On the Adam-Gibbs-Wolynes scenario for the viscosity increase in glasses

We reformulate the interpretation of the mean-field glass transition scenario for finite dimensional systems, proposed by Wolynes and collaborators. This allows us to establish clearly a temperature dependent length xi* above which the mean-field glass transition picture has to be modified. We argue in favor of the mosaic state introduced by Wolynes and collaborators, which leads to the Adam-Gibbs relation between the viscosity and configurational entropy of glass forming liquids. Our argument is a mixture of thermodynamics and kinetics, partly inspired by the Random Energy Model: small clusters of particles are thermodynamically frozen in low energy states, whereas large clusters are kinetically frozen by large activation energies. The relevant relaxation time is that of the smallest `liquid' clusters. Some physical consequences are discussed.Comment: 8 page

Numerical study of the temperature and porosity effects on the fracture propagation in a 2D network of elastic bonds

This article reports results concerning the fracture of a 2d triangular lattice of atoms linked by springs. The lattice is submitted to controlled strain tests and the influence of both porosity and temperature on failure is investigated. The porosity is found on one hand to decrease the stiffness of the material but on the other hand it increases the deformation sustained prior to failure. Temperature is shown to control the ductility due to the presence of cavities that grow and merge. The rough surfaces resulting from the propagation of the crack exhibit self-affine properties with a roughness exponent $\zeta = 0.59 \pm 0.07$ over a range of length scales which increases with temperature. Large cavities also have rough walls which are found to be fractal with a dimension, $D$, which evolves with the distance from the crack tip. For large distances, $D$ is found to be close to 1.5, and close to 1.0 for cavities just before their coalescence with the main crack

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

Financial Applications of Random Matrix Theory: a short review

We discuss the applications of Random Matrix Theory in the context of financial markets and econometric models, a topic about which a considerable number of papers have been devoted to in the last decade. This mini-review is intended to guide the reader through various theoretical results (the Marcenko-Pastur spectrum and its various generalisations, random SVD, free matrices, largest eigenvalue statistics, etc.) as well as some concrete applications to portfolio optimisation and out-of-sample risk estimation.Comment: To appear in the "Handbook on Random Matrix Theory", Oxford University Pres

SCALING AND INTERMITTENCY IN BURGERS' TURBULENCE

We use the mapping between Burgers' equation and the problem of a directed polymer in a random medium in order to study the fully developped turbulence in the $N$ dimensional forced Burgers' equation. The stirring force corresponds to a quenched (spatio temporal) random potential for the polymer. The properties of the inertial regime are deduced from a study of the directed polymer on length scales smaller than the correlation length of the potential. From this study we propose an Ansatz for the velocity field in the large Reynolds number limit of the forced Burgers' equation in $N$ dimensions. This Ansatz allows us to compute exactly the full probability distribution of the velocity difference $u(r)$ between points separated by a distance $r$ much smaller than the correlation length of the forcing. We find that the moments $$ scale as $r^{\zeta(q)}$ with $\zeta(q) \equiv 1$ for all $q \geq 1$. This strong `intermittency' is related to the large scale singularities of the velocity field, which is concentrated on a $N-1$ dimensional froth-like structure.Comment: 35 pages latex, 4 ps figures in separate uufiles package

Statistical Mechanics of a Two-Dimensional System with Long Range Interaction

We analyse the statistical physics of a two dimensional lattice based gas with long range interactions. The particles interact in a way analogous to Queens on a chess board. The long range nature of the interaction gives the mathematics of the problem a simple geometric structure which simplifies both the analytic and numerical study of the system. We present some analytic calculations for the statics of the problem and also we perform Monte Carlo simulations which exhibit a dynamical transition between a high temperature liquid regime and a low temperature glassy regime exhibiting aging in the two time correlation functions.Comment: 9 pages, 8 figure

Continuum mesoscale theory inspired by plasticity

We present a simple mesoscale field theory inspired by rate-independent plasticity that reflects the symmetry of the deformation process. We parameterize the plastic deformation by a scalar field which evolves with loading. The evolution equation for that field has the form of a Hamilton-Jacobi equation which gives rise to cusp-singularity formation. These cusps introduce irreversibilities analogous to those seen in plastic deformation of real materials: we observe a yield stress, work hardening, reversibility under unloading, and cell boundary formation.Comment: 7 pages, 5 .eps figures. submitted to Europhysics Letter

Self Induced Quenched Disorder: A Model for the Glass Transition

We consider a simple spin system without disorder which exhibits a glassy regime. We show that this model can be well approximated by a system with quenched disorder which is studied with the standard methods developped in spin glasses. We propose that the glass transition is a point where quenched disorder is self induced, a scenario for which the `cavity' method might be particularly well suited.Comment: Latex, LPTENS 94/14, three figures upon reques