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

Moving and staying together without a leader

A microscopic, stochastic, minimal model for collective and cohesive motion of identical self-propelled particles is introduced. Even though the particles interact strictly locally in a very noisy manner, we show that cohesion can be maintained, even in the zero-density limit of an arbitrarily large flock in an infinite space. The phase diagram spanned by the two main parameters of our model, which encode the tendencies for particles to align and to stay together, contains non-moving "gas", "liquid"' and "solid" phases separated from their moving counterparts by the onset of collective motion. The "gas/liquid" and "liquid/solid" are shown to be first-order phase transitions in all cases. In the cohesive phases, we study also the diffusive properties of individuals and their relation to the macroscopic motion and to the shape of the flock

When dunes move together, structure of deserts emerges

Crescent shaped barchan dunes are highly mobile dunes that are usually presented as a prototypical model of sand dunes. Although they have been theoretically shown to be unstable when considered separately, it is well known that they form large assemblies in desert. Collisions of dunes have been proposed as a mechanism to redistribute sand between dunes and prevent the formation of heavily large dunes, resulting in a stabilizing effect in the context of a dense barchan field. Yet, no models are able to explain the spatial structures of dunes observed in deserts. Here, we use an agent-based model with elementary rules of sand redistribution during collisions to access the full dynamics of very large barchan dune fields. Consequently, stationnary, out of equilibrium states emerge. Trigging the dune field density by a sand load/lost ratio, we show that large dune fields exhibit two assymtotic regimes: a dilute regime, where sand dune nucleation is needed to maintain a dune field, and a dense regime, where dune collisions allow to stabilize the whole dune field. In this dense regime, spatial structures form: the dune field is structured in narrow corridors of dunes extending in the wind direction, as observed in dense barchan deserts

Boltzmann and hydrodynamic description for self-propelled particles

We study analytically the emergence of spontaneous collective motion within large bidimensional groups of self-propelled particles with noisy local interactions, a schematic model for assemblies of biological organisms. As a central result, we derive from the individual dynamics the hydrodynamic equations for the density and velocity fields, thus giving a microscopic foundation to the phenomenological equations used in previous approaches. A homogeneous spontaneous motion emerges below a transition line in the noise-density plane. Yet, this state is shown to be unstable against spatial perturbations, suggesting that more complicated structures should eventually appear.Comment: 4 pages, 3 figures, final versio

Polynomial root finding over local rings and application to error correcting codes

International audienceThis article is devoted to algorithms for computing all the roots of a univariate polynomial with coefficients in a complete commutative Noetherian unramified regular local domain, which are given to a fixed common finite precision. We study the cost of our algorithms, discuss their practical performances, and apply our results to the Guruswami and Sudan list decoding algorithm over Galois rings

Active and passive particles: Modeling beads in a bacterial bath

International audienceA simple model for the motion of passive particles in a bath of active, self-propelled ones is introduced. It is argued that this approach provides the correct framework within which to cast the recent experimental results obtained by Wu and Libchaber [Phys Rev. Lett. 84, 3017 (2000)] for the diffusive properties of polystyrene beads displaced by bacteria suspended in a two-dimensional fluid film. Our results suggest that superdiffusive behavior should indeed be generically observed in the transition region marking the onset of collective motion

Collective motion of self-propelled particles interacting without cohesion

We present a comprehensive study of Vicsek-style self-propelled particle models in two and three space dimensions. The onset of collective motion in such stochastic models with only local alignment interactions is studied in detail and shown to be discontinuous (first-order like). The properties of the ordered, collectively moving phase are investigated. In a large domain of parameter space including the transition region, well-defined high-density and high-order propagating solitary structures are shown to dominate the dynamics. Far enough from the transition region, on the other hand, these objects are not present. A statistically-homogeneous ordered phase is then observed, which is characterized by anomalously-strong density fluctuations, superdiffusion, and strong intermittency.Comment: Submitted to Physical Review

Onset of collective and cohesive motion

We study the onset of collective motion, with and without cohesion, of groups of noisy self-propelled particles interacting locally. We find that this phase transition, in two space dimensions, is always discontinuous, including for the minimal model of Vicsek et al. [Phys. Rev. Lett. {\bf 75},1226 (1995)] for which a non-trivial critical point was previously advocated. We also show that cohesion is always lost near onset, as a result of the interplay of density, velocity, and shape fluctuations.Comment: accepted for publication in Phys. Rev. Let

Modèles minimaux aux interfaces de la physique

Collective motions, deserts of mobile dunes and flows of giant micellles share in common the fact that the local injection of energy leads to complex collective dynamics. At a microscopic level, interactions may remain unknown or they reach a such level of complexity that it is necessary to simplify the elementary ingredients. Models allow to understand the weight of each ingredients on the global dynamics. We then get an understandable picture. This is the main goal of minimal models.But the underlying ideas on universality and minimal models have a narrower and a more accurate meaning in the framework of at-equilibrium statistical physics. Such concepts are linked to the existence of continuous transition. Similar theoretical results do not exist for driven systems. Then the data analysis of numerical simulations are usually done following analogies with critical phenomena.Here, we present three cases at three different steps of study. For collective motions, we show that analogies with ferromagnetic materials lead to wrong conclusions. A long careful study of numerical simulations reveals a discontinuous phase transition. An instability leads to a non-linear dynamical pattern which gets similar characteristics to solitary waves. Other recent studies make analogies with smectic phases.Models of deserts of dunes allow to understand the effects of the different dunes interactions. Thus we explained how deserts could self-organise in time and in space. When models are used far from the geophysical hypotheses, we get behaviours which have already been observed in other out-of-equilibrium physical systems: percolation, reaction-diffusion, mass transfer. However we show that none of those analogies are fully conclusive in regard to our results.Last, in considering flows of solutions of giant micelles, we propose a minimal model in the aim to give a better understanding of the mechanisms of shear banding.Les mouvements collectifs d'animaux, les déserts de dunes mobiles etles écoulements de micelles géantes ont ceci de commun que l'injection d'énergie au niveau local conduit à une dynamique collective complexe. Les interactions au niveau microscopique peuvent être inconnues, ou alors sont tellement complexes qu'il est nécessaire de simplifier les ingrédients élémentaires. La modélisation permet de comprendre le poids de chacun des ingrédients sur la dynamique globale. On en obtient ainsi un tableau causal intelligible. C'est le premier intérêt des modèles minimaux.Mais les concepts d'universalité et de modèles minimaux ont une signification bien établie et plus restreinte dans le cadre de la physique statistique des systèmes à l'équilibre. Ils sont attachés à l'existence de transitions continues. Un cadre théorique équivalent à celui des phénomènes critiques n'existe pas lorsque le système est maintenu loin de l'équilibre. L'analyse des données issues des simulations numériques est habituellement réalisée par analogie en suivant les résultats analytiques obtenus à l'équilibre.Nous présentons trois cas à différentes étapes du projet de recherche. Dans le cas des mouvements collectifs, nous montrons que les analogies avec les matériaux ferromagnétiques ont mené à des conclusions erronées. Une longue étude critique des simulations numériques a montré que la transition est discontinue. Une instabilité dans les assemblées en mouvement produit un motif spatio-temporel similaire à une onde solitaire. D'autres études récentes proposent une nouvelle analogie avec les phases smectiques.Les modèles de déserts de dunes permettent d'ordonner les effets des différentes interactions entre dunes. Ainsi, nous avons donné une explication à l'auto-organisation des déserts. Lorsque les modèles sont étudiés sans prendre en compte leur dimension géophysique, nous obtenons des comportements déjà observés dans d'autres modèles de physique statistique hors d'équilibre~: percolation, réaction-diffusion, transfert de masse. Cependant nous montrons qu'aucune analogie ne permet d'expliquer de manière convainquante nos résultats.Enfin, considérant les écoulements de solutions de micelles géantes, nous proposons un modèle minimal permettant de mieux comprendre les mécanismes à l'oeuvre dans les écoulements en bande de cisaillement

Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis

Considering a gas of self-propelled particles with binary interactions, we derive the hydrodynamic equations governing the density and velocity fields from the microscopic dynamics, in the framework of the associated Boltzmann equation. Explicit expressions for the transport coefficients are given, as a function of the microscopic parameters of the model. We show that the homogeneous state with zero hydrodynamic velocity is unstable above a critical density (which depends on the microscopic parameters), signaling the onset of a collective motion. Comparison with numerical simulations on a standard model of self-propelled particles shows that the phase diagram we obtain is robust, in the sense that it depends only slightly on the precise definition of the model. While the homogeneous flow is found to be stable far from the transition line, it becomes unstable with respect to finite-wavelength perturbations close to the transition, implying a non trivial spatio-temporal structure for the resulting flow. We find solitary wave solutions of the hydrodynamic equations, quite similar to the stripes reported in direct numerical simulations of self-propelled particles.Comment: 33 pages, 11 figures, submitted to J. Phys.