Related papers: Nonlinear response theory for Markov processes II:…
The effective nonlinear response of films of random composites consisting of a binary composite with nonlinear particles randomly embedded in a linear host is theoretically and numerically studied. A theoretical expression for the effective…
A new systematic approach to the construction of approximate solutions to a class of nonlinear singularly perturbed feedback control systems using the boundary layer functions especially with regard to the possible occurrence of the…
Within the framework of the effective potential theory of the structural glass transition, we calculate for the p-spin model a static nonlinear susceptibility related to a four-point density correlation function, and show that it grows and…
In recent years, nonlinear transport phenomena have garnered significant interest in both theoretical explorations and experiments. In this work, we utilize the semi-classical wave packet theory to calculate disorder-induced second-order…
A nonlinear dynamical system model that approximates a microscopic Gibbs field model for the yielding of a viscoplastic material subjected to varying external stress recently reported in [1] is presented. The predictions of the model are in…
In this paper we consider interacting particle systems which are frequently used to model collective behavior in animal swarms and other applications. We study the stability of orientationally aligned formations called flock solutions, one…
We are interested in assessing the order of a finite-state Hidden Markov Model (HMM) with the only two assumptions that the transition matrix of the latent Markov chain has full rank and that the density functions of the emission…
A granular assembly composed of a collection of identical grains may pack under different microscopic configurations with microscopic features that are sensitive to the preparation history. A given configuration may also change in response…
An adaptive nonparametric estimation procedure is constructed for the estimation problem of heteroscedastic regression when the noise variance depends on the unknown regression. A non-asymptotic upper bound for a quadratic risk (an oracle…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
We study the so-called two-time-scale stochastic approximation, a simulation-based approach for finding the roots of two coupled nonlinear operators. Our focus is to characterize its finite-time performance in a Markov setting, which often…
Nonparametric estimation for semilinear SPDEs, namely stochastic reaction-diffusion equations in one space dimension, is studied. We consider observations of the solution field on a discrete grid in time and space with infill asymptotics in…
A possibility of tuning the phase of the third-order Kerr-type nonlinear susceptibility in a system consisting of two interacting metal nanospheres and a nonlinearly polarizable molecule is investigated theoretically and numerically. It is…
Two-time-scale stochastic approximation, a generalized version of the popular stochastic approximation, has found broad applications in many areas including stochastic control, optimization, and machine learning. Despite its popularity,…
We investigate the static charge response for the Hubbard model. Using the Slave-Boson method in the saddle-point approximation we calculate the charge susceptibility. We find that RPA works quite well close to half-filling, breaking, of…
Along the lines of the nonlinear response theory developed by Ruelle, in a previous paper we have proved under rather general conditions that Kramers-Kronig dispersion relations and sum rules apply for a class of susceptibilities describing…
Nonlinear response theory is employed to derive a closure to the polymer reference interaction site model (PRISM) equation. The closure applies to a liquid of neutral polymers at melt densities. It can be considered a molecular…
The linear response of non-equilibrium systems with Markovian dynamics satisfies a generalized fluctuation-dissipation relation derived from time symmetry and antisymmetry properties of the fluctuations. The relation involves the sum of two…
We develop a linear response theory by computing the asymptotic value of the order parameter from the linearized equation of continuity around the nonsynchronized reference state using the Laplace transform in time. The proposed theory is…
The obtention (up to five or six loop orders) of nonasymptotic critical behavior, above and below Tc, from the field theoretical framework is presented and discussed.