Adéquation et choix de modele de marche aléatoire des trajectoires des navires de peches

L'étude du mouvement des organismes est essentiel pour la compréhension du fonctionnement des écosystèmes. Dans le cas des écosystèmes marins exploités, cela amène à s'intéresser aux stratégies spatiales des pêcheurs. L'une des approches les plus utilisées pour la modélisation du mouvement des prédateurs supé- rieurs est la marche aléatoire de Lévy. Une marche aléatoire est un modèle mathématique composé par des déplacements aléatoires. Dans le cas de Lévy, les longueurs des déplacements suivent une loi stable de Lévy. Dans ce cas également, les longueurs, lorsqu'elles tendent vers l'in ni (in praxy lorsqu'elles sont grandes, grandes par rapport à la médiane ou au troisième quartile par exemple), suivent une loi puissance caractéristique du type de marche aléatoire de Lévy (Cauchy, Brownien ou strictement Lévy). Dans la pratique, outre que cette propriété est utilisée de façon réciproque sans fondement théorique, les queues de distribution, notion par ailleurs imprécise, sont modélisée par des lois puissances sans que soient discutées la sensibilité des résultats à la dé nition de la queue de distribution, et la pertinence des tests d'ajustement et des critères de choix de modèle. Dans ce travail portant sur les déplacements observés de trois bateaux de pêche à l'anchois du Pérou, plusieurs modèles de queues de distribution (log-normal, exponentiel, exponentiel tronqué, puissance et puissance tronqué) ont été comparés ainsi que deux dé nitions possible de queues de distribution (de la médiane à l'in ni ou du troisième quartile à l'in ni). Au plan des critères et tests statistiques utilisés, les lois tronquées (exponentielle et puissance) sont apparues les meilleures. Elles intègrent en outre le fait que, dans la pratique, les bateaux ne dépassent pas une certaine limite de longueur de déplacement. Le choix de modèle est apparu sensible au choix du début de la queue de distribution : pour un même bateau, le choix d'un modèle tronqué ou l'autre dépend de l'intervalle des valeurs de la variable sur lequel le modèle est ajusté. Pour nir, nous discutons les implications en écologie des résultats de ce travail.

Incremental neural networks for function approximation

A new strategy for incremental building of multilayer feedforward neural networks is proposed in the context of approximation of functions from R-p to R-q using noisy data. A stopping criterion based on the properties of the noise is also proposed. Experimental results for both artificial and real data are performed and two alternatives of the proposed construction strategy are compared.

A fully adaptive numerical approximation for a two-dimensional epidemic model with nonlinear cross-diffusion

An epidemic model is formulated by a reactionâeuro"diffusion system where the spatial pattern formation is driven by cross-diffusion. The reaction terms describe the local dynamics of susceptible and infected species, whereas the diffusion terms account for the spatial distribution dynamics. For both self-diffusion and cross-diffusion, nonlinear constitutive assumptions are suggested. To simulate the pattern formation two finite volume formulations are proposed, which employ a conservative and a non-conservative discretization, respectively. An efficient simulation is obtained by a fully adaptive multiresolution strategy. Numerical examples illustrate the impact of the cross-diffusion on the pattern formation.

Surface collective oscillations of metal clusters and spheres: Random-phase-approximation sum-rules approach

Using the once and thrice energy-weighted moments of the random-phase-approximation strength function, we have derived compact expressions for the average energy of surface collective oscillations of clusters and spheres of metal atoms. The L=0 volume mode has also been studied. We have carried out quantal and semiclassical calculations for Na and Ag systems in the spherical-jellium approximation. We present a rather thorough discussion of surface diffuseness and quantal size effects on the resonance energies.

Spin and density longitudinal response of quantum dots in the time-dependent local-spin-density approximation

The longitudinal dipole response of a quantum dot has been calculated in the far-infrared regime using local-spin-density-functional theory. We have studied the coupling between the collective spin and density modes as a function of the magnetic field. We have found that the spin dipole mode and single-particle excitations have a sizable overlap, and that the magnetoplasmon modes can be excited by the dipole spin operator if the dot is spin polarized. The frequency of the dipole spin edge mode presents an oscillation which is clearly filling factor (v) related. We have found that the spin dipole mode is especially soft for even-n values. Results for selected numbers of electrons and confining potentials are discussed.

Spin polarized neutron matter and magnetic susceptibility within the Brueckner-Hartree-Fock approximation

The Brueckner-Hartree-Fock formalism is applied to study spin polarized neutron matter properties. Results of the total energy per particle as a function of the spin polarization and density are presented for two modern realistic nucleon-nucleon interactions, Nijmegen II and Reid93. We find that the dependence of the energy on the spin polarization is practically parabolic in the full range of polarizations. The magnetic susceptibility of the system is computed. Our results show no indication of a ferromagnetic transition which becomes even more difficult as the density increases.

Quasilocal density functional theory and its application within the extended Thomas-Fermi approximation

In this paper we propose a generalization of the density functional theory. The theory leads to single-particle equations of motion with a quasilocal mean-field operator, which contains a quasiparticle position-dependent effective mass and a spin-orbit potential. The energy density functional is constructed using the extended Thomas-Fermi approximation and the ground-state properties of doubly magic nuclei are considered within the framework of this approach. Calculations were performed using the finite-range Gogny D1S forces and the results are compared with the exact Hartree-Fock calculations

Double folding with a density-dependent effective interaction and it s analytical approximation

The real part of the optical potential for heavy ion elastic scattering is obtained by double folding of the nuclear densities with a density-dependent nucleon-nucleon effective interaction which was successful in describing the binding, size, and nucleon separation energies in spherical nuclei. A simple analytical form is found to differ from the resulting potential considerably less than 1% all through the important region. This analytical potential is used so that only few points of the folding need to be computed. With an imaginary part of the Woods-Saxon type, this potential predicts the elastic scattering angular distribution in very good agreement with experimental data, and little renormalization (unity in most cases) is needed.

Classical solutions of the leading-logarithm approximation with non-trivial topology

Exact solutions of the classical equations corresponding to the leading-logarithm approximation are obtained. They are classified by an (integer) topological number.