Electrical conductance of a 2D packing of metallic beads under thermal perturbation

Electrical conductivity measurements on a 2D packing of metallic beads have been performed to study internal rearrangements in weakly pertubed granular materials. Small thermal perturbations lead to large non gaussian conductance fluctuations. These fluctuations are found to be intermittent and gathered in bursts. The distributions of the waiting time between to peaks is found to be a power law inside bursts. The exponent is independent of the bead network, the intensity of the perturbation and external stress. these bursts are interpreted as the signature of individual bead creep rather than collective vaults reorganisations. We propose a simple model linking the exponent of the waiting time distribution to the roughness exponent of the surface of the beads.Comment: 7 pages, 6 figure

Rejuvenation in the Random Energy Model

We show that the Random Energy Model has interesting rejuvenation properties in its frozen phase. Different `susceptibilities' to temperature changes, for the free-energy and for other (`magnetic') observables, can be computed exactly. These susceptibilities diverge at the transition temperature, as (1-T/T_c)^-3 for the free-energy.Comment: 9 pages, 1 eps figur

Classical diffusion of N interacting particles in one dimension: General results and asymptotic laws

I consider the coupled one-dimensional diffusion of a cluster of N classical particles with contact repulsion. General expressions are given for the probability distributions, allowing to obtain the transport coefficients. In the limit of large N, and within a gaussian approximation, the diffusion constant is found to behave as N^{-1} for the central particle and as (\ln N)^{-1} for the edge ones. Absolute correlations between the edge particles increase as (\ln N)^{2}. The asymptotic one-body distribution is obtained and discussed in relation of the statistics of extreme events.Comment: 6 pages, 2 eps figure

Elements for a Theory of Financial Risks

Estimating and controlling large risks has become one of the main concern of financial institutions. This requires the development of adequate statistical models and theoretical tools (which go beyond the traditionnal theories based on Gaussian statistics), and their practical implementation. Here we describe three interrelated aspects of this program: we first give a brief survey of the peculiar statistical properties of the empirical price fluctuations. We then review how an option pricing theory consistent with these statistical features can be constructed, and compared with real market prices for options. We finally argue that a true `microscopic' theory of price fluctuations (rather than a statistical model) would be most valuable for risk assessment. A simple Langevin-like equation is proposed, as a possible step in this direction.Comment: 22 pages, to appear in `Order, Chance and Risk', Les Houches (March 1998), to be published by Springer/EDP Science

Influence of humidity on granular packings with moving walls

A significant dependence on the relative humidity H for the apparent mass (Mapp) measured at the bottom of a granular packing inside a vertical tube in relative motion is demonstrated experimentally. While the predictions of Janssen's model are verified for all values of H investigated (25%< H <80%), Mapp increases with time towards a limiting value at high relative humidities (H>60%) but remains constant at lower ones (H=25%). The corresponding Janssen length is nearly independent of the tube velocity for H>60% but decreases markedly for H=25%. Other differences are observed on the motion of individual beads in the packing. For H=25%, they are almost motionless while the mean particle fraction of the packing remains constant; for H>60% the bead motion is much more significant and the mean particle fraction decreases. The dependence of these results on the bead diameter and their interpretation in terms of the influence of capillary forces are discussed.Comment: 6 pages, 6 figure

Experimental study of granular surface flows via a fast camera: a continuous description

Depth averaged conservation equations are written for granular surface flows. Their application to the study of steady surface flows in a rotating drum allows to find experimentally the constitutive relations needed to close these equations from measurements of the velocity profile in the flowing layer at the center of the drum and from the flowing layer thickness and the static/flowing boundary profiles. The velocity varies linearly with depth, with a gradient independent of both the flowing layer thickness and the static/flowing boundary local slope. The first two closure relations relating the flow rate and the momentum flux to the flowing layer thickness and the slope are then deduced. Measurements of the profile of the flowing layer thickness and the static/flowing boundary in the whole drum explicitly give the last relation concerning the force acting on the flowing layer. Finally, these closure relations are compared to existing continuous models of surface flows.Comment: 20 pages, 11 figures, submitted to Phys. FLuid

Exact Solutions of a Model for Granular Avalanches

We present exact solutions of the non-linear {\sc bcre} model for granular avalanches without diffusion. We assume a generic sandpile profile consisting of two regions of constant but different slope. Our solution is constructed in terms of characteristic curves from which several novel predictions for experiments on avalanches are deduced: Analytical results are given for the shock condition, shock coordinates, universal quantities at the shock, slope relaxation at large times, velocities of the active region and of the sandpile profile.Comment: 7 pages, 2 figure

Against Chaos in Temperature in Mean-Field Spin-Glass Models

We study the problem of chaos in temperature in some mean-field spin-glass models by means of a replica computation over a model of coupled systems. We propose a set of solutions of the saddle point equations which are intrinsically non-chaotic and solve a general problem regarding the consistency of their structure. These solutions are relevant in the case of uncoupled systems too, therefore they imply a non-trivial overlap distribution $P(q_{T1T2})$ between systems at different temperatures. The existence of such solutions is checked to fifth order in an expansion near the critical temperature through highly non-trivial cancellations, while it is proved that a dangerous set of such cancellations holds exactly at all orders in the Sherrington-Kirkpatrick (SK) model. The SK model with soft-spin distribution is also considered obtaining analogous results. Previous analytical results are discussed.Comment: 20 pages, submitted to J.Phys.

Renormalization flow in extreme value statistics

The renormalization group transformation for extreme value statistics of independent, identically distributed variables, recently introduced to describe finite size effects, is presented here in terms of a partial differential equation (PDE). This yields a flow in function space and gives rise to the known family of Fisher-Tippett limit distributions as fixed points, together with the universal eigenfunctions around them. The PDE turns out to handle correctly distributions even having discontinuities. Remarkably, the PDE admits exact solutions in terms of eigenfunctions even farther from the fixed points. In particular, such are unstable manifolds emanating from and returning to the Gumbel fixed point, when the running eigenvalue and the perturbation strength parameter obey a pair of coupled ordinary differential equations. Exact renormalization trajectories corresponding to linear combinations of eigenfunctions can also be given, and it is shown that such are all solutions of the PDE. Explicit formulas for some invariant manifolds in the Fr\'echet and Weibull cases are also presented. Finally, the similarity between renormalization flows for extreme value statistics and the central limit problem is stressed, whence follows the equivalence of the formulas for Weibull distributions and the moment generating function of symmetric L\'evy stable distributions.Comment: 21 pages, 9 figures. Several typos and an upload error corrected. Accepted for publication in JSTA