A shape optimization formulation of weld pool determination

International audienceIn this paper, we propose a shape optimization formulation for a problem modeling a process of welding. We show the existence of an optimal solution. The finite element method is used for the discretization of the problem. The discrete problem is solved by an identification technique using a parameterization of the weld pool by Bézier curves and Genetic algorithms

On a shape derivative formula for star-shaped domains using Minkowski deformation

We consider the shape derivative formula for a volume cost functional studied in previous papers where we used the Minkowski deformation and support functions in the convex setting. In this work, we extend it to some non-convex domains, namely the star-shaped ones. The formula happens to be also an extension of a well-known one in the geometric Brunn-Minkowski theory of convex bodies. At the end, we illustrate the formula by applying it to some model shape optimization problem

The evolving SARS-CoV-2 epidemic in Africa: Insights from rapidly expanding genomic surveillance

INTRODUCTION Investment in Africa over the past year with regard to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) sequencing has led to a massive increase in the number of sequences, which, to date, exceeds 100,000 sequences generated to track the pandemic on the continent. These sequences have profoundly affected how public health officials in Africa have navigated the COVID-19 pandemic. RATIONALE We demonstrate how the first 100,000 SARS-CoV-2 sequences from Africa have helped monitor the epidemic on the continent, how genomic surveillance expanded over the course of the pandemic, and how we adapted our sequencing methods to deal with an evolving virus. Finally, we also examine how viral lineages have spread across the continent in a phylogeographic framework to gain insights into the underlying temporal and spatial transmission dynamics for several variants of concern (VOCs). RESULTS Our results indicate that the number of countries in Africa that can sequence the virus within their own borders is growing and that this is coupled with a shorter turnaround time from the time of sampling to sequence submission. Ongoing evolution necessitated the continual updating of primer sets, and, as a result, eight primer sets were designed in tandem with viral evolution and used to ensure effective sequencing of the virus. The pandemic unfolded through multiple waves of infection that were each driven by distinct genetic lineages, with B.1-like ancestral strains associated with the first pandemic wave of infections in 2020. Successive waves on the continent were fueled by different VOCs, with Alpha and Beta cocirculating in distinct spatial patterns during the second wave and Delta and Omicron affecting the whole continent during the third and fourth waves, respectively. Phylogeographic reconstruction points toward distinct differences in viral importation and exportation patterns associated with the Alpha, Beta, Delta, and Omicron variants and subvariants, when considering both Africa versus the rest of the world and viral dissemination within the continent. Our epidemiological and phylogenetic inferences therefore underscore the heterogeneous nature of the pandemic on the continent and highlight key insights and challenges, for instance, recognizing the limitations of low testing proportions. We also highlight the early warning capacity that genomic surveillance in Africa has had for the rest of the world with the detection of new lineages and variants, the most recent being the characterization of various Omicron subvariants. CONCLUSION Sustained investment for diagnostics and genomic surveillance in Africa is needed as the virus continues to evolve. This is important not only to help combat SARS-CoV-2 on the continent but also because it can be used as a platform to help address the many emerging and reemerging infectious disease threats in Africa. In particular, capacity building for local sequencing within countries or within the continent should be prioritized because this is generally associated with shorter turnaround times, providing the most benefit to local public health authorities tasked with pandemic response and mitigation and allowing for the fastest reaction to localized outbreaks. These investments are crucial for pandemic preparedness and response and will serve the health of the continent well into the 21st century

A shape optimization approach for a class of free boundary problems of Bernoulli type

summary:We are interested in an optimal shape design formulation for a class of free boundary problems of Bernoulli type. We show the existence of the optimal solution of this problem by proving continuity of the solution of the state problem with respect to the domain. The main tools in establishing such a continuity are a result concerning uniform continuity of the trace operator with respect to the domain and a recent result on the uniform Poincaré inequality for variable domains

Supervised learning as an inverse problem based on non-smooth loss function

International audienc

Supervised learning as an inverse problem based on non-smooth loss function

International audienc

Etude théorique et approximation numérique d'un problème inverse de transfert de chaleur

Nous nous intéressons à l étude d un problème d analyse des transferts de chaleur qui modélise une opération de soudage. L approche que nous considérons ne s occupe que de la partie solide de la plaque. Elle consiste à résoudre un problème à frontière libre. Pour cela, nous proposons une formulation en optimisation de forme. Le problème d état est gouverné par un opérateur qui, pour certaines données, n est pas coercif. Cela complique l étude de la continuité du problème d état. Nous surmontons cette difficulté en utilisant le degré topologique de Leray-Shauder, ainsi nous montrons l existence d un domaine optimal. Ensuite, nous considérons une discrétisation de ce problème basée sur les éléments finis linéaires. Nous prouvons alors que le problème discret admet une solution et nous montrons qu une sous-suite des solutions de ce problème convergence vers la solution du problème continu. Enfin, nous présentons des résultats numériques réalisés par deux méthodes : la méthode déterministe basée sur le calcul du gradient de forme, et les algorithmes génétiques combinés avec la logique floue et le calcul parallèle. Ainsi une étude comparative de ces deux méthodes aux niveaux qualitatif et quantitatif a été présentée.We are interested in studying a heat transfer problem which modeling a welding process. The approach that we consider deals only with the solid part of the plate. It consists in solving a free boundary problem. For this, we propose a shape optimization formulation. The state problem governed by an operator which for some data is not coercif. This complicates the study of the continuity of the state problem.We overcome this difficulty using the topological degree of Leray-Schauder and we show the existence of an optimal domain. Next, we consider a discretization of this problem based on linear finite elements. We prove that the approximate problem is solvable and we show that a subsequence of the solution of this approximate problem converges to the solution of the continuous problem. Finally, we present numerical results achieved by two methods : the deterministic method based on the gradient-likes method and genetic algorithms combined with fuzzy logic and parallel computing. A comparative study of two methods for qualitative and quantitative levels was presented.NANTES-BU Sciences (441092104) / SudocSudocFranceF

On a numerical approximation of a highly nonlinear parabolic inverse problem in hydrology

International audienceIn this paper, we consider an inverse problem in hydrology governed by a highly nonlinear parabolic equation called Richards equation. This inverse problem consists of determine a set of hydrological parameters describing the flow of water in porous media, from some additional observations on pressure. We propose an approximation method of this problem based on its optimal control formulation and a temporal discretization of its state problem. The obtained discrete nonlinear state problem is approached by the finite difference method and solved by Picard's method. Then, for the resolution of the discrete associated optimization problem, we opt for an evolutionary algorithm. Finally, we give some numerical results showing the efficiency of the proposed approach

Homogenization of parabolic nonlinear coupled problem in heat exchange

International audienceThis work deals with the homogenization of heat transfer nonlinear parabolic problem in a periodic composite medium consisting in two-component (fluid/solid). This problem presents some difficulties due to the presence of a nonlinear Neumann condition modeling a radiative heat transfer on the interface between the two parts of the medium and to the fact that the problem is strongly coupled. In order to justify rigorously the homogenization process, we use two scale convergence. For this, we show first the existence and uniqueness of the homogenization problem by topological degree of Leray-Schauder, Then we establish the two scale convergence, and identify the limit problems