Related papers: Homogenized dynamics of stochastic partial differe…
Stochastic dynamical systems arise naturally across nearly all areas of science and engineering. Typically, a dynamical system model is based on some prior knowledge about the underlying dynamics of interest in which probabilistic features…
Boltzmann provided a scenario to explain why individual macroscopic systems composed of a large number $N$ of microscopic constituents are inevitably (i.e., with overwhelming probability) observed to approach a unique macroscopic state of…
A stochastic telegraph equation is defined by adding a random inhomogeneity to the classical (second order linear hyperbolic) telegraph differential equation. The inhomogeneities we consider are proportional to the two-dimensional white…
We consider a multicontinuum model in porous media applications, which is described as a system of coupled flow equations. The coupling between different continua depends on many factors and its modeling is important for porous media…
We present an approximate and heuristic scheme for the derivation of continuum kinetic equations from microscopic dynamics for stochastic, interacting systems. The method consists of a mean-field type, decoupled approximation of the master…
Molecular dynamics simulations use statistical mechanics at the atomistic scale to enable both the elucidation of fundamental mechanisms and the engineering of matter for desired tasks. The behavior of molecular systems at the microscale is…
Stochastic diffusion is the noisy and uncertain process through which dynamics like epidemics, or agents like animal species, disperse over a larger area. Understanding these processes is becoming increasingly important as we attempt to…
Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified…
We study stochastic particle systems made up of heterogeneous units. We introduce a general framework suitable to analytically study this kind of systems and apply it to two particular models of interest in economy and epidemiology. We show…
Confined granular fluids, placed in a shallow box that is vibrated vertically, can achieve homogeneous stationary states thanks to energy injection mechanisms that take place throughout the system. These states can be stable even at high…
Motivated by the fact that in nature almost all phenomena behave randomly in some scales and deterministically in some other scales, we build up a framework suitable to tackle both deterministic and stochastic homogenization problems…
We address the reachability problem for continuous-time stochastic dynamic systems. Our objective is to present a unified framework that characterizes the reachable set of a dynamic system in the presence of both stochastic disturbances and…
Dynamics of many-body Hamiltonian systems with long range interactions is studied, in the context of the so called $\alpha-$HMF model. Building on the analogy with the related mean field model, we construct stationary states of the…
A central question in numerical homogenization of partial differential equations with multiscale coefficients is the accurate computation of effective quantities, such as the homogenized coefficients. Computing homogenized coefficients…
A number of simplified dynamical problems is studied in an attempt to clarify some of the mechanisms leading to turbulence and the existing proposals to control this transition. A simplified set of boundary layer equations displays a…
We consider the homogenization of the Poisson and the Stokes equations in the whole space perforated with periodically distributed small holes. The periodic homogenization in bounded domains is well understood, following the classical…
One considers linearly thermoelastic composite media, which consist of a homogeneous matrix containing a statistically homogeneous random set of ellipsoidal uncoated or coated inclusions. Effective properties (such as compliance and thermal…
The Allen-Cahn equation, coupled with dynamic boundary conditions, has recently received a good deal of attention. The new issue of this paper is the setting of a rather general mass constraint which may involve either the solution inside…
In this manuscript we prove quantitative homogenization results for the obstacle problem with bounded measurable coefficients. As a consequence, large-scale regularity results both for the solution and the free boundary for the…
We are concerned with homogenization of stochastic differential equations (SDE) with stationary coefficients driven by Poisson random measures and Brownian motions in the critical case, that is when the limiting equation admits both a…