Related papers: Stochastic sigma-convergence and applications
In this paper we prove a general homogenization result for monotone parabolic problems with an arbitrary number of microscopic scales in space as well as in time, where the scale functions are not necessarily powers of epsilon. The main…
We study generically stable types/measures in both classical and continuous logics, and their connection with randomization and modes of convergence of types/measures.
The problem of pattern formation in a generic two species reaction--diffusion model is studied, under the hypothesis that only one species can diffuse. For such a system, the classical Turing instability cannot take place. At variance, by…
The aim of this paper is to examine the large-scale behavior of dynamical optimal transport on stationary random graphs embedded in $\R^n$. Our primary contribution is a stochastic homogenization result that characterizes the effective…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
We consider variational problems that model the bending behavior of curves that are constrained to belong to given hypersurfaces. Finite element discretizations of corresponding functionals are justified rigorously via Gamma-convergence.…
Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency,…
Consider a fast-slow system of ordinary differential equations of the form $\dot x=a(x,y)+\varepsilon^{-1}b(x,y)$, $\dot y=\varepsilon^{-2}g(y)$, where it is assumed that $b$ averages to zero under the fast flow generated by $g$. We give…
The homogenization of a metamaterial made of a collection of scatterers periodically disposed is studied from three different points of view. Specifically tools for multiple scattering theory, functional analysis, differential geometry and…
Since Kolmogorov's theory, turbulence has been studied using various methods, many of which could be now be understood in a probabilistic framework. Herein, a comprehensive review of the advances made on stochastic theory of turbulence…
Stochastic geometric mechanics (SGM) is known for its potential utility in quantifying uncertainty in global climate modelling of the Earth's ocean and atmosphere while also preserving the fundamental advective transport properties of ideal…
Convergence of stochastic processes with jumps to diffusion processes is investigated in the case when the limit process has discontinuous coefficients. An example is given in which the diffusion approximation of a queueing model yields a…
We formulate conditions for convergence of Laws of Large Numbers and show its links with of the parts of mathematical analysis such as summation theory, convergence of orthogonal series. We present also applications of the Law of Large…
This short survey article stems from recent progress on critical cases of stochastic evolution equations in variational formulation with additive, multiplicative or gradient noises. Typical examples appear as the limit cases of the…
We study the finite-size scaling behaviour at the critical point, resulting from the addition of a homogeneous size-dependent perturbation, decaying as an inverse power of the system size. The scaling theory is first formulated in a general…
Deterministic simulations of the rate equations governing cluster dynamics in materials are limited by the number of equations to integrate. Stochastic simulations are limited by the high frequency of certain events. We propose a coupling…
We develop a formalism to discuss the properties of GENERIC systems in terms of corresponding Hamiltonians that appear in the characterization of large-deviation limits. We demonstrate how the GENERIC structure naturally arises from a…
We analyze convergence rates of stochastic optimization procedures for non-smooth convex optimization problems. By combining randomized smoothing techniques with accelerated gradient methods, we obtain convergence rates of stochastic…
The starting point for this work is a static macroscopic model for a high-contrast layered material in single-slip finite crystal plasticity, identified in [Christowiak & Kreisbeck, Calc. Var. PDE (2017)] as a homogenization limit via…
The four types of homogeneity -- additive, multiplicative, exponential, and logarithmic -- are generalized as transformations describing how a function $f$ changes under scaling or shifting of its arguments. These generalized homogeneity…