Dispersion for the wave equation inside strictly convex domains I: the Friedlander model case

We consider a model case for a strictly convex domain of dimension $d\geq 2$ with smooth boundary and we describe dispersion for the wave equation with Dirichlet boundary conditions. More specifically, we obtain the optimal fixed time decay rate for the smoothed out Green function: a $t^{1/4}$ loss occurs with respect to the boundary less case, due to repeated occurrences of swallowtail type singularities in the wave front set.Comment: 53 pages, 4 figures, to appear in Annals of Math. Fixed typos, added remark

Analysis of Steiner subtrees of Random Trees for Traceroute Algorithms

We consider in this paper the problem of discovering, via a traceroute algorithm, the topology of a network, whose graph is spanned by an infinite branching process. A subset of nodes is selected according to some criterion. As a measure of efficiency of the algorithm, the Steiner distance of the selected nodes, i.e. the size of the spanning sub-tree of these nodes, is investigated. For the selection of nodes, two criteria are considered: A node is randomly selected with a probability, which is either independent of the depth of the node (uniform model) or else in the depth biased model, is exponentially decaying with respect to its depth. The limiting behavior the size of the discovered subtree is investigated for both models

O stars with weak winds: the Galactic case

We study the stellar and wind properties of a sample of Galactic O dwarfs to track the conditions under which weak winds (i.e mass loss rates lower than ~ 1e-8 Msol/yr) appear. The sample is composed of low and high luminosity dwarfs including Vz stars and stars known to display qualitatively weak winds. Atmosphere models including non-LTE treatment, spherical expansion and line blanketing are computed with the code CMFGEN. Both UV and Ha lines are used to derive wind properties while optical H and He lines give the stellar parameters. Mass loss rates of all stars are found to be lower than expected from the hydrodynamical predictions of Vink et al. (2001). For stars with log L/Lsol > 5.2, the reduction is by less than a factor 5 and is mainly due to the inclusion of clumping in the models. For stars with log L/Lsol < 5.2 the reduction can be as high as a factor 100. The inclusion of X-ray emission in models with low density is crucial to derive accurate mass loss rates from UV lines. The modified wind momentum - luminosity relation shows a significant change of slope around this transition luminosity. Terminal velocities of low luminosity stars are also found to be low. The physical reason for such weak winds is still not clear although the finding of weak winds in Galactic stars excludes the role of a reduced metallicity. X-rays, through the change in the ionisation structure they imply, may be at the origin of a reduction of the radiative acceleration, leading to lower mass loss rates. A better understanding of the origin of X-rays is of crucial importance for the study of the physics of weak winds.Comment: 31 pages, 42 figures. A&A accepted. A version of the paper with full resolution figures is available at http://www.mpe.mpg.de/~martins/publications.htm

Stationary analysis of the Shortest Queue First service policy

We analyze the so-called Shortest Queue First (SQF) queueing discipline whereby a unique server addresses queues in parallel by serving at any time that queue with the smallest workload. Considering a stationary system composed of two parallel queues and assuming Poisson arrivals and general service time distributions, we first establish the functional equations satisfied by the Laplace transforms of the workloads in each queue. We further specialize these equations to the so-called "symmetric case", with same arrival rates and identical exponential service time distributions at each queue; we then obtain a functional equation $$M(z) = q(z) \cdot M \circ h(z) + L(z)$$ for unknown function $M$, where given functions $q$, $L$ and $h$ are related to one branch of a cubic polynomial equation. We study the analyticity domain of function $M$ and express it by a series expansion involving all iterates of function $h$. This allows us to determine empty queue probabilities along with the tail of the workload distribution in each queue. This tail appears to be identical to that of the Head-of-Line preemptive priority system, which is the key feature desired for the SQF discipline

Transgressive bodies in the work of Julie Doucet, Fabrice Neaud and Jean-Christophe Menu: towards a theory of the 'autobioBD'

As the comic book, and more precisely its exceptionally francophone doppelganger, la bande dessinée, begins to fulfil its potential as 'the Ninth Art', the range of styles, reading contexts, and genres which constitute the form as a signifying practice has consequently expanded. Consideration of 'what a comic is', such as is found in the works of Thierry Groensteen and Benoît Peeters1 needs therefore to be complemented by a range of subsidiary questions addressing not only 'what kinds of comics there are', but, as an integral part of those inquiries, how different comic genres signify, and how the enunciative and representational functions deployed by each might be conceptualised. This paper considers the work of three Francophone comic artists, Fabrice Neaud and Jean-Christophe Menu, both French, and the Québecoise Julie Doucet, all of whom could be considered as proponents of the genre of BD we will call 'autobiocomics'. It will be argued that Neaud and Doucet, through their exploration of ontologies of presence and self-representation, work against the visual order of the phallocentric and heteronormative, an order which Menu appears to replicate but ultimately calls into question

Gradient Bounds for Solutions of Stochastic Differential Equations Driven by Fractional Brownian Motions

We study some functional inequalities satisfied by the distribution of the solution of a stochastic differential equation driven by fractional Brownian motions. Such functional inequalities are obtained through new integration by parts formulas on the path space of a fractional Brownian motion.Comment: The paper is dedicated to Pr. David Nualart 60th's birthda

A sub-Riemannian curvature-dimension inequality, volume doubling property and the Poincar\'e inequality

Let $\mathbb{M}$ be a smooth connected manifold endowed with a smooth measure $\mu$ and a smooth locally subelliptic diffusion operator $L$ satisfying $L1=0$, and which is symmetric with respect to $\mu$. We show that if $L$ satisfies, with a non negative curvature parameter, the generalized curvature inequality introduced by the first and third named authors in \cite{BG}, then the following properties hold: 1 The volume doubling property; 2 The Poincar\'e inequality; 3 The parabolic Harnack inequality. The key ingredient is the study of dimensional reverse log-Sobolev inequalities for the heat semigroup and corresponding non-linear reverse Harnack type inequalities. Our results apply in particular to all Sasakian manifolds whose horizontal Webster-Tanaka-Ricci curvature is non negative, all Carnot groups with step two, and to wide subclasses of principal bundles over Riemannian manifolds whose Ricci curvature is non negative