Role of beam propagation in Goos-H\"{a}nchen and Imbert-Fedorov shifts

We derive the polarization-dependent displacements parallel and perpendicular to the plane of incidence, for a Gaussian light beam reflected from a planar interface, taking into account the propagation of the beam. Using a classical-optics formalism we show that beam propagation may greatly affect both Goos-H\"{a}nchen and Imbert-Fedorov shifts when the incident beam is focussed.Comment: 3 pages, 1 figure, submitted to Opt. Let

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

Effects of Force Distribution and Rebound on Electromagnetically Formed Sheet Metal

Electromagnetic forming (EMF) is a high speed forming process that has been shown to increase the formability of aluminum alloys under certain conditions. Many authors have reported significant increases in formability; however, there is as of yet no complete understanding of the process. Obtaining a gain in formability is not the only factor that must be considered when studying EMF. The process rapidly generates significant forces which lead to the deformation of the material at very high rates. The applied forces depend on the shape of the electromagnetic coil used, which leads to force distributions that may not be ideal for forming a particular part. Once the sheet is accelerated it will travel at high speeds until it impacts the die. This high speed impact results in the sheet rebounding from the die. Both the force distribution and the rebound affect the final shape of the part. This paper presents the results of experimental and numerical study carried out to determine the effect of the force distribution and the rebound on samples of conical and "v-channel" geometry. It was found that both sample geometries are affected by the force distribution and the rebound, with the v-channel samples being considerably more affected. The results indicate that these effects must be carefully considered when EMF processes are designed

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

Electromagnetic Forming of AZ31B Magnesium Alloy Sheet

In the first stage of this work, polycrystalline specimens of AZ31B magnesium alloy have been characterized by uniaxial tensile tests at quasi-static and dynamic strain rates at room temperature. The influence of the strain rate is outlined and experimental results were fitted to the parameters of Johnson-Cook constitutive material model. In the second stage of the present study, sheets of AZ31B magnesium alloy have been biaxially formed by electromagnetic forming using different coil and die configurations. Deformation values measured from electromagnetic formed parts are compared to the ones achieved with uniaxial tensile tests and also with the values obtained by conventional forming technologies. Finally, numerical simulations have been carried out using an alternative method for computing the electromagnetic fields in the EMF process simulation, a combination of Finite Element Method (FEM) for conductor parts and Boundary Element Method (BEM) for the surrounding air (or more generally insulators) that is being implemented into commercial code LS-DYNA®

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

Absence of zero field muon spin relaxation induced by superconductivity in the B phase of UPt3_3

We present muon spin relaxation measurements performed on crystals of the heavy fermion superconductor UPt$_3$. In zero applied field, contrary to a previous report, we do not observe an increase of the internal magnetic field in the lower superconducting phase (the B phase). Our result gives an experimental upper bound of the magnetic field that could be associated with the superconducting state.Comment: 4 pages, REVTeX 3.0, 2 PostScript figure