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Homogeneous Cooling with Repulsive and Attractive Long-Range Potentials

M. K. Müller, S. Luding (2011)

Mathematical Modelling of Natural Phenomena

The interplay between dissipation and long-range repulsive/attractive forces in homogeneous, dilute, mono-disperse particle systems is studied. The pseudo-Liouville operator formalism, originally introduced for hard-sphere interactions, is modified such that it provides very good predictions for systems with weak long-range forces at low densities, with the ratio of potential to fluctuation kinetic energy as control parameter. By numerical simulations, ...

Homogenization and diffusion asymptotics of the linear Boltzmann equation

Thierry Goudon, Antoine Mellet (2003)

ESAIM: Control, Optimisation and Calculus of Variations

We investigate the diffusion limit for general conservative Boltzmann equations with oscillating coefficients. Oscillations have a frequency of the same order as the inverse of the mean free path, and the coefficients may depend on both slow and fast variables. Passing to the limit, we are led to an effective drift-diffusion equation. We also describe the diffusive behaviour when the equilibrium function has a non-vanishing flux.

Homogenization and Diffusion Asymptotics of the Linear Boltzmann Equation

Thierry Goudon, Antoine Mellet (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We investigate the diffusion limit for general conservative Boltzmann equations with oscillating coefficients. Oscillations have a frequency of the same order as the inverse of the mean free path, and the coefficients may depend on both slow and fast variables. Passing to the limit, we are led to an effective drift-diffusion equation. We also describe the diffusive behaviour when the equilibrium function has a non-vanishing flux.

Homogenization in perforated domains with rapidly pulsing perforations

Doina Cioranescu, Andrey L. Piatnitski (2003)

ESAIM: Control, Optimisation and Calculus of Variations

The aim of this paper is to study a class of domains whose geometry strongly depends on time namely. More precisely, we consider parabolic equations in perforated domains with rapidly pulsing (in time) periodic perforations, with a homogeneous Neumann condition on the boundary of the holes. We study the asymptotic behavior of the solutions as the period ε of the holes goes to zero. Since standard conservation laws do not hold in this model, a first difficulty is to get a priori estimates of the...

Homogenization in perforated domains with rapidly pulsing perforations

Doina Cioranescu, Andrey L. Piatnitski (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The aim of this paper is to study a class of domains whose geometry strongly depends on time namely. More precisely, we consider parabolic equations in perforated domains with rapidly pulsing (in time) periodic perforations, with a homogeneous Neumann condition on the boundary of the holes. We study the asymptotic behavior of the solutions as the period ε of the holes goes to zero. Since standard conservation laws do not hold in this model, a first difficulty is to get a priori estimates...

Homogenization of a capillary phenomena.

N. Labani, Mongi Mabrouk (1998)

Publicacions Matemàtiques

We study the height of a liquid in a tube when it contains a great number of thin vertical bars and when its border is finely strained. For this, one uses an epi-convergence method.

Homogenization of a dual-permeability problem in two-component media with imperfect contact

Abdelhamid Ainouz (2015)

Applications of Mathematics

In this paper, we study the macroscopic modeling of a steady fluid flow in an ε -periodic medium consisting of two interacting systems: fissures and blocks, with permeabilities of different order of magnitude and with the presence of flow barrier formulation at the interfacial contact. The homogenization procedure is performed by means of the two-scale convergence technique and it is shown that the macroscopic model is a one-pressure field model in a one-phase flow homogenized medium.

Homogenization of a one-dimensional model for compressible miscible flow in porous media

Catherine Choquet (2003)

Bollettino dell'Unione Matematica Italiana

We discuss the homogenization of a one-dimensional model problem describing the motion of a compressible miscible flow in porous media. The flow is governed by a nonlinear system of parabolic type coupling the pressure and the concentration. Using the technique of renormalized solutions for parabolic equations and a compensated compactness argument, we prove the stability of the homogenization process.

Homogenization of a three-phase composites of double-porosity type

Ahmed Boughammoura, Yousra Braham (2021)

Czechoslovak Mathematical Journal

In this work we consider a diffusion problem in a periodic composite having three phases: matrix, fibers and interphase. The heat conductivities of the medium vary periodically with a period of size ε β ( ε > 0 and β > 0 ) in the transverse directions of the fibers. In addition, we assume that the conductivity of the interphase material and the anisotropy contrast of the material in the fibers are of the same order ε 2 (the so-called double-porosity type scaling) while the matrix material has a conductivity of...

Homogenization of the compressible Navier–Stokes equations in a porous medium

Nader Masmoudi (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We study the homogenization of the compressible Navier–Stokes system in a periodic porous medium (of period ε ) with Dirichlet boundary conditions. At the limit, we recover different systems depending on the scaling we take. In particular, we rigorously derive the so-called “porous medium equation”.

Homogenization of the compressible Navier–Stokes equations in a porous medium

Nader Masmoudi (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We study the homogenization of the compressible Navier–Stokes system in a periodic porous medium (of period ε) with Dirichlet boundary conditions. At the limit, we recover different systems depending on the scaling we take. In particular, we rigorously derive the so-called “porous medium equation”.

Homogenization of the transport equation describing convection-diffusion processes in a material with fine periodic structure

Šilhánek, David, Beneš, Michal (2023)

Programs and Algorithms of Numerical Mathematics

In the present contribution we discuss mathematical homogenization and numerical solution of the elliptic problem describing convection-diffusion processes in a material with fine periodic structure. Transport processes such as heat conduction or transport of contaminants through porous media are typically associated with convection-diffusion equations. It is well known that the application of the classical Galerkin finite element method is inappropriate in this case since the discrete solution...

Homogenized double porosity models for poro-elastic media with interfacial flow barrier

Abdelhamid Ainouz (2011)

Mathematica Bohemica

In the paper a Barenblatt-Biot consolidation model for flows in periodic porous elastic media is derived by means of the two-scale convergence technique. Starting with the fluid flow of a slightly compressible viscous fluid through a two-component poro-elastic medium separated by a periodic interfacial barrier, described by the Biot model of consolidation with the Deresiewicz-Skalak interface boundary condition and assuming that the period is too small compared with the size of the medium, the limiting...

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