arXiv subjects

Dan Polisevski

Publications and source records attributed to Dan Polisevski.

3 recordsLinked to original sources

arXiv2009

Homogenizing media containing a highly conductive honeycomb substructure

The present paper deals with the homogenization of the heat conduction which takes place in a binary three-dimensional medium consisting of an ambiental phase having conductivity of unity order and a rectangular honeycomb structure formed by a set of thin layers crossing orthogonally and periodically. We consider the case when the conductivity of the thin layers is in inverse proportion to the vanishing volume of the rectangular honeycomb structure. We find the system that governs the asymptotic behaviour of the temperature distribution of this binary medium. The dependence with respect to the thicknesses of the layers is also emphasized. We use an energetic method associated to a natural control-zone of the vanishing domain.

math.AP↗

arXiv2007

The Div-Curl Lemma Revisited

The Div-Curl Lemma, which is the basic result of the compensated compactness theory in Sobolev spaces, was introduced by F. Murat (1978) with distinct proofs for the $L^2(Ω)$ and $L^p(Ω)$, $p \neq 2$, cases. In this note we present a slightly different proof, relying only on a Green-Gauss integral formula and on the usual Rellich-Kondrachov compactness properties.

math.FA↗

arXiv2005

Homogenization of a diffusion process in a rarefied binary structure

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 distribution of the concentration is determined for both phases, as $\veps\to 0$, assuming that the suspension has mass of unity order and vanishing volume. Three cases are distinguished according to the values of a certain limit capacity. When it is positive and finite, the macroscopic system involves a two-concentration system, coupled through a term accounting for the non local effects. In the other two cases, where the capacity is either infinite or going to zero, although the form of the system is much simpler, some peculiar effects still account for the presence of the suspension.

math.AP↗