Related papers: Homogenization: in Mathematics or Physics?
A description of physical reality in which wholeness is the foundation is discussed along with the motivation for such an attempt. As a possible mathematical framework within which a physical theory based on wholeness may be expressed,…
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…
The paper studies homogenization problem for a non-autonomous parabolic equation with a large random rapidly oscillating potential in the case of one dimensional spatial variable. We show that if the potential is a statistically homogeneous…
We perform the homogenization process avoiding the necessity of testing the weak formulation of the initial and homogenized systems by corresponding weak solutions. We show that the stress tensor for homogenized problem depends on the…
This paper studies homogenization of stochastic differential systems. The standard example of this phenomenon is the small mass limit of Hamiltonian systems. We consider this case first from the heuristic point of view, stressing the role…
We study homogenisation problems for divergence form equations with rapidly sign-changing coefficients. With a focus on problems with piecewise constant, scalar coefficients in a ($d$-dimensional) crosswalk type shape, we will provide a…
We study the homogenization of a diffusion process which takes place in a binary structure formed by an ambiental connected phase surrounding a suspension of very small spheres distributed in an $\veps$-periodic network. The asymptotic…
In this paper, we discuss the question whether a physical "simplification" of a model makes it always easier to study, at least from a mathematical and numerical point of view. To this end, we give different examples showing that these…
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…
In porous media physics, calibrating model parameters through experiments is a challenge. This process is plagued with errors that come from modelling, measurement and computation of the macroscopic observables through random homogenization…
The purpose of this short paper is to identify the mathematical essence of the superiorization methodology. This methodology has been developed in recent years while attempting to solve specific application-oriented problems. Consequently,…
We explore the interplay between symmetry and randomness in quantum information. Adopting a geometric approach, we consider states as $H$-equivalent if related by a symmetry transformation characterized by the group $H$. We then introduce…
We revisit the classical problem of diffusion of a scalar (or heat) released in a two-dimensional medium with an embedded periodic array of impermeable obstacles such as perforations. Homogenisation theory provides a coarse-grained…
An overview of some recent developments in inhomogeneous models is presented. As the volume and precision of cosmological data improves, it will become more and more essential to understand the non-linear behaviour of the Einstein field…
A homogeneous mass-fragmentation, as it has been defined in \cite{RFC}, describes the evolution of the collection of masses of fragments of an object which breaks down into pieces as time passes. Here, we show that this model can be…
We consider linear problems in the worst case setting. That is, given a linear operator and a pool of admissible linear measurements, we want to approximate the values of the operator uniformly on a convex and balanced set by means of…
The test of homogeneity for normal mixtures has been conducted in diverse research areas, but constructing a theory of the test of homogeneity is challenging because the parameter set for the null hypothesis corresponds to singular points…
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 the context of infinitesimal strain plasticity with hardening, we derive a stochastic homogenization result. We assume that the coefficients of the equation are random functions: elasticity tensor, hardening parameter and flow-rule…
The paper deals with homogenization of a model problem describing an immiscible compressible two-phase flow in random statistically homogeneous porous media. We derive the effective (macroscopic) problem and prove the convergence of…