ITERATED QUASI-REVERSIBILITY METHOD APPLIED TO ELLIPTIC AND PARABOLIC DATA COMPLETION PROBLEMS

International audienceWe study the iterated quasi-reversibility method to regularize ill-posed elliptic and parabolic problems: data completion problems for Poisson's and heat equations. We define an abstract setting to treat both equations at once. We demonstrate the convergence of the regularized solution to the exact one, and propose a strategy to deal with noise on the data. We present numerical experiments for both problems: a two-dimensional corrosion detection problem and the one-dimensional heat equation with lateral data. In both cases, the method prove to be efficient even with highly corrupted data

Ion exchange effect on asymmetric dioxins adsorption onto FAU-type X-zeolites

International audienceThe effect of trivalent cation exchange on fully dehydrated (activated) FAU-type X-zeolites with respect to the adsorption of the sterically biggest, asymmetric dioxin-molecules (1,2,3,4 TeCDD) in iso-octane solvent was investigated. FAU 13X Na zeolites were selected due to their pore openings, close to the diameter of the 2,3-DCDD (0.74 nm) as well as their high adsorption affinity for this dioxin molecule. This zeolite also adsorbed 1,4 DCDD, but with significantly lower affinity.With the aim to eventually liberate the channel's access for the sterically biggest dioxin molecule 1,2,3,4 TeCDD, Na+ cations were replaced by trivalent cation species Y3+, Ce3+ and La3+. Symmetric dioxins were not tested in this study due to their high toxicity.Analyses performed indicate that cation exchange reaches 80% on the zeolite, while the zeolite structure is preserved during the process. La3+-FAU-type X-zeolites showed the same extreme affinity towards 1,2,3,4 TeCDD as Na+ - FAU-type X-zeolites did for 2,3-DCDD. At the same time it could be shown that both dioxins could be separated by adsorption, while 1,2,3,4 TeCDD only interacts with the external surface of Na+-FAU-type X-zeolite, not entering the zeolite pores. (C) 2015 Elsevier Inc. All rights reserved

Topological sensitivity analysis for the location of small cavities in Stokes flow

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A Dirichlet–Neumann cost functional approach for the Bernoulli problem

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Solving Cauchy problems by minimizing an energy-like functional

International audienceAn energy-like error functional is introduced in the context of the ill-posed problem of boundary data recovering, which is well known as a Cauchy problem. Links with existing methods for data completion are detailed. Here the problem is converted into an optimization problem; the computation of the gradients of the energy-like functional is given for both the continuous and the discrete problems. Numerical experiments highlight the efficiency of the proposed method as well as its robustness in the model context of Laplace's equation, but also for anisotropic conductivity problems

Investigating the interaction of two asymmetric dioxins with FAU 13X zeolites using calorimetry and solid-state NMR

International audienceWe report on the characterization of dioxin adsorption, notably 2,3-DCDD and 1,2,3,4-TeCDD, from isooctane onto zeolite FAU 13X Na+ and FAU 13X La3+, with 80% Na+- La3+ exchange level. Adsorption isotherms showed extreme affinities of 2,3-DCDD towards FAU 13X Na+ and 1,2,3,4-TeCDD towards FAU 13X La3+ in the experimentally accessible concentration range, which is limited by dioxin solubility in isooctane.Thermogravimetric studies were employed to understand the effect of water content level of zeolites onto the affinity and capacity of adsorption, but also to determine the temperature range of eventual dioxin regeneration.Moreover, microcalorimetric investigations indicated that high dioxin adsorption affinities of 2,3-DCDD towards FAU 13X Na+ and 1,2,3,4-TeCDD towards FAU 13X La3+, respectively, were combined with quite different levels of adsorption enthalpies. Cross polarization magic angle spinning (CP-MAS) NMR experiments recorded with dynamic nuclear polarization (DNP) revealed that 1,2,3,4-TeCDD was adsorbed simultaneously with isooctane in the micropores of the zeolites, without chemical alteration

The topological gradient method : from optimal design to image processing

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