Claudia Timofte

Effective Chemical Processes in Porous Media

In the book by Hornung, Chap. 6, the author proposes a homogenization strategy for the effective behavior of some chemical processes involving adsorption and reactions arising in porous media. Rigorous proofs of the convergence results are given in the case of linear adsorption rates and linear chemical reactions. The author leaves as an open question the case of a nonlinear adsorption rate. Our goal in this paper is to study two well-known examples of such nonlinear models, namely the so-called Freundlich and Langmuir kinetics.

Multiscale analysis of diffusion processes in composite media

The goal of this paper is to present some homogenization results for a nonlinear problem arising in the modeling of diffusion in a periodic structure formed by two media with different properties, separated by an active interface. 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.

Homogenization results for enzyme catalyzed reactions through porous media

Abstract The aim of this article is to study the effective behavior of the solution of a nonlinear problem arising in the modelling of enzyme catalyzed reactions through the exterior of a domain containing periodically distributed reactive solid obstacles, with period ɛ. The asymptotic behavior of the solution of such a problem is governed by a new elliptic boundary-value problem, with an extra zero-order term that captures the effect of the enzymatic reactions.

Homogenization results for the calcium dynamics in living cells

Via the periodic unfolding method, the effective behavior of a nonlinear system of coupled reaction–diffusion equations arising in the modeling of the dynamics of calcium ions in living cells is analyzed. We deal, at the microscale, with two reaction–diffusion equations governing the concentration of calcium ions in the endoplasmic reticulum and, respectively, in the cytosol, coupled through an interfacial exchange term. Depending on the magnitude of this term, various models arise at the macroscale. In particular, we obtain, at the limit, a bidomain model. Such a model is widely used for studying the dynamics of the calcium ions, which are recognized to be important intracellular messengers between the endoplasmic reticulum and the cytosol inside the biological cells.

Homogenization results for ionic transport in periodic porous media

The effective behavior of the solution of a nonlinear system of coupled partial differential equations arising in the modeling of ionic transport phenomena in electrically charged periodic porous media is rigorously analyzed. Our model can be useful for biophysicists to describe the ionic transport through protein channels. Also, this setting proves to be relevant in the modeling of the flow of electrons and holes in semiconductor devices. The main tool for obtaining our macroscopic model is the use of the periodic unfolding method, which enables us to deal with a large class of heterogeneous media.

Multiscale analysis in nonlinear thermal diffusion problems in composite structures

The aim of this paper is to analyze the asymptotic behavior of the solution of a nonlinear problem arising in the modelling of thermal diffusion in a two-component composite material. We consider, at the microscale, a periodic structure formed by two materials with different thermal properties. We assume that we have nonlinear sources and that at the interface between the two materials the flux is continuous and depends in a dynamical nonlinear way on the jump of the temperature field. We shall be interested in describing the asymptotic behavior of the temperature field in the periodic composite as the small parameter which characterizes the sizes of our two regions tends to zero. We prove that the effective behavior of the solution of this system is governed by a new system, similar to Barenblatt’s model, with additional terms capturing the effect of the interfacial barrier, of the dynamical boundary condition, and of the nonlinear sources.

Robust packing in cyclopalladated primary amines: isomorphous crystal structures of four complexes with varying substitution patterns.

The crystal structures of (SP-4-4)-[rac-2-(1-aminoethyl)phenyl-kappa(2)C(1),N]chlorido(pyridine-kappaN)palladium(II), [Pd(C(8)H(10)N)Cl(C(5)H(5)N)], (I), (SP-4-4)-[rac-2-(1-aminoethyl)phenyl-kappa(2)C(1),N]bromido(pyridine-kappaN)palladium(II), [PdBr(C(8)H(10)N)(C(5)H(5)N)], (II), (SP-4-4)-[rac-2-(1-aminoethyl)-5-bromophenyl-kappa(2)C(1),N]bromido(4-methylpyridine-kappaN)palladium(II), [PdBr(C(8)H(9)BrN)(C(6)H(7)N)], (III), and (SP-4-4)-[rac-2-(1-aminoethyl)-5-bromophenyl-kappa(2)C(1),N]iodido(4-methylpyridine-kappaN)palladium(II), [Pd(C(8)H(9)BrN)I(C(6)H(7)N)], (IV), are reported. The latter is the first iodide complex in this class of compounds. All four complexes crystallize in the same space group, viz. I4(1)/a, with very similar lattice parameters a and more flexible lattice parameters c. Their packing corresponds to that of their enantiomerically pure congeners, which crystallize in the t2 subgroup I4(1).

The Effectiveness Factor of Reaction-Diffusion Equations: Homogenization and Existence of Optimal Pellet Shapes

We study the asymptotic behaviour of the so-called effectiveness factor ηε of a nonlinear diffusion equation that occurs on the boundary of periodically distributed inclusions (or particles) in an ε-periodic medium. Here, ε is a small parameter related to the characteristic size of the inclusions, which, in the homogenization process, will tend to 0. The inclusions are modeled as homothecy of a fixed pellet T, rescaled by a factor r(ε). We study the cases in which r(ε) = O(εα), known as big holes, for α = 1, as well as non-critical small holes, for

Homogenization results for elliptic problems in periodically perforated domains with mixed-type boundary conditions

1 > \alpha \frac{n}{{n - 2}}