Spontaneously ordered motion of self-propelled particles

Finite-size scaling in kinetics of phase separation in certain models of aligning active particles

To study the kinetics of phase separation in active matter systems, we consider models that impose a Vicsek-type self-propulsion rule on otherwise passive particles interacting via the Lennard-Jones potential. Two types of kinetics are of interest: one conserves the total momentum of all the constituents and the other does not. We carry out molecular dynamics simulations to obtain results on structural, growth, and aging properties. Results from our studies, with various finite boxes, show that there exist scalings with respect to the system sizes, in both the latter quantities, as in the standard passive cases. We have exploited this scaling picture to accurately estimate the corresponding exponents, in the thermodynamically large system size limit, for power-law time dependences. It is shown that certain analytical functions describe the behavior of these quantities quite accurately, including the finite-size limits. Our results demonstrate that even though the conservation of velocity has at best weak effects on the dynamics of evolution in the thermodynamic limit, the finite-size behavior is strongly influenced by the presence (or the absence) of it.

Human Crowds as Social Networks: Collective Dynamics of Consensus and Polarization

A ubiquitous type of collective behavior and decision-making is the coordinated motion of bird flocks, fish schools, and human crowds. Collective decisions to move in the same direction, turn right or left, or split into subgroups arise in a self-organized fashion from local interactions between individuals without central plans or designated leaders. Strikingly similar phenomena of consensus (collective motion), clustering (subgroup formation), and bipolarization (splitting into extreme groups) are also observed in opinion formation. As we developed models of crowd dynamics and analyzed crowd networks, we found ourselves going down the same path as models of opinion dynamics in social networks. In this article, we draw out the parallels between human crowds and social networks. We show that models of crowd dynamics and opinion dynamics have a similar mathematical form and generate analogous phenomena in multiagent simulations. We suggest that they can be unified by a common collective dynamics, which may be extended to other psychological collectives. Models of collective dynamics thus offer a means to account for collective behavior and collective decisions without appealing to a priori mental structures.

Using neuronal models to capture burst-and-glide motion and leadership in fish

While mathematical models, in particular self-propelled particle models, capture many properties of large fish schools, they do not always capture the interactions of smaller shoals. Nor do these models tend to account for the use of intermittent locomotion, often referred to as burst-and-glide, by many species. In this paper, we propose a model of social burst-and-glide motion by combining a well-studied model of neuronal dynamics, the FitzHugh-Nagumo model, with a model of fish motion. We first show that our model can capture the motion of a single fish swimming down a channel. Extending to a two-fish model, where visual stimulus of a neighbour affects the internal burst or glide state of the fish, we observe a rich set of dynamics found in many species. These include: leader-follower behaviour; periodic changes in leadership; apparently random (i.e. chaotic) leadership change; and tit-for-tat turn taking. Moreover, unlike previous studies where a randomness is required for leadership switching to occur, we show that this can instead be the result of deterministic interactions. We give several empirically testable predictions for how bursting fish interact and discuss our results in light of recently established correlations between fish locomotion and brain activity.

Phase behavior and dynamics in a colloid-polymer mixture under spherical confinement

From studies via molecular dynamics simulations, we report results on structure and dynamics in mixtures of active colloids and passive polymers that are confined inside a spherical container with a repulsive boundary. All interactions in the fully passive limit are chosen in such a way that in equilibrium coexistence between colloid-rich and polymer-rich phases occurs. For most part of the studies the chosen compositions give rise to Janus-like structure: nearly one side of the sphere is occupied by the colloids and the rest by the polymers. This partially wet situation mimics approximately a neutral wall in the fully passive scenario. Following the introduction of a velocity-aligning activity to the colloids, the shape of the polymer-rich domain changes to that of an ellipsoid, around the long axis of which the colloid-rich domain attains a macroscopic angular momentum. In the steady state, the orientation of this axis evolves via diffusion, magnitude of which depends upon the strength of activity, but only weakly.

Ontogeny of collective behaviour

During their lifetime, superorganisms, like unitary organisms, undergo transformations that change the machinery of their collective behaviour. Here, we suggest that these transformations are largely understudied and propose that more systematic research into the ontogeny of collective behaviours is needed if we hope to better understand the link between proximate behavioural mechanisms and the development of collective adaptive functions. In particular, certain social insects engage in self-assemblage, forming dynamic and physically connected architectures with striking similarities to developing multicellular organisms, making them good model systems for ontogenetic studies of collective behaviour. However, exhaustive time series and three-dimensional data are required to thoroughly characterize the different life stages of the collective structures and the transitions between these stages. The well-established fields of embryology and developmental biology offer practical tools and theoretical frameworks that could speed up the acquisition of new knowledge about the formation, development, maturity and dissolution of social insect self-assemblages and, by extension, other superorganismal behaviours. We hope that this review will encourage an expansion of the ontogenetic perspective in the field of collective behaviour and, in particular, in self-assemblage research, which has far-reaching applications in robotics, computer science and regenerative medicine. This article is part of a discussion meeting issue 'Collective behaviour through time'.

Flocking of two unfriendly species: The two-species Vicsek model

We consider the two-species Vicsek model (TSVM) consisting of two kinds of self-propelled particles, A and B, that tend to align with particles from the same species and to antialign with the other. The model shows a flocking transition that is reminiscent of the original Vicsek model: it has a liquid-gas phase transition and displays micro-phase-separation in the coexistence region where multiple dense liquid bands propagate in a gaseous background. The interesting features of the TSVM are the existence of two kinds of bands, one composed of mainly A particles and one mainly of B particles, the appearance of two dynamical states in the coexistence region: the PF (parallel flocking) state in which all bands of the two species propagate in the same direction, and the APF (antiparallel flocking) state in which the bands of species A and species B move in opposite directions. When PF and APF states exist in the low-density part of the coexistence region they perform stochastic transitions from one to the other. The system size dependence of the transition frequency and dwell times show a pronounced crossover that is determined by the ratio of the band width and the longitudinal system size. Our work paves the way for studying multispecies flocking models with heterogeneous alignment interactions.

Collective motion of active particles exhibiting non-reciprocal orientational interactions

We present a Brownian dynamics study of a 2D bath of active particles interacting among each other through usual steric interactions and, additionally, via non-reciprocal avoidant orientational interactions. We motivate them by the fact that the two flagella of the alga Chlamydomonas interact sterically with nearby surfaces such that a torque acts on the alga. As expected, in most cases such interactions disrupt the motility-induced particle clustering in active baths. Surprisingly, however, we find that the active particles can self-organize into collectively moving flocks if the range of non-reciprocal interactions is close to that of steric interactions. We observe that the flocking motion can manifest itself through a variety of structural forms, spanning from single dense bands to multiple moderately-dense stripes, which are highly dynamic. The flocking order parameter is found to be only weakly dependent on the underlying flock structure. Together with the variance of the local-density distribution, one can clearly group the flocking motion into the two separate band and dynamic-stripes states.

Information conduction and convection in noiseless Vicsek flocks

Physical interactions generally respect certain symmetries, such as reciprocity and energy conservation, which survive in coarse-grained isothermal descriptions. Active many-body systems usually break such symmetries intrinsically, on the particle level, so that their collective behavior is often more naturally interpreted as a result of information exchange. Here we study numerically how information spreads from a "leader" particle through an initially aligned flock, described by the Vicsek model without noise. In the low-speed limit of a static spin lattice, we find purely conductive spreading, reminiscent of heat transfer. Swarm motility and heterogeneity can break reciprocity and spin conservation. But what seems more consequential for the swarm response is that the dispersion relation acquires a significant convective contribution along the leader's direction of motion.

A broad perspective to particle-laden fluid interfaces systems: from chemically homogeneous particles to active colloids

Particles adsorbed to fluid interfaces are ubiquitous in industry, nature or life. The wide range of properties arising from the assembly of particles at fluid interface has stimulated an intense research activity on shed light to the most fundamental physico-chemical aspects of these systems. These include the mechanisms driving the equilibration of the interfacial layers, trapping energy, specific inter-particle interactions and the response of the particle-laden interface to mechanical perturbations and flows. The understanding of the physico-chemistry of particle-laden interfaces becomes essential for taking advantage of the particle capacity to stabilize interfaces for the preparation of different dispersed systems (emulsions, foams or colloidosomes) and the fabrication of new reconfigurable interface-dominated devices. This review presents a detailed overview of the physico-chemical aspects that determine the behavior of particles trapped at fluid interfaces. This has been combined with some examples of real and potential applications of these systems in technological and industrial fields. It is expected that this information can provide a general perspective of the topic that can be exploited for researchers and technologist non-specialized in the study of particle-laden interfaces, or for experienced researcher seeking new questions to solve.

Robust weighted averaging accounts for recruitment into collective motion in human crowds

Agent-based models of 'flocking' and 'schooling' have shown that a weighted average of neighbor velocities, with weights that decay gradually with distance, yields emergent collective motion. Weighted averaging thus offers a potential mechanism of self-organization that recruits an increasing, but self-limiting, number of individuals into collective motion. Previously, we identified and modeled such a 'soft metric' neighborhood of interaction in human crowds that decays exponentially to zero at a distance of 4-5m. Here we investigate the limits of weighted averaging in humans and find that it is surprisingly robust: pedestrians align with the mean heading direction in their neighborhood, despite high levels of noise and diverging motions in the crowd, as predicted by the model. In three Virtual Reality experiments, participants were immersed in a crowd of virtual humans in a mobile head-mounted display and were instructed to walk with the crowd. By perturbing the heading (walking direction) of virtual neighbors and measuring the participant's trajectory, we probed the limits of weighted averaging. (1) In the 'Noisy Neighbors' experiment, the neighbor headings were randomized (range 0-90°) about the crowd's mean direction (±10° or ±20°, left or right); (2) in the 'Splitting Crowd' experiment, the crowd split into two groups (heading difference = 10-40°) and the proportion of the crowd in one group was varied (50-84%); (3) in the 'Coherent Subgroup' experiment, a perturbed subgroup varied in its coherence (heading SD = 0-2°) about a mean direction (±10° or ±20°) within a noisy crowd (heading range = 180°), and the proportion of the crowd in the subgroup was varied. In each scenario, the results were predicted by the weighted averaging model, and attraction strength (turning rate) increased with the participant's deviation from the mean heading direction, not with group coherence. However, the results indicate that humans ignore highly discrepant headings (45-90°). These findings reveal that weighted averaging in humans is highly robust and generates a common heading direction that acts as a positive feedback to recruit more individuals into collective motion, in a self-reinforcing cascade. Therefore, this 'soft' metric neighborhood serves as a mechanism of self-organization in human crowds.

Phase transitions in biology: from bird flocks to population dynamics

Phase transitions are an important and extensively studied concept in physics. The insights derived from understanding phase transitions in physics have recently and successfully been applied to a number of different phenomena in biological systems. Here, we provide a brief review of phase transitions and their role in explaining biological processes ranging from collective behaviour in animal flocks to neuronal firing. We also highlight a new and exciting area where phase transition theory is particularly applicable: population collapse and extinction. We discuss how phase transition theory can give insight into a range of extinction events such as population decline due to climate change or microbial responses to stressors such as antibiotic treatment.

Why animals swirl and how they group

We report a possible solution for the long-standing problem of the biological function of swirling motion, when a group of animals orbits a common center of the group. We exploit the hypothesis that learning processes in the nervous system of animals may be modelled by reinforcement learning (RL) and apply it to explain the phenomenon. In contrast to hardly justified models of physical interactions between animals, we propose a small set of rules to be learned by the agents, which results in swirling. The rules are extremely simple and thus applicable to animals with very limited level of information processing. We demonstrate that swirling may be understood in terms of the escort behavior, when an individual animal tries to reside within a certain distance from the swarm center. Moreover, we reveal the biological function of swirling motion: a trained for swirling swarm is by orders of magnitude more resistant to external perturbations, than an untrained one. Using our approach we analyze another class of a coordinated motion of animals-a group locomotion in viscous fluid. On a model example we demonstrate that RL provides an optimal disposition of coherently moving animals with a minimal dissipation of energy.

Pattern stabilization in swarms of programmable active matter: A probe for turbulence at large length scales

We propose an algorithm for creating stable, ordered, swarms of active robotic agents arranged in any given pattern. The strategy involves suppressing a class of fluctuations known as "nonaffine" displacements, viz., those involving nonlinear deformations of a reference pattern, while all (or most) affine deformations are allowed. We show that this can be achieved using precisely calculated, fluctuating, thrust forces associated with a vanishing average power input. A surprising outcome of our study is that once the structure of the swarm is maintained at steady state, the statistics of the underlying flow field is determined solely from the statistics of the forces needed to stabilize the swarm.

Spontaneous response of a self-organized fish school to a predator

While the collective movements of fish schools evading predators in nature are complex, they can be fundamentally represented by simplified mathematical models. Here we develop a numerical model, which considers self-propelled particles subject to phenomenological behavioural rules and the hydrodynamic interactions between individuals. We introduce a predator in this model, to study the spontaneous response of a group of simulated fish to the threat. A self-organized fish school with a milling pattern is considered, which was expected to be efficient to evade the threat of predators. Four different attack tactics are adopted by the predator. We find that the simulated fish form transiently smaller structures as some prey individuals split from the main group, but eventually they will re-organize, sometimes into sub groups when the simulated predator approaches the fish school unidirectionally or take a reciprocating action. As the predator is programmed to target the centroid, the school ends in a gradually enlarging circle. For the fourth tactic, as the predator chases its nearest prey, the fish school's response varies with the predator's delay factor. Moreover, the average speed of the group and the distance between individuals have also been studied, both demonstrating that the fish school is able to respond spontaneously to the predator's invasion. We demonstrate that the currently adopted model can predict prey-predator interactions.

Non-local interactions in collective motion

The collective motion of animal groups often exhibits velocity-velocity correlations between nearest neighbours, with the strongest velocity correlations observed at the shortest inter-animal spacings. This may have been a motivational factor in the development of models based primarily on short-ranged interactions. Here we ask whether such observations necessarily mean that the interactions are short-ranged. We develop a minimal model of collective motion capable of supporting interactions of arbitrary range and show that it represents a counterexample: the strongest velocity correlations emerge at the shortest distances, even when the interactions are explicitly non-local.

Swirlonic state of active matter

We report a novel state of active matter-a swirlonic state. It is comprised of swirlons, formed by groups of active particles orbiting their common center of mass. These quasi-particles demonstrate a surprising behavior: In response to an external load they move with a constant velocity proportional to the applied force, just as objects in viscous media. The swirlons attract each other and coalesce forming a larger, joint swirlon. The coalescence is extremely slow, decelerating process, resulting in a rarified state of immobile quasi-particles. In addition to the swirlonic state, we observe gaseous, liquid and solid states, depending on the inter-particle and self-driving forces. Interestingly, in contrast to molecular systems, liquid and gaseous states of active matter do not coexist. We explain this unusual phenomenon by the lack of fast particles in active matter. We perform extensive numerical simulations and theoretical analysis. The predictions of the theory agree qualitatively and quantitatively with the simulation results.

Speed inhomogeneity accelerates information transfer in polar flock

A collection of self-propelled particles (SPPs) shows coherent motion and exhibits a true long-range-ordered state in two dimensions. Various studies show that the presence of spatial inhomogeneities can destroy the usual long-range ordering in the system. However, the effects of inhomogeneity due to the intrinsic properties of the particles are barely addressed. In this paper we consider a collection of polar SPPs moving at inhomogeneous speed (IS) on a two-dimensional substrate, which can arise due to varying physical strengths of the individual particles. To our surprise, the IS not only preserves the usual long-range ordering present in homogeneous speed models but also induces faster ordering in the system. Furthermore, the response of the flock to an external perturbation is also faster, compared to the Vicsek-like model systems, due to the frequent update of neighbors of each SPP in the presence of the IS. Therefore, our study shows that an IS can promote information transfer in a moving flock.

Effect of particle fraction on phase transitions in an active-passive particles system

We study phase transition in a binary system of monodisperse active and passive particles. The particles are initially randomly positioned inside a fixed boundary square enclosure. The active particles can move with their self-propulsion force. Whereas, the passive particles do not have any self-propulsion force, and they move by the spatial interactions with other particles. An alignment force in our discrete element model causes the emergence of collective milling motion. Without this alignment interaction, the particle system remains in a disordered phase. Whereas, the ordered milling phase is attained after achieving a minimum coordination among neighboring particles. The phase transition from disordered to ordered depends upon the relative effect of self-propulsion and the alignment, initial states of the particles, noise level, and the fraction of the active particles present in the system. The phase transition we observed is of first-order nature.

Decentralized Control for Swarm Robots That Can Effectively Execute Spatially Distributed Tasks

A swarm robotic system is a system in which multiple robots cooperate to fulfill a macroscopic function. Many swarm robots have been developed for various purposes. This study aims to design swarm robots capable of executing spatially distributed tasks effectively, which can be potentially used for tasks such as search-and-rescue operation and gathering scattered garbage in rooms. We propose a simple decentralized control scheme for swarm robots by extending our previously proposed non-reciprocal-interaction-based model. Each robot has an internal state, called its workload. Each robot first moves randomly to find a task, and when it does, its workload increases, and then it attracts its neighboring robots to ask for their help. We demonstrate, via simulations, that the proposed control scheme enables the robots to effectively execute multiple tasks in parallel under various environments. Fault tolerance of the proposed system is also demonstrated.

Multiple Particle Correlation Analysis of Many-Particle Systems: Formalism and Application to Active Matter

We introduce a fast spatial point pattern analysis technique that is suitable for systems of many identical particles giving rise to multiparticle correlations up to arbitrary order. The obtained correlation parameters allow us to quantify the quality of mean field assumptions or theories that incorporate correlations of limited order. We study the Vicsek model of self-propelled particles and create a correlation map marking the required correlation order for each point in phase space incorporating up to ten-particle correlations. We find that multiparticle correlations are important even in a large part of the disordered phase. Furthermore, the two-particle correlation parameter serves as an excellent order parameter to locate both phase transitions of the system, whereas two different order parameters were required before.

Transport coefficients of self-propelled particles: Reverse perturbations and transverse current correlations

The reverse perturbation method [Phys. Rev. E 59, 4894 (1999)1063-651X10.1103/PhysRevE.59.4894] for shearing simple liquids and measuring their viscosity is extended to the Vicsek model (VM) of active particles [Phys. Rev. Lett. 75, 1226 (1995)PRLTAO0031-900710.1103/PhysRevLett.75.1226] and its metric-free version. The sheared systems exhibit a phenomenon that is similar to the skin effect of an alternating electric current: Momentum that is fed into the boundaries of a layer decays mostly exponentially toward the center of the layer. It is shown how two transport coefficients, i.e., the shear viscosity ν and the momentum amplification coefficient λ, can be obtained by fitting this decay with an analytical solution of the hydrodynamic equations for the VM. The viscosity of the VM consists of two parts, a kinetic and a collisional contribution. While analytical predictions already exist for the former, a novel expression for the collisional part is derived by an Enskog-like kinetic theory. To verify the predictions for the transport coefficients, Green-Kubo relations were evaluated and transverse current correlations were measured in independent simulations. Not too far to the transition to collective motion, we find excellent agreement between the different measurements of the transport coefficients. However, the measured values of ν and 1-λ are always slightly higher than the mean-field predictions, even at large mean free paths and at state points quite far from the threshold to collective motion, that is, far in the disordered phase. These findings seem to indicate that the mean-field assumption of molecular chaos is much less reliable in systems with velocity-alignment rules such as the VM, compared to models obeying detailed balance such as multiparticle collision dynamics.

Self-propelled Vicsek particles at low speed and low density

We study through numerical simulation the Vicsek model for very low speeds and densities. We consider scalar noise in two and three dimensions and vector noise in three dimensions. We focus on the behavior of the critical noise with density and speed, trying to clarify seemingly contradictory earlier results. We find that, for scalar noise, the critical noise is a power law in both density and speed, but although we confirm the density exponent in two dimensions, we find a speed exponent different from earlier reports (we consider lower speeds than previous studies). On the other hand, for the vector noise case we find that the dependence of the critical noise cannot be separated as a product of power laws in speed and density. Finally, we study the dependence of the relaxation time with speed. At the critical point we find a power law, with the same exponent in two and three dimensions.

Additivity and density fluctuations in Vicsek-like models of self-propelled particles

We study coarse-grained density fluctuations in the disordered phase of the paradigmatic Vicsek-like models of self-propelled particles with alignment interactions and random self-propulsion velocities. By numerically integrating a fluctuation-response relation-the direct consequence of an additivity property-we compute logarithm of the large-deviation probabilities of the coarse-grained subsystem density, while the system is in the disordered fluid phase with vanishing macroscopic velocity. The large-deviation probabilities, computed within additivity, agree remarkably well with that obtained from direct microscopic simulations of the models. Our results provide evidence of the existence of an equilibriumlike chemical potential, which governs the coarse-grained density fluctuations in the Vicsek-like models. Moreover, comparison of the particle-number fluctuations among several self-propelled particle systems suggests a common mechanism through which the number fluctuations arise in such systems.

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.

How do fire ants control the rheology of their aggregations? A statistical mechanics approach

Active networks are omnipresent in nature, from the molecular to the macro-scale. In this study, we explore the mechanical behaviour of fire ant aggregations, closely knit swarms that display impressive dynamics culminating with the aggregations' capacity to self-heal and adapt to the environment. Although the combined elasticity and rheology of the ant aggregation can be characterized by phenomenological mechanical models (e.g. linear Maxwell or Kelvin-Voigt model), it is not clear how the behaviour of individual ants affects the aggregations' emerging responses. Here, we explore an alternative way to think about these materials, describing them as a collection of individuals connected via elastic chains that associate and dissociate over time. Using our knowledge of these connections-e.g. their elasticity and attachment/dissociation rates-we construct a statistical description of connection stretch and derive an evolution equation for the corresponding stretch distribution. This time-evolving stretch distribution is then used to determine important macroscopic measures, e.g. stress, energy storage and energy dissipation, in the network. In this context, we show how the physical characteristics and activities of individual ants can explain the elasticity, flow and shear thinning of the aggregation. In particular, we find that experimental results are matched if the detachment rate between two individuals increases with tension in the connection.

Active dumbbells: Dynamics and morphology in the coexisting region

With the help of molecular dynamics simulations we study an ensemble of active dumbbells in purely repulsive interaction. We derive the phase diagram in the density-activity plane and we characterise the various phases with liquid, hexatic and solid character. The analysis of the structural and dynamical properties, such as enstrophy, mean-square displacement, polarisation, and correlation functions, shows the continuous character of liquid and hexatic phases in the coexisting region when the activity is increased starting from the passive limit.

Exact Hydrodynamic Description of Active Lattice Gases

We introduce lattice gas models of active matter systems whose coarse-grained "hydrodynamic" description can be derived exactly. We illustrate our approach by considering two systems exhibiting two of the most studied collective behaviors in active matter: the motility-induced phase separation and the transition to collective motion. In both cases, we derive coupled partial differential equations describing the dynamics of the local density and polarization fields and show how they quantitatively predict the emerging properties of the macroscopic lattice gases.

Experimental Investigation of the Self-Propelled Motion of a Sodium Oleate Tablet and Boat at an Oil-Water Interface

The self-propelled behaviors of macroscopic inanimate objects at surfaces and interfaces are ubiquitous phenomena of fundamental interest in interface science. However, given the existence of a large variety of systems with their own inherent chemical properties, the kinematics of the self-propelled motion and the dynamics of the forces driving these systems often remain largely unknown. Here, we experimentally investigate the spontaneous motion of a sodium oleate tablet at a water-nitrobenzene interface, under nonequilibrium and global isothermal conditions, through measurements of the interfacial tension with the noninvasive, quasi-elastic laser scattering method. The sodium oleate tablet was self-propelled due to an imbalance in the interfacial tension induced by the inhomogeneous adsorption of oleate/oleic acid molecules. The kinetics of the self-propelled motion of a boat-shaped plastic sheet bearing sodium oleate tablets at a sodium oleate aqueous solution-nitrobenzene interface was also studied. The interfacial tension difference between the front and rear of the boat was quantitatively identified as the force pushing the boat forward, although the Marangoni flow due to the uneven distribution of the interfacial tension behind the boat tended to decelerate the motion.

Brownian dynamics of self-regulated particles with additional degrees of freedom: Symmetry breaking and homochirality

We consider the Brownian motion of a collection of particles each with an additional degree of freedom. The degree of freedom of a particle (or, in general, a molecule) can assume distinct values corresponding to certain states or conformations. The time evolution of the additional degree of freedom of a particle is guided by those of its neighbors as well as the temperature of the system. We show that the local averaging over these degrees of freedom results in emergence of a collective order in the dynamics in the form of selection or dominance of one of the isomers leading to a symmetry-broken state. Our statistical model captures the basic features of homochirality, e.g., autocatalysis and chiral inhibition.

Effect of form of obstacle on speed of crowd evacuation

This paper investigates the effect of the form of an obstacle on the time that a crowd takes to evacuate a room, using a toy model. Pedestrians are modeled as active soft matter moving toward a point with intended velocities. An obstacle is placed in front of the exit, and it has one of four shapes: a cylindrical column, a triangular prism, a quadratic prism, or a diamond prism. Numerical results indicate that the evacuation-completion time depends on the shape of the obstacle. Obstacles with a circular cylinder (C.C.) shape yield the shortest evacuation-completion time in the proposed model.

Vortex dynamics and Lagrangian statistics in a model for active turbulence

Cellular suspensions such as dense bacterial flows exhibit a turbulence-like phase under certain conditions. We study this phenomenon of "active turbulence" statistically by using numerical tools. Following Wensink et al. (Proc. Natl. Acad. Sci. U.S.A. 109, 14308 (2012)), we model active turbulence by means of a generalized Navier-Stokes equation. Two-point velocity statistics of active turbulence, both in the Eulerian and the Lagrangian frame, is explored. We characterize the scale-dependent features of two-point statistics in this system. Furthermore, we extend this statistical study with measurements of vortex dynamics in this system. Our observations suggest that the large-scale statistics of active turbulence is close to Gaussian with sub-Gaussian tails.

Effects of Heterogeneous Social Interactions on Flocking Dynamics

Social relationships characterize the interactions that occur within social species and may have an important impact on collective animal motion. Here, we consider a variation of the standard Vicsek model for collective motion in which interactions are mediated by an empirically motivated scale-free topology that represents a heterogeneous pattern of social contacts. We observe that the degree of order of the model is strongly affected by network heterogeneity: more heterogeneous networks show a more resilient ordered state, while less heterogeneity leads to a more fragile ordered state that can be destroyed by sufficient external noise. Our results challenge the previously accepted equivalence between the static Vicsek model and the equilibrium XY model on the network of connections, and point towards a possible equivalence with models exhibiting a different symmetry.

Nonequilibrium transition and pattern formation in a linear reaction-diffusion system with self-regulated kinetics

We consider a reaction-diffusion system with linear, stochastic activator-inhibitor kinetics where the time evolution of concentration of a species at any spatial location depends on the relative average concentration of its neighbors. This self-regulating nature of kinetics brings in spatial correlation between the activator and the inhibitor. An interplay of this correlation in kinetics and disparity of diffusivities of the two species leads to symmetry breaking non-equilibrium transition resulting in stationary pattern formation. The role of initial noise strength and the linear reaction terms has been analyzed for pattern selection.

Gaussian theory for spatially distributed self-propelled particles

Obtaining a reduced description with particle and momentum flux densities outgoing from the microscopic equations of motion of the particles requires approximations. The usual method, we refer to as truncation method, is to zero Fourier modes of the orientation distribution starting from a given number. Here we propose another method to derive continuum equations for interacting self-propelled particles. The derivation is based on a Gaussian approximation (GA) of the distribution of the direction of particles. First, by means of simulation of the microscopic model, we justify that the distribution of individual directions fits well to a wrapped Gaussian distribution. Second, we numerically integrate the continuum equations derived in the GA in order to compare with results of simulations. We obtain that the global polarization in the GA exhibits a hysteresis in dependence on the noise intensity. It shows qualitatively the same behavior as we find in particles simulations. Moreover, both global polarizations agree perfectly for low noise intensities. The spatiotemporal structures of the GA are also in agreement with simulations. We conclude that the GA shows qualitative agreement for a wide range of noise intensities. In particular, for low noise intensities the agreement with simulations is better as other approximations, making the GA to an acceptable candidates of describing spatially distributed self-propelled particles.

Clusterflock: a flocking algorithm for isolating congruent phylogenomic datasets

BACKGROUND

Collective animal behavior, such as the flocking of birds or the shoaling of fish, has inspired a class of algorithms designed to optimize distance-based clusters in various applications, including document analysis and DNA microarrays. In a flocking model, individual agents respond only to their immediate environment and move according to a few simple rules. After several iterations the agents self-organize, and clusters emerge without the need for partitional seeds. In addition to its unsupervised nature, flocking offers several computational advantages, including the potential to reduce the number of required comparisons.

FINDINGS

In the tool presented here, Clusterflock, we have implemented a flocking algorithm designed to locate groups (flocks) of orthologous gene families (OGFs) that share an evolutionary history. Pairwise distances that measure phylogenetic incongruence between OGFs guide flock formation. We tested this approach on several simulated datasets by varying the number of underlying topologies, the proportion of missing data, and evolutionary rates, and show that in datasets containing high levels of missing data and rate heterogeneity, Clusterflock outperforms other well-established clustering techniques. We also verified its utility on a known, large-scale recombination event in Staphylococcus aureus. By isolating sets of OGFs with divergent phylogenetic signals, we were able to pinpoint the recombined region without forcing a pre-determined number of groupings or defining a pre-determined incongruence threshold.

CONCLUSIONS

Clusterflock is an open-source tool that can be used to discover horizontally transferred genes, recombined areas of chromosomes, and the phylogenetic 'core' of a genome. Although we used it here in an evolutionary context, it is generalizable to any clustering problem. Users can write extensions to calculate any distance metric on the unit interval, and can use these distances to 'flock' any type of data.

Linear response to leadership, effective temperature, and decision making in flocks

Large collections of autonomously moving agents, such as animals or micro-organisms, are able to flock coherently in space even in the absence of a central control mechanism. While the direction of the flock resulting from this critical behavior is random, this can be controlled by a small subset of informed individuals acting as leaders of the group. In this article we use the Vicsek model to investigate how flocks respond to leadership and make decisions. Using a combination of numerical simulations and continuous modeling we demonstrate that flocks display a linear response to leadership that can be cast in the framework of the fluctuation-dissipation theorem, identifying an effective temperature reflecting how promptly the flock reacts to the initiative of the leaders. The linear response to leadership also holds in the presence of two groups of informed individuals with competing interests, indicating that the flock's behavioral decision is determined by both the number of leaders and their degree of influence.

Mapping two-dimensional polar active fluids to two-dimensional soap and one-dimensional sandblasting

Active fluids and growing interfaces are two well-studied but very different non-equilibrium systems. Each exhibits non-equilibrium behaviour distinct from that of their equilibrium counterparts. Here we demonstrate a surprising connection between these two: the ordered phase of incompressible polar active fluids in two spatial dimensions without momentum conservation, and growing one-dimensional interfaces (that is, the 1+1-dimensional Kardar–Parisi–Zhang equation), in fact belong to the same universality class. This universality class also includes two equilibrium systems: two-dimensional smectic liquid crystals, and a peculiar kind of constrained two-dimensional ferromagnet. We use these connections to show that two-dimensional incompressible flocks are robust against fluctuations, and exhibit universal long-ranged, anisotropic spatio-temporal correlations of those fluctuations. We also thereby determine the exact values of the anisotropy exponent ζ and the roughness exponents χ_x,y that characterize these correlations.

In many groups of moving organisms, such as swarms of bacteria, their constituents pack so tightly that density cannot change. Here, Chen et al. map such incompressible flocks in two dimensions onto the growth of a one-dimensional interface, and thereby compute the large-distance behaviour of such flocks.

Collective Motion in a Network of Self-Propelled Agent Systems

Collective motions of animals that move towards the same direction is a conspicuous feature in nature. Such groups of animals are called a self-propelled agent (SPA) systems. Many studies have been focused on the synchronization of isolated SPA systems. In real scenarios, different SPA systems are coupled with each other forming a network of SPA systems. For example, a flock of birds and a school of fish show predator-prey relationships and different groups of birds may compete for food. In this work, we propose a general framework to study the collective motion of coupled self-propelled agent systems. Especially, we study how three different connections between SPA systems: symbiosis, predator-prey, and competition influence the synchronization of the network of SPA systems. We find that a network of SPA systems coupled with symbiosis relationship arrive at a complete synchronization as all its subsystems showing a complete synchronization; a network of SPA systems coupled by predator-prey relationship can not reach a complete synchronization and its subsystems converges to different synchronized directions; and the competitive relationship between SPA systems could increase the synchronization of each SPA systems, while the network of SPA systems coupled by competitive relationships shows an optimal synchronization for small coupling strength, indicating that small competition promotes the synchronization of the entire system.

Modelling the emergence of coordinated collective motion by minimizing dissatisfaction

Coordinated collective motion (CCM) has been recently studied using agent-based simulations by applying three behavioural rules: repulsion, attraction and alignment. But these rules are so similar to the expected group behaviour that it can hardly be labelled emergent. We developed an agent-based model that produces CCM using a set of low-level dyadic interaction rules. The agents change their positions with regard to other agents in order to minimize their own dissatisfaction with their inter-individual distances. To test the emergence of CCM, several simulation experiments were performed. The results show that the agents were able to achieve CCM after a few thousand time steps, and that the bigger the area perceived by them, the more coordinated and cohesive the group motion became. An increased memory span and capacity to remember other agents' identities improved cohesion and coordination. The relationship with biological referents is discussed.

Topological-distance-dependent transition in flocks with binary interactions

We have studied a flocking model with binary interactions (binary flock), where the velocity of an agent depends on the velocity of only another agent and its own velocity, topped by the angular noise. The other agent is selected as the nth topological neighbor; the specific value of n being a fixed parameter of the problem. On the basis of extensive numerical simulation results, we argue that for n = 1, the phase transition from the ordered to the disordered phase of the flock is a special kind of discontinuous transition. Here, the order parameter does not flip-flop between multiple metastable states. It continues its initial disordered state for a period t(c), then switches over to the ordered state and remains in this state ever after. For n = 2, it is the usual discontinuous transition between two metastable states. Beyond this range, the continuous transitions are observed for n≥3. Such a system of binary flocks has been further studied using the hydrodynamic equations of motion. Linear stability analysis of the homogeneous polarized state shows that such a state is unstable close to the critical point and above some critical speed, which increases as we increase n. The critical noise strengths, which depend on the average correlation between a pair of topological neighbors, are estimated for five different values of n, which match well with their simulated values.

Flocking with discrete symmetry: The two-dimensional active Ising model

We study in detail the active Ising model, a stochastic lattice gas where collective motion emerges from the spontaneous breaking of a discrete symmetry. On a two-dimensional lattice, active particles undergo a diffusion biased in one of two possible directions (left and right) and align ferromagnetically their direction of motion, hence yielding a minimal flocking model with discrete rotational symmetry. We show that the transition to collective motion amounts in this model to a bona fide liquid-gas phase transition in the canonical ensemble. The phase diagram in the density-velocity parameter plane has a critical point at zero velocity which belongs to the Ising universality class. In the density-temperature "canonical" ensemble, the usual critical point of the equilibrium liquid-gas transition is sent to infinite density because the different symmetries between liquid and gas phases preclude a supercritical region. We build a continuum theory which reproduces qualitatively the behavior of the microscopic model. In particular, we predict analytically the shapes of the phase diagrams in the vicinity of the critical points, the binodal and spinodal densities at coexistence, and the speeds and shapes of the phase-separated profiles.

Beyond Corroboration: Strengthening Model Validation by Looking for Unexpected Patterns

Models of emergent phenomena are designed to provide an explanation to global-scale phenomena from local-scale processes. Model validation is commonly done by verifying that the model is able to reproduce the patterns to be explained. We argue that robust validation must not only be based on corroboration, but also on attempting to falsify the model, i.e. making sure that the model behaves soundly for any reasonable input and parameter values. We propose an open-ended evolutionary method based on Novelty Search to look for the diverse patterns a model can produce. The Pattern Space Exploration method was tested on a model of collective motion and compared to three common a priori sampling experiment designs. The method successfully discovered all known qualitatively different kinds of collective motion, and performed much better than the a priori sampling methods. The method was then applied to a case study of city system dynamics to explore the model’s predicted values of city hierarchisation and population growth. This case study showed that the method can provide insights on potential predictive scenarios as well as falsifiers of the model when the simulated dynamics are highly unrealistic.

Shape control and compartmentalization in active colloidal cells

Small autonomous machines like biological cells or soft robots can convert energy input into control of function and form. It is desired that this behavior emerges spontaneously and can be easily switched over time. For this purpose we introduce an active matter system that is loosely inspired by biology and which we term an active colloidal cell. The active colloidal cell consists of a boundary and a fluid interior, both of which are built from identical rotating spinners whose activity creates convective flows. Similarly to biological cell motility, which is driven by cytoskeletal components spread throughout the entire volume of the cell, active colloidal cells are characterized by highly distributed energy conversion. We demonstrate that we can control the shape of the active colloidal cell and drive compartmentalization by varying the details of the boundary (hard vs. flexible) and the character of the spinners (passive vs. active). We report buckling of the boundary controlled by the pattern of boundary activity, as well as formation of core-shell and inverted Janus phase-separated configurations within the active cell interior. As the cell size is increased, the inverted Janus configuration spontaneously breaks its mirror symmetry. The result is a bubble-crescent configuration, which alternates between two degenerate states over time and exhibits collective migration of the fluid along the boundary. Our results are obtained using microscopic, non-momentum-conserving Langevin dynamics simulations and verified via a phase-field continuum model coupled to a Navier-Stokes equation.

Active matter beyond mean-field: ring-kinetic theory for self-propelled particles

Recently, Hanke et al. [Phys. Rev. E 88, 052309 (2013)] showed that mean-field kinetic theory fails to describe collective motion in soft active colloids and that correlations must not be neglected. Correlation effects are also expected to be essential in systems of biofilaments driven by molecular motors and in swarms of midges. To obtain correlations in an active matter system from first principles, we derive a ring-kinetic theory for Vicsek-style models of self-propelled agents from the exact N-particle evolution equation in phase space. The theory goes beyond mean-field and does not rely on Boltzmann's approximation of molecular chaos. It can handle precollisional correlations and cluster formation, which are both important to understand the phase transition to collective motion. We propose a diagrammatic technique to perform a small-density expansion of the collision operator and derive the first two equations of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. An algorithm is presented that numerically solves the evolution equation for the two-particle correlations on a lattice. Agent-based simulations are performed and informative quantities such as orientational and density correlation functions are compared with those obtained by ring-kinetic theory. Excellent quantitative agreement between simulations and theory is found at not-too-small noises and mean free paths. This shows that there are parameter ranges in Vicsek-like models where the correlated closure of the BBGKY hierarchy gives correct and nontrivial results. We calculate the dependence of the orientational correlations on distance in the disordered phase and find that it seems to be consistent with a power law with an exponent around -1.8, followed by an exponential decay. General limitations of the kinetic theory and its numerical solution are discussed.

Tricritical points in a Vicsek model of self-propelled particles with bounded confidence

We study the orientational ordering in systems of self-propelled particles with selective interactions. To introduce the selectivity we augment the standard Vicsek model with a bounded-confidence collision rule: a given particle only aligns to neighbors who have directions quite similar to its own. Neighbors whose directions deviate more than a fixed restriction angle α are ignored. The collective dynamics of this system is studied by agent-based simulations and kinetic mean-field theory. We demonstrate that the reduction of the restriction angle leads to a critical noise amplitude decreasing monotonically with that angle, turning into a power law with exponent 3/2 for small angles. Moreover, for small system sizes we show that upon decreasing the restriction angle, the kind of the transition to polar collective motion changes from continuous to discontinuous. Thus, an apparent tricritical point with different scaling laws is identified and calculated analytically. We investigate the shifting and vanishing of this point due to the formation of density bands as the system size is increased. Agent-based simulations in small systems with large particle velocities show excellent agreement with the kinetic theory predictions. We also find that at very small interaction angles, the polar ordered phase becomes unstable with respect to the apolar phase. We derive analytical expressions for the dependence of the threshold noise on the restriction angle. We show that the mean-field kinetic theory also permits stationary nematic states below a restriction angle of 0.681π. We calculate the critical noise, at which the disordered state bifurcates to a nematic state, and find that it is always smaller than the threshold noise for the transition from disorder to polar order. The disordered-nematic transition features two tricritical points: At low and high restriction angle, the transition is discontinuous but continuous at intermediate α. We generalize our results to systems that show fragmentation into more than two groups and obtain scaling laws for the transition lines and the corresponding tricritical points. A numerical method to evaluate the nonlinear Fredholm integral equation for the stationary distribution function is also presented. This method is shown to give excellent agreement with agent-based simulations, even in strongly ordered systems at noise values close to zero.

Aspects of the density field in an active nematic

Active nematics are conceptually the simplest orientationally ordered phase of self-driven particles, but have proved to be a perennial source of surprises. We show here through numerical solution of coarse-grained equations for the order parameter and density that the growth of the active nematic phase from the isotropic phase is necessarily accompanied by a clumping of the density. The growth kinetics of the density domains is shown to be faster than the [Formula: see text] law expected for variables governed by a conservation law. Other results presented include the suppression of density fluctuations in the stationary ordered nematic by the imposition of an orienting field. We close by posing some open questions.