arXiv subjects
Publications and source records attributed to Denis Boyer.
Edwards et al. [Nature 449, 1044-1048 (2007)] revisited well-known studies reporting power-laws in the frequency distribution of flight duration of wandering albatrosses, and concluded that no Lévy process could model recent observations with higher resolution. Here we show that this re-analysis suffers from a conceptual misunderstanding, and that the new albatross data remain consistent with a biological Lévy flight.
Precisely how ecological factors influence animal social structure is far from clear. We explore this question using an agent-based model inspired by the fission-fusion society of Spider monkeys (Ateles spp). Our model introduces a realistic, complex foraging environment composed of many resource patches with size varying according to an inverse power-law frequency distribution with exponent $β$. Foragers do not interact among them and start from random initial locations. They have either a complete or partial knowledge of the environment and maximize the ratio between the size of the next visited patch and the distance traveled to it, ignoring previously visited patches. At intermediate values of $β$, when large patches are neither too scarce nor too abundant, foragers form groups (coincide at the same patch) with a similar size frequency distribution as the spider monkey's subgroups. Fission-fusion events create a network of associations that contains weak bonds among foragers that meet only rarely and strong bonds among those that repeat associations more frequently than would be expected by chance. The latter form sub-networks with the highest number of bonds and a high clustering coefficient at intermediate values of $β$. The weak bonds enable the whole social network to percolate. Some of our results are similar to those found in long-term field studies of spider monkeys and other fission-fusion species. We conclude that hypotheses about the ecological causes of fission-fusion and the origin of complex social structures should consider the heterogeneity and complexity of the environment in which social animals live.
Scale-free foraging patterns are widespread among animals. These may be the outcome of an optimal searching strategy to find scarce randomly distributed resources, but a less explored alternative is that this behaviour may result from the interaction of foraging animals with a particular distribution of resources. We introduce a simple foraging model where individuals follow mental maps and choose their displacements according to a maximum efficiency criterion, in a spatially disordered environment containing many trees with a heterogeneous size distribution. We show that a particular tree size frequency distribution induces non-Gaussian movement patterns with multiple spatial scales (Lévy walks). These results are consistent with tree size variation and Spider monkey (Ateles geoffroyi) foraging patterns. We discuss the consequences that our results may have for the patterns of seed dispersal by foraging primates.
The complex arrangements of atoms near grain boundaries are difficult to understand theoretically. We propose a phenomenological (Ginzburg-Landau-like) description of crystalline phases based on symmetries and fairly general stability arguments. This method allows a very detailed description of defects at the lattice scale with virtually no tunning parameters, unlike usual phase-field methods. The model equations are directly inspired from those used in a very different physical context, namely, the formation of periodic patterns in systems out-of-equilibrium ({\it e.g.} Rayleigh-Bénard convection, Turing patterns). We apply the formalism to the study of symmetric tilt boundaries. Our results are in quantitative agreement with those predicted by a recent crystallographic theory of grain boundaries based on a geometrical quasicrystal-like construction. These results suggest that frustration and competition effects near defects in crystalline arrangements have some universal features, of interest in solids or other periodic phases.
We study the coarsening of two-dimensional smectic polycrystals characterized by grains of oblique stripes with only two possible orientations. For this purpose, an anisotropic Swift-Hohenberg equation is solved. For quenches close enough to the onset of stripe formation, the average domain size increases with time as $t^{1/2}$. Further from onset, anisotropic pinning forces similar to Peierls stresses in solid crystals slow down defects, and growth becomes anisotropic. In a wide range of quench depths, dislocation arrays remain mobile and dislocation density roughly decays as $t^{-1/3}$, while chevron boundaries are totally pinned. We discuss some agreements and disagreements found with recent experimental results on the coarsening of anisotropic electroconvection patterns.
We revisit the Swift-Hohenberg model for two-dimensional hexagonal patterns in the bistability region where hexagons coexist with the uniform quiescent state. We both analyze the law of motion of planar interfaces (separating hexagons and uniform regions), and the stability of localized structures. Interfaces exhibit properties analogous to that of interfaces in crystals, such as faceting, grooving and activated growth or " melting". In the nonlinear regime, some spatially disordered heterogeneous configurations do not evolve in time. Frozen states are essentially composed of extended polygonal domains of hexagons with pinned interfaces, that may coexist with isolated localized structures randomly distributed in the quiescent background. Localized structures become metastable at the pinning/depinning transition of interfaces. In some region of the parameter space, localized structures shrink meanwhile interfaces are still pinned. The region where localized structures have an infinite life-time is relatively limited.
We show that the nonequilibrium dynamics of systems with many interacting elements located on a small-world network can be much slower than on regular networks. As an example, we study the phase ordering dynamics of the Ising model on a Watts-Strogatz network, after a quench in the ferromagnetic phase at zero temperature. In one and two dimensions, small-world features produce dynamically frozen configurations, disordered at large length scales, analogous of random field models. This picture differs from the common knowledge (supported by equilibrium results) that ferromagnetic short-cuts connections favor order and uniformity. We briefly discuss some implications of these results regarding the dynamics of social changes.
We study the motion of a grain boundary separating two otherwise stationary domains of hexagonal symmetry. Starting from an order parameter equation appropriate for hexagonal patterns, a multiple scale analysis leads to an analytical equation of motion for the boundary that shares many properties with that of a crystalline solid. We find that defect motion is generically opposed by a pinning force that arises from non-adiabatic corrections to the standard amplitude equation. The magnitude of this force depends sharply on the mis-orientation angle between adjacent domains so that the most easily pinned grain boundaries are those with an angle between four and eight degrees. Although pinning effects may be small, they do not vanish asymptotically near the onset of this subcritical bifurcation, and can be orders of magnitude larger than those present in smectic phases that bifurcate supercritically.
We study numerically and analytically the coarsening of stripe phases in two spatial dimensions, and show that transient configurations do not achieve long ranged orientational order but rather evolve into glassy configurations with very slow dynamics. In the absence of thermal fluctuations, defects such as grain boundaries become pinned in an effective periodic potential that is induced by the underlying periodicity of the stripe pattern itself. Pinning arises without quenched disorder from the non-adiabatic coupling between the slowly varying envelope of the order parameter around a defect, and its fast variation over the stripe wavelength. The characteristic size of ordered domains asymptotes to a finite value $R_g \sim λ_0\ ε^{-1/2}\exp(|a|/\sqrtε)$, where $ε\ll 1$ is the dimensionless distance away from threshold, $λ_0$ the stripe wavelength, and $a$ a constant of order unity. Random fluctuations allow defect motion to resume until a new characteristic scale is reached, function of the intensity of the fluctuations. We finally discuss the relationship between defect pinning and the coarsening laws obtained in the intermediate time regime.
We study domain coarsening of two dimensional stripe patterns by numerically solving the Swift-Hohenberg model of Rayleigh-Benard convection. Near the bifurcation threshold, the evolution of disordered configurations is dominated by grain boundary motion through a background of largely immobile curved stripes. A numerical study of the distribution of local stripe curvatures, of the structure factor of the order parameter, and a finite size scaling analysis of the grain boundary perimeter, suggest that the linear scale of the structure grows as a power law of time with a craracteristic exponent z=3. We interpret theoretically the exponent z=3 from the law of grain boundary motion.
We study the motion of a grain boundary that separates two sets of mutually perpendicular rolls in Rayleigh-Bénard convection above onset. The problem is treated either analytically from the corresponding amplitude equations, or numerically by solving the Swift-Hohenberg equation. We find that if the rolls are curved by a slow transversal modulation, a net translation of the boundary follows. We show analytically that although this motion is a nonlinear effect, it occurs in a time scale much shorter than that of the linear relaxation of the curved rolls. The total distance traveled by the boundary scales as $ε^{-1/2}$, where $ε$ is the reduced Rayleigh number. We obtain analytical expressions for the relaxation rate of the modulation and for the time dependent traveling velocity of the boundary, and especially their dependence on wavenumber. The results agree well with direct numerical solutions of the Swift-Hohenberg equation. We finally discuss the implications of our results on the coarsening rate of an ensemble of differently oriented domains in which grain boundary motion through curved rolls is the dominant coarsening mechanism.
We point out some similitudes between the statistics of high Reynolds number turbulence and critical phenomena. An analogy is developed for two-dimensional decaying flows, in particular by studying the scaling properties of the two-point vorticity correlation function within a simple phenomenological framework. The inverse of the Reynolds number is the analogue of the small parameter that separates the system from criticality. It is possible to introduce a set of three critical exponents; for the correlation length, the autocorrelation function and a so-called susceptibility, respectively. The exponents corresponding to the well-known enstrophy cascade theory of Kraichnan and Batchelor are, remarkably, the same as the Gaussian approximation exponents for spin models. The limitations of the analogy, in particular the lack of universal scaling functions, are also discussed.
In an idealized way, some turbulent flows can be pictured by assemblies of many vortices characterized by a set of particle distribution functions. Ultrasound provide an useful, nonintrusive, tool to study the spatial structure of vorticity in flows. This is analogous to the use of elastic neutron scattering to determine liquid structure. We express the dispersion relation, as well as the scattering cross section, of sound waves propagating in a ``liquid'' of identical vortices as a function of vortex pair correlation functions. In two dimensions, formal analogies with ionic liquids are pointed out.