66 research outputs found
Periodic homogenization of an elliptic system involving non-local and equi-valued interface conditions
No full textIn this paper, we analyze the effective behaviour of the solution of an elliptic problem in a two-phase composite material
with non-standard imperfect contact conditions between its constituents. More specifically, we consider on the interface
an equi-valued surface condition and a non-local flux condition involving a scaling parameter .
We perform a homogenization procedure by using the periodic unfolding technique.
As a result, we obtain two different effective models, depending on the scaling parameter .
More precisely, in the case \alpha>-1, we are led to a standard Dirichlet problem for an elliptic equation,
while in the case , we get a bidomain system, consisting in the coupling of an elliptic equation with an algebraic one
Homogenization results for a class of parabolic problems with a non-local interface condition via time-periodic unfolding
No full textWe study the thermal properties of a composite material in which a periodic array of finely mixed perfect thermal conductors is inserted.
The suitable model describing the behaviour of such physical materials leads to the so-called equivalued surface boundary value problem.
To analyze the overall conductivity of the composite medium (when the size of the inclusions tends to zero),
we make use of the homogenization theory, employing the unfolding technique.
The peculiarity of the problem under investigation asks for a particular care in developing the unfolding procedure,
giving rise to a non-standard two-scale problem
Concentration and homogenization in electrical conduction in heterogeneous media involving the Laplace-Beltrami operator
No full textWe study a concentration and homogenization problem modelling electrical conduction in a composite material. The novelty of the problem is due to the specific scaling of the physical quantities characterizing the dielectric component of the composite. This leads to the appearance of a peculiar displacement current governed by a Laplace-Beltrami pseudo-parabolic equation. This pseudo-parabolic character is present also in the homogenized equation, which is obtained by the unfolding technique
Homogenization in heterogeneous media modeled by the Laplace-Beltrami operator
No full textThe study of thermal, mechanical and electrical properties of composite materials plays an increasingly important role in material sciences because of their wide spectrum of applica-
tions, for instance, in industrial processes, biomathematics, medical diagnosis. In this talk, we discuss some models which describe the thermal diffusivity or the electrical
conductivity in a composite medium with a nely mixed periodic structure, assuming that the microstructure of the materials under consideration is made by two different diffusive
or conductive regions separated by an active interface ([1, 2, 3]). From the mathematical point of view, these models are described by a system of parabolic or elliptic equations in the two bulk phases, coupled through the interface by means of an equation involving the Laplace-Beltrami operator. Since the characteristic length of the microstructure is very small, we are led to study the limit behaviour of the medium, when the spatial period of the medium goes to zero, in order to produce the so-called \macroscopic" or \homogenized" models
A degenerate pseudo-parabolic equation with memory
No full textWe prove the existence and uniqueness for a degenerate pseudo-parabolic problem with memory. This kind of problem arises in the study of the homogenization of some differential systems involving the Laplace-Beltrami operator and describes the effective behaviour of the electrical conduction in some composite materials
Multiscale Analysis of Ionic Transport in Periodic Charged Media
No full textA macroscopic model for describing the ion transport in periodic charged porous media is rigorously derived. Our results can serve as a tool for biophysicists to analyze the ion transport through protein channels. Also, such a model is useful for describing the flow of electrons and holes in a semiconductor device
Multiscale Analysis of Composite Structures
No full textThe goal of this paper is to present some homogenization results for diffusion problems in composite structures, formed by two media with different features. Our setting is relevant for modeling heat diffusion in composite materials with imperfect interfaces or electrical conduction in biological tissues. The approach we follow is based on the periodic unfolding method, which allows us to deal with general media
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