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The basic problem in equilibrium statistical mechanics is to compute phase space average, in which Monte Carlo method plays a very important role. We begin with a review of nonlocal algorithms for Markov chain Monte Carlo simulation in…
A semi-classical non-Hamiltonian model of a spontaneous collapse of unstable quantum system is given. The time evolution of the system becomes non-Hamiltonian at random instants of transition of pure states to reduced ones, given by a…
This paper deals with the numerical (finite volume) approximation of reaction-diffusion systems with relaxation, among which the hyperbolic extension of the Allen--Cahn equation represents a notable prototype. Appropriate discretizations…
Qualitatively new aspects of the (linear and non-linear) stability of sheared relativistic (slab) jets are analyzed. The linear problem has been solved for a wide range of jet models well inside the ultrarelativistic domain (flow Lorentz…
We present a numerical method of analyzing possibly singular incompressible 3D Euler flows using massively parallel high-resolution adaptively refined numerical simulations up to 8192^3 mesh points. Geometrical properties of Lagrangian…
In this note we study the numerical stability problem that may take place when calculating the cumulative distribution function of the {\it Hypoexponential} random variable. This computation is extensively used during the execution of Monte…
We are concerned with the stability of steady multi-wave configurations for the full Euler equations of compressible fluid flow. In this paper, we focus on the stability of steady four-wave configurations that are the solutions of the…
A numerical study of the Kelvin-Helmholtz instability in compressible magnetohydrodynamics is presented. The three-dimensional simulations consider shear flow in a cylindrical jet configuration, embedded in a uniform magnetic field directed…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
We investigate a one dimensional flow described with the non-compressible coupled Euler and non-compressible Navier-Stokes equations in Cartesian coordinate systems. We couple the two fluids through the continuity equation where different…
We study distributionally robust optimization (DRO) problems with uncertainty sets consisting of high-dimensional random vectors that are close in the multivariate Wasserstein distance to a reference random vector. We give conditions when…
We study shell models that conserve the analogues of energy and enstrophy, hence designed to mimic fluid turbulence in 2D. The main result is that the observed state is well described as a formal statistical equilibrium, closely analogous…
A simplified thermodynamic approach of the incompressible axisymmetric Euler equations is considered based on the conservation of helicity, angular momentum and microscopic energy. Statistical equilibrium states are obtained by maximizing…
We introduce new probabilistic and variational constructions of (twisted) K\"ahler-Einstein metrics on complex projective algebraic varieties, drawing inspiration from Onsager's statistical mechanical model of turbulence in two-dimensional…
We investigate Monte Carlo based algorithms for solving stochastic control problems with probabilistic constraints. Our motivation comes from microgrid management, where the controller tries to optimally dispatch a diesel generator while…
Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…
As a natural approach to modeling system safety conditions, chance constraint (CC) seeks to satisfy a set of uncertain inequalities individually or jointly with high probability. Although a joint CC offers stronger reliability certificate,…
Motivated by the difficulty to solve numerically the weakly compressible 1D isentropic Euler equations with classical methods, we develop in this paper a two scale numerical method on this model. This method is based on two scale…
In this paper we address the use of rare event computation techniques to estimate small over-threshold probabilities of observables in determin-istic dynamical systems. We demonstrate that the genealogical particle analysis algorithms can…
Asymptotic behavior of a class of nonlinear Schr\"odinger equations are studied. Particular cases of 1D weakly focusing and Bose-Einstein condensates are considered. A statistical approach is presented to describe the stationary probability…