Stochastic and deterministic models for age-structured populations with genetically variable traits

Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in continuous time of a population with (continuous) age and trait structures. The individuals reproduce asexually, age, interact and die. The 'trait' is an individual heritable property (d-dimensional vector) that may influence birth and death rates and interactions between individuals, and vary by mutation. In a large population limit, the random process converges to the solution of a Gurtin-McCamy type PDE. We show that the random model has a long time behavior that differs from its deterministic limit. However, the results on the limiting PDE and large deviation techniques \textit{\`a la} Freidlin-Wentzell provide estimates of the extinction time and a better understanding of the long time behavior of the stochastic process. This has applications to the theory of adaptive dynamics used in evolutionary biology. We present simulations for two biological problems involving life-history trait evolution when body size is plastic and individual growth is taken into account.Comment: This work is a proceeding of the CANUM 2008 conferenc

A numerical approach for modelling thin cracked plates with XFEM

The modelization of bending plates with through the thickness cracks is investigated. We consider the Kirchhoff-Love plate model which is valid for very thin plates. We apply the eXtended Finite Element Method (XFEM) strategy: enrichment of the finite element space with the asymptotic bending and with the discontinuity across the crack. We present two variants and their numerical validations and also a numerical computation of the stress intensity factors

Spatially resolved phase objects using Mach–Zehnder interferometry

Phase characterization with a good spatial resolution is crucial for focused beams in nonlinear media. The phase-shifting interferometry technique, using the least-squares error criterion for several interferograms, is implemented using a reflective spatial light modulator (SLM). The method provides a convenient calibration for any phase-shift steps. The reliability of the proposed method is checked by direct comparison with results obtained by the Fourier transform method as well as using a previously characterized circular phase object

The isolation of gravitational instantons: Flat tori V flat R^4

The role of topology in the perturbative solution of the Euclidean Einstein equations about flat instantons is examined.Comment: 15 pages, ICN-UNAM 94-1

Toric anti-self-dual Einstein metrics via complex geometry

Using the twistor correspondence, we give a classification of toric anti-self-dual Einstein metrics: each such metric is essentially determined by an odd holomorphic function. This explains how the Einstein metrics fit into the classification of general toric anti-self-dual metrics given in an earlier paper (math.DG/0602423). The results complement the work of Calderbank-Pedersen (math.DG/0105263), who describe where the Einstein metrics appear amongst the Joyce spaces, leading to a different classification. Taking the twistor transform of our result gives a new proof of their theorem.Comment: v2. Published version. Additional references. 14 page

A Barren Landscape?

We consider the generation of a non-perturbative superpotential in F-theory compactifications with flux. We derive a necessary condition for the generation of such a superpotential in F-theory. For models with a single volume modulus, we show that the volume modulus is never stabilized by either abelian instantons or gaugino condensation. We then comment on how our analysis extends to a larger class of compactifications. From our results, it appears that among large volume string compactifications, metastable de Sitter vacua (should any exist) are non-generic.Comment: 14 pages, comments adde

Taille de la population d’Avahi laniger dans la réserve d’Ambodiriana-Manompana, Nord-est de Madagascar

Avahi laniger est le seul lémurien nocturne appartenant à la famille des Indriidae qui habite les forêts humides de l’est de Madagascar (Mittermeier et. al., 2010) dont une partie disparaît chaque année (exploitation du bois, pratique du «tavy» ou culture sur brûlis) (Beaucent and Fayolle, 2011; Lehman and Wright, 2000). La fragmentation et la destruction de leur habitat ainsi que la chasse menacent la survie de nombreuses espèces de lémuriens incluant celle de A. laniger (Jenkins et. al., 2011; Rakotondravony and Rabenandrasana, 2011; Anderson, Rowcliffe and Cowlishaw, 2007). Nous avons réalisé, entre fin Avril et Mai 2012, une étude de densité de la population de A. laniger au sein de l’aire protégée de Manompana-Ambodiriana afin d’estimer la taille de la population totale et de déterminer l’impact du projet de conservation menée par l’Association de Défense de la Forêt d’Ambodiriana (ADEFA) qui recherche l’évolution démographique à moyen terme de cette espèce."LABEX" TULIP: (ANR-10-LABX-41), fct fellowship: (SFRH/BD/64875/2009)