Time-harmonic acoustic propagation in the presence of a shear flow

This work deals with the numerical simulation, by means of a finite element method, of the time-harmonic propagation of acoustic waves in a moving fluid, using the Galbrun equation instead of the classical linearized Euler equations. This work extends a previous study in the case of a uniform flow to the case of a shear flow. The additional difficulty comes from the interaction between the propagation of acoustic waves and the convection of vortices by the fluid. We have developed a numerical method based on the regularization of the equation which takes these two phenomena into account. Since it leads to a partially full matrix, we use an iterative algorithm to solve the linear system.     

Clustering via minimum volume ellipsoids

We propose minimum volume ellipsoids (MVE) clustering as an alternative clustering technique to k-means for data clusters with ellipsoidal shapes and explore its value and practicality. MVE clustering allocates data points into clusters in a way that minimizes the geometric mean of the volumes of each cluster’s covering ellipsoids. Motivations for this approach include its scale-invariance, its ability to handle asymmetric and unequal clusters, and our ability to formulate it as a mixed-integer semidefinite programming problem that can be solved to global optimality. We present some preliminary empirical results that illustrate MVE clustering as an appropriate method for clustering data from mixtures of “ellipsoidal” distributions and compare its performance with the k-means clustering algorithm as well as the MCLUST algorithm (which is based on a maximum likelihood EM algorithm) available in the statistical package R. Research of the first author was supported in part by a Discovery Grant from NSERC and a research grant from Faculty of Mathematics, University of Waterloo. Research of the second author was supported in part by a Discovery Grant from NSERC and a PREA from Ontario, Canada.     

Measuring stress intensity factors with a camera: Integrated digital image correlation (I-DIC)Mesure de facteurs d'intensité des contraintes avec une caméra : corrélation d'images numériques intégrée (CINI)

A novel ‘integrated’ approach coupling image correlation and elastic displacement field identification provides a powerful and accurate tool to evaluate mode I and II stress intensity factors. This technique is applied to silicon carbide subjected to a sandwiched three-point bend test, using digital pictures obtained in optical microscopy where the pixel physical scale is about 2 μm. A crack whose maximum opening is 500 nm can be detected and its geometry identified. The toughness is determined well within a 10%uncertainty. To cite this article: F. Hild, S. Roux, C. R. Mecanique 334 (2006).     

A Necklace of Wulff Shapes

In a probabilistic model of a film over a disordered substrate, Monte-Carlo simulations show that the film hangs from peaks of the substrate. The film profile is well approximated by a necklace of Wulff shapes. Such a necklace can be obtained as the infimum of a collection of Wulff shapes resting on the substrate. When the random substrate is given by iid heights with exponential distribution, we prove estimates on the probability density of the resulting peaks, at small density.AMS subject classification: 60K35, 60K37, 82B24, 82B41     

Surface chemkin: A general formalism and software for analyzing heterogeneous chemical kinetics at a gas-surface interface

This article describes a general kinetic formalism for treating the details of heterogeneous reactions at a gas-solid interface. We develop a nomenclature for treating reactions between the gas phase and surface species residing on any number of surface site types and bulk-phase species residing in bulk-phase mixtures or in pure bulk phases. The rate of progress of surface reactions follows the law of mass-action. We discuss the relationship between macroscopic conservation laws for mass and energy and the microscopic surface reaction rates as they might appear in boundary conditions for a chemically reacting flow. The formalism developed has been implemented in a general package of Fortran computer codes for the evaluation of complex surface-reaction kinetics called Surface Chemkin.