Generation and near-field imaging of Airy surface plasmons

We demonstrate experimentally the generation and near-field imaging of nondiffracting surface waves - plasmonic Airy beams, propagating on the surface of a gold metal film. The Airy plasmons are excited by an engineered nanoscale phase grating, and demonstrate significant beam bending over their propagation. We show that the observed Airy plasmons exhibit self-healing properties, suggesting novel applications in plasmonic circuitry and surface optical manipulation.Comment: 4 pages, 4 figure

An O(M(n) log n) algorithm for the Jacobi symbol

The best known algorithm to compute the Jacobi symbol of two n-bit integers runs in time O(M(n) log n), using Sch\"onhage's fast continued fraction algorithm combined with an identity due to Gauss. We give a different O(M(n) log n) algorithm based on the binary recursive gcd algorithm of Stehl\'e and Zimmermann. Our implementation - which to our knowledge is the first to run in time O(M(n) log n) - is faster than GMP's quadratic implementation for inputs larger than about 10000 decimal digits.Comment: Submitted to ANTS IX (Nancy, July 2010

Fronts and interfaces in bistable extended mappings

We study the interfaces' time evolution in one-dimensional bistable extended dynamical systems with discrete time. The dynamics is governed by the competition between a local piece-wise affine bistable mapping and any couplings given by the convolution with a function of bounded variation. We prove the existence of travelling wave interfaces, namely fronts, and the uniqueness of the corresponding selected velocity and shape. This selected velocity is shown to be the propagating velocity for any interface, to depend continuously on the couplings and to increase with the symmetry parameter of the local nonlinearity. We apply the results to several examples including discrete and continuous couplings, and the planar fronts' dynamics in multi-dimensional Coupled Map Lattices. We eventually emphasize on the extension to other kinds of fronts and to a more general class of bistable extended mappings for which the couplings are allowed to be nonlinear and the local map to be smooth.Comment: 27 pages, 3 figures, submitted to Nonlinearit

Challenges for creating magnetic fields by cosmic defects

We analyse the possibility that topological defects can act as a source of magnetic fields through the Harrison mechanism in the radiation era. We give a detailed relativistic derivation of the Harrison mechanism at first order in cosmological perturbations, and show that it is only efficient for temperatures above T ~ 0.2 keV. Our main result is that the vector metric perturbations generated by the defects cannot induce vorticity in the matter fluids at linear order, thereby excluding the production of currents and magnetic fields. We show that anisotropic stress in the matter fluids is required to source vorticity and magnetic fields. Our analysis is relevant for any mechanism whereby vorticity is meant to be transferred purely by gravitational interactions, and thus would also apply to dark matter or neutrinos.Comment: 9 pages, 1 figure; minor corrections and additions; accepted for publication in Physical Review

Reducible valgus flat-foot: Assessment of posterior subtalar joint surface displacement by posterior arthroscopy during sinus tarsi expansion screwing

AbstractIntroductionSubtalar arthroereisis corrects childhood and adult reducible valgus flat-foot in certain indications. Inserting an expansion screw in the sinus tarsi simultaneously corrects the calcaneal valgus of the talocalcaneal divergence and first-ray pronation if these are reducible. The displacement induced in the posterior subtalar joint (decoaptation, translation, rotation) is, however, poorly known. The present study involved arthroscopic assessment of posterior subtalar joint surface displacement during insertion of a talocalcaneal arthroereisis screw, with the hypothesis that displacement varies in three dimensions according to screw size.Material and methodEight specimens were used for the study. All ankles were supple, taken from adult subjects. A 4.5-mm arthroscope was used and measurements were taken with a graduated palpator in the posterior subtalar joint. Three sinus tarsi expansion screws of incremental diameter were assessed. Before and after insertion measurements were made of posterolateral and posteromedial talar exposure on the calcaneus, anteroposterior and lateromedial translation, and talocalcaneal joint-line opening.ResultsMedial rotation, varization and anterior translation of the calcaneus were comparable in all cases. Mean lateral opening of the posterior subtalar joint was 0.88mm with 8-mm screws and 1.25mm with 16-mm screws. Significant differences between 8 and 16mm screws were found for lateral subtalar joint opening (P=0.028) and for lateromedial translation (P=0.004).ConclusionSinus tarsi expansion screwing corrects hindfoot valgus and talocalcaneal divergence by inducing medial translation of the calcaneus under the talus and talar medial rotation and varization, proportional to screw size (medial translation and lateral opening of the subtalar joint).Level of evidenceIII

Multidomain spectral method for the Gauss hypergeometric function

We present a multidomain spectral approach for Fuchsian ordinary differential equations in the particular case of the hypergeometric equation. Our hybrid approach uses Frobenius’ method and Moebius transformations in the vicinity of each of the singular points of the hypergeometric equation, which leads to a natural decomposition of the real axis into domains. In each domain, solutions to the hypergeometric equation are constructed via the well-conditioned ultraspherical spectral method. The solutions are matched at the domain boundaries to lead to a solution which is analytic on the whole compactified real line R∪∞ , except for the singular points and cuts of the Riemann surface on which the solution is defined. The solution is further extended to the whole Riemann sphere by using the same approach for ellipses enclosing the singularities. The hypergeometric equation is solved on the ellipses with the boundary data from the real axis. This solution is continued as a harmonic function to the interior of the disk by solving the Laplace equation in polar coordinates with an optimal complexity Fourier–ultraspherical spectral method. In cases where logarithms appear in the solution, a hybrid approach involving an analytical treatment of the logarithmic terms is applied. We show for several examples that machine precision can be reached for a wide class of parameters, but also discuss almost degenerate cases where this is not possible

Magnetic Helicity Generation from the Cosmic Axion Field

The coupling between a primordial magnetic field and the cosmic axion field generates a helical component of the magnetic field around the time in which the axion starts to oscillate. If the energy density of the seed magnetic field is comparable to the energy density of the universe at that time, then the resulting magnetic helicity is about |H_B| \simeq (10^{-20} G)^2 kpc and remains constant after its generation. As a corollary, we find that the standard properties of the oscillating axion remain unchanged even in the presence of very strong magnetic fields.Comment: 6 pages, 2 figures. Accepted for publication in Phys. Rev. D. Minor revisions and new references adde

Ellipsoidal Universe Can Solve The CMB Quadrupole Problem

The recent three-year WMAP data have confirmed the anomaly concerning the low quadrupole amplitude compared to the best-fit \Lambda CDM prediction. We show that, allowing the large-scale spatial geometry of our universe to be plane-symmetric with eccentricity at decoupling or order 10^{-2}, the quadrupole amplitude can be drastically reduced without affecting higher multipoles of the angular power spectrum of the temperature anisotropy.Comment: 4 pages, 2 figures, minor changes, reference added, to appear in Phys. Rev. Let

Pulsar rotation measures and the magnetic structure of our Galaxy

We have obtained 63 rotation measures (RMs) from polarization observations of southern pulsars, of which 54 are new measurements and 3 are varied from previous values. The new pulsar RM data at high Galactic latitudes are mostly consistent with the antisymmetric RM distribution found previously. For the Galactic disc, evidence for a field reversal near the Perseus arm, and possibly another beyond it, is presented. Inside the Solar Circle, in addition to the two known field reversals in or near the Carina-Sagittartus arm and the Crux-Scutum arm, a further reversal in the Norma arm is tentatively identified. These reversals, together with the pitch angle derived from pulsar RM and stellar polarization distributions, are consistent with bisymmetric spiral (BSS) models for the large-scale magnetic field structure in the disc of our Galaxy. However, discrimination between models is complicated by the presence of smaller-scale irregularities in the magnetic field, as well as uncertainties in the theoretical modelling.Comment: 10pages; 8 figures; Accepted by MNRA