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

The Physics of the Vicsek Model

Peer reviewedPublisher PD

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

Evidence of a Critical Phase Transition in Purely Temporal Dynamics with Long-Delayed Feedback

We wish to thank S. Lepri and A. Politi for useful discussions. MF and FG acknowledge support from EU Marie Curie ITN grant n. 64256 (COSMOS).Peer reviewedPublisher PD

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

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

Covariant Lyapunov vectors

The recent years have witnessed a growing interest for covariant Lyapunov vectors (CLVs) which span local intrinsic directions in the phase space of chaotic systems. Here we review the basic results of ergodic theory, with a specific reference to the implications of Oseledets' theorem for the properties of the CLVs. We then present a detailed description of a "dynamical" algorithm to compute the CLVs and show that it generically converges exponentially in time. We also discuss its numerical performance and compare it with other algorithms presented in literature. We finally illustrate how CLVs can be used to quantify deviations from hyperbolicity with reference to a dissipative system (a chain of H\'enon maps) and a Hamiltonian model (a Fermi-Pasta-Ulam chain)