The Novikov conjecture on Cheeger spaces

We prove the Novikov conjecture on oriented Cheeger spaces whose fundamental group satisfies the strong Novikov conjecture. A Cheeger space is a stratified pseudomanifold admitting, through a choice of ideal boundary conditions, an L2-de Rham cohomology theory satisfying Poincare duality. We prove that this cohomology theory is invariant under stratified homotopy equivalences and that its signature is invariant under Cheeger space cobordism. Analogous results, after coupling with a Mishchenko bundle associated to any Galois covering, allow us to carry out the analytic approach to the Novikov conjecture: we define higher analytic signatures of a Cheeger space and prove that they are stratified homotopy invariants whenever the assembly map is rationally injective. Finally we show that the analytic signature of a Cheeger space coincides with its topological signature as defined by Banagl.Comment: To appear in JNC

Hodge theory on Cheeger spaces

We extend the study of the de Rham operator with ideal boundary conditions from the case of isolated conic singularities, as analyzed by Cheeger, to the case of arbitrary stratified pseudomanifolds. We introduce a class of ideal boundary operators and the notion of mezzoperversity, which intermediates between the standard lower and upper middle perversities in intersection theory, as interpreted in this de Rham setting, and show that the de Rham operator with these boundary conditions is Fredholm and has compact resolvent. We also prove an isomorphism between the resulting Hodge and L2 de Rham cohomology groups, and that these are independent of the choice of iterated edge metric. On spaces which admit ideal boundary conditions of this type which are also self-dual, which we call `Cheeger spaces', we show that these Hodge/de Rham cohomology groups satisfy Poincare Duality.Comment: v2: Slight changes to improve exposition, v3: Improved discussion of core domain, to appear in Crelle's journa

influence of wall radiation in 2D cavities heated from below

International audienceThis study investigates numerically the effects of wall radiation on Bénard cells in cavities heated from below using Chebyshev spectral methods. Bifurcation theory is also used to describe and analyse the cellular flow solutions obtained in a square and a rectangle cavities filled with air. As wall radiation modifies the flow via the adiabatic vertical wall condition, the motionless and thermally stratified solution no longer exists at low Rayleigh numbers and is replaced by a very weak 2 × 2 cellular solution. This 4-cell weak flow undergoes pitchfork bifurcations at higher Rayleigh numbers: both perfect and imperfect pitchfork bifurcations are observed in the presence of wall radiation. Bifurcations to cellular flows with a reflection symmetry become imperfect because the cellular flows with the opposite rotating directions are no more equivalent. Therefore the resulting convective and radiative Nusselt numbers of the two bifurcated branches are no longer the same on the top or bottom wall. Note also that Nusselt numbers (either convective or radiative) of any bifurcated branch at one Rayleigh number are different on the bottom and top walls with wall radiation. Results obtained are analysed and some recommendations are given to describe Bénard flows with wall radiation

Ricci flow of conformally compact metrics

In this paper we prove that given a smoothly conformally compact metric there is a short-time solution to the Ricci flow that remains smoothly conformally compact. We adapt recent results of Schn\"urer, Schulze and Simon to prove a stability result for conformally compact Einstein metrics sufficiently close to the hyperbolic metric.Comment: 26 pages, 2 figures. Version 2 includes stronger stability result and fixes several typo

Systematically Searching for New Resonances at the Energy Frontier using Topological Models

We propose a new strategy to systematically search for new physics processes in particle collisions at the energy frontier. An examination of all possible topologies which give identifiable resonant features in a specific final state leads to a tractable number of `topological models' per final state and gives specific guidance for their discovery. Using one specific final state, $\ell\ell jj$, as an example, we find that the number of possibilities is reasonable and reveals simple, but as-yet-unexplored, topologies which contain significant discovery potential. We propose analysis techniques and estimate the sensitivity for $pp$ collisions with $\sqrt{s}=14$ TeV and $\mathcal{L}=300$ fb$^{-1}$

Etude comparative des méthodes de suivi d'interface pour les écoulements diphasiques

Les écoulements diphasiques, omniprésents dans la nature et dans de nombreux processus industriels, font intervenir différentes phases (liquide et gaz) et sont souvent caractérisés par des rapports de densité et de viscosité élevés. L'une des principales difficultés rencontrées lors de la simulation numérique de ces écoulements réside dans la bonne représentation de l'interface qui sépare les fluides immiscibles mis en jeu. Un grand nombre de méthodes de suivi d'interface existent dans la littérature, mais les études comparatives permettant de choisir l'approche la mieux adaptée sont peu nombreuses. Dans ce travail, nous comparons plusieurs méthodes Eulériennes de suivi d'interface à savoir la méthode Volume Of Fluid (VOF), Level set (LS), et les méthodes couplées CLSVOF, VOSET et MCLS. Cette comparaison originale a permis de dégager quelques points forts et faibles de chacune des approches