Flux-limited solutions for quasi-convex Hamilton-Jacobi equations on networks

We study Hamilton-Jacobi equations on networks in the case where Hamiltonians are quasi-convex with respect to the gradient variable and can be discontinuous with respect to the space variable at vertices. First, we prove that imposing a general vertex condition is equivalent to imposing a specific one which only depends on Hamiltonians and an additional free parameter, the flux limiter. Second, a general method for proving comparison principles is introduced. This method consists in constructing a vertex test function to be used in the doubling variable approach. With such a theory and such a method in hand, we present various applications, among which a very general existence and uniqueness result for quasi-convex Hamilton-Jacobi equations on networks.Comment: 104 pages. Version final

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

V(RI)sub(c) Photometry of Cepheids in the Magellanic Clouds

We present V(RI)sub data for thirteen Cepheids in the Large Magellanic Cloud ans fifty-five in each wavelength band. The median uncertainty in the photometry iy Moffett, Gieren & Barnes (1998) which contained 1000 measures ($\pm 0.01$ mag) in each wavelength band on 22 variables with periods in the range 8--133 days.Comment: LaTeX file (9 pages), LaTeX table (1 page), 2 figures of 3 panels eacs PASP (July

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

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

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)

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

Diffusion as a singular homogenization of the Frenkel-Kontorova model

International audienceIn this work, we consider a general fully overdamped Frenkel-Kontorova model. This model describes the dynamics of a infinite chain of particles, moving in a periodic landscape. Our aim is to describe the macroscopic behavior of this system. We study a singular limit corresponding to a high density of particles moving in a vanishing periodic landscape. We identify the limit equation which is a nonlinear diffusion equation. Our homogenization approach is done in the framework of viscosity solutions

Immunisation des génisses contre l’infection par Brucella abortus. Comparaison de quatre vaccins

Renoux G., Nicolas J. A., Imbert R., Quéchon M. Immunisation des génisses contre l’infection par Brucella Abortus. Comparaison de quatre vaccins. In: Bulletin de l'Académie Vétérinaire de France tome 117 n°3, 1964. pp. 139-147

Immunisation des génisses contre la brucellose par l’association du vaccin antibrucellique tué, en excipient et de vaccin anti-aphteux

Quinze génisses de race limousine, âgées de 7 à 9 mois, indemnes de brucellose et de tuberculose sont vaccinées par un mélange de vaccin antibrucellique Br. melitensis H. 38 formolé en excipient et d’un vaccin anti-aphteux polyvalent du commerce. Trois mois plus tard, ces animaux vaccinés sont infectés par l’inoculation conjonctivale de 15 x 10 6 Br. abortus souche 544, en même temps qu’un lot témoin de 20 génisses non vaccinées. Tous ces bovins sont sacrifiés et autopsiés 6 à 8 semaines plus tard. La culture en masse des échantillons prélevés (ganglions lymphatiques, rate et foie) donne les résultats suivants : 20 génisses témoins = 20 infectées, 0 protégées. 15 génisses vaccinées = 2 infectées, 13 protégées. La protection étant vérifiée par l’absence de culture de Brucella. Les deux génisses qui, quoique vaccinées, sont infectées ont donné un total de 10 colonies de Br. abortus ; cependant le nombre moyen de colonies de Br. abortus par génisse témoin est de 200. Ainsi, la protection relative est considérable. On peut conclure que l’association de vaccin antibrucellique, Br. melitensis H. 38 formolé en excipient, au vaccin anti-aphteux protège les génisses aussi bien que ce vaccin antibrucellique seul