrates exhibit transitions among a variety of different states. In particular, from a phase separated cluster state, the disks can spread out and homogeneously cover the substrate in what can be viewed as an example of an active matter wetting transition. We map the location of this transition as a function of activity, disk density, and substrate strength, and we also identify other phases including a cluster state, coexistence between a cluster and a labyrinth wetted phase, and a pinned liquid. Convenient measures of these phases include the cluster size, which dips at the wetting-dewetting transition, and the fraction of sixfold coordinated particles, which drops when dewetting occurs.

Dynamic phases of active matter systems with quenched disorder

Depinning and nonequilibrium transitions within sliding states in systems driven over quenched disorder arise across a wide spectrum of size scales ranging from atomic friction at the nanoscale, flux motion in type II superconductors at the mesoscale, colloidal motion in disordered media at the microscale, and plate tectonics at geological length scales. Here we show that active matter or self-propelled particles interacting with quenched disorder under an external drive represents a class of system that can also exhibit pinning-depinning phenomena, plastic flow phases, and nonequilibrium sliding transitions that are correlated with distinct morphologies and velocity-force curve signatures. When interactions with the substrate are strong, a homogeneous pinned liquid phase forms that depins plastically into a uniform disordered phase and then dynamically transitions first into a moving stripe coexisting with a pinned liquid and then into a moving phase-separated state at higher drives. We numerically map the resulting dynamical phase diagrams as a function of external drive, substrate interaction strength, and self-propulsion correlation length. These phases can be observed for active matter moving through random disorder. Our results indicate that intrinsically nonequilibrium systems can exhibit additional nonequilibrium transitions when subjected to an external drive.

Depinning and nonequilibrium dynamic phases of particle assemblies driven over random and ordered substrates: a review

We review the depinning and nonequilibrium phases of collectively interacting particle systems driven over random or periodic substrates. This type of system is relevant to vortices in type-II superconductors, sliding charge density waves, electron crystals, colloids, stripe and pattern forming systems, and skyrmions, and could also have connections to jamming, glassy behaviors, and active matter. These systems are also ideal for exploring the broader issues of characterizing transient and steady state nonequilibrium flow phases as well as nonequilibrium phase transitions between distinct dynamical phases, analogous to phase transitions between different equilibrium states. We discuss the differences between elastic and plastic depinning on random substrates and the different types of nonequilibrium phases which are associated with specific features in the velocity-force curves, fluctuation spectra, scaling relations, and local or global particle ordering. We describe how these quantities can change depending on the dimension, anisotropy, disorder strength, and the presence of hysteresis. Within the moving phase we discuss how there can be a transition from a liquid-like state to dynamically ordered moving crystal, smectic, or nematic states. Systems with periodic or quasiperiodic substrates can have multiple nonequilibrium second or first order transitions in the moving state between chaotic and coherent phases, and can exhibit hysteresis. We also discuss systems with competing repulsive and attractive interactions, which undergo dynamical transitions into stripes and other complex morphologies when driven over random substrates. Throughout this work we highlight open issues and future directions such as absorbing phase transitions, nonequilibrium work relations, inertia, the role of non-dissipative dynamics such as Magnus effects, and how these results could be extended to the broader issues of plasticity in crystals, amorphous solids, and jamming phenomena.

Active Brownian particles moving in a random Lorentz gas

Biological microswimmers often inhabit a porous or crowded environment such as soil. In order to understand how such a complex environment influences their spreading, we numerically study non-interacting active Brownian particles (ABPs) in a two-dimensional random Lorentz gas. Close to the percolation transition in the Lorentz gas, they perform the same subdiffusive motion as ballistic and diffusive particles. However, due to their persistent motion they reach their long-time dynamics faster than passive particles and also show superdiffusive motion at intermediate times. While above the critical obstacle density [Formula: see text] the ABPs are trapped, their long-time diffusion below [Formula: see text] is strongly influenced by the propulsion speed v₀. With increasing v₀, ABPs are stuck at the obstacles for longer times. Thus, for large propulsion speed, the long-time diffusion constant decreases more strongly in a denser obstacle environment than for passive particles. This agrees with the behavior of an effective swimming velocity and persistence time, which we extract from the velocity autocorrelation function.

Spatial heterogeneity can facilitate the target search of self-propelled particles

A numerical investigation of the target search dynamics of self-propelled particles (SPPs) in heterogeneous environments is presented in this work. We show that the spatial heterogeneity has a dramatic effect on the target search dynamics of SPPs. The relative magnitude of the self-propulsion length l_p and the radius of the circular domain R_c determines how the mean search time of SPPs τ depends on the area fraction of fixed obstacles ϕ_ob. For l_p < R_c, the target search process is diffusion-dominated so that a monotonic increase in τ with increasing ϕ_ob is observed. For l_p > R_c, τ is shown to be a non-monotonic convex function as a function of ϕ_ob due to the interplay of the distribution-dominated and diffusion-dominated dynamic regimes. Furthermore, at fixed ϕ_ob, τ shows a minimum upon increasing the self-propulsion velocity v₀ of a SPP of a slow rotational diffusion when it searches for a target at low ϕ_ob, while it decreases monotonically at high ϕ_ob. The present work highlights that the introduction of spatial heterogeneity causes rich dynamic behaviors of a SPP searching for a target, and deepens our understanding of the transport of active matter in heterogeneous media.

Collective transport for active matter run-and-tumble disk systems on a traveling-wave substrate

We examine numerically the transport of an assembly of active run-and-tumble disks interacting with a traveling-wave substrate. We show that as a function of substrate strength, wave speed, disk activity, and disk density, a variety of dynamical phases arise that are correlated with the structure and net flux of disks. We find that there is a sharp transition into a state in which the disks are only partially coupled to the substrate and form a phase-separated cluster state. This transition is associated with a drop in the net disk flux, and it can occur as a function of the substrate speed, maximum substrate force, disk run time, and disk density. Since variation of the disk activity parameters produces different disk drift rates for a fixed traveling-wave speed on the substrate, the system we consider could be used as an efficient method for active matter species separation. Within the cluster phase, we find that in some regimes the motion of the cluster center of mass is in the opposite direction to that of the traveling wave, while when the maximum substrate force is increased, the cluster drifts in the direction of the traveling wave. This suggests that swarming or clustering motion can serve as a method by which an active system can collectively move against an external drift.

The effect of changing topography on the coordinated marching of locust nymphs

Collective motion has traditionally been studied in the lab in homogeneous, obstacle-free environments, with little work having been conducted with changing landscapes or topography. Here, the impact of spatial heterogeneity on the collective motion exhibited by marching desert locust nymphs was studied under controlled lab conditions. Our experimental circular arenas, incorporating a funnel-like narrowing followed by re-widening, did not constitute a major barrier to the locusts but, rather, mimicked a changing topography in the natural environment. We examined its effects on macroscopic features of the locust collective behavior, as well as the any changes in their marching kinematics. A major finding was that of the limited extent to which the changing topography affected system-level features of the marching locust group, such as the order parameter and the fraction of walking individuals, despite increased crowding at the funnel. Overall, marching kinematics was also very little affected, suggesting that locust marching bands adjust to the environment, with little effect on the overall dynamics of the group. These findings are in contrast to recent theoretical results predicting that environmental heterogeneities qualitatively alter the dynamics of collectively moving particles; and highlight the crucial role of rapid individual plasticity and adaptability in the dynamics of flocks and swarms. Our study has revealed other important features of the marching behavior of the desert locust in addition to its robustness: the locusts demonstrated both, clear thigmotaxis and a tendency to spread-out and fill the available space.

Self-organized sorting limits behavioral variability in swarms

Swarming is a phenomenon where collective motion arises from simple local interactions between typically identical individuals. Here, we investigate the effects of variability in behavior among the agents in finite swarms with both alignment and cohesive interactions. We show that swarming is abolished above a critical fraction of non-aligners who do not participate in alignment. In certain regimes, however, swarms above the critical threshold can dynamically reorganize and sort out excess non-aligners to maintain the average fraction close to the critical value. This persists even in swarms with a distribution of alignment interactions, suggesting a simple, robust and efficient mechanism that allows heterogeneously mixed populations to naturally regulate their composition and remain in a collective swarming state or even differentiate among behavioral phenotypes. We show that, for evolving swarms, this self-organized sorting behavior can couple to the evolutionary dynamics leading to new evolutionarily stable equilibrium populations set by the physical swarm parameters.

Disorder-mediated crowd control in an active matter system

Living active matter systems such as bacterial colonies, schools of fish and human crowds, display a wealth of emerging collective and dynamic behaviours as a result of far-from-equilibrium interactions. The dynamics of these systems are better understood and controlled considering their interaction with the environment, which for realistic systems is often highly heterogeneous and disordered. Here, we demonstrate that the presence of spatial disorder can alter the long-term dynamics in a colloidal active matter system, making it switch between gathering and dispersal of individuals. At equilibrium, colloidal particles always gather at the bottom of any attractive potential; however, under non-equilibrium driving forces in a bacterial bath, the colloids disperse if disorder is added to the potential. The depth of the local roughness in the environment regulates the transition between gathering and dispersal of individuals in the active matter system, thus inspiring novel routes for controlling emerging behaviours far from equilibrium.

Many living systems, such as bacterial colonies, exhibit collective and dynamic behaviours that are sensitive to the change in environmental conditions. Here, the authors show that a colloidal active matter system switches between gathering and dispersal of individuals in response to a disordered potential.

Collective Motion of Swarming Agents Evolving on a Sphere Manifold: A Fundamental Framework and Characterization

Collective motion of self-propelled agents has attracted much attention in vast disciplines. However, almost all investigations focus on such agents evolving in the Euclidean space, with rare concern of swarms on non-Euclidean manifolds. Here we present a novel and fundamental framework for agents evolving on a sphere manifold, with which a variety of concrete cooperative-rules of agents can be designed separately and integrated easily into the framework, which may perhaps pave a way for considering general spherical collective motion (SCM) of a swarm. As an example, one concrete cooperative-rule, i.e., the spherical direction-alignment (SDA), is provided, which corresponds to the usual and popular direction-alignment rule in the Euclidean space. The SCM of the agents with the SDA has many unique statistical properties and phase-transitions that are unexpected in the counterpart models evolving in the Euclidean space, which unveils that the topology of the sphere has an important impact on swarming emergence.

Obstacle avoidance in social groups: new insights from asynchronous models

For moving animals, the successful avoidance of hazardous obstacles is an important capability. Despite this, few models of collective motion have addressed the relationship between behavioural and social features and obstacle avoidance. We develop an asynchronous individual-based model for social movement which allows social structure within groups to be included. We assess the dynamics of group navigation and resulting collision risk in the context of information transfer through the system. In agreement with previous work, we find that group size has a nonlinear effect on collision risk. We implement examples of possible network structures to explore the impact social preferences have on collision risk. We show that any social heterogeneity induces greater obstacle avoidance with further improvements corresponding to groups containing fewer influential individuals. The model provides a platform for both further theoretical investigation and practical application. In particular, we argue that the role of social structures within bird flocks may have an important role to play in assessing the risk of collisions with wind turbines, but that new methods of data analysis are needed to identify these social structures.

Absorbing phase transitions and dynamic freezing in running active matter systems

We examine a two-dimensional system of sterically repulsive interacting disks where each particle runs in a random direction. This system is equivalent to a run-and-tumble dynamics system in the limit where the run time is infinite. At low densities, we find a strongly fluctuating state composed of transient clusters. Above a critical density that is well below the density at which non-active particles would crystallize, the system can organize into a drifting quiescent or frozen state where the fluctuations are lost and large crystallites form surrounded by a small density of individual particles. Although all the particles are still moving, their paths form closed orbits. The average transient time to organize into the quiescent state diverges as a power law upon approaching the critical density from above. We compare our results to the random organization observed for periodically sheared systems that can undergo an absorbing transition from a fluctuating state to a dynamical non-fluctuating state. In the random organization studies, the system organizes to a state in which the particles no longer interact; in contrast, we find that the randomly running active matter organizes to a strongly interacting dynamically jammed state. We show that the transition to the frozen state is robust against a certain range of stochastic fluctuations. We also examine the effects of adding a small number of pinned particles to the system and find that the transition to the frozen state shifts to significantly lower densities and arises via the nucleation of faceted crystals centered at the obstacles.

Hydrodynamic suppression of phase separation in active suspensions

We simulate with hydrodynamics a suspension of active disks squirming through a Newtonian fluid. We explore numerically the full range of squirmer area fractions from dilute to close packed and show that "motility induced phase separation," which was recently proposed to arise generically in active matter, and which has been seen in simulations of active Brownian disks, is strongly suppressed by hydrodynamic interactions. We give an argument for why this should be the case and support it with counterpart simulations of active Brownian disks in a parameter regime that provides a closer counterpart to hydrodynamic suspensions than in previous studies.

Active matter transport and jamming on disordered landscapes

We numerically examine the transport of active run-and-tumble particles with steric particle-particle interactions driven with a drift force over random disordered landscapes composed of fixed obstacles. For increasing run lengths, the net particle transport initially increases before reaching a maximum and decreasing at larger run lengths. The transport reduction is associated with the formation of cluster or living crystal states that become locally jammed or clogged by the obstacles. We also find that the system dynamically jams at lower particle densities when the run length is increased. Our results indicate that there is an optimal activity level for transport of run-and-tumble type active matter through quenched disorder and could be important for understanding biological transport in complex environments or for applications of active matter particles in random media.

Residence times and boundary-following behavior in animals

Many animals in heterogeneous environments bias their trajectories displaying a preference for the vicinity of boundaries. Here we propose a criterion, relying on recent invariance properties of residence times for microreversible Boltzmann's walks, that permits detecting and quantifying boundary-following behaviors. On this basis we introduce a boundary-following model that is a nonmicroreversible Boltzmann's walk and that can represent all kinds of boundary-following distributions. This allows us to perform a theoretical analysis of field-resolved boundary following in animals. Two consequences are pointed out and are illustrated: A systematic procedure can now be used for extraction of individual properties from experimental field measurements, and boundary-curvature influence can be recovered as an emerging property without the need for individuals perceiving the curvature via complex physiological mechanisms. The presented results apply to any memoryless correlated random walk, such as the run-and-tumble models that are widely used in cell motility studies.

Diffusion, subdiffusion, and trapping of active particles in heterogeneous media

We study the transport properties of a system of active particles moving at constant speed in a heterogeneous two-dimensional space. The spatial heterogeneity is modeled by a random distribution of obstacles, which the active particles avoid. Obstacle avoidance is characterized by the particle turning speed γ. We show, through simulations and analytical calculations, that the mean square displacement of particles exhibits two regimes as function of the density of obstacles ρ(o) and γ. We find that at low values of γ, particle motion is diffusive and characterized by a diffusion coefficient that displays a minimum at an intermediate obstacle density ρ(o). We observe that in high obstacle density regions and for large γ values, spontaneous trapping of active particles occurs. We show that such trapping leads to genuine subdiffusive motion of the active particles. We indicate how these findings can be used to fabricate a filter of active particles.