Related papers: Local scale-invariance in disordered systems

The goal of this chapter is to review recent analytical results about the growth of a (static) correlation length in glassy systems, and the connection that can be made between this length scale and the equilibrium correlation time of its…

We discuss the method of folding for discrete planar systems and use it to establish the existence or non-existence of cycles or chaos in planar systems of rational difference equations with variable coefficients. These include some systems…

In this article we discuss several aspects of the stochastic dynamics of spin models. The paper has two independent parts. Firstly, we explore a few properties of the multi-point correlations and responses of generic systems evolving in…

A simple, non-disordered spin model has been studied in an effort to understand the origin of the precipitous slowing down of dynamics observed in supercooled liquids approaching the glass transition. A combination of Monte Carlo…

The topological nature of the disorder of glasses and supercooled liquids strongly affects their high-frequency dynamics. In order to understand its main features, we analytically studied a simple topologically disordered model, where the…

Ageing in systems without detailed balance is studied in bosonic contact and pair-contact processes with Levy diffusion. In the ageing regime, the dynamical scaling of the two-time correlation function and two-time response function is…

The study of spin-glass dynamics, long considered the paradigmatic complex system, has reached important milestones. The availability of single crystals has allowed the experimental measurement of spin-glass coherence lengths of almost…

The dynamics of a nonequilibrium system can become complex because the system has many components (e.g., a human brain), because the system is strongly driven from equilibrium (e.g., large Reynolds-number flows), or because the system…

The local minima (inherent structures) of a system and their associated transition links give rise to a network. Here we consider the topological and distance properties of such a network in the context of spin glasses. We use steepest…

In this work, sample-based observability of linear discrete-time systems is studied. That is, we consider the case where the system output measurements are not available at every time instance. It is shown that some discrete-time systems…

It is shown that the description of anomalous scaling in turbulent systems requires the simultaneous use of two normalization scales. This phenomenon stems from the existence of two independent (infinite) sets of anomalous scaling exponents…

In various disordered systems or non-equilibrium dynamical models, the large deviations of some observables have been found to display different scalings for rare values bigger or smaller than the typical value. In the present paper, we…

We propose a simplified version of the Multi-Scale Analysis of tight-binding Anderson models with strongly mixing random potentials which leads directly to uniform exponential bounds on decay of eigenfunctions in arbitrarily large finite…

We study the behavior of fracture in disordered systems close to the breakdown point. We simulate numerically both scalar (resistor network) and vectorial (spring network) models with threshold disorder, driven at constant current and…

We study the time evolution of perturbations in spatially extended chaotic systems in the presence of quenched disorder. We find that initially random perturbations tend to exponentially localize in space around static pinning centers that…

Using Monte Carlo simulations, we have studied aging phenomena in three-dimensional Gaussian Ising spin-glass model focusing on quasi-equilibrium behavior of the spin auto-correlation functions. Weak violation of the time translational…

The dynamical behaviours of a kinetically constrained spin model (Fredrickson-Andersen model) on a Bethe lattice are investigated by a perturbation analysis that provides exact final states above the nonergodic transition point. It is…

This paper is concerned with the study of scalability in nonlinear heterogeneous networks affected by communication delays and disturbances. After formalizing the notion of scalability, we give two sufficient conditions to assess this…

Scaling describes how a given quantity $Y$ that characterizes a system varies with its size $P$. For most complex systems it is of the form $Y\sim P^\beta$ with a nontrivial value of the exponent $\beta$, usually determined by regression…

In past works, various schemes for adaptive synchronization of chaotic systems have been proposed. The stability of such schemes is central to their utilization. As an example addressing this issue, we consider a recently proposed adaptive…