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Abstract: We study the steady-state potential in a high contrast medium with a resistive thin layer. We provide asymptotic expansions of the potential at any order, whatever small the layer conductivity is. Approximate transmission conditions at any order and the corresponding variational formulation are given. We prove uniform estimates with respect to the thickness of the layer and with respect to its resistivity. The main insight consists in this expansion at any order and in the corresponding non-standard variational formulation whatever small the layer conductivity is. In particular the limit potential is not continuous across the limit surface (when the membrane thickness shrinks to zero) unlike the soft contrast case and its jump is proportional to the electric flux. Numerical simulations illustrate the theoretical results. [Copyright &y& Elsevier]

Abstract: We study the behaviour of the steady-state voltage potential in a material composed of a two-dimensional object surrounded by a very rough thin layer and embedded in an ambient medium. The roughness of the layer is described by a quasi ε-periodic function, ε being a small parameter, while the mean thickness of the layer is of magnitude , where . Using the two-scale analysis, we replace the very rough thin layer by appropriate transmission conditions on the boundary of the object, which lead to an explicit characterization of the polarization tensor as defined in Vogelius and Capdeboscq [Y. Capdeboscq, M.S. Vogelius, A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction, M2AN Math. Model. Numer. Anal. 37 (2003) 159–173]. The main result of this paper is quite unexpected, and the approximate transmission conditions are not intuitive since they mix in a complex way both conductivities of the exterior medium and of the membrane. This paper extends the previous works of Poignard [C. Poignard, Approximate transmission conditions through a weakly oscillating thin layer, Math. Meth. Appl. Sci. 32 (2009) 435–453] and of Ciuperca et al. [I. Ciuperca, M. Jai, C. Poignard, Approximate transmission conditions through a rough thin layer. The case of periodic roughness, Euro. J. Appl. Math. 21 (2010) 51–75], in which . [Copyright &y& Elsevier]

We propose an asynchronous method for the explicit integration of multi-scale partial differential equations. This method is restricted by a local CFL (Courant Friedrichs Lewy) condition rather than the traditional global CFL condition. Moreover, contrary to other local time-stepping (LTS) methods, the asynchronous algorithm permits the selection of independent time steps in each mesh element. We derived an asynchronous Runge–Kutta 2 (ARK2) scheme from a standard explicit Runge–Kutta method and we proved that the ARK2 scheme is second order convergent. Comparing with the classical integration, the asynchronous scheme is effective in terms of computation time. [ABSTRACT FROM AUTHOR]

Abstract: The arrival of chemicals in a soil or groundwater ecosystem could upset the natural balance of the microbial community. Since soil microorganisms are the first to be exposed to the chemicals released into the soil environment, we evaluated the use of a phylogenetic microarray as a bio-indicator of community perturbations due to the exposure to trichloroethylene (TCE). The phylogenetic microarray, which measures the presence of different members of the soil community, was used to evaluate unpolluted soils exposed to TCE as well as to samples from historically TCE polluted sites. We were able to determine an apparent threshold at which the microbial community structure was significantly affected (about 1ppm). In addition, the members of the microbial community most affected were identified. This approach could be useful for assessing environmental impact of chemicals on the biosphere as well as important members of the microbial community involved in TCE degradation. [Copyright &y& Elsevier]