Related papers: Introduction to the dynamics of disordered systems…
We discuss the properties of the distributions of energies of minima obtained by gradient descent in complex energy landscapes. We find strikingly similar phenomenology across several prototypical models. We particularly focus on the…
These notes are for the proceedings of the NATO Advanced Study Insitutue on "Scale Invariance, Interfaces, and Non--Equilibrium Dynamics", held at the Isaac Newton Institute, 20--30 June 1994. The four lectures address a number of issues…
Exploring structural order in disordered systems including liquids and glasses is an intriguing but challenging issue in condensed matter physics. Here we construct a new parameter based on the angular distribution function of particles and…
We endow a system of interacting particles with two distinct, local, Markovian and reversible microscopic dynamics. Using common field-theoretic techniques used to investigate the presence of a glass transition, we find that while the…
We introduce a set of theoretical ideas that form the basis for an analytical framework capable of describing nonequilibrium dynamics in glassy systems. We test the resulting scenario by comparing its predictions with numerical simulations…
Gradient descent (GD) is a collection of continuous optimization methods that have achieved immeasurable success in practice. Owing to data science applications, GD with diminishing step sizes has become a prominent variant. While this…
We study slow dynamics of particles moving in a matrix of immobile obstacles using molecular dynamics simulations. The glass transition point decreases drastically as the obstacle density increases. At higher obstacle densities, the…
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…
Exploration of the structure formation and dynamics of animate and inanimate matter on the nanometer scale is a highly interdisciplinary field of rapidly emerging research. It is relevant for various molecular and nanoscale systems of…
The rapid progress in machine learning in recent years has been based on a highly productive connection to gradient-based optimization. Further progress hinges in part on a shift in focus from pattern recognition to decision-making and…
We review the mechanism for transport in strongly anharmonic chains of oscillators near the atomic limit where all oscillators are decoupled. In this regime, the motion of most oscillators remains close to integrable, i.e. quasi-periodic,…
We analyse the Langevin dynamics of the random walk, the scalar field, the X-Y model and the spinoidal decomposition. We study the deviations from the equilibrium dynamics theorems (FDT and homogeneity), the asymptotic behaviour of the…
In recent years dynamical systems (of deterministic and stochastic nature), describing many models in mathematics, physics, engineering and finances, become more and more complex. Numerical analysis narrowed only to deterministic algorithms…
This paper is based on three tutorial lectures given at the CRM Summer School in Banff, Alberta, June 27-July 10, 1999 on "Theoretical Physics at the End of the Twentieth Century". They will be published by Springer-Verlag. Lecture I gives…
Several key questions remain unanswered regarding overparameterized learning models. It is unclear how (stochastic) gradient descent finds solutions that generalize well, and in particular the role of small random initializations. Matrix…
Granular simulations are used to probe the particle scale dynamics at short, intermediate, and long time scales for gravity driven, dense granular flows down an inclined plane. On approach to the angle of repose, where motion ceases, the…
This article contains the lecture notes for the short course ``Introduction to Econophysics,'' delivered at the II Brazilian School on Statistical Mechanics, held in Sao Carlos, Brazil, in February 2004. The main goal of the present notes…
Notes of the lectures delivered in Les Houches during the Summer School on Complex Systems (July 2006).
We describe some general results that constrain the dynamical fluctuations that can occur in non-equilibrium steady states, with a focus on molecular dynamics. That is, we consider Hamiltonian systems, coupled to external heat baths, and…
In this expository paper, which covers material presented at the NATO Advanced Study Institute "Nonlinear Analysis, Differential Equations, and Control" (Montreal, Jul/Aug 1998), we deal with several questions related to stability and…