On the well-posedness of higher order viscous Burgers' equations

We consider higher order viscous Burgers' equations with generalized nonlinearity and study the associated initial value problems for given data in the L²$L^2$-based Sobolev spaces. We introduce appropriate time weighted spaces to derive multilinear estimates and use them in the contraction mapping principle   argument to prove local well-posedness for data with Sobolev regularity below L²$L^2$. We also prove ill-posedness for this type of models and show that the local well-posedness results are sharp in some particular cases viz., when the orders of dissipation p  , and nonlinearity k+1$k+1$, satisfy a relation p=2k+1$p=2k+1$.     

Valuation of power plants by utility indifference and numerical computation

This paper presents a real option valuation model of a power plant, which accounts for physical constraints and market incompleteness. Switching costs, minimum on-off times, ramp rates, or non-constant heat rates are important characteristics that can lead, if neglected, to overestimated values. The existence of non-hedgeable uncertainties is also a feature of energy markets that can impact assets value. We use the utility indifference approach to define the value of the physical asset. We derive the associated mixed optimal switching-control problem and provide a characterization of its solution by means of a coupled system of reflected Backward Stochastic Differential Equations (BSDE). We relate this system to a system of variational inequalities, and we provide a numerical comparative study by implementing BSDE simulation algorithms, and PDE finite differences schemes.     

Application de méthodes intégrales au calcul du bruit de cavitéComputation of cavity noise using integral methods

A direct numerical simulation of the sound radiated by a flow over a 2-D subsonic cavity is performed using Computational AeroAcoustics tools. The simulation is consistent with Karamcheti's experiments. The numerical results are used as a reference to study two integral formulations: the Ffowcs Williams and Hawkings acoustic analogy and a wave extrapolation method based on FW-H equation. These hybrid approaches agree with the direct computation by DNS data and provide powerful tools to compute far-field noise. To cite this article: X. Gloerfelt et al., C. R. Mecanique 330 (2002) 13–20     

Dynamics of structural transformations between lamellar and inverse bicontinuous cubic lyotropic phases

The liquid crystalline lamellar (L(alpha)) to double-diamond inverse bicontinuous cubic (Q(D)(pi)) phase transition for the amphiphile monoelaidin in excess water exhibits a remarkable sequence of structural transformations for pressure or temperature jumps. Our data imply that the transition dynamics depends on a coupling between changes in molecular shape and the geometrical and topological constraints of domain size. We propose a qualitative model for this coupling based on theories of membrane fusion via stalks and existing knowledge of the structure and energetics of bicontinuous cubic phases.     

Fast topological imaging

Mathematical optimization methods based on the topological sensitivity analysis have been used to develop innovative ultrasonic imaging methods. With a single illumination of the medium, they have proved experimentally to yield a lateral resolution comparable to classical multiple-illumination techniques. As these methods are based on the numerical simulations of two wave fields, they require extensive computation. A time-domain finite-difference scheme is usually used for that purpose. This paper presents the development of an experimental imaging method based on the topological sensitivity. The numerical cost is reduced by replacing the numerical simulations by simple mathematical operations between the radiation patterns of the array’s transducers and the frequency-domain signals to be emitted. These radiation patterns are preliminary computed once and for all. They were obtained with a finite element model for the anisotropic elastodynamic case and with semi-analytical integrations for the acoustic case. Experimental results are presented for a composite material sample and for a prefractal network immersed in water. A lateral resolution below 2.5 times the wavelength is obtained with a single plane wave illumination. The method is also applied with multiple illuminations, so that objects hidden in complex media can be investigated.     

Hybrid dynamics of two coupled oscillators that can impact a fixed stop

We consider two linearly coupled masses, where one mass can have inelastic impacts with a fixed, rigid stop. This leads to the study of a two degree of freedom, piecewise linear, frictionless, unforced, constrained mechanical system. The system is governed by three types of dynamics: coupled harmonic oscillation, simple harmonic motion and discrete rebounds. Energy is dissipated discontinuously in discrete amounts, through impacts with the stop. We prove the existence of a non-zero measure set of orbits that lead to infinite impacts with the stop in a finite time. We show how to modify the mathematical model so that forward existence and uniqueness of solutions for all time is guaranteed. Existence of hybrid periodic orbits is shown. A geometrical interpretation of the dynamics based on action coordinates is used to visualize numerical simulation results for the asymptotic dynamics.     

Approximative solution methods for multiobjective combinatorial optimization

In this paper we present a review of approximative solution methods, that is, heuristics and metaheuristics designed for the solution of multiobjective combinatorial optimization problems (MOCO). First, we discuss questions related to approximation in this context, such as performance ratios, bounds, and quality measures. We give some examples of heuristics proposed for the solution of MOCO problems. The main part of the paper covers metaheuristics and more precisely non-evolutionary methods. The pioneering methods and their derivatives are described in a unified way. We provide an algorithmic presentation of each of the methods together with examples of applications, extensions, and a bibliographic note. Finally, we outline trends in this area. The research of M. Ehrgott has been partially supported by University of Auckland grant 3602178/9275 and grant Ka 477/27-1 of the Deutsche Forschungsgemeinschaft (DFG).     

The Energy of Some Microscopic Stochastic Lattices

We introduce a notion of energy for some microscopic stochastic lattices. Such lattices are broad generalizations of simple periodic lattices, for which the question of the definition of an energy was examined in a series of previous works [14–18]. Note that slightly more general deterministic geometries were also considered in [6]. These lattices are involved in the modelling of materials whose microscopic structure is a perturbation, in a sense made precise in the article, of the periodic structure of a perfect crystal. The modelling considered here is either a classical modelling, where the sites of the lattice are occupied by ball-like atomic systems that interact by pair potentials, or a quantum modelling where the sites are occupied by nuclei equipped with an electronic structure spread all over the ambient space. The corresponding energies for the infinite stochastic lattices are derived consistently with truncated systems of finite size, by application of a thermodynamic limit process. Subsequent works [7, 8] will be devoted to the macroscopic limits of the energies of such microscopic lattices, thereby extending to a stochastic context the results of [4, 5]. Such convergences in a stochastic setting (in dimension 1) have been studied in [21, 22]. We will also study in [8] some variants and extensions of the stationary setting presented here.