A one-dimensional rule-based model for flocking, that combines velocity alignment and long-range centering interactions, is presented and studied. The induced cohesion in the collective motion of the self-propelled agents leads to a unique group behaviour that contrasts with previous studies. Our results show that the largest cluster of particles, in the condensed states, develops a mean velocity slower than the preferred one in the absence of noise. For strong noise, the system also develops a non-vanishing mean velocity, alternating its direction of motion stochastically. This allows us to address the directional switching phenomenon. The effects of different sources of stochasticity on the system are also discussed.
Collective motion - or flocking - is an emergent phenomena that underlies many biological processes of relevance, from cellular migrations to animal groups movement. In this work, we derive scaling relations for the fluctuations of the mean direction of motion and for the static density structure factor (which encodes static density fluctuations) in the presence of a homogeneous, small external field. This allows us to formulate two different and complementary criteria capable of detecting instances of directed motion exclusively from easily measurable dynamical and static signatures of the co…
We generalize the Vicsek model to describe the collective behaviour of polar circle swimmers with local alignment interactions. While the phase transition leading to collective motion in 2D (flocking) occurs at the same interaction to noise ratio as for linear swimmers, as we show, circular motion enhances the polarization in the ordered phase (enhanced flocking) and induces secondary instabilities leading to structure formation. Slow rotations result in phase separation whereas fast rotations generate patterns which consist of phase synchronized microflocks of controllable self-limited size. …
The spontaneous emergence of collective motion patterns is usually associated with the presence of a velocity alignment mechanism that mediates the interactions among the moving individuals. Despite of this widespread view, it has been shown recently that several flocking behaviors can emerge in the absence of velocity alignment and as a result of short-range, position-based, attractive forces that act inside a vision cone. Here, we derive the corresponding hydrodynamic equations of a microscopic position-based flocking model, reviewing and extending previously reported results. In particular,…
We study the $q$-state active Potts model (APM) on a two-dimensional lattice in which self-propelled particles have $q$ internal states corresponding to the $q$ directions of motion. A local alignment rule inspired by the ferromagnetic $q$-state Potts model and self-propulsion via biased diffusion according to the internal particle states leads to a collective motion at high densities and low noise. We formulate a coarse-grained hydrodynamic theory of the model, compute the phase diagrams of the APM for $q=4$ and $q=6$ and explore the flocking dynamics in the region, in which the high-density …
Random walkers characterized by random positions and random velocities lead to normal diffusion. A random walk was originally proposed by Einstein to model Brownian motion and to demonstrate the existence of atoms and molecules. Such a walker represents an inanimate particle driven by environmental fluctuations. On the other hand, there are many examples of so-called "persistent random walkers", including self-propelled particles that are able to move with almost constant speed while randomly changing their direction of motion. Examples include living entities (ranging from flagellated unicell…
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 c…
We study a minimal cognitive flocking model, which assumes that the moving entities navigate using exclusively the available instantaneous visual information. The model consists of active particles, with no memory, that interact by a short-ranged, position-based, attractive force that acts inside a vision cone (VC) and lack velocity-velocity alignment. We show that this active system can exhibit -- due to the VC that breaks Newton's third law -- various complex, large-scale, self-organized patterns. Depending on parameter values, we observe the emergence of aggregates or milling-like patterns,…
We study the collective motion of a large set of self-propelled particles subject to voter-like interactions. Each particle moves on a two-dimensional space at a constant speed in a direction that is randomly assigned initially. Then, at every step of the dynamics, each particle adopts the direction of motion of a randomly chosen neighboring particle. We investigate the time evolution of the global alignment of particles measured by the order parameter $φ$, until complete order $φ=1.0$ is reached (polar consensus). We find that $φ$ increases as $t^{1/2}$ for short times and approaches exponent…
The effect of quenched (frozen) orientational disorder on the collective motion of active particles is analyzed. We find that, as with annealed disorder (Langevin noise), active polar systems are far more robust against quenched disorder than their equilibrium counterparts. In particular, long ranged order (i.e., the existence of a non-zero average velocity $\langle {\bf v} \rangle$) persists in the presence of quenched disorder even in spatial dimensions $d=3$, while it is destroyed even by arbitrarily weak disorder in $d \le 4$ in equilibrium systems. Furthermore, in $d=2$, quasi-long-ranged…
Flocking and turning: a new model for self-organized collective motion
a Istituto Sistemi Complessi (ISC--CNR), Via dei Taurini 19, 00185 Roma, Italy b Dipartimento di Fisica, ``Sapienza'' Universit\'a di Roma, P.le Aldo Moro 2, 00185 Roma, Italy c Initiative for the Theoretical Sciences, The Graduate Center, 365 Fifth Avenue, New York, NY 10016 USA d Instituto de Investigaciones Fisicoqu \' micas Te \'o ricas y Aplicadas (INIFTA)；Departamento de F \' sica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, c.c. 16, suc. 4, 1900 La Plata, Argentina e CONICET La Plata, Consejo Nacional de Investigaciones Cient \' ficas y T \'e cnicas, Argentina f Laboratoire de Physique Statistique de l' \' E cole Normale Sup\'erieure, CNRS；h Laboratoire de Physique Th\'eorique de l'\'Ecole Normale Sup\'erieure, CNRS；University Paris VI, 24 rue Lhomond, 75231 Paris Cedex 05, France
From Global Flocking to Local Clustering: Interplay between Velocity Alignment and Visual Perception of Active Particles
Department of Physics and Astrophysics, University of Delhi（德里大学物理与天体物理学系）；Department of Physics, University of Calcutta（加尔各答大学物理系）；Laboratoire de Physique Théorique et Modélisation, UMR 8089, CY Cergy Paris Université（CY塞尔吉巴黎大学理论物理与建模实验室）
Flocks of birds, schools of fish, insects swarms are examples of coordinated motion of a group that arises spontaneously from the action of many individuals. Here, we study flocking behavior from the viewpoint of multi-agent reinforcement learning. In this setting, a learning agent tries to keep contact with the group using as sensory input the velocity of its neighbors. This goal is pursued by each learning individual by exerting a limited control on its own direction of motion. By means of standard reinforcement learning algorithms we show that: i) a learning agent exposed to a group of teac…
