57 research outputs found
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
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
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