Relevance of Metric-Free Interactions in Flocking Phenomena

We show that the collective properties of self-propelled particles aligning with their "topological" (Voronoi) neighbors are qualitatively different from those of usual models where metric interaction ranges are used. This relevance of metric-free interactions, shown in a minimal setting, indicate that realistic models for the cohesive motion of cells, bird flocks, and fish schools may have to incorporate them, as suggested by recent observations.Comment: To appear on Physical Review Letter

Comment on ``Phase Transitions in Systems of Self-Propelled Agents and Related Network Models''

In this comment we show that the transition to collective motion in Vicsek-like systems with angular noise remain discontinuous for large velocity values. Thus, the networks studied by Aldana {\et al.} [Phys. Rev. Lett. {\bf 98}, 095702 (2007)] at best constitute a singular, large velocity limit of these systems.Comment: To appear on Physical Review Letter

Competing ferromagnetic and nematic alignment in self-propelled polar particles

We study a Vicsek-style model of self-propelled particles where ferromagnetic and nematic alignment compete in both the usual "metric" version and in the "metric-free" case where a particle interacts with its Voronoi neighbors. We show that the phase diagram of this out-of-equilibrium XY model is similar to that of its equilibrium counterpart: the properties of the fully-nematic model, studied before in [F. Ginelli, F. Peruani, M. Baer, and H. Chat\'e, Phys. Rev. Lett. 104, 184502 (2010)], are thus robust to the introduction of a modest bias of interactions towards ferromagnetic alignment. The direct transitions between polar and nematic ordered phases are shown to be discontinuous in the metric case, and continuous, belonging to the Ising universality class, in the metric-free version

Nonlinearly driven transverse synchronization in coupled chaotic systems

Synchronization transitions are investigated in coupled chaotic maps. Depending on the relative weight of linear versus nonlinear instability mechanisms associated to the single map two different scenarios for the transition may occur. When only two maps are considered we always find that the critical coupling $\epsilon_l$ for chaotic synchronization can be predicted within a linear analysis by the vanishing of the transverse Lyapunov exponent $\lambda_T$. However, major differences between transitions driven by linear or nonlinear mechanisms are revealed by the dynamics of the transient toward the synchronized state. As a representative example of extended systems a one dimensional lattice of chaotic maps with power-law coupling is considered. In this high dimensional model finite amplitude instabilities may have a dramatic effect on the transition. For strong nonlinearities an exponential divergence of the synchronization times with the chain length can be observed above $\epsilon_l$, notwithstanding the transverse dynamics is stable against infinitesimal perturbations at any instant. Therefore, the transition takes place at a coupling $\epsilon_{nl}$ definitely larger than $\epsilon_l$ and its origin is intrinsically nonlinear. The linearly driven transitions are continuous and can be described in terms of mean field results for non-equilibrium phase transitions with long range interactions. While the transitions dominated by nonlinear mechanisms appear to be discontinuous.Comment: 29 pages, 14 figure

Leading birds by their beaks : the response of flocks to external perturbations

Acknowledgments We have benefited from discussions with H Chaté and A Cavagna. We acknowledge support from the Marie Curie Career Integration Grant (CIG) PCIG13-GA-2013-618399. JT also acknowledges support from the SUPA distinguished visitor program and from the National Science Foundation through awards # EF-1137815 and 1006171, and thanks the University of Aberdeen for their hospitality while this work was underway. FG acknowledges support from EPSRC First Grant EP/K018450/1.Peer reviewedPublisher PD

Synchronization of spatio-temporal chaos as an absorbing phase transition: a study in 2+1 dimensions

The synchronization transition between two coupled replicas of spatio-temporal chaotic systems in 2+1 dimensions is studied as a phase transition into an absorbing state - the synchronized state. Confirming the scenario drawn in 1+1 dimensional systems, the transition is found to belong to two different universality classes - Multiplicative Noise (MN) and Directed Percolation (DP) - depending on the linear or nonlinear character of damage spreading occurring in the coupled systems. By comparing coupled map lattice with two different stochastic models, accurate numerical estimates for MN in 2+1 dimensions are obtained. Finally, aiming to pave the way for future experimental studies, slightly non-identical replicas have been considered. It is shown that the presence of small differences between the dynamics of the two replicas acts as an external field in the context of absorbing phase transitions, and can be characterized in terms of a suitable critical exponent.Comment: Submitted to Journal of Statistical Mechanics: Theory and Experimen

The Physics of the Vicsek Model

Peer reviewedPublisher PD

Intertangled stochastic motifs in networks of excitatory-inhibitory units

We have benefited from discussions with A. Politi. The authors acknowledge financial support from H2020- MSCA-ITN-2015 project COSMOS 642563.Peer reviewedPostprin

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

Large-scale collective properties of self-propelled rods

We study, in two space dimensions, the large-scale properties of collections of constant-speed polar point particles interacting locally by nematic alignment in the presence of noise. This minimal approach to self-propelled rods allows one to deal with large numbers of particles, revealing a phenomenology previously unseen in more complicated models, and moreover distinctively different from both that of the purely polar case (e.g. the Vicsek model) and of active nematics.Comment: Submitted to Phys. Rev. Let