Geometric optics and boundary layers for Nonlinear Schrodinger equations

We justify supercritical geometric optics in small time for the defocusing semiclassical Nonlinear Schrodinger Equation for a large class of non-necessarily homogeneous nonlinearities. The case of a half-space with Neumann boundary condition is also studied.Comment: 44 page

The boundary Riemann solver coming from the real vanishing viscosity approximation

We study a family of initial boundary value problems associated to mixed hyperbolic-parabolic systems: v^{\epsilon} _t + A (v^{\epsilon}, \epsilon v^{\epsilon}_x ) v^{\epsilon}_x = \epsilon B (v^{\epsilon} ) v^{\epsilon}_{xx} The conservative case is, in particular, included in the previous formulation. We suppose that the solutions $v^{\epsilon}$ to these problems converge to a unique limit. Also, it is assumed smallness of the total variation and other technical hypotheses and it is provided a complete characterization of the limit. The most interesting points are the following two. First, the boundary characteristic case is considered, i.e. one eigenvalue of $A$ can be $0$. Second, we take into account the possibility that $B$ is not invertible. To deal with this case, we take as hypotheses conditions that were introduced by Kawashima and Shizuta relying on physically meaningful examples. We also introduce a new condition of block linear degeneracy. We prove that, if it is not satisfied, then pathological behaviours may occur.Comment: 84 pages, 6 figures. Text changes in Sections 1 and 3.2.3. Added Section 3.1.2. Minor changes in other section

Environmental factors influence both abundance and genetic diversity in a widespread bird species.

Genetic diversity is one of the key evolutionary variables that correlate with population size, being of critical importance for population viability and the persistence of species. Genetic diversity can also have important ecological consequences within populations, and in turn, ecological factors may drive patterns of genetic diversity. However, the relationship between the genetic diversity of a population and how this interacts with ecological processes has so far only been investigated in a few studies. Here, we investigate the link between ecological factors, local population size, and allelic diversity, using a field study of a common bird species, the house sparrow (Passer domesticus). We studied sparrows outside the breeding season in a confined small valley dominated by dispersed farms and small-scale agriculture in southern France. Population surveys at 36 locations revealed that sparrows were more abundant in locations with high food availability. We then captured and genotyped 891 house sparrows at 10 microsatellite loci from a subset of these locations (N = 12). Population genetic analyses revealed weak genetic structure, where each locality represented a distinct substructure within the study area. We found that food availability was the main factor among others tested to influence the genetic structure between locations. These results suggest that ecological factors can have strong impacts on both population size per se and intrapopulation genetic variation even at a small scale. On a more general level, our data indicate that a patchy environment and low dispersal rate can result in fine-scale patterns of genetic diversity. Given the importance of genetic diversity for population viability, combining ecological and genetic data can help to identify factors limiting population size and determine the conservation potential of populations

Constraining the orbit of the possible companion to Beta Pictoris: New deep imaging observations

We recently reported on the detection of a possible planetary-mass companion to Beta Pictoris at a projected separation of 8 AU from the star, using data taken in November 2003 with NaCo, the adaptive-optics system installed on the Very Large Telescope UT4. Eventhough no second epoch detection was available, there are strong arguments to favor a gravitationally bound companion rather than a background object. If confirmed and located at a physical separation of 8 AU, this young, hot (~1500 K), massive Jovian companion (~8 Mjup) would be the closest planet to its star ever imaged, could be formed via core-accretion, and could explain the main morphological and dynamical properties of the dust disk. Our goal was to return to Beta Pic five years later to obtain a second-epoch observation of the companion or, in case of a non-detection, constrain its orbit. Deep adaptive-optics L'-band direct images of Beta Pic and Ks-band Four-Quadrant-Phase-Mask (4QPM) coronagraphic images were recorded with NaCo in January and February 2009. We also use 4QPM data taken in November 2004. No point-like signal with the brightness of the companion candidate (apparent magnitudes L'=11.2 or Ks ~ 12.5) is detected at projected distances down to 6.5 AU from the star in the 2009 data. As expected, the non-detection does not allow to rule out a background object; however, we show that it is consistent with the orbital motion of a bound companion that got closer to the star since first observed in 2003 and that is just emerging from behind the star at the present epoch. We place strong constraints on the possible orbits of the companion and discuss future observing prospects.Comment: 8 pages, 8 figures, 1 table, accepted for publication in Astronomy and Astrophysic

The phase shift of line solitons for the KP-II equation

The KP-II equation was derived by [B. B. Kadomtsev and V. I. Petviashvili,Sov. Phys. Dokl. vol.15 (1970), 539-541] to explain stability of line solitary waves of shallow water. Stability of line solitons has been proved by [T. Mizumachi, Mem. of vol. 238 (2015), no.1125] and [T. Mizumachi, Proc. Roy. Soc. Edinburgh Sect. A. vol.148 (2018), 149--198]. It turns out the local phase shift of modulating line solitons are not uniform in the transverse direction. In this paper, we obtain the $L^\infty$-bound for the local phase shift of modulating line solitons for polynomially localized perturbations

The mode of host-parasite interaction shapes coevolutionary dynamics and the fate of host cooperation

Antagonistic coevolution between hosts and parasites can have a major impact on host population structures, and hence on the evolution of social traits. Using stochastic modelling techniques in the context of bacteria-virus interactions, we investigate the impact of coevolution across a continuum of host-parasite genetic specificity (specifically, where genotypes have the same infectivity/resistance ranges (matching alleles, MA) to highly variable ranges (gene-for-gene, GFG)) on population genetic structure, and on the social behaviour of the host. We find that host cooperation is more likely to be maintained towards the MA end of the continuum, as the more frequent bottlenecks associated with an MA-like interaction can prevent defector invasion, and can even allow migrant cooperators to invade populations of defectors.Comment: 8 pages, 4 figures, 1 Supplementary Material file attached (to view it, please download the source file listed under "Other formats"

2-D constrained Navier-Stokes equation and intermediate asymptotics

We introduce a modified version of the two-dimensional Navier-Stokes equation, preserving energy and momentum of inertia, which is motivated by the occurrence of different dissipation time scales and related to the gradient flow structure of the 2-D Navier-Stokes equation. The hope is to understand intermediate asymptotics. The analysis we present here is purely formal. A rigorous study of this equation will be done in a forthcoming paper

Detection of the Sgr A* activity at 3.8 and 4.8 microns with NACO

L'-band (lambda=3.8 microns) and M'-band (lambda=4.8 microns) observations of the Galactic Center region, performed in 2003 at VLT (ESO) with the adaptive optics imager NACO, have lead to the detection of an infrared counterpart of the radio source Sgr A* at both wavelengths. The measured fluxes confirm that the Sgr A* infrared spectrum is dominated by the synchrotron emission of nonthermal electrons. The infrared counterpart exhibits no significant short term variability but demonstrates flux variations on daily and yearly scales. The observed emission arises away from the position of the dynamical center of the S2 orbit and would then not originate from the closest regions of the black hole.Comment: 5 pages, 3 figures, accepted in Astronomy & Astrophysic