Related papers: Relaxation to the equilibrium in the hard disk dyn…
We study, using both theory and molecular dynamics simulations, the relaxation dynamics of a microcanonical two dimensional self-gravitating system. After a sufficiently large time, a gravitational cluster of N particles relaxes to the…
We present a new numerical Monte Carlo approach to determine the scaling behavior of lattice field theories far from equilibrium. The presented methods are generally applicable to systems where classical-statistical fluctuations dominate…
We study a two-dimensional fluid of dipolar hard disks by Monte Carlo simulations in a square with periodic boundary conditions and on the surface of a sphere. The theory of the dielectric constant and the asymptotic behaviour of the…
In this paper, we present a comprehensive investigation of stress propagation in a two-dimensional elastic circular disk. To accurately describe the displacements and stress fields within the disk, we employ a scalar and vector potential…
Elastic systems that are spatially heterogeneous in their mechanical response pose special challenges for molecular simulations. Standard methods for sampling thermal fluctuations of a system's size and shape proceed through a series of…
Evidently, some relaxation dynamics, e.g. exponential decays, are much more common in nature than others. Recently there have been attempts to explain this observation on the basis of ``typicality of perturbations'' with respect to their…
We study diffusion in systems of classical particles whose dynamics conserves the total center of mass. This conservation law leads to several interesting consequences. In finite systems, it allows for equilibrium distributions that are…
Among random sampling methods, Markov Chain Monte Carlo algorithms are foremost. Using a combination of analytical and numerical approaches, we study their convergence properties towards the steady state, within a random walk Metropolis…
In high dimensions, reflective Hamiltonian Monte Carlo with inexact reflections exhibits slow mixing when the particle ensemble is initialised from a Dirac delta distribution and the uniform distribution is targeted. By quantifying the…
We present simple and practical strategies to reduce the variance of Monte Carlo estimators. Our focus is on variational Monte Carlo calculations of atomic forces and pressure in electronic systems, although we show that the underlying…
The histogram reweighting technique, widely used to analyze Monte Carlo data, is shown to be applicable to dynamic properties obtained from Molecular Dynamics simulations. The theory presented here is based on the fact that the correlation…
This paper considers an infinite-horizon Markov decision process (MDP) that allows for general non-exponential discount functions, in both discrete and continuous time. Due to the inherent time inconsistency, we look for a randomized…
We study nonequilibrium critical relaxation properties of systems with quenched extended defects, correlated in $\epsilon_d$ dimensions and randomly distributed in the remaining $d-\epsilon_d$ dimensions. Using a field-theoretic…
We prove approach to thermal equilibrium for the fully Hamiltonian dynamics of a dynamical Lorentz gas, by which we mean an ensemble of particles moving through a $d$-dimensional array of fixed soft scatterers that each possess an internal…
We introduce a theoretical approach to study the quantum-dissipative dynamics of electronic excitations in macromolecules, which enables to perform calculations in large systems and cover long time intervals. All the parameters of the…
We compute the exact relaxation and $\Lambda$-convex hull of the kinematic dynamo equations and show that they coincide. We also find the relaxation in the stationary case.
We study well-posedness for the relaxed linear elastic micromorphic continuum model with symmetric Cauchy force-stresses and curvature contribution depending only on the micro-dislocation tensor. In contrast to classical micromorphic models…
Based on global conservation principles, magnetohydrodynamic (MHD) relaxation theory predicts the existence of several equilibria, such as the Taylor state or global dynamic alignment. These states are generally viewed as very long-time and…
We investigate the diffusive properties of energy fluctuations in a one-dimensional diatomic chain of hard-point particles interacting through a square--well potential. The evolution of initially localized infinitesimal and finite…
The stochastic differential equations for a model of dissipative particle dynamics, with both total energy and total momentum conservation at every time-step, are presented. The algorithm satisfies detailed balance as well as the…