Swarms of particle agents with harmonic interactions

Inverse Bayesian inference in swarming behaviour of soldier crabs

Animals making a group sometimes approach and sometimes avoid a dense area of group mates, and that reveals the ambiguity of density preference. Although the ambiguity is not expressed by a simple deterministic local rule, it seems to be implemented by probabilistic inference that is based on Bayesian and inverse Bayesian inference. In particular, the inverse Bayesian process refers to perpetual changing of hypotheses. We here analyse a time series of swarming soldier crabs and show that they are employed to Bayesian and inverse Bayesian inference. Comparing simulation results with data of the real swarm, we show that the interpretation of the movement of soldier crabs which can be based on the inference can lead to the identification of a drastic phase shift-like transition of gathering and dispersing.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)'.

A simple game-theoretic model for upstream fish migration

A simple game-theoretic model for upstream fish migration, which is a key element in life history of diadromous fishes, is proposed. Foundation of the model is a minimization problem on the cost of migration with the swimming speed and school size as the variables to be simultaneously optimized. Finding the optimizer ultimately reduces to solving a self-consistency equation without explicit solutions. Mathematical analytical results lead to the sufficient condition that the self-consistency equation has a unique solution, which turns out to be identified with the condition where the unique optimizer exists. Behavior of the optimizer is analyzed both mathematically and numerically to show its biophysical and ecological consequences. The analytical results demonstrate reasonable agreement between the present mathematical model and the theoretical and experimental results of upstream migration of fish schools reported in the past research.

Swarming in viscous fluids: Three-dimensional patterns in swimmer- and force-induced flows

We derive a three-dimensional theory of self-propelled particle swarming in a viscous fluid environment. Our model predicts emergent collective behavior that depends critically on fluid opacity, mechanism of self-propulsion, and type of particle-particle interaction. In "clear fluids" swimmers have full knowledge of their surroundings and can adjust their velocities with respect to the lab frame, while in "opaque fluids" they control their velocities only in relation to the local fluid flow. We also show that "social" interactions that affect only a particle's propensity to swim towards or away from neighbors induces a flow field that is qualitatively different from the long-ranged flow fields generated by direct "physical" interactions. The latter can be short-ranged but lead to much longer-ranged fluid-mediated hydrodynamic forces, effectively amplifying the range over which particles interact. These different fluid flows conspire to profoundly affect swarm morphology, kinetically stabilizing or destabilizing swarm configurations that would arise in the absence of fluid. Depending upon the overall interaction potential, the mechanism of swimming ( e.g., pushers or pullers), and the degree of fluid opaqueness, we discover a number of new collective three-dimensional patterns including flocks with prolate or oblate shapes, recirculating pelotonlike structures, and jetlike fluid flows that entrain particles mediating their escape from the center of mill-like structures. Our results reveal how the interplay among general physical elements influence fluid-mediated interactions and the self-organization, mobility, and stability of new three-dimensional swarms and suggest how they might be used to kinetically control their collective behavior.

Swarming and pattern formation due to selective attraction and repulsion

We discuss the collective dynamics of self-propelled particles with selective attraction and repulsion interactions. Each particle, or individual, may respond differently to its neighbours depending on the sign of their relative velocity. Thus, it is able to distinguish approaching (coming closer) and retreating (moving away) individuals. This differentiation of the social response is motivated by the response to looming visual stimuli and may be seen as a generalization of the previously proposed escape and pursuit interactions motivated by empirical evidence for cannibalism as a driving force of collective migration in locusts and Mormon crickets. The model can account for different types of behaviour such as pure attraction, pure repulsion or escape and pursuit, depending on the values (signs) of the different response strengths. It provides, in the light of recent experimental results, an interesting alternative to previously proposed models of collective motion with an explicit velocity-alignment interaction. We discuss the derivation of a coarse-grained description of the system dynamics, which allows us to derive analytically the necessary condition for emergence of collective motion. Furthermore, we analyse systematically the onset of collective motion and clustering in numerical simulations of the model for varying interaction strengths. We show that collective motion arises only in a subregion of the parameter space, which is consistent with the analytical prediction and corresponds to an effective escape and/or pursuit response.

Canonical active Brownian motion

Active Brownian motion is the complex motion of active Brownian particles. They are "active" in the sense that they can transform their internal energy into energy of motion and thus create complex motion patterns. Theories of active Brownian motion so far imposed couplings between the internal energy and the kinetic energy of the system. We investigate how this idea can be naturally taken further to include also couplings to the potential energy, which finally leads to a general theory of canonical dissipative systems. Explicit analytical and numerical studies are done for the motion of one particle in harmonic external potentials. Apart from stationary solutions, we study nonequilibrium dynamics and show the existence of various bifurcation phenomena.

Finite-size scaling analysis and dynamic study of the critical behavior of a model for the collective displacement of self-driven individuals

The Vicsek model (VM) [T. Vicsek, Phys. Rev. Lett. 75, 1226 (1995)], for the description of the collective behavior of self-driven individuals, assumes that each of them adopts the average direction of movement of its neighbors, perturbed by an external noise. A second-order transition between a state of ordered collective displacement (low-noise limit) and a disordered regime (high-noise limit) was found early on. However, this scenario has recently been challenged by Grégory and Chaté [G. Grégory and H. Chaté, Phys. Rev. Lett. 92, 025702 (2004)] who claim that the transition of the VM may be of first order. By performing extensive simulations of the VM, which are analyzed by means of both finite-size scaling methods and a dynamic scaling approach, we unambiguously demonstrate the critical nature of the transition. Furthermore, the complete set of critical exponents of the VM, in d=2 dimensions, is determined. By means of independent methods--i.e., stationary and dynamic measurements--we provide two tests showing that the standard hyperscaling relationship dnu-2beta=gamma holds, where beta, nu, and gamma are the order parameter, correlation length, and "susceptibility" critical exponents, respectively. Furthermore, we established that at criticality, the correlation length grows according to xi-t1z, with z approximately = 1.27(3) , independently of the degree of order of the initial configuration, in marked contrast with the behavior of the XY model.

Modeling vortex swarming in Daphnia

Based on experimental observations in Daphnia, we introduce an agent-based model for the motion of single and swarms of animals. Each agent is described by a stochastic equation that also considers the conditions for active biological motion. An environmental potential further reflects local conditions for Daphnia, such as attraction to light sources. This model is sufficient to describe the observed cycling behavior of single Daphnia. To simulate vortex swarming of many Daphnia, i.e. the collective rotation of the swarm in one direction, we extend the model by considering avoidance of collisions. Two different ansatzes to model such a behavior are developed and compared. By means of computer simulations of a multi-agent system we show that local avoidance - as a special form of asymmetric repulsion between animals - leads to the emergence of a vortex swarm. The transition from uncorrelated rotation of single agents to the vortex swarming as a function of the swarm size is investigated. Eventually, some evidence of avoidance behavior in Daphnia is provided by comparing experimental and simulation results for two animals.

Vortex formation by active agents as a model for Daphnia swarming

We propose a self-propelled particle model for the swarming of Daphnia that takes into account mutual repulsion and attraction to a center. Surprisingly, a vortex is formed only for an intermediate strength of propulsion. The phase diagram and the transitions between states with and without a vortex are analyzed, and the nature of the phase boundaries is discussed based on a linear stability analysis of the motion of individual swimmers. This allows us to identify various key parameters determining the characteristic features of the collective motion.