The primal-dual method for approximation algorithms

In this survey, we give an overview of a technique used to design and analyze algorithms that provide approximate solutions to NP-hard problems in combinatorial optimization. Because of parallels with the primal-dual method commonly used in combinatorial optimization, we call it the primal-dual method for approximation algorithms. We show how this technique can be used to derive approximation algorithms for a number of different problems, including network design problems, feedback vertex set problems, and facility location problems. Received: June 19, 2000 / Accepted: February 7, 2001?Published online October 2, 2001     

Vibration of a pre-constrained elastic thin shell I: Modeling and regularity of the solutionsVibration d'une coque élastique mince pré-contrainte I

We study the vibration of an elastic thin shell which is pre-constrained by a large displacement with a small deformation. In this first Note we prove the solutions exist and we investigate both the interior regularity and the boundary regularity which is known to be important in the shape differentiation of hyperbolic equations. To cite this article: J. Cagnol, J.-P. Zolésio, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 161–166     

Influence of Particle Morphology and Flow Conditions on the Dispersion Behavior of Fumed Silica in Silicone Polymers

The dispersion behavior of agglomerates of several grades of fumed silica in poly(dimethyl siloxane) liquids has been studied as a function of particle morphology and applied flow conditions. The effects of primary particle size and aggregate density and structure on cohesivity were probed through tensile and shear strength tests on particle compacts. These cohesivity tests indicated that the shear strength of particle compacts was two orders of magnitude higher than the tensile strength at the same overall packing density. Experiments carried out in both steady and time‐varying simple‐shear flows indicate that dispersion occurs through tensile failure. In the steady‐shear experiments,enhanced dispersion was obtained at higher levels of applied stress and, at comparable levels of applied stress, dispersion was found to proceed faster at higher shear rates. Experiments conducted in time‐varying flows further corroborated the results obtained in tensile cohesivity tests. Experiments in which the mean and maximum stresses in the time‐varying flows were matched to the stresses produced in steady shear flows highlight the influence of flow dynamics on dispersion behavior.