Repeated games for eikonal equations, integral curvature flows and non-linear parabolic integro-differential equations

The main purpose of this paper is to approximate several non-local evolution equations by zero-sum repeated games in the spirit of the previous works of Kohn and the second author (2006 and 2009): general fully non-linear parabolic integro-differential equations on the one hand, and the integral curvature flow of an interface (Imbert, 2008) on the other hand. In order to do so, we start by constructing such a game for eikonal equations whose speed has a non-constant sign. This provides a (discrete) deterministic control interpretation of these evolution equations. In all our games, two players choose positions successively, and their final payoff is determined by their positions and additional parameters of choice. Because of the non-locality of the problems approximated, by contrast with local problems, their choices have to "collect" information far from their current position. For integral curvature flows, players choose hypersurfaces in the whole space and positions on these hypersurfaces. For parabolic integro-differential equations, players choose smooth functions on the whole space

High Mass Triple Systems: The Classical Cepheid Y Car

We have obtained an HST STIS ultraviolet high dispersion Echelle mode spectrum the binary companion of the double mode classical Cepheid Y Car. The velocity measured for the hot companion from this spectrum is very different from reasonable predictions for binary motion, implying that the companion is itself a short period binary. The measured velocity changed by 7 km/ s during the 4 days between two segments of the observation confirming this interpretation. We summarize "binary" Cepheids which are in fact members of triple system and find at least 44% are triples. The summary of information on Cepheids with orbits makes it likely that the fraction is under-estimated.Comment: accepted by A

Existence of solutions for a higher order non-local equation appearing in crack dynamics

In this paper, we prove the existence of non-negative solutions for a non-local higher order degenerate parabolic equation arising in the modeling of hydraulic fractures. The equation is similar to the well-known thin film equation, but the Laplace operator is replaced by a Dirichlet-to-Neumann operator, corresponding to the square root of the Laplace operator on a bounded domain with Neumann boundary conditions (which can also be defined using the periodic Hilbert transform). In our study, we have to deal with the usual difficulty associated to higher order equations (e.g. lack of maximum principle). However, there are important differences with, for instance, the thin film equation: First, our equation is nonlocal; Also the natural energy estimate is not as good as in the case of the thin film equation, and does not yields, for instance, boundedness and continuity of the solutions (our case is critical in dimension $1$ in that respect)

The Binary Fraction of Low Mass White Dwarfs

We describe spectroscopic observations of 21 low-mass (<0.45 M_sun) white dwarfs (WDs) from the Palomar-Green Survey obtained over four years. We use both radial velocities and infrared photometry to identify binary systems, and find that the fraction of single, low-mass WDs is <30%. We discuss the potential formation channels for these single stars including binary mergers of lower-mass objects. However, binary mergers are not likely to explain the observed number of single low-mass WDs. Thus additional formation channels, such as enhanced mass loss due to winds or interactions with substellar companions, are likely.Comment: 9 pages, accepted to Ap

The OSACA Database and a Kinematic Analysis of Stars in the Solar Neighborhood

We transformed radial velocities compiled from more than 1400 published sources, including the Geneva--Copenhagen survey of the solar neighborhood (CORAVEL-CfA), into a uniform system based on the radial velocities of 854 standard stars in our list. This enabled us to calculate the average weighted radial velocities for more than 25~000 HIPPARCOS stars located in the local Galactic spiral arm (Orion arm) with a median error of +-1 km/s. We use these radial velocities together with the stars' coordinates, parallaxes, and proper motions to determine their Galactic coordinates and space velocities. These quantities, along with other parameters of the stars, are available from the continuously updated Orion Spiral Arm CAtalogue (OSACA) and the associated database. We perform a kinematic analysis of the stars by applying an Ogorodnikov-Milne model to the OSACA data. The kinematics of the nearest single and multiple main-sequence stars differ substantially. We used distant (r\approx 0.2 kpc) stars of mixed spectral composition to estimate the angular velocity of the Galactic rotation -25.7+-1.2 km/s/kpc, and the vertex deviation,l=13+-2 degrees, and detect a negative K effect. This negative K effect is most conspicuous in the motion of A0-A5 giants, and is equal to K=-13.1+-2.0 km/s/kpc.Comment: 16 pages, 8 figure

Molecular Dynamics Simulation of Semiflexible Polyampholyte Brushes - The Effect of Charged Monomers Sequence

Planar brushes formed by end-grafted semiflexible polyampholyte chains, each chain containing equal number of positively and negatively charged monomers is studied using molecular dynamics simulations. Keeping the length of the chains fixed, dependence of the average brush thickness and equilibrium statistics of the brush conformations on the grafting density and the salt concentration are obtained with various sequences of charged monomers. When similarly charged monomers of the chains are arranged in longer blocks, the average brush thickness is smaller and dependence of brush properties on the grafting density and the salt concentration is stronger. With such long blocks of similarly charged monomers, the anchored chains bond to each other in the vicinity of the grafting surface at low grafting densities and buckle toward the grafting surface at high grafting densities.Comment: 8 pages,7 figure

Structure and Evolution of Nearby Stars with Planets. I. Short-Period Systems

Using the Yale stellar evolution code, we have calculated theoretical models for nearby stars with planetary-mass companions in short-period nearly circular orbits: 51 Pegasi, Tau Bootis, Upsilon Andromedae, Rho Cancri, and Rho Coronae Borealis. We present tables listing key stellar parameters such as mass, radius, age, and size of the convective envelope as a function of the observable parameters (luminosity, effective temperature, and metallicity), as well as the unknown helium fraction. For each star we construct best models based on recently published spectroscopic data and the present understanding of galactic chemical evolution. We discuss our results in the context of planet formation theory, and, in particular, tidal dissipation effects and stellar metallicity enhancements.Comment: 48 pages including 13 tables and 5 figures, to appear in Ap

Darwin’s wind hypothesis: does it work for plant dispersal in fragmented habitats?

Using the wind-dispersed plant Mycelis muralis, we examined how landscape fragmentation affects variation in seed traits contributing to dispersal. Inverse terminal velocity (Vt−1) of field-collected achenes was used as a proxy for individual seed dispersal ability. We related this measure to different metrics of landscape connectivity, at two spatial scales: in a detailed analysis of eight landscapes in Spain and along a latitudinal gradient using 29 landscapes across three European regions. In the highly patchy Spanish landscapes, seed Vt−1 increased significantly with increasing connectivity. A common garden experiment suggested that differences in Vt−1 may be in part genetically based. The Vt−1 was also found to increase with landscape occupancy, a coarser measure of connectivity, on a much broader (European) scale. Finally, Vt−1 was found to increase along a south–north latitudinal gradient. Our results for M. muralis are consistent with ‘Darwin’s wind dispersal hypothesis’ that high cost of dispersal may select for lower dispersal ability in fragmented landscapes, as well as with the ‘leading edge hypothesis’ that most recently colonized populations harbour more dispersive phenotypes.

Transiting exoplanets from the CoRoT space mission VIII. CoRoT-7b: the first Super-Earth with measured radius

We report the discovery of very shallow (DF/F = 3.4 10-4), periodic dips in the light curve of an active V = 11.7 G9V star observed by the CoRoT satellite, which we interpret as due to the presence of a transiting companion. We describe the 3-colour CoRoT data and complementary ground-based observations that support the planetary nature of the companion. Methods. We use CoRoT color information, good angular resolution ground-based photometric observations in- and out- of transit, adaptive optics imaging, near-infrared spectroscopy and preliminary results from Radial Velocity measurements, to test the diluted eclipsing binary scenarios. The parameters of the host star are derived from optical spectra, which were then combined with the CoRoT light curve to derive parameters of the companion. We examine carefully all conceivable cases of false positives, and all tests performed support the planetary hypothesis. Blends with separation larger than 0.40 arcsec or triple systems are almost excluded with a 8 10-4 risk left. We conclude that, as far as we have been exhaustive, we have discovered a planetary companion, named CoRoT-7b, for which we derive a period of 0.853 59 +/- 3 10-5 day and a radius of Rp = 1.68 +/- 0.09 REarth. Analysis of preliminary radial velocity data yields an upper limit of 21 MEarth for the companion mass, supporting the finding. CoRoT-7b is very likely the first Super-Earth with a measured radius.Comment: Accepted in Astronomy and Astrophysics; typos and language corrections; version sent to the printer w few upgrade

Technical design and performance of the NEMO3 detector

The development of the NEMO3 detector, which is now running in the Frejus Underground Laboratory (L.S.M. Laboratoire Souterrain de Modane), was begun more than ten years ago. The NEMO3 detector uses a tracking-calorimeter technique in order to investigate double beta decay processes for several isotopes. The technical description of the detector is followed by the presentation of its performance.Comment: Preprint submitted to Nucl. Instrum. Methods A Corresponding author: Corinne Augier ([email protected]