Related papers: Projecting Low Dimensional Chaos from Spatio-tempo…
We perform the linear stability analysis for a new model for poromechanical processes with inertia (formulated in mixed form using the solid deformation, fluid pressure, and total pressure) interacting with diffusing and reacting solutes…
A method to estimate Lyapunov spectra from spatio-temporal data is presented, which is well-suited to be applied to experimental situations. It allows to characterize the high-dimensional chaotic states, with possibly a large number of…
The technique of distributed dislocations proved to be in the past an effective approach in studying crack problems within classical elasticity. The present work is intended to extend this technique in studying crack problems within…
We study a disordered network of bistable bonds subjected to periodic strain. The model is inspired by experiments on crumpled sheets and it features behaviors associated with glasses, including a complex energy landscape, memories, and…
Experimental measurements of the response of a two dimensional system of plastic beads subjected to steady shear are reported. The beads float at the surface of a fluid substrate and are subjected to a slow, steady-shear in a Couette…
Because of the enormous range of time and space scales involved in dislocation dynamics, plastic modeling at macroscale requires a continuous formulation. In this paper, we present a rigorous formulation of the transition between the…
We develop a numerical method for the time evolution of Gaussian wave packets on flat-band lattices in the presence of correlated disorder. To achieve this, we introduce a method to generate random on-site energies with prescribed…
Developing a macroscopic theory of elasto-plasticity in amorphous solids calls for (i) identifying the relevant macro state-variables and (ii) discriminating the different time-scales which characterize these variables. In current theories…
Shear banding, or localization of intense strains along narrow bands, is a plastic instability in solids with important implications for material failure in a wide range of materials and across length-scales. In this paper, we report on a…
We investigate instabilities in a stochastic mathematical model of cochlear dynamics. The cochlea is modeled as a spatio-temporal dynamical system made up of a spatially distributed array of coupled oscillators, together with the cochlear…
Theoretical foundations of chaos have have been predominantly laid out for finite-dimensional dynamical systems, such as the three-body problem in classical mechanics and the Lorenz model in dissipative systems. In contrast, many real-world…
We study the probability densities of finite-time or \local Lyapunov exponents (LLEs) in low-dimensional chaotic systems. While the multifractal formalism describes how these densities behave in the asymptotic or long-time limit, there are…
In dislocation-free martensites the components of the elastic strain tensor are constrained by the Saint-Venant compatibility condition which guarantees continuity of the body during external loading. However, in dislocated materials the…
The slow flow of amorphous solids exhibits striking heterogeneities: swift localised particle rearrangements take place in the midst of a more or less homogeneously deforming medium. Recently, experimental as well as numerical work has…
Analytic scaling relations are derived for a phenomenological model of the plasmoid instability in an evolving current sheet, including the effects of reconnection outflow. Two scenarios are considered, where the plasmoid instability can be…
Plastic deformation of heterogeneous solid structures is often characterized by random intermittent local plastic events. On the mesoscale this feature can be represented by a spatially fluctuating local yield threshold. Here we study the…
We consider simple examples illustrating some new features of the linear response theory developed by Ruelle for dissipative and chaotic systems [{\em J. of Stat. Phys.} {\bf 95} (1999) 393]. In this theory the concepts of linear response,…
This paper develops a new approach to the estimation of the degree of boundedness or stability of multidimensional nonlinear systems with time-dependent nonperiodic coefficients-an essential task in various engineering and natural science…
In problems where the temporal evolution of a nonlinear system cannot be followed, a method for studying the fluctuations of spatial patterns has been developed. That method is applied to well-known problems in deterministic chaos (the…
The statistical-thermodynamic dislocation theory developed in our earlier studies is used here in an analysis of the experimental observations of adiabatic shear banding in steel by Marchand and Duffy (1988). Employing a small set of…