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

The cyclic ground state structure of the HF trimer revealed by far infrared jet-cooled Fourier transform spectroscopy.

International audienceThe rovibrationally resolved Fourier transform (FT) far infrared (FIR) spectra of two intermolecular librations of (HF)3, namely the in-plane ν6 and out-of-plane ν4 bending fundamentals centered, respectively, at about 494 cm(-1) and 602 cm(-1), have been recorded for the first time under jet-cooled conditions using the supersonic jet of the Jet-AILES apparatus. The simultaneous rotational analysis of 245 infrared transitions belonging to both bands enabled us to determine the ground state (GS), ν6 and ν4 rotational and centrifugal distortion constants. These results provided definite experimental answers to the structure of such a weakly bound trimer: firstly the vibrationally averaged planarity of cyclic (HF)3, also supported by the very small value of the inertia defect obtained in the GS, secondly the slight weakening of the hydrogen bond in the intermolecular excited states evidenced from the center of mass separations of the HF constituents determined in the ground, ν6 = 1 and ν4 = 1 states of (HF)3 as well as the decrease of the fitted rotational constants upon excitation. Finally, lower bounds of about 2 ns on ν6 and ν4 state lifetimes could be derived from the deconvolution of experimental linewidths. Such long lifetimes highlight the interest in probing low frequency intermolecular motions of molecular complexes to get rid of constraints related to the vibrational dynamics of coupled anharmonic vibrations at higher energy, resulting in loss of rotational information

Quantum Zakharov Model in a Bounded Domain

We consider an initial boundary value problem for a quantum version of the Zakharov system arising in plasma physics. We prove the global well-posedness of this problem in some Sobolev type classes and study properties of solutions. This result confirms the conclusion recently made in physical literature concerning the absence of collapse in the quantum Langmuir waves. In the dissipative case the existence of a finite dimensional global attractor is established and regularity properties of this attractor are studied. For this we use the recently developed method of quasi-stability estimates. In the case when external loads are $C^\infty$ functions we show that every trajectory from the attractor is $C^\infty$ both in time and spatial variables. This can be interpret as the absence of sharp coherent structures in the limiting dynamics.Comment: 27 page

Travelling waves for the Gross-Pitaevskii equation II

The purpose of this paper is to provide a rigorous mathematical proof of the existence of travelling wave solutions to the Gross-Pitaevskii equation in dimensions two and three. Our arguments, based on minimization under constraints, yield a full branch of solutions, and extend earlier results, where only a part of the branch was built. In dimension three, we also show that there are no travelling wave solutions of small energy.Comment: Final version accepted for publication in Communications in Mathematical Physics with a few minor corrections and added remark

The Stromal Processing Peptidase of Chloroplasts is Essential in Arabidopsis, with Knockout Mutations Causing Embryo Arrest after the 16-Cell Stage

Stromal processing peptidase (SPP) is a metalloendopeptidase located in the stroma of chloroplasts, and it is responsible for the cleavage of transit peptides from preproteins upon their import into the organelle. Two independent mutant Arabidopsis lines with T-DNA insertions in the SPP gene were analysed (spp-1 and spp-2). For both lines, no homozygous mutant plants could be detected, and the segregating progeny of spp heterozygotes contained heterozygous and wild-type plants in a ratio of 2∶1. The siliques of heterozygous spp-1 and spp-2 plants contained many aborted seeds, at a frequency of ∼25%, suggesting embryo lethality. By contrast, transmission of the spp mutations through the male and female gametes was found to be normal, and so gametophytic effects could be ruled out. To further elucidate the timing of the developmental arrest, mutant and wild-type seeds were cleared and analysed by Nomarski microscopy. A significant proportion (∼25%) of the seeds in mutant siliques exhibited delayed embryogenesis compared to those in wild type. Moreover, the mutant embryos never progressed normally beyond the 16-cell stage, with cell divisions not completing properly thereafter. Heterozygous spp mutant plants were phenotypically indistinguishable from the wild type, indicating that the spp knockout mutations are completely recessive and suggesting that one copy of the SPP gene is able to produce sufficient SPP protein for normal development under standard growth conditions

Nearly inviscid Faraday waves

Many powerful techniques from Hamiltonian mechanics are available for the study of ideal hydrodynamics. This article explores some of the consequences of including small viscosity in a study of surface gravity-capillary waves excited by the vertical vibration of a container. It is shown that in this system, as in others, the addition of small viscosity provides a singular perturbation of the ideal fluid system, and that as a result its effects are nontrivial. The relevance of existing studies of ideal fluid problems is discussed from this point of view

Contrasted Patterns of Molecular Evolution in Dominant and Recessive Self-Incompatibility Haplotypes in Arabidopsis

Self-incompatibility has been considered by geneticists a model system for reproductive biology and balancing selection, but our understanding of the genetic basis and evolution of this molecular lock-and-key system has remained limited by the extreme level of sequence divergence among haplotypes, resulting in a lack of appropriate genomic sequences. In this study, we report and analyze the full sequence of eleven distinct haplotypes of the self-incompatibility locus (S-locus) in two closely related Arabidopsis species, obtained from individual BAC libraries. We use this extensive dataset to highlight sharply contrasted patterns of molecular evolution of each of the two genes controlling self-incompatibility themselves, as well as of the genomic region surrounding them. We find strong collinearity of the flanking regions among haplotypes on each side of the S-locus together with high levels of sequence similarity. In contrast, the S-locus region itself shows spectacularly deep gene genealogies, high variability in size and gene organization, as well as complete absence of sequence similarity in intergenic sequences and striking accumulation of transposable elements. Of particular interest, we demonstrate that dominant and recessive S-haplotypes experience sharply contrasted patterns of molecular evolution. Indeed, dominant haplotypes exhibit larger size and a much higher density of transposable elements, being matched only by that in the centromere. Overall, these properties highlight that the S-locus presents many striking similarities with other regions involved in the determination of mating-types, such as sex chromosomes in animals or in plants, or the mating-type locus in fungi and green algae