A reaction-diffusion system modeling concrete corrosion in sewer pipes is discussed. The system is coupled, semi-linear, and partially dissipative. It is defined on a locally periodic perforated domain with nonlinear Robin-type boundary conditions at water-air and solid-water interfaces. Asymptotic homogenization techniques are applied to obtain upscaled reaction-diffusion models together with explicit formulae for the effective transport and reaction coefficients. It is shown that the averaged system contains additional terms appearing due to the deviation of the assumed geometry from a purely periodic distribution of perforations for two relevant parameter regimes: (a) all diffusion coefficients are of order of O(1) and (b) all diffusion coefficients are of order of O(ε 2 ) except the one for H 2 S(g) which is of order of O(1). In case (a) a set of macroscopic equations is obtained, while in case (b) a two-scale reaction-diffusion system is derived that captures the interplay between microstructural reaction effects and the macroscopic transport.

The choice of excipients constitutes a major part of preformulation and formulation studies during the preparation of pharmaceutical dosage forms. The physical, mechanical, and chemical properties of excipients affect various formulation parameters, such as disintegration, dissolution, and shelf life, and significantly influence the final product. Therefore, several studies have been performed to evaluate the effect of drug-excipient interactions on the overall formulation. This article reviews the information available on the physical and chemical instabilities of excipients and their incompatibilities with the active pharmaceutical ingredient in solid oral dosage forms, during various drug-manufacturing processes. The impact of these interactions on the drug formulation process has been discussed in detail. Examples of various excipients used in solid oral dosage forms have been included to elaborate on different drug-excipient interactions.

We explore the homogenization limit and rigorously derive upscaled equations for a microscopic reaction-diffusion system modeling sulfate corrosion in sewer pipes made of concrete. The system, defined in a periodically-perforated domain, is semilinear, partially dissipative and weakly coupled via a non-linear ordinary differential equation posed on the solid-water interface at the pore level. Firstly, we show the well-posedness of the microscopic model. We then apply homogenization techniques based on two-scale convergence for an uniformly periodic domain and derive upscaled equations together with explicit formulae for the effective diffusion coefficients and reaction constants. We use a boundary unfolding method to pass to the homogenization limit in the non-linear ordinary differential equation. Finally, besides giving its strong formulation, we also prove that the upscaled two-scale model admits a unique solution.

This paper is aimed to elaborate the problem of energy-momentum in General Relativity. In this connection, we use the prescriptions of Einstein, Landau-Lifshitz, Papapetrou and Möller to compute the energy-momentum densities for two exact solutions of Einstein field equations. The spacetimes under consideration are the non-null Einstein-Maxwell solutions and the singularity-free cosmological model. The electromagnetic generalization of the Gödel solution and the Gödel metric become special cases of the non-null Einstein-Maxwell solutions. It turns out that these prescriptions do not provide consistent results for any of these spacetimes. These inconsistence results verify the well-known proposal that the idea of localization does not follow the lines of pseudo-tensorial construction but instead follows from the energy-momentum tensor itself. These differences can also be understood with the help of the Hamiltonian approach.

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