Searcharxiv⌕ Search

arXiv subjects

Laurent Krähenbühl

Publications and source records attributed to Laurent Krähenbühl.

2 recordsLinked to original sources
arXiv2022

Corner asymptotics of the magnetic potential in the eddy-current model

In this paper, we describe the magnetic potential in the vicinity of a corner of a conducting body embedded in a dielectric medium in a bidimensional setting. We make explicit the corner asymptotic expansion for this potential as the distance to the corner goes to zero. This expansion involves singular functions and singular coefficients. We introduce a method for the calculation of the singular functions near the corner and we provide two methods to compute the singular coefficients: the method of moments and the method of quasi-dual singular functions. Estimates for the convergence of both approximate methods are proven. We eventually illustrate the theoretical results with finite element computations. The specific non-standard feature of this problem lies in the structure of its singular functions: They have the form of series whose first terms are harmonic polynomials and further terms are genuine non-smooth functions generated by the piecewise constant zeroth order term of the operator.

math.NA↗
arXiv2006

Les représentations génétiques d'objets : simples analogies ou modèles pertinents ? Le point de vue de l' "évolutique". ––– Genetic representations of objects : simple analogies or efficient models ? The "evolutic" point of view

Depuis une trentaine d'années, les ingénieurs utilisent couramment des analogies avec l'évolution naturelle pour optimiser des dispositifs techniques. Le plus souvent, ces méthodes "génétiques" ou "évolutionnaires" sont considérées uniquement du point de vue pratique, comme des méthodes d'optimisation performantes, qu'on peut utiliser à la place d'autres méthodes (gradients, simplexes, ...). Dans cet article, nous essayons de montrer que les sciences et les techniques, mais aussi les organisations humaines, et généralement tous les systèmes complexes, obéissent à des lois d'évolution dont la génétique est un bon modèle représentatif, même si gênes et chromosomes sont "virtuels" : ainsi loin d'être seulement un outil ponctuel d'aide à la synthèse de solutions technologiques, la représentation génétique est-elle un modèle dynamique global de l'évolution du monde façonné par l'agitation humaine.––––For thirty years, engineers commonly use analogies with natural evolution to optimize technical devices. More often that not, these "genetic" or "evolutionary" methods are only view as efficient tools, which could replace other optimization techniques (gradient methods, simplex, ...). In this paper, we try to show that sciences, techniques, human organizations, and more generally all complex systems, obey to evolution rules, whose the genetic is a good representative model, even if genes and chromosomes are "virtual". Thus, the genetic representation is not only a specific tool helping for the design of technological solutions, but also a global and dynamic model for the action of the human agitation on our world.

cs.AI↗