English
Related papers

Related papers: Homogenized dynamics of stochastic partial differe…

200 papers

Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale.…

Condensed Matter · Physics 2009-11-07 Gregor Diezemann , Gerald Hinze , Hans Sillescu

A central feature of complex systems is the relevance and entanglement of different levels of description. For instance, the dynamics of ecosystems can be alternatively described in terms of large ecological processes and classes of…

Populations and Evolution · Quantitative Biology 2025-10-06 Juan Giral Martínez , Silvia de Monte , Matthieu Barbier

The homogeneous partly pinned fluid systems are simple models of a fluid confined in a disordered porous matrix obtained by arresting randomly chosen particles in a one-component bulk fluid or one of the two components of a binary mixture.…

Soft Condensed Matter · Physics 2010-12-07 Vincent Krakoviack

We investigate systems of interacting stochastic differential equations with two kinds of heterogeneity: one originating from different weights of the linkages, and one concerning their asymptotic relevance when the system becomes large. To…

Probability · Mathematics 2020-06-02 Carsten Chong , Claudia Klüppelberg

We study the homogenization of the Poisson equation in randomly perforated domains and obtain the strange term effect in the homogenized equation. The perforations are modeled by rescaled germ-grain processes, and the main assumption is…

Analysis of PDEs · Mathematics 2026-02-24 Naoto Sato

We perform the periodic homogenization (i.e. $\eps\to 0$) of the non-stationary Stokes-Nernst-Planck-Poisson system using two-scale convergence, where $\eps$ is a suitable scale parameter. The objective is to investigate the influence of…

Analysis of PDEs · Mathematics 2011-11-08 Nadja Ray , Adrian Muntean , Peter Knabner

This work develops a dynamic homogenization approach for metamaterials. It finds an approximate macroscopic homogenized equation with constant coefficients posed in space and time; however, the resulting homogenized equation is higher order…

Analysis of PDEs · Mathematics 2022-06-23 Kshiteej Deshmukh , Timothy Breitzman , Kaushik Dayal

We consider the homogenisation of the Stokes equations in a porous medium which is evolving in time. At the interface of the pore space and the solid part, we prescribe an inhomogeneous Dirichlet boundary condition, which enables to model a…

Analysis of PDEs · Mathematics 2021-09-14 David Wiedemann , Malte A. Peter

The macroscopic behavior of dissipative stochastic partial differential equations usually can be described by a finite dimensional system. This article proves that a macroscopic reduced model may be constructed for stochastic…

Mathematical Physics · Physics 2008-12-11 Wei Wang , A. J. Roberts

We consider a system of differential equations in a fast long range dependent random environment and prove a homogenization theorem involving multiple scaling constants. The effective dynamics solves a rough differential equation, which is…

Probability · Mathematics 2019-12-02 Johann Gehringer , Xue-Mei Li

We aim at studying a novel mathematical model associated to a physical phenomenon of infiltration in an homogeneous porous medium. The particularities of our system are connected to the presence of a gravitational acceleration term…

Analysis of PDEs · Mathematics 2024-05-22 Ioana Ciotir , Dan Goreac , Juan Li , Antoine Tonnoir

In this paper we study homogenization of a class of control problems in a stationary and ergodic random environment. This problem has been mostly studied in the calculus of variations setting in connection to the homogenization of the…

Analysis of PDEs · Mathematics 2018-06-21 Alexander Van-Brunt

Fully resolving dynamics of materials with rapidly-varying features involves expensive fine-scale computations which need to be conducted on macroscopic scales. The theory of homogenization provides an approach to derive effective…

Numerical Analysis · Mathematics 2022-06-07 Kaushik Bhattacharya , Burigede Liu , Andrew M. Stuart , Margaret Trautner

Homogenisation empowers the efficient macroscale system level prediction of physical scenarios with intricate microscale structures. Here we develop an innovative powerful, rigorous and flexible framework for asymptotic homogenisation of…

Dynamical Systems · Mathematics 2025-04-08 A. J. Roberts

For microscale heterogeneous PDEs, this article further develops novel theory and methodology for their macroscale mathematical/asymptotic homogenization. This article specifically encompasses the case of quasi-periodic heterogeneity with…

Analysis of PDEs · Mathematics 2022-09-08 A. J. Roberts

In our recent work [8], we have studied the homogenization of the Poisson equation in a class of non periodically perforated domains. In this paper, we examine the case of the Stokes system. We consider a porous medium in which the…

Analysis of PDEs · Mathematics 2021-01-13 Sylvain Wolf

A stochastic system of particles is considered in which the sizes of the particles increase by successive binary mergers with the constraint that each coagulation event involves a particle with minimal size. Convergence of a suitably…

Probability · Mathematics 2011-10-31 Anne-Laure Basdevant , Philippe Laurencot , James R. Norris , Clement Rau

Computational models in cardiac electrophysiology are notorious for long runtimes, restricting the numbers of nodes and mesh elements in the numerical discretisations used for their solution. This makes it particularly challenging to…

Simulation of stochastic spatially-extended systems is a challenging problem. The fundamental quantities in these models are individual entities such as molecules, cells, or animals, which move and react in a random manner. In big systems,…

Quantitative Methods · Quantitative Biology 2024-09-24 Tomás Alarcón , Natalia Briñas-Pascual , Juan Calvo , Pilar Guerrero , Daria Stepanova

This article investigates an energy balance model coupled to the primitive equations by a dynamic boundary condition with and without noise on the boundary. It is shown that this system is globally strongly well-posed both in the…

Analysis of PDEs · Mathematics 2025-10-29 Gianmarco Del Sarto , Matthias Hieber , Tarek Zöchling