Comparison principles and applications to mathematical modelling of vegetal meta-communities

This article partakes of the PEGASE project the goal of which is a better understanding of the mechanisms explaining the behaviour of species living in a network of forest patches linked by ecological corridors (hedges for instance). Actually we plan to study the effect of the fragmentation of the habitat on biodiversity. A simple neutral model for the evolution of abundances in a vegetal metacommunity is introduced. Migration between the communities is explicitely modelized in a deterministic way, while the reproduction process is dealt with using Wright-Fisher models, independently within each community. The large population limit of the model is considered. The hydrodynamic limit of this split-step method is proved to be the solution of a partial differential equation with a deterministic part coming from the migration process and a diffusion part due to the Wright-Fisher process. Finally, the diversity of the metacommunity is adressed through one of its indicator, the mean extinction time of a species. At the limit, using classical comparison principles, the exchange process between the communities is proved to slow down extinction. This shows that the existence of corridors seems to be good for the biodiversity

Evidence of a boundary layer instability at very high Rayleigh number

In 1997, a Rayleigh-B\'enard experiment evidenced a significant increase of the heat transport efficiency for Rayleigh numbers larger than $Ra \sim 10^{12}$ and interpreted this observation as the signature of the Kraichnan's ``Ultime Regime'' of convection. According to Kraichnan's 1962 prediction, the flow boundary layers above the cold and hot plates -in which most of the fluid temperature drop is localized- become unstable for large enough $Ra$ and this instability boosts the heat transport compared to the other turbulent regimes. Using the same convection cell as in the 1997 experiment, we show that the reported heat transport increase is accompanied with enhanced temperature fluctuations of the bottom plate, which was heated at constant power levels. Indeed, for $Ra < 10^{12}$, the bottom plate fluctuations can simply be accounted from those in the bulk of the flow. In particular, they share the same spectral density at low frequencies, as if the bottom plate was following the slow temperature fluctuations of the bulk, modulo a constant temperature drop across the bottom boundary layer. Conversely, to account for the plate's temperature fluctuations at higher $Ra$, we no-longuer can ignore the fluctuations of the temperature drop across the boundary layer. The negative skewness of fluctuations at high $Ra$ supports the picture of a boundary layer instability. These observations provide new evidence that the transition reported in 1997 corresponds to the triggering of the Ultimate Regime of convection.Comment: Submitted for publicatio

d13C tracing of dissolved inorganic carbon sources in Patagonian rivers (Argentina)

The main Patagonian rivers (Colorado, Negro, Chubut, Deseado, Coyle, Chico, Santa Cruz and Gallegos) were sampled between September 1995 and November 1998 to determine their chemical and isotopic compositions, the origins of the suspended and dissolved river loads and their inputs to the South Atlantic Ocean. This paper focuses on the dissolved inorganic carbon (DIC) transport and its υ13C isotopic signature. The υ13CDIC values vary between 12Ð8 and 1Ð8‰ and allow one to distinguish two river groups: (i) the Colorado, Negro, Chubut and Santa Cruz, which display the highest values and the lowest seasonal variations; (ii) the Deseado, Coyle, Chico and Gallegos, which show the lowest values and the highest seasonal variations. For the first group, υ13CDIC is mainly controlled by important exchanges between the river waters and atmospheric CO2, due to the presence of lakes and dams. For the second group, υ13CDIC also appears to be controlled by the oxidation of organic carbon, showing a negative relationship between υ13CDIC and the dissolved organic carbon. These biogeochemical processes interfere with the contribution of carbonate and silicate weathering to the riverine DIC and do not allow use of υ13CDIC alone to distinguish these contributions. The annual DIC flux exported by Patagonian Rivers to the South Atlantic Ocean averages 621 ð 109 g. of C, i.e. a specific yield of 2Ð7 g m2 year1. The mean υ13CDIC can be estimated to 4Ð9‰, which is high compared with other rivers of the world

Observability, Identifiability and Epidemiology -- A survey

In this document we introduce the concepts of Observability and Iden-tifiability in Mathematical Epidemiology. We show that, even for simple and well known models, these properties are not always fulfilled. We also consider the problem of practical observability and identi-fiability which are connected to sensitivity and numerical condition numbers

Méthodes de développement de systèmes multi-agents

http://www.emse.fr/~picard/publications/gleizes08glis.pdfNational audienceLes systèmes multi-agents (SMA) ont montré leur pertinence pour la conception d'applications distribuées (logiquement ou physiquement), complexes et robustes. Le concept d'agent est aujourd'hui plus qu'une technologie efficace, il représente un nouveau paradigme pour le développement de logiciels dans lesquels l'agent est un logiciel autonome qui possède un objectif, évolue dans un environnement dynamique et interagit avec d'autres agents au moyen de langages et de protocoles. Souvent, l'agent est considéré comme un objet " intelligent " ou comme un niveau d'abstraction au-dessus des objets et des composants. Les méthodes de développement orientées objet - au vu des différences entre les objets et les agents - ne sont pas directement applicables au développement de SMA. Il est alors devenu nécessaire d'étendre ou de développer de nouveaux modèles, de nouvelles méthodes et de nouveaux outils adaptés au développement de systèmes multi-agents. L'objectif de cet article est d'établir la spécificité du paradigme multi-agent, de donner un aperçu du processus de développement d'un SMA au travers de la méthode ADELFE et de donner les caractéristiques des principales méthodes de conception de SMA en donnant les caractéristiques essentielles de chacune

On the triggering of the Ultimate Regime of convection

Rayleigh-B\'enard cells are one of the simplest systems to explore the laws of natural convection in the highly turbulent limit. However, at very high Rayleigh numbers (Ra > 1E12) and for Prandtl numbers of order one, experiments fall into two categories: some evidence a steep enhancement of the heat transfer while others do not. The origin of this apparent disagreement is presently unexplained. This puzzling situation motivated a systematic study of the triggering of the regime with an enhanced heat transfer, originally named the "Ultimate Regime" of convection. High accuracy heat transfer measurements have been conducted in convection cells with various aspect ratios and different specificities, such as altered boundary conditions or obstacles inserted in the flow. The two control parameters, the Rayleigh and Prandtl numbers have been varied independently to disentangle their relative influence. Among other results, it is found that i) most experiments reaching very high $Ra$ are not in disagreement if small differences in Prandtl numbers are taken into account, ii) the transition is not directly triggered by the large scale circulation present in the cell, iii) the sidewall of the cell have a significant influence on the transition. The characteristics of this Ultimate regime are summarized and compared with R. Kraichnan prediction for the asymptotic regime of convection.Comment: 25 pages, 14 figure

Addition of tethered nonaromatic carbon nucleophiles to chemoselectively activated amides

Abstract: In an effort to develop new ways of synthesizing polycyclic alkaloids, we successfully added silyl enol ethers, allylsilanes, and enamines to iminium ions generated from amides. Because of their higher oxidation state, such iminiums show a yet unexploited advantage of potential double cyclizations over standard Mannich monocyclizations. We report herein the first example of tethered nonaromatic carbon nucleophiles adding to activated amides for the generation of enaminals of various ring sizes, with endo- or exo-cyclic nitrogen