Related papers: Multicontinuum homogenization. General theory and …
The present paper is concerned with a space-time homogenization problem for nonlinear diffusion equations with periodically oscillating (in space and time) coefficients. Main results consist of a homogenization theorem (i.e., convergence of…
The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying…
This paper presents a thermodynamically consistent model for multicomponent electrolyte solutions. The first part of this paper derives the general governing equations for nonequilibrium systems within the theory of nonequilibrium…
We consider in this paper a challenging problem of simulating fluid flows, in complex multiscale media possessing multi-continuum background. As an effort to handle this obstacle, model reduction is employed. In \cite{rh2}, homogenization…
The article studies the reiterated homogenization of linear elliptic variational inequalities arising in problems with unilateral constrains. We assume that the coefficients of the equations satisfy and abstract hypothesis covering on each…
In this paper, we propose multicontinuum splitting schemes for multiscale problems, focusing on a parabolic equation with a high-contrast coefficient. Using the framework of multicontinuum homogenization, we introduce spatially smooth…
This paper presents a homogenization framework for elastomeric metamaterials exhibiting long-range correlated fluctuation fields. Based on full-scale numerical simulations on a class of such materials, an ansatz is proposed that allows to…
In this work, we propose multicontinuum splitting schemes for the wave equation with a high-contrast coefficient, extending our previous research on multiscale flow problems. The proposed approach consists of two main parts: decomposing the…
A model of multicellular systems with several types of cells is developed from the phase field model. The model is presented as a set of partial differential equations of the field variables, each of which expresses the shape of one cell.…
In this work, we review the connection between the subjects of homogenization and nonlocal modeling and discuss the relevant computational issues. By further exploring this connection, we hope to promote the cross fertilization of ideas…
We study a cell problem arising in homogenization for a Hamilton-Jacobi equation whose Hamiltonian is not coercive. We introduce a generalized notion of effective Hamiltonians by approximating the equation and characterize the solvability…
A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for…
This work is devoted to the homogenization of elliptic equations in high-contrast media in the so-called 'double-porosity' resonant regime, for which we solve two open problems of the literature. First, we prove qualitative stochastic…
Homogenization theory is used to calculate the macroscopic dielectric constant from the quantum microscopic dielectric function in a periodic medium. The method can be used to calculate any macroscopic constitutive relation, but it is…
In this paper, we study a multiscale method for simulating a dual-continuum unsaturated flow problem within complex heterogeneous fractured porous media. Mathematically, each of the dual continua is modeled by a multiscale Richards equation…
In this paper homogenization of a mathematical model for plant tissue biomechanics is presented. The microscopic model constitutes a strongly coupled system of reaction-diffusion-convection equations for chemical processes in plant cells,…
In this paper we study homogenization for a class of monotone systems of first-order time-dependent periodic Hamilton-Jacobi equations. We characterize the Hamiltonians of the limit problem by appropriate cell problems. Hence we show the…
This paper develops a general approach to nonlinear circuit modelling aimed at preserving the intrinsic symmetry of electrical circuits when formulating reduced models. The goal is to provide a framework accommodating such reductions in a…
Asymptotic homogenisation is considered for problems with integral constraints imposed on a slowly-varying microstructure; an insulator with an array of perfectly dielectric inclusions of slowly varying size serves as a paradigm. Although…
The aim of the paper is to introduce an alternative notion of two-scale convergence which gives a more natural modeling approach to the homogenization of partial differential equations with periodically oscillating coefficients: while…