Comportement macroscopique des matériaux poreux à microstructure en feuilletsMacroscopic behavior of porous materials with lamellar microstructure

The solid phase of the porous material considered in this Note is made up of lamellar particles. The influence of interaction forces between platelets on the macroscopic behavior is addressed. The results provide a micromechanical basis to the modelling of the behavior of clays of the smectite group, for which repulsive forces arise from the electrical interaction between the solid platelets and the interstitial fluid. To cite this article: L. Dormieux et al., C. R. Mecanique 334 (2006).     

Estimation of three-dimensional flame surface densities from planar images in turbulent premixed combustion

Turbulence motions are, by nature, three-dimensional while planar imaging techniques, widely used in turbulent combustion, give only access to two-dimensional information. For example, to extract flame surface densities, a key ingredient of some turbulent combustion models, from planar images implicitly assumes an instantaneously two-dimensional flow, neglecting the unresolved flame front wrinkling. The objective here is to estimate flame surface densities from two-dimensional measurements assuming that (1) the flow is statistically two dimensional; (2) the measuring plane is a plane of symmetry of the mean flow, either by translation (homogeneous third direction as in slot burners for example) or by rotation (axi-symmetrical flows such as jets) and (3) flame movements in transverse directions are similar. The unknown flame front wrinkling is then modelled from known quantities. An excellent agreement is achieved against direct numerical simulation (DNS) data where all three-dimensional quantities are known, but validations in other conditions (larger DNS, experiments) are required.     

Effects of notches on the surface pressure field downstream of a wall-mounted spoiler

Notched spoilers have been observed to be more effective than uniform spoilers to suppress the flow-induced cavity resonance of vehicles with open sunroofs. In this study, a few mechanisms possibly involved in buffeting suppression from notched spoilers were investigated experimentally and numerically. One objective was to investigate the spatial coherence and phase of the wall pressure fluctuations downstream of notched spoilers in comparison with the same quantities for uniform spoilers. Another objective was to gather detailed measured data to allow the verification of computer simulations of the flow over the notched spoiler. Experiments were performed to measure the velocity and wall pressure fields downstream of spoilers mounted on the rigid floor of a closed test section wind tunnel. Efforts were made to reproduce the spoiler and wind tunnel geometry and boundary conditions of the experimental setup in the numerical simulations. The numerical investigation used the Lattice Boltzmann Method (LBM), with the so-called Very Large Eddy Simulation (VLES) viscosity turbulence model. The results of the numerical investigation were in satisfactory agreement with measured data at low frequencies, where buffeting is expected to occur. The results suggested that the notches break down the homogeneity of the leading edge cross-stream vortices predominantly responsible for the cavity excitation. This decreased the cross-stream coherence of the surface pressure field, thereby reducing the magnitude of the net equivalent excitation force acting over the surface downstream.     

Uniqueness of Kottler spacetime and the Besse conjecture

We establish a black hole uniqueness theorem for Schwarzschild–de Sitter spacetime, also called Kottler spacetime, which satisfies Einstein's field equations of general relativity with positive cosmological constant. Our result concerns the class of static vacuum spacetimes with compact spacelike slices and regular maximal level set of the lapse function. We provide a characterization of the interior domain of communication of the Kottler spacetime, which surrounds an inner horizon and is surrounded by a cosmological horizon. The proof combines arguments from the theory of partial differential equations and differential geometry, and is centered on a detailed study of a possibly singular foliation. We also apply our technique in the Riemannian setting, and establish the validity of the so-called Besse conjecture.     

Improvements to a large neighborhood search heuristic for an integrated aircraft and passenger recovery problem

Because most commercial passenger airlines operate on a hub-and-spoke network, small disturbances can cause major disruptions in their planned schedules and have a significant impact on their operational costs and performance. When a disturbance occurs, the airline often applies a recovery policy in order to quickly resume normal operations. We present in this paper a large neighborhood search heuristic to solve an integrated aircraft and passenger recovery problem. The problem consists of creating new aircraft routes and passenger itineraries to produce a feasible schedule during the recovery period. The method is based on an existing heuristic, developed in the context of the 2009 ROADEF Challenge, which alternates between three phases: construction, repair and improvement. We introduce a number of refinements in each phase so as to perform a more thorough search of the solution space. The resulting heuristic performs very well on the instances introduced for the challenge, obtaining the best known solution for 17 out of 22 instances within five minutes of computing time and 21 out of 22 instances within 10 minutes of computing time.     

Harnack Inequalities and Bôcher‐Type Theorems for Conformally Invariant,Fully Nonlinear Degenerate Elliptic Equations

We give a generalization of a theorem of Bôcher for the Laplace equation to a class of conformally invariant fully nonlinear degenerate elliptic equations. We also prove a Harnack inequality for locally Lipschitz viscosity solutions and a classification of continuous radially symmetric viscosity solutions. © 2014 Wiley Periodicals, Inc.     

Methods for generating random variates with Polya characteristic functions

Polya has shown that real even continuous functions that are convex on (0,∞), for 1 t = 0, and decreasing to 0 as t → ∞ are characteristic functions. Dugué and Girault (1955) have shown that the corresponding random variables are distributed as $\text{Y}\text{Z}$ where Y is a random variable with density (2π)^?1$\text{(}\text{sin}\text{(}\text{x}\text{2}\text{)/(}\text{x}\text{2}\text{))}{}^2$, and Z is independent of Y and has distribution function 1 ? φ + tφ′, t > 0. This property allows us to develop fast algorithms for this class of distributions. This is illustrated for the symmetric stable distribution, Linnik's distribution and a few other distributions. We pay special attention to the generation of Y.     

Local and global Carleman estimates for parabolic operators with coefficients with jumps at interfaces

In (0,T)×Ω, Ω open subset of ? ⁿ , n≥2, we consider a parabolic operator P=? _t ?? _x δ(t,x)? _x , where the (scalar) coefficient δ(t,x) is piecewise smooth in space yet discontinuous across a smooth interface S. We prove a global in time, local in space Carleman estimate for P in the neighborhood of any point of the interface. The “observation” region can be chosen independently of the sign of the jump of the coefficient δ at the considered point. The derivation of this estimate relies on the separation of the problem into three microlocal regions related to high and low tangential frequencies at the interface. In the high-frequency regime we use Calderón projectors. In the low-frequency regime we follow a more classical approach. Because of the parabolic nature of the problem we need to introduce Weyl-Hörmander anisotropic metrics, symbol classes and pseudo-differential operators. Each frequency regime and the associated technique require a different calculus. A global in time and space Carleman estimate on (0,T)×M, M a manifold, is also derived from the local result.     

Long and short paths in uniform random recursive dags

In a uniform random recursive k-directed acyclic graph, there is a root, 0, and each node in turn, from 1 to n, chooses k uniform random parents from among the nodes of smaller index. If S _n is the shortest path distance from node n to the root, then we determine the constant σ such that S _n /log n→σ in probability as n→∞. We also show that max _1≤i≤n S _i /log n→σ in probability.     

Centroaffine surfaces in -geodesics

For (positive) definite surfaces in there is a canonical choice of a centroaffine normal plane bundle, which induces a centroaffine invariant Ricci-symmetric connection . We classify all surfaces in with planar -geodesics. It turns out that the resulting class of surfaces is umbilical with projectively flat induced connection and flat normal plane bundle.