laboratoire de physique statistique
laboratoire de physique statistique




P A R M I :

Fourier analysis of wave turbulence in a thin elastic plate - Mordant, N.

Abstract : The spatio-temporal dynamics of the deformation of a vibrated plate is measured by a high speed Fourier transform profilometry technique. The space-time Fourier spectrum is analyzed. It displays a behavior consistent with the premises of the Weak Turbulence theory. A isotropic continuous spectrum of waves is excited with a non linear dispersion relation slightly shifted from the linear dispersion relation. The spectral width of the dispersion relation is also measured. The non linearity of this system is weak as expected from the theory. Finite size effects are discussed. Despite a qualitative agreement with the theory, a quantitative mismatch is observed which origin may be due to the dissipation that ultimately absorbs the energy flux of the Kolmogorov-Zakharov casade.
Observation of the condensation of a gas of interacting grains - Laroche, C. and Petrelis, F.

Abstract : We consider an ensemble of grains that interact through a dipole-dipole interaction. A granular gas is formed by the vertical motion of a piston at the bottom boundary of the system. The interaction between the grains is controlled by an horizontally applied magnetic field. When the speed of the piston is decreased, we observe a transition from a low density to a high density phase. When the interaction between grains is weak, the transition is continuous. It is discontinuous for stronger interaction. The phase diagram displays strong similarities with the ones observed for usual equilibrium phase transitions.
Dynamo regimes and transitions in the VKS experiment - Berhanu, M. and Verhille, G. and Boisson, J. and Gallet, B. and Gissinger, C. and Fauve, S. and Mordant, N. and Petrelis, F. and Bourgoin, M. and Odier, P. and Pinton, J. -F. and Plihon, N. and Aumaitre, S. and Chiffaudel, A. and Daviaud, F. and Dubrulle, B. and Pirat, C.

Abstract : The Von Karman Sodium experiment yields a variety of dynamo regimes, when asymmetry is imparted to the flow by rotating impellers at different speed F (1) and F (2). We show that as the intensity of forcing, measured as F (1)+F (2), is increased, the transition to a self-sustained magnetic field is always observed via a supercritical bifurcation to a stationary state. For some values of the asymmetry parameter theta = (F (1)-F (2))/(F (1)+F (2)), time dependent dynamo regimes develop. They are observed either when the forcing is increased for a given value of asymmetry, or when the amount of asymmetry is varied at sufficiently high forcing. Two qualitatively different transitions between oscillatory and stationary regimes are reported, involving or not a strong divergence of the period of oscillations. These transitions can be interpreted using a low dimensional model based on the interactions of two dynamo modes.
Superfluid density in a two-dimensional model of supersolid - Sepulveda, N. and Josserand, C. and Rica, S.

Abstract : We study in 2-dimensions the superfluid density of periodically modulated states in the framework of the mean-field Gross-Pitaevskii model of a quantum solid. We obtain a full agreement for the superfluid fraction between a semi-theoretical approach and direct numerical simulations. As in 1-dimension, the superfluid density decreases exponentially with the amplitude of the particle interaction. We discuss the case when defects are present in this modulated structure. In the case of isolated defects (e.g. dislocations) the superfluid density only shows small changes. Finally, we report an increase of the superfluid fraction up to 50\% in the case of extended macroscopical defects. We show also that this excess of superfluid fraction depends on the length of the complex network of grain boundaries in the system.
Crime and punishment: the economic burden of impunity - Gordon, M. B. and Iglesias, J. R. and Semeshenko, V. and Nadal, J. P.

Abstract : Crime is an economically relevant activity. It may represent a mechanism of wealth distribution but also a social and economic burden because of the interference with regular legal activities and the cost of the law enforcement system. Sometimes it may be less costly for the society to allow for some level of criminality. However, a drawback of such a policy is that it may lead to a high increase of criminal activity, that may become hard to reduce later on. Here we investigate the level of law enforcement required to keep crime within acceptable limits. A sharp phase transition is observed as a function of the probability of punishment. We also analyze other consequences of criminality as the growth of the economy, the inequality in the wealth distribution (the Gini coefficient) and other relevant quantities under different scenarios of criminal activity and probabilities of apprehension.
Phase diagram of a Schelling segregation model - Gauvin, L. and Vannimenus, J. and Nadal, J. -P.

Abstract : The collective behavior in a variant of Schelling's segregation model is characterized with methods borrowed from statistical physics, in a context where their relevance was not conspicuous. A measure of segregation based on cluster geometry is defined and several quantities analogous to those used to describe physical lattice models at equilibrium are introduced. This physical approach allows to distinguish quantitatively several regimes and to characterize the transitions between them, leading to the building of a phase diagram. Some of the transitions evoke empirical sudden ethnic turnovers. We also establish links with `spin-1' models in physics. Our approach provides generic tools to analyze the dynamics of other socio-economic systems.
Cycles of cooperation and free-riding in social systems - Ma, Y. P. and Goncalves, S. and Mignot, S. and Nadal, J. -P. and Gordon, M. B.

Abstract : Basic evidences on non-profit making and other forms of benevolent-based organizations reveal a rough partition of members between some pure consumers of the public good (free-riders) and benevolent individuals (cooperators). We study the relationship between the community size and the level of cooperation in a simple model where the utility of joining the community is proportional to its size. We assume an idiosyncratic willingness to join the community ; cooperation bears a fixed cost while free-riding bears a (moral) idiosyncratic cost proportional to the fraction of cooperators. We show that the system presents two types of equilibria: fixed points (Nash equilibria) with a mixture of cooperators and free-riders and cycles where the size of the community, as well as the proportion of cooperators and free-riders, vary periodically.
Life at ultralow interfacial tension: wetting, waves and droplets in demixed colloid-polymer mixtures - Lekkerkerker, H. N. W. and de Villeneuve, V. W. A. and de Folter, J. W. J. and Schmidt, M. and Hennequin, Y. and Bonn, D. and Indekeu, J. O. and Aarts, D. G. A. L.

Abstract : Mixtures of colloids and polymers display a rich phase behavior, involving colloidal gas (rich in polymer, poor in colloid), colloidal liquid (poor in polymer, rich in colloid) and colloidal crystal phases (poor in polymer, highly ordered colloids). Recently, the colloidal gas-colloidal liquid interface received considerable attention as well. Due to the colloidal length scale the interfacial tension is much lower than in the atomic or molecular analog (nN/m instead of mN/m). This ultra-low interfacial tension has pronounced effects on the kinetics of phase separation, the colloidal gas-liquid profile near a single wall and the thermally induced fluctuations of the interface. The amplitudes of these thermally excited capillary waves are restrained by the interfacial tension and are for that reason of the order of the particle diameter. Therefore, in molecular systems, the capillary waves can only be seen indirectly in scattering experiments. In colloidal systems, however, the wave amplitudes are on a (sub) micrometer scale. This fact enables the direct observation of capillary waves in both real space and real time using confocal scanning laser microscopy. Moreover, the real space technique enables us to demonstrate the strong influence of interface fluctuations on droplet coalescence and droplet break up.
Statistics of power injection in a plate set into chaotic vibration - Cadot, O. and Boudaoud, A. and Touze, C.

Abstract : A vibrating plate is set into a chaotic state of wave turbulence by either a periodic or a random local forcing. Correlations between the forcing and the local velocity response of the plate at the forcing point are studied. Statistical models with fairly good agreement with the experiments are proposed for each forcing. Both distributions of injected power have a logarithmic cusp for zero power, while the tails are Gaussian for the periodic driving and exponential for the random one. The distributions of injected work over long time intervals are investigated in the framework of the fluctuation theorem, also known as the Gallavotti-Cohen theorem. It appears that the conclusions of the theorem are verified only for the periodic, deterministic forcing. Using independent estimates of the phase space contraction, this result is discussed in the light of available theoretical framework.