We establish some quantitative concentration estimates for the empirical measure of many independent variables, in transportation distances. As an application, we provide some error bounds for particle simulations in a model mean field problem. The tools include coupling arguments, as well as regularity and moments estimates for solutions of certain diffusive partial differential equations.

molecular dynamics simulation has been performed to analyze the effect of the presence of gold nanoparticle on dynamics of kob-anderson binary lennard-jones (blj) mixture upon supercooling within the framework of the mode coupling theory of the dynamic glass transition. the presence of gold nanoparticle has a direct effect on the liquid structure and causes the peaks of the radial distribution ...

Chains of N FitzHugh–Nagumo oscillators with a gradient in natural frequencies and strong diffusive coupling are analyzed in this paper. We study the system’s dynamics in the limit of infinitely large coupling and then treat the case when the coupling is large but finite as a perturbation of the former case. In the large coupling limit, the 2N -dimensional phase space has an unexpected structur...

molecular dynamics simulation has been performed to analyze the effect of the presence of gold nanoparticle on dynamics of kob-anderson binary lennard-jones (blj) mixture upon supercooling within the framework of the mode coupling theory of the dynamic glass transition. the presence of gold nanoparticle has a direct effect on the liquid structure and causes the peaks of the radial distribution ...

Systems of strongly coupled chaotic maps generically exhibit collective behavior emerging out of extensive chaos. We show how the well-known renormalization group (RG) of unimodal maps can be extended to the coupled systems, and in particular to coupled map lattices (CMLs) with local diffusive coupling. The RG relation derived for CMLs is nonperturbative, i.e., not restricted to a particular cl...

Large ensembles of heterogeneous oscillators often exhibit collective synchronization as a result of mutual interactions. If the oscillators have distributed natural frequencies and common shear (or nonisochronicity), the transition from incoherence to collective synchronization is known to occur at large enough values of the coupling strength. However, here we demonstrate that shear diversity ...

Within the framework of a (1 + 1)-dimensional model which mimics high-energy QCD, we study the behavior of the cross sections for inclusive and diffractive deep inelastic γ ∗h scattering cross sections. We analyze the cases of both fixed and running coupling within the mean-field approximation, in which the evolution of the scattering amplitude is described by the Balitsky–Kovchegov equation, a...

The central pattern generator (CPG) is a group of interconnected neurons, existing in biological systems as control center for oscillatory behaviors. We propose new approach based on the multivariable harmonic balance to characterize relationship between oscillation profile (frequency, amplitude, phase) and interconnections within CPG, modeled weakly coupled oscillators. In particular, taking a...

We deduce rigorous conditions for the onset of amplitude death (AD) and oscillation death (OD) in a system of identical coupled paradigmatic Stuart-Landau oscillators. A nonscalar coupling and high frequency are beneficial for the onset of AD. In strong contrast, scalar diffusive coupling and low intrinsic frequency are in favor of the emergence of OD. Our finding contributes to clearly disting...