Phasefield theory for fractional diffusion-reaction equations and applications

This paper is concerned with diffusion-reaction equations where the classical diffusion term, such as the Laplacian operator, is replaced with a singular integral term, such as the fractional Laplacian operator. As far as the reaction term is concerned, we consider bistable non-linearities. After properly rescaling (in time and space) these integro-differential evolution equations, we show that the limits of their solutions as the scaling parameter goes to zero exhibit interfaces moving by anisotropic mean curvature. The singularity and the unbounded support of the potential at stake are both the novelty and the challenging difficulty of this work.Comment: 41 page

Ground-based time-guidance algorithm for control of airplanes in a time-metered air traffic control environment: A piloted simulation study

The rapidly increasing costs of flight operations and the requirement for increased fuel conservation have made it necessary to develop more efficient ways to operate airplanes and to control air traffic for arrivals and departures to the terminal area. One concept of controlling arrival traffic through time metering has been jointly studied and evaluated by NASA and ONERA/CERT in piloted simulation tests. From time errors attained at checkpoints, airspeed and heading commands issued by air traffic control were computed by a time-guidance algorithm for the pilot to follow that would cause the airplane to cross a metering fix at a preassigned time. These tests resulted in the simulated airplane crossing a metering fix with a mean time error of 1.0 sec and a standard deviation of 16.7 sec when the time-metering algorithm was used. With mismodeled winds representing the unknown in wind-aloft forecasts and modeling form, the mean time error attained when crossing the metering fix was increased and the standard deviation remained approximately the same. The subject pilots reported that the airspeed and heading commands computed in the guidance concept were easy to follow and did not increase their work load above normal levels

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

Homogenization and enhancement for the G-equation

We consider the so-called G-equation, a level set Hamilton-Jacobi equation, used as a sharp interface model for flame propagation, perturbed by an oscillatory advection in a spatio-temporal periodic environment. Assuming that the advection has suitably small spatial divergence, we prove that, as the size of the oscillations diminishes, the solutions homogenize (average out) and converge to the solution of an effective anisotropic first-order (spatio-temporal homogeneous) level set equation. Moreover we obtain a rate of convergence and show that, under certain conditions, the averaging enhances the velocity of the underlying front. We also prove that, at scale one, the level sets of the solutions of the oscillatory problem converge, at long times, to the Wulff shape associated with the effective Hamiltonian. Finally we also consider advection depending on position at the integral scale

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)

Neonatal infections with multidrug-resistant ESBL-producing E. cloacae and K. pneumoniae in Neonatal Units of two different Hospitals in Antananarivo, Madagascar

Background: We investigated the molecular mechanism of ß-lactam resistance in extended-spectrum ß-lactamase (ESBL)-producing Enterobacterial strains isolated in neonatal units of different hospitals in Anatnanarivo, Madagascar.Methods: Bacteria were identified by standard biochemical methods, disc diffusion antibiograms and Etest. Resistance genes were sought by PCR. Strains were characterized by Rep- PCR (Diversilab), plasmid analysis and rep-typing.Results: From April 2012 to March 2013, 29 ESBL-producing E. cloacae and 15 K. pneumoniae were isolated from blood culture (n = 32) or gastric samples (n = 12) performed at day 0 or 2 from 39/303 newborns suspected of early neonatal infection. These infants were treated with expanded spectrum cephalosporins, due to lack of carbapenems, leading to a high mortality rate (45 %). Isolates recovered were all, but 4, multidrug resistant, particularly to fluoroquinolones (FQ) except for 21 E. cloacae isolates. Isolates produced TEM-1 and CTX-M-15 ß-lactamases and their genes were located on several self- transferable plasmids of variable sizes sizes that could not be linked to a major plasmid incompatibility group. E. cloacae isolates belonged to 6 Rep-types among which two counted for 11 isolates each. The FQ resistant E. cloacae isolates belonged to one clone, whereas the FQ susceptible E. cloacae isolates belonged to four clones. The K. pneumoniae isolates belonged to 9 Rep-types among which one included five isolates.Conclusion: This study is the first molecular characterization of ESBL- producing isolates from neonatology units in Madagascar, a country with limited epidemiological data. It revealed an important multi-clonal dissemination of CTX-M-15- producing isolates reflecting both the high community carriage and the very early nosocomial contamination of the neonates

Increased intensity of treatment and decreased mortality in elderly patients in an intensive care unit over a decade

Objectives: Data collected from two cohorts of patients aged ≥80 yrs and admitted to an intensive care unit in France were compared to determine whether intensive care unit care and survival had evolved from the 1990s to the 2000s.Design: Retrospective cohort study on patient data attained during intensive care unit stays. Setting: 18-bed intensive care unit in an academic medical center. Patients: Two cohorts of patients aged ≥80 yrs, admitted to an intensive care unit at a 10-yr interval. Interventions: None. Measurements and Main Results: The first cohort comprised 348 patients admitted between January 1992 and December 1995, and the second cohort, 373 patients admitted between January 2001 and December 2004. There was no difference in age between the two cohorts, but patients in the second had significantly less history of functional limitation and significantly more acute illness (Simplified Acute Physiology Score II 43 ± 18 vs. 57 ± 25, respectively, p < .0001). Patients in the second cohort had a significantly higher Omega Score, had a higher occurrence of renal replacement therapy, and received vasopressors more frequently than the patients in the first cohort, even when adjusted for age, sex, Knaus classification, Simplified Acute Physiology Score II, and intensive care unit admission cause. Intensive care unit mortality was 65% and 64% for the first and second cohorts, respectively. In multivariate analysis (including age, Knaus classification, Simplified Acute Physiology Score II and first vs. second period) for association with intensive care unit survival, the 2001–2004 period was associated with a near tripling of chances of survival (odds ratio 2.9; 95% confidence interval, 1.92–4.47, p < .0001). Conclusions: The characteristics and intensity of treatment for elderly people admitted to the intensive care unit changed significantly over a decade. The intensity of treatments has increased over time and survival has improved over time as well. A potential link between increased treatment and improved survival in the elderly may be evoked

A kinetic formulation for multidimensional scalar conservation laws with boundary conditions and applications

International audienceWe state a kinetic formulation of weak entropy solutions of a general multidimensional scalar conservation law with initial and boundary conditions. We first associate with any weak entropy solution a entropy defect measure; the analysis of this measure at the boundary of the domain relies on the study of weak entropy sub and supersolutions and implies the introduction of the notion of sided boundary defect measures. As a first application, we prove that any weak entropy subsolution of the initial-boundary value problem is bounded above by any weak entropy supersolution (Comparison Theorem). We next study a BGK-like kinetic model that approximates the scalar conservation law. We prove that such a model converges by adapting the proof of the Comparison Theorem

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