[Show abstract][Hide abstract] ABSTRACT: Recent research in animal behaviour has contributed to determine how alignment, turning responses, and changes of speed mediate flocking and schooling interactions in different animal species. Here, we propose a complementary approach to the analysis of flocking phenomena, based on the idea that animals occupy preferential, anysotropic positions with respect to their neighbours, and devote a large amount of their interaction responses to maintaining their mutual positions. We test our approach by deriving the apparent alignment and attraction responses from simulated trajectories of animals moving side by side, or one in front of the other. We show that the anisotropic positioning of individuals, in combination with noise, is sufficient to reproduce several aspects of the movement responses observed in real animal groups. This anisotropy at the level of interactions should be considered explicitly in future models of flocking and schooling. By making a distinction between interaction responses involved in maintaining a preferred flock configuration, and interaction responses directed at changing it, our work provides a frame to discriminate movement interactions that signal directional conflict from interactions underlying consensual group motion.
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[Show abstract][Hide abstract] ABSTRACT: In order to test parameters of the peculiar dynamics occurring in
barchan fields, and compute statistical analysis over large numbers of
dunes, we build and study an agent-based model, which includes the
well-known physics of an isolated barchan, and observations of
interactions between dunes. We showed in a previous study that such a
model, where barchans interact through short-range sand recapture and
collisions, reproduces the peculiar behaviours of real fields, namely
its spatial structuring along the wind direction, and the size selection
by the local density. In this paper we focus on the mechanisms that
drives these features. In particular, we show that eolian remote sand
transfer between dunes ensures that a dense field structures itself into
a very heterogeneous pattern, which alternates dense and diluted stripes
in the wind direction. In these very dense clusters of dunes, the
accumulation of collisions leads to the local emergence of a new size
for the dunes.
[Show abstract][Hide abstract] ABSTRACT: Crescent-shaped barchan dunes are highly mobile dunes which are
ubiquitous on Earth and other solar system bodies. Although they are
unstable when considered separately, they form large assemblies in
deserts and spatially organize in narrow corridors that extend in the
wind direction. Collision of barchans has been proposed as a mechanism
to redistribute sand between dunes and prevent the formation of very
large dunes. Here we use an agent-based model with elementary rules of
sand redistribution during collisions to access the full dynamics of
very large barchan fields. We tune the dune field density by changing
the sand load/lost ratio and follow the transition between dilute
fields, where barchans barely interact, and dense fields, where dune
collisions control and stabilize the dune field. In this dense regime,
barchans have a small, well-selected size and form flocks: the dune
field self-organizes in narrow corridors of dunes, as it is observed in
real dense barchan deserts.
Geophysical Research Letters 08/2013; 40(15):3909-3914. DOI:10.1002/grl.50757 · 4.20 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: 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. A
Journal of Physics A Mathematical and Theoretical 07/2009; 42(44). DOI:10.1088/1751-8113/42/44/445001 · 1.58 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We argue that the model introduced by Vicsek et al. in which self-propelled particles align locally with neighbors is, because of its simplicity, central to most studies of collective motion or "active" matter. After reviewing briefly its main properties, we show how it can be expanded into three main directions: changing the symmetry of the particles and/or of their interactions, adding local cohesion, and taking into account the fluid in which the particles move.
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: 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. 75,1226 (1995)10.1103/PhysRevLett.75.1226] for which a nontrivial 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.
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: The reverse transition from turbulent to laminar flow is studied in very large aspect ratio plane Couette and Taylor–Couette experiments. We show that laminar-turbulence coexistence dynamics (turbulent spots, spiral turbulence, etc.) can be seen as the ultimate stage of a modulation of the turbulent flows present at higher Reynolds number leading to regular, long-wavelength, inclined stripes. This new type of instability, whose originality is to arise within a macroscopically fluctuating state, can be described in the framework of Ginzburg–Landau equations to which noise is heuristically added to take into account the intrinsic fluctuations of the basic state.
[Show abstract][Hide abstract] ABSTRACT: We show that turbulent "spirals" and "spots" observed in Taylor-Couette and plane Couette flow correspond to a turbulence-intensity modulated finite-wavelength pattern which in every respect fits the phenomenology of coupled noisy Ginzburg-Landau (amplitude) equations with noise. This suggests the existence of a long-wavelength instability of the homogeneous turbulence regime.
[Show abstract][Hide abstract] ABSTRACT: A 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.