A penalization method applied to the wave equation

In this Note we investigate the mathematical properties of the volume penalization method applied to the one-dimensional wave equation. Generally speaking, the penalization method allows one to handle complex geometries by simply adding a term to the equation to impose the boundary conditions. We study the convergence of the method with regards to the penalization parameter and we present error and stability analyses for the wave equation. Numerical simulations using a finite difference scheme illustrate the results. To cite this article: A. Paccou et al., C. R. Mecanique 333 (2005).     

Spectral methods for compressible reactive flows

High order simulations are necessary in order to capture fine details in resolving supersonic reactive flows. However, high Mach number compressible flows feature sharp gradients and discontinuities, which present a challenge to successful simulations using high order methods. Spectral methods have proven a powerful tool in simulation of incompressible turbulent flows, and recent advances allow the application of spectral methods to compressible reactive flows. We review the recent advances in the theory and application of spectral methods which allow stable computations of discontinuous phenomena, and the recovery of high order information via postprocessing, and present applications of high Mach number reactive flows. To cite this article: D. Gottlieb, S. Gottlieb, C. R. Mecanique 333 (2005).     

Quelques modèles diffusifs capillaires de type KortewegSome diffusive capillary models of Korteweg type.

The purpose of this Note is to propose new diffusive capillary models of Korteweg type and discuss their mathematical properties. More precisely, we introduce viscous models which provide some additional information on the behavior of the density close to vacuum. We actually prove that if some compatibility conditions between diffusion and capillarity are satisfied, some extra regularity information on a quantity involving the density is available. We obtain a non-trivial equality deduced from the special structure of the momentum equation. This Note generalizes to some extent the authors' previous works on the Korteweg model (with constant capillary coefficient) and on the shallow water equation. To cite this article: D. Bresch, B. Desjardins, C. R. Mecanique 332 (2004).     

Dynamique multi-contact d'un système de solides tridimensionnels rigidesMulti-contact dynamics of a set of three-dimensional rigid bodies

This study is in keeping with the general pattern of dynamical simulations of a set of rigid three-dimensional bodies submitted to unilateral contact constraints with dry friction. An exact formulation (respecting the contact and friction laws) of the problem of predicting the system accelerations and the contact status, in further evolution is proposed. A numerical treatment of this kind of nonlinear problem is presented. This approach is applied to a simple multi-contact example, and yields results in agreement with those of analytical and numerical type, known for this example. To cite this article: C. Le Saux et al., C. R. Mecanique 331 (2003).     

A Comparison of Electron Transfer Kinetics of Three Common Carbon Electrode Surfaces in Acetonitrile and in Room Temperature Ionic Liquid 1‐Butyl‐3‐Methylimidiazonium Hexafluorophosphate: Correlation to Surface Structure and the Limit of the Diffusion Domain Approximation

We report the comparison of electron transfer kinetic parameters of the ferrocene redox couple in both acetonitrile and in room temperature ionic liquid (RTIL) 1‐butyl‐3‐methylimidiazonium hexafluorophosphate ([C₄mim] [PF₆]), using edge plane pyrolytic graphite (EPPG), basal plane pyrolytic graphite (BPPG) and glassy carbon (GC) electrodes. Each electrode surface was characterized using SEM and AFM and the surface morphology was analyzed in terms of surface heterogeneity including the distribution of edge plane defects. The experimental data were modeled using both one and two dimensional simulations to correlate the electron transfer parameters obtained with the different surface structure of each electrode. Furthermore, we show that the diffusion domain approximation (commonly used to accurately simulate electron transfer kinetics at graphitic surfaces) breaks down when a BPPG electrode is used in RTIL and demonstrate the near impossibility of assigning rate constant to the basal plane surface.     

Solving the logit-based stochastic user equilibrium problem with elastic demand based on the extended traffic network model

This paper proposes a novel extended traffic network model to solve the logit-based stochastic user equilibrium (SUE) problem with elastic demand. In this model, an extended traffic network is established by properly adding dummy nodes and links to the original traffic network. Based on the extended traffic network, the logit-based SUE problem with elastic demand is transformed to the SUE problem with fixed demand. Such problem is then further converted to a linearly constrained convex programming and addressed by a predictor–corrector interior point algorithm with polynomial complexity. A numerical example is provided to compare the proposed model with the method of successive averages (MSA). The numerical results indicate that the proposed model is more efficient and has a better convergence than the MSA.     

An explicit recursive formula for computing the normal forms associated with semisimple cases

This paper presents an explicit, computationally efficient, recursive formula for computing the normal forms, center manifolds and nonlinear transformations for general n-dimensional systems, associated with semisimple singularities. Based on the formula, we develop a Maple program, which is very convenient for an end-user who only needs to prepare an input file and then execute the program to “automatically” generate the result. Several examples are presented to demonstrate the computational efficiency of the algorithm.     

Gene tree correction for reconciliation and species tree inference: Complexity and algorithms

Reconciliation consists in mapping a gene tree T into a species tree S, and explaining the incongruence between the two as evidence for duplication, loss and other events shaping the gene family represented by the leaves of T. When S is unknown, the Species Tree Inference Problem is to infer, from a set of gene trees, a species tree leading to a minimum reconciliation cost. As reconciliation is very sensitive to errors in T, gene tree correction prior to reconciliation is a fundamental task. In this paper, we investigate the complexity of four different combinatorial approaches for deleting misplaced leaves from T. First, we consider two problems (Minimum Leaf Removal and Minimum Species Removal) related to the reconciliation of T with a known species tree S. In the former (latter respectively) we want to remove the minimum number of leaves (species respectively) so that T is “MD-consistent” with S. Second, we consider two problems (Minimum Leaf Removal Inference and Minimum Species Removal Inference) related to species tree inference. In the former (latter respectively) we want to remove the minimum number of leaves (species respectively) from T so that there exists a species tree S such that T is MD-consistent with S. We prove that Minimum Leaf Removal and Minimum Species Removal are APX-hard, even when each label has at most two occurrences in the input gene tree, and we present fixed-parameter algorithms for the two problems. We prove that Minimum Leaf Removal Inference is not only NP-hard, but also W[2]-hard and inapproximable within factor $c\ln n$, where n is the number of leaves in the gene tree. Finally, we show that Minimum Species Removal Inference is NP-hard and W[2]-hard, when parameterized by the size of the solution, that is the minimum number of species removals.