Can past gamma-ray bursts explain both INTEGRAL and ATIC/PAMELA/Fermi anomalies simultaneously?

Gamma-ray bursts (GRBs) have been invoked to explain both the 511 keV emission from the galactic bulge and the high-energy positron excess inferred from the ATIC, PAMELA, and Fermi data. While independent explanations can be responsible for these phenomena, we explore the possibility of their common GRB-related origin by modeling the GRB distribution and estimating the rates. For an expected Milky Way long GRB rate, neither of the two signals is generic; the local excess requires a 2% coincidence, while the signal from the galactic center requires a 20% coincidence with respect to the timing of the latest GRB. The simultaneous explanation requires a 0.4% coincidence. Considering the large number of statistical "trials" created by multiple searches for new physics, the coincidences of a few per cent cannot be dismissed as unlikely. Alternatively, both phenomena can be explained by GRBs if the galactic rate is higher than expected. We also show that a similar result is difficult to obtain assuming a simplified short GRB distribution.Comment: 4 pages; version accepted for publicatio

Eigenelements of a General Aggregation-Fragmentation Model

We consider a linear integro-differential equation which arises to describe both aggregation-fragmentation processes and cell division. We prove the existence of a solution (\lb,\U,\phi) to the related eigenproblem. Such eigenelements are useful to study the long time asymptotic behaviour of solutions as well as the steady states when the equation is coupled with an ODE. Our study concerns a non-constant transport term that can vanish at $x=0,$ since it seems to be relevant to describe some biological processes like proteins aggregation. Non lower-bounded transport terms bring difficulties to find $a\ priori$ estimates. All the work of this paper is to solve this problem using weighted-norms

Particle approximation of the one dimensional Keller-Segel equation, stability and rigidity of the blow-up

We investigate a particle system which is a discrete and deterministic approximation of the one-dimensional Keller-Segel equation with a logarithmic potential. The particle system is derived from the gradient flow of the homogeneous free energy written in Lagrangian coordinates. We focus on the description of the blow-up of the particle system, namely: the number of particles involved in the first aggregate, and the limiting profile of the rescaled system. We exhibit basins of stability for which the number of particles is critical, and we prove a weak rigidity result concerning the rescaled dynamics. This work is complemented with a detailed analysis of the case where only three particles interact

Performances des stations de pompages en irrigation : application aux forages de petits périmètres irrigués de la plaine de Kairouan (Tunisie) et impact des dysfonctionnements sur le prix de l'eau

International audienceLorsqu'une élévation de l'eau de nappes ou une mise en pression est nécessaire au fonctionnement des systèmes modernes d'irrigation dans un périmètre, on utilise presque exclusivement des pompes centrifuges. La facture énergétique représente donc une part importante du coût de l'eau. Or, le rendement de ces machines est très dépendant de leurs conditions de fonctionnement et de leur usure et toute déviation par rapport aux conditions optimales entraîne des surcoûts énergétiques importants. L'objectif est de proposer une méthodologie pour évaluer les performances de ces équipements. Des indicateurs accessibles (énergie unitaire, énergie volumique absorbée réelle, volume spécifique pompé, coefficient de volume spécifique pompé) sont définis et des valeurs de référence fournies à partir des données des constructeurs. Les différentes méthodes d'estimation des volumes pompés sont critiquées. Les tests proposés sur les données volumiques indiquent le type de mesure réalisé pour les volumes pompés ainsi que leur dérive dans le temps (utilisation du débit nominal, compteur volumétrique). Pour les mesures d'énergie, l'absence de synchronisation entre les relevés temporels et énergétiques implique de cumuler les données pour obtenir la puissance consommée - lors de conditions stables de fonctionnement des pompes et si chaque pompe dispose d'un compteur d'énergie. Un ensemble de 18 stations de pompage sur forage alimentant des petits périmètres irrigués de la plaine de Kairouan en Tunisie centrale a été testé. La vétusté des équipements peut engendrer des rendements très faibles dont la conséquence principale est une augmentation des coûts de pompage (consommation énergétique et surcoût de maintenance). Ce diagnostic met donc bien en évidence l'intérêt d'un suivi précis de chaque ouvrage. Les divergences observées dans les ratios entre les volumes pompés et l'énergie consommée par rapport à ceux attendus en conditions optimales de fonctionnement conduisent au raisonnement suivant : si les données obtenues sont justes, le dysfonctionnement provient de l'inadaptation de l'équipement hydroélectrique au fonctionnement hydraulique de l'installation ; ou bien si les données sont fausses, ce dysfonctionnement provient des erreurs de gestion des pompistes et les quantités d'eau pompées sont alors sous-estimées. Dans les deux cas, un surcoût est payé par l'Administration. Dans la moitié des stations, les surcoûts d'énergie dépassent 20 %, voire 50 % pour près du quart d'entre elles

GaN directional couplers for integrated quantum photonics

Large cross-section GaN waveguides are proposed as a suitable architecture to achieve integrated quantum photonic circuits. Directional couplers with this geometry have been designed with aid of the beam propagation method and fabricated using inductively coupled plasma etching. Scanning electron microscopy inspection shows high quality facets for end coupling and a well defined gap between rib pairs in the coupling region. Optical characterization at 800 nm shows single-mode operation and coupling-length-dependent splitting ratios. Two photon interference of degenerate photon pairs has been observed in the directional coupler by measurement of the Hong-Ou-Mandel dip with 96% visibility.Comment: 4 pages, 5 figure

A mathematical model for mechanotransduction at the early steps of suture formation

Growth and patterning of craniofacial sutures are subjected to the effects of mechanical stress. Mechanotransduction processes occurring at the margins of the sutures are not precisely understood. Here, we propose a simple theoretical model based on the orientation of collagen fibres within the suture in response to local stress. We demonstrate that fibre alignment generates an instability leading to the emergence of interdigitations. We confirm the appearance of this instability both analytically and numerically. To support our model, we use histology and synchrotron x-ray microtomography and reveal the fine structure of fibres within the sutural mesenchyme and their insertion into the bone. Furthermore, using a mouse model with impaired mechanotransduction, we show that the architecture of sutures is disturbed when forces are not interpreted properly. Finally, by studying the structure of sutures in the mouse, the rat, an actinopterygian (\emph{Polypterus bichir}) and a placoderm (\emph{Compagopiscis croucheri}), we show that bone deposition patterns during dermal bone growth are conserved within jawed vertebrates. In total, these results support the role of mechanical constraints in the growth and patterning of craniofacial sutures, a process that was probably effective at the emergence of gnathostomes, and provide new directions for the understanding of normal and pathological suture fusion

Strictly Toral Dynamics

This article deals with nonwandering (e.g. area-preserving) homeomorphisms of the torus $\mathbb{T}^2$ which are homotopic to the identity and strictly toral, in the sense that they exhibit dynamical properties that are not present in homeomorphisms of the annulus or the plane. This includes all homeomorphisms which have a rotation set with nonempty interior. We define two types of points: inessential and essential. The set of inessential points $ine(f)$ is shown to be a disjoint union of periodic topological disks ("elliptic islands"), while the set of essential points $ess(f)$ is an essential continuum, with typically rich dynamics (the "chaotic region"). This generalizes and improves a similar description by J\"ager. The key result is boundedness of these "elliptic islands", which allows, among other things, to obtain sharp (uniform) bounds of the diffusion rates. We also show that the dynamics in $ess(f)$ is as rich as in $\mathbb{T}^2$ from the rotational viewpoint, and we obtain results relating the existence of large invariant topological disks to the abundance of fixed points.Comment: Incorporates suggestions and corrections by the referees. To appear in Inv. Mat

The one-dimensional Keller-Segel model with fractional diffusion of cells

We investigate the one-dimensional Keller-Segel model where the diffusion is replaced by a non-local operator, namely the fractional diffusion with exponent $0<\alpha\leq 2$. We prove some features related to the classical two-dimensional Keller-Segel system: blow-up may or may not occur depending on the initial data. More precisely a singularity appears in finite time when $\alpha<1$ and the initial configuration of cells is sufficiently concentrated. On the opposite, global existence holds true for $\alpha\leq1$ if the initial density is small enough in the sense of the $L^{1/\alpha}$ norm.Comment: 12 page