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Abdelhamid Ainouz

Publications and source records attributed to Abdelhamid Ainouz.

7 recordsLinked to original sources
arXiv2021

Homogenization of a thermo-poro-elastic medium with two-components and interfacial hydraulic/thermal exchange barrier

The paper addresses the homogenization of a micro-model of poroelasticity coupled with thermal effects for two-constituent media and with imperfect interfacial contact.The homogenized model is obtained by means of the two-scale convergence technique. It is shown that the macro-thermo-poro-elasticity model with double porosity/diffusivity contains in particular some extra terms accounting for the micro-heterogeneities and imperfect contact at the local scale. Finally, a corrector result is given under more regularity assumptions on the data.

math.AP↗
arXiv2015

Stable capillary hypersurfaces in a half-space or a slab

We study stable immersed capillary hypersurfaces in a domain $\mathcal B$ which is either a half-space or a slab in the Euclidean space $\Bbb R^{n+1}.$ We prove that such a hypersurface $Σ$ is rotationally symmetric in the following cases: (1) $n=2$, $\mathcal B$ is a slab and $Σ$ has genus zero, (2) $n\geq 2$, $\mathcal B$ is a slab, the angle of contact is $π/2$ and each component of $\partialΣ$ is embedded, (3) $n\geq 2,$ $\mathcal B$ is a half-space, the angle of contact is $<π/2$ and each component of $\partialΣ$ is embedded. Moreover, in case (2), if not a right circular cylinder, the hypersurface has to be graphical over a domain in $\partial\mathcal B.$ In case (3), the hypersurface is a spherical cap.

math.DG↗
arXiv2014

On a Multiscale Analysis of a Micro-Model of Heat Transfer in Biological Tissues

A bio-heat transfer model for biological tissues in a micro-scale and periodical settings is investigated . It is assumed that the model is a two-component system consisting of solid particles representing tissue cells and interconnected pores containing either arterial or venous blood. This tissue-blood system is described by two energy equations, one equation for the solid tissues and the other for the surrounding blood. On the interface between them, it is assumed that the heat transfer is governed by Newton's cooling law. Using homogenization techniques, it is shown that the obtained macro-model presents some extra-terms and it can be seen as a new mathematical model for human thermotherapy and human thermoregulation system.

math.AP↗
arXiv2012

Homogenization of a Double Porosity Model In Deformable Media

The paper addresses the homogenization of a family of micro-models for the flow of a slightly compressible fluid in a poroelastic matrix containing periodically distibuted poroelastic inclusions, with low permeabilities and with imperfect contact on the interface. The micro-models are based on Biot's system for consolidation processes in each phase, with interfacial barrier formulation. Using the two-scale convergence technique, it is shown that the derived system is a general model of that proposed by Aifantis, plus an extra memory term.

math.AP↗
arXiv2007

Derivation of a Convection Process in a Steady Diffusion-Transfer Problem by Homogenization

We study the homogenization of a steady diffusion equation in a highly heterogeneous medium made of two subregions separated by a periodic barrier through which the flow is proportional to the jump of the temperature by a layer conductance of the same order of magnitude of the materials in consideration. The macroscopic governing equations and the effective conductivity of the homogenized model are obtained by means of the two scale convergence technique. We show that under some hypothesis the homogenized systems contain convective terms of order one.

math.AP↗
arXiv2006

Two-Scale limit of the solution to a Robin Problem in Perforated Media

The two scale convergence of the solution to a Robin's type-like problem of a stationary diffusion problem in a periodically perforated domain is investigated. It is shown that the Robin's problem converges to a problem associated to a new operator which is the sum of a standard homogenized operator plus an extra first order "strange" term; its appearance is due to the non-symmetry of the diffusion matrix and to the non rescaled resistivity.

math.AP↗