Related papers: Interacting Steps With Finite-Range Interactions: …
Role of range of interactions in a model of charged particles diffusing on a two-dimensional lattice is studied. We investigate, via Monte Carlo simulations, three models. In the first one interactions are restricted to nearest neighbors,…
The goal of this paper is to describe the various kinetic equations which arise from scaling limits of interacting particle systems. We provide a formalism which allows us to determine the kinetic equation for a given interaction potential…
Recent work showed that the exact exchange-correlation potential of time-dependent density functional theory generically displays dynamical step structures. These have a spatially non-local and time-non-local dependence on the density in…
Large ensembles of stochastically evolving interacting particles describe phenomena in diverse fields including statistical physics, neuroscience, biology, and engineering. In such systems, the infinitesimal evolution of each particle…
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 Pairwise Einstein Model (PEM) of steps not only justifies the use of the Generalized Wigner Distribution (GWD) for Terrace Width Distributions (TWDs), it also predicts a specific form for the Step Position Distribution (SPD), i.e., the…
The models in statistical physics such as an Ising model offer a convenient way to characterize stationary activity of neural populations. Such stationary activity of neurons may be expected for recordings from in vitro slices or…
The stacking problem is approached by computational mechanics, using an Ising next nearest neighbor model. Computational mechanics allows to treat the stacking arrangement as an information processing system in the light of a symbol…
The equilibrium statistical mechanics of one-dimensional lattice gases with interactions of arbitrary range and shape between first-neighbor atoms is solved exactly on the basis of statistically interacting vacancy particles. Two sets of…
We obtain exact analytical results for lattices of maps with couplings that decay with distance as $r^{-\alpha}$. We analyze the effect of the coupling range on the system dynamics through the Lyapunov spectrum. For lattices whose elements…
In this paper we continue the study of the derivation of different types of kinetic equations which arise from scaling limits of interacting particle systems. We began this study in \cite{NVW}. More precisely, we consider the derivation of…
Most infectious diseases spread on a dynamic network of human interactions. Recent studies of social dynamics have provided evidence that spreading patterns may depend strongly on detailed micro-dynamics of the social system. We have…
Analyses of urban scaling laws assume that observations in different cities are independent of the existence of nearby cities. Here we introduce generative models and data-analysis methods that overcome this limitation by modelling…
As is well known, one-dimensional systems with interactions restricted to first nearest neighbors admit a full analytically exact statistical-mechanical solution. This is essentially due to the fact that the knowledge of the first…
Motivated by the role that spectral properties play for the dynamical evolution of a quantum many-body system, we investigate the level spacing statistic of the extended Bose-Hubbard model. In particular, we focus on the distribution of the…
The result of 2-dimensional Gaussian lattice fit to a speckle intensity pattern based on a linear model that includes nearest-neighbor interactions is presented. We also include a Monte Carlo simulation of the same spatial speckle pattern…
We introduce a model of long-range interacting particles evolving under a stochastic Monte Carlo dynamics, in which possible increase or decrease in the values of the dynamical variables is accepted with preassigned probabilities. For…
One approach to monitoring a dynamic system relies on decomposition of the system into weakly interacting subsystems. An earlier paper introduced a notion of weak interaction called separability, and showed that it leads to exact…
Recently it has been recognized that the so-called generalized Wigner distribution may provide at least as good a description of terrace width distributions (TWDs) on vicinal surfaces as the standard Gaussian fit and is particularly…
Correlation of interacting particles is studied in their dynamics and localization in ideal and disordered lattice systems with the help of numerical tools. Both 1D and 2D systems are considered. In 1D lattices with long-range hopping,…