Flocking Regimes in a Simple Lattice Model

We study a one-dimensional lattice flocking model incorporating all three of the flocking criteria proposed by Reynolds [Computer Graphics vol.21 4 (1987)]: alignment, centring and separation. The model generalises that introduced by O. J. O' Loan and M. R. Evans [J. Phys. A. vol. 32 L99 (1999)]. We motivate the dynamical rules by microscopic sampling considerations. The model exhibits various flocking regimes: the alternating flock, the homogeneous flock and dipole structures. We investigate these regimes numerically and within a continuum mean-field theory.Comment: 24 pages 7 figure

Emergence of macroscopic directed motion in populations of motile colloids

From the formation of animal flocks to the emergence of coordinate motion in bacterial swarms, at all scales populations of motile organisms display coherent collective motion. This consistent behavior strongly contrasts with the difference in communication abilities between the individuals. Guided by this universal feature, physicists have proposed that solely alignment rules at the individual level could account for the emergence of unidirectional motion at the group level. This hypothesis has been supported by agent-based simulations. However, more complex collective behaviors have been systematically found in experiments including the formation of vortices, fluctuating swarms, clustering and swirling. All these model systems predominantly rely on actual collisions to display collective motion. As a result, the potential local alignment rules are entangled with more complex, often unknown, interactions. The large-scale behavior of the populations therefore depends on these uncontrolled microscopic couplings. Here, we demonstrate a new phase of active matter. We reveal that dilute populations of millions of colloidal rollers self-organize to achieve coherent motion along a unique direction, with very few density and velocity fluctuations. Identifying the microscopic interactions between the rollers allows a theoretical description of this polar-liquid state. Comparison of the theory with experiment suggests that hydrodynamic interactions promote the emergence of collective motion either in the form of a single macroscopic flock at low densities, or in that of a homogenous polar phase at higher densities. Furthermore, hydrodynamics protects the polar-liquid state from the giant density fluctuations. Our experiments demonstrate that genuine physical interactions at the individual level are sufficient to set homogeneous active populations into stable directed motion

Flowing active liquids in a pipe: Hysteretic response of polar flocks to external fields

We investigate the response of colloidal flocks to external fields. We first show that individual colloidal rollers align with external flows as would a classical spin with magnetic fields. Assembling polar active liquids from colloidal rollers, we experimentally demonstrate their hysteretic response: confined colloidal flocks can proceed against external flows. We theoretically explain this collective robustness, using an active hydrodynamic description, and show how orientational elasticity and confinement protect the direction of collective motion. Finally, we exploit the intrinsic bistability of confined active flows to devise self-sustained microfluidic oscillators.Comment: 12 pages, 7 figure; accepted for publication in Physical Review

Boltzmann-Ginzburg-Landau approach for continuous descriptions of generic Vicsek-like models

We describe a generic theoretical framework, denoted as the Boltzmann-Ginzburg-Landau approach, to derive continuous equations for the polar and/or nematic order parameters describing the large scale behavior of assemblies of point-like active particles interacting through polar or nematic alignment rules. Our study encompasses three main classes of dry active systems, namely polar particles with 'ferromagnetic' alignment (like the original Vicsek model), nematic particles with nematic alignment ("active nematics"), and polar particles with nematic alignment ("self-propelled rods"). The Boltzmann-Ginzburg-Landau approach combines a low-density description in the form of a Boltzmann equation, with a Ginzburg-Landau-type expansion close to the instability threshold of the disordered state. We provide the generic form of the continuous equations obtained for each class, and comment on the relationships and differences with other approaches.Comment: 30 pages, 3 figures, to appear in Eur. Phys. J. Special Topics, in a Discussion and Debate issue on active matte

Collective Motion with Anticipation: Flocking, Spinning, and Swarming

We investigate the collective dynamics of self-propelled particles able to probe and anticipate the orientation of their neighbors. We show that a simple anticipation strategy hinders the emergence of homogeneous flocking patterns. Yet, anticipation promotes two other forms of self-organization: collective spinning and swarming. In the spinning phase, all particles follow synchronous circular orbits, while in the swarming phase, the population condensates into a single compact swarm that cruises coherently without requiring any cohesive interactions. We quantitatively characterize and rationalize these phases of polar active matter and discuss potential applications to the design of swarming robots.Comment: 6 pages, 4 figure

Mean-field theory of collective motion due to velocity alignment

We introduce a system of self-propelled agents (active Brownian particles) with velocity alignment in two spatial dimensions and derive a mean-field theory from the microscopic dynamics via a nonlinear Fokker-Planck equation and a moment expansion of the probability distribution function. We analyze the stationary solutions corresponding to macroscopic collective motion with finite center of mass velocity (ordered state) and the disordered solution with no collective motion in the spatially homogeneous system. In particular, we discuss the impact of two different propulsion functions governing the individual dynamics. Our results predict a strong impact of the individual dynamics on the mean field onset of collective motion (continuous vs discontinuous). In addition to the macroscopic density and velocity field we consider explicitly the dynamics of an effective temperature of the agent system, representing a measure of velocity fluctuations around the mean velocity. We show that the temperature decreases strongly with increasing level of collective motion despite constant fluctuations on individual level, which suggests that extreme caution should be taken in deducing individual behavior, such as, state-dependent individual fluctuations from mean-field measurements [Yates {\em et al.}, PNAS, 106 (14), 2009].Comment: corrected version, Ecological Complexity (2011) in pres