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

Caractérisation et réactivité au chlore des particules relarguées par les baigneurs en piscine

International audienceDisinfecting swimming pool water is essential for preventing waterborne diseases. An unforeseen consequence of treating water with disinfectants is the formation of disinfection byproducts (DPBs) that can cause harmful effects to health through the interactions between the added disinfectant and organic matter in the water. The present work focuses on the chlorine reactivity with particles released by bathers. Such particles are collected in the filter backwash water of swimming pools and this study intends to distinguish DPBs generated from dissolved chemicals from those formed by particulate matter. Therefore, filtered and unfiltered backwash waters were collected from several swimming pools, analyzed physicochemically and chemically, and then chlorinated as is (79 mgL-1) and as diluted suspensions (36.2 and 11.9 mgL-1) at varying concentrations of chlorine (1.2 mg and 24 mgCl2L-1). Utilizing a DPD colorimetric technique and GC-ECD, respectively, the kinetics of chlorine consumption and DPBs production have been investigated. Up to 25.7 µgL-1 of chloroform was produced within 96 h at 1.2 mgCl2L-1 , followed by haloacetic acids (HAAs) and haloacetonitriles (HANs). Within 96 h, the concentration of trichloroacetic acid reached a maximum of 231.8 µgL-1 at a chlorine concentration of 231.8 µgL-1. The formations of 0.13 µmol THMs, 0.31 µmol HAAs, and 0.04 µmol HANs per mg of dissolved organic carbon (DOC) were finally determined by correlating the organic content of particles with the nature of the DBPs generated. Comparing the quantities of DBPs generated in filtered and unfiltered samples helps us conclude that ~50% of DBPs formed during the chlorination of swimming pool water are derived from particles brought by bathers

Characterization of the Bernoulli-Navier model for a rectangular section beam as the limit of the Kirchhoff-Love model for a plate

In this paper we compare the Kirchhoff-Love model for a linearly elastic rectangular plate Ωtε = (0, L) × (−t, t) × (−ε, ε) of thickness 2ε with the Bernoulli-Navier model for the same solid considered as a linearly elastic beam of length L and cross-section ω tε 1 = (−t, t) × (−ε, ε). We assume that the solid is clamped on both ends {0, L} × [−t, t] × [−ε, ε]. We show that the scaled version of the displacements field ζ t in the middle plane, solution of the Kirchhoff-Love model, converges strongly to the unique solution of a one-dimensional problem when the plate width parameter t tends to zero. Moreover, after re-scaling this limit, we show that, as a matter of fact, it is the solution of the Bernoulli-Navier model for the beam. This means that, under appropriate assumptions on the order of magnitude of the data, the Bernoulli-Navier displacement field is the natural approximation of the Kirchhoff-Love displacement field when the cross-section of the plate is rectangular and its width is sufficiently small and homothetic to thickness.This research was partially supported by the Research Centre of Mathematics of the University of Minho through the FEDER Funds “Programa Operacional Factores de Competitividade COMPETE”, and by the Portuguese Funds through FCT - “Funda¸c˜ao para a Ciˆencia e a Tecnologia”, within the Project PEst-OE/MAT/UI0013/2014, and by the project “Modelizaci´on y simulaci´on num´erica de s´olidos y fluidos en dominios con peque˜nas dimensiones. Aplicaciones en estructuras, biomec´anica y aguas someras”, MTM2012-36452-C02-01 financed by the Spanish Ministry of Econom´ıa y Competitividad with the participation of FEDER

Quasi-bounded mappings and complementarity problems depending of parameters

Quasi-bounded mappings, Complementarity problems depending of parameters,