Honeycomb pattern formation by laser-beam filamentation in atomic sodium vapor

We have observed transverse pattern formation leading to highly regular structures in both the near and far fields when a near-resonant laser beam propagates without feedback through an atomic sodium vapor. One example is a regular far-field honeycomb pattern, which results from the transformation of the laser beam within the vapor into a stable three-lobed structure with a uniform phase distribution and highly correlated power fluctuations. The predictions of a theoretical model of the filamentation process are in good agreement with these observations.     

Study of an ultrahigh-numerical-aperture fiber continuum generation source for optical coherence tomography

The axial resolution of optical coherence tomography images is primarily dependent on the bandwidth of the illumination source. Continuum generation is one way to generate the single-mode, high-bandwidth light needed for point illumination. We present an inexpensive and easy-to-implement augmentation to a Ti:sapphire laser that widens the bandwidth from 20 to over 200 nm with commerically available ultrahigh-numerical-aperture fiber. This technique can provide a readily available broad-bandwidth source for researchers and a practical enhancement to a fiber-optic optical coherence tomography system.     

Unitary Correlations and the Fejér Kernel

Let M be a unitary matrix with eigenvalues t _j , and let f be a function on the unit circle. Define X _f (M)=f(t _j ). We derive exact and asymptotic formulae for the covariance of X _f and X _g with respect to the measures |(M)|²dM where dM is Haar measure and an irreducible character. The asymptotic results include an analysis of the Fejér kernel which may be of independent interest.     

Jules Horowitz Reactor: a high performance material testing reactor

The physical modelling of materials' behaviour under severe conditions is an indispensable element for developing future fission and fusion systems: screening, design, optimisation, processing, licensing, and lifetime assessment of a new generation of structure materials and fuels, which will withstand high fast neutron flux at high in-service temperatures with the production of elements like helium and hydrogen.JANNUS and other analytical experimental tools are developed for this objective. However, a purely analytical approach is not sufficient: there is a need for flexible experiments integrating higher scales and coupled phenomena and offering high quality measurements; these experiments are performed in material testing reactors (MTR). Moreover, complementary representative experiments are usually performed in prototypes or dedicated facilities such as IFMIF for fusion. Only such a consistent set of tools operating on a wide range of scales, can provide an actual prediction capability. A program such as the development of silicon carbide composites (600–1200 °C) illustrates this multiscale strategy.Facing the long term needs of experimental irradiations and the ageing of present MTRs, it was thought necessary to implement a new generation high performance MTR in Europe for supporting existing and future nuclear reactors. The Jules Horowitz Reactor (JHR) project copes with this context. It is funded by an international consortium and will start operation in 2014. JHR will provide improved performances such as high neutron flux (10¹⁵ n/cm²/s above 0.1 MeV) in representative environments (coolant, pressure, temperature) with online monitoring of experimental parameters (including stress and strain control). Experimental devices designing, such as high dpa and small thermal gradients experiments, is now a key objective requiring a broad collaboration to put together present scientific state of art, end-users requirements and advanced instrumentation. To cite this article: D. Iracane et al., C. R. Physique 9 (2008).     

Phase Retrieval for Probability Distributions on Quantum Groups and Braided Groups

For nilpotent quantum groups [as introduced by Franz et al. ⁽⁷⁾], we show that (in sharp contrast to the classical case) the symmetrization of a probability distribution and the first moments of together determine uniquely the original distribution .     

A Hahn-Banach theorem for integral polynomials

We study the problem of extendibility of polynomials over Banach spaces: when can a polynomial defined over a Banach space be extended to a polynomial over any larger Banach space? To this end, we identify all spaces of polynomials as the topological duals of a space spanned by evaluations, with Hausdorff locally convex topologies. We prove that all integral polynomials over a Banach space are extendible. Finally, we study the Aron-Berner extension of integral polynomials, and give an equivalence for non-containment of .

     

QPECgen, a MATLAB Generator for Mathematical Programs with Quadratic Objectives and Affine Variational Inequality Constraints

We describe a technique for generating a special class, called QPEC, of mathematical programs with equilibrium constraints, MPEC. A QPEC is a quadratic MPEC, that is an optimization problem whose objective function is quadratic, first-level constraints are linear, and second-level (equilibrium) constraints are given by a parametric affine variational inequality or one of its specialisations. The generator, written in MATLAB, allows the user to control different properties of the QPEC and its solution. Options include the proportion of degenerate constraints in both the first and second level, ill-conditioning, convexity of the objective, monotonicity and symmetry of the second-level problem, and so on. We believe these properties may substantially effect efficiency of existing methods for MPEC, and illustrate this numerically by applying several methods to generator test problems. Documentation and relevant codes can be found by visiting http://www.ms.unimelb.edu.au/danny/qpecgendoc.html.     

On the optimal local regularity for the Yang-Mills equations in

The aim of the paper is to develop the Fourier Analysis techniques needed in the study of optimal well-posedness and global regularity properties of the Yang-Mills equations in Minkowski space-time , for the case of the critical dimension . We introduce new functional spaces and prove new bilinear estimates for solutions of the homogeneous wave equation, which can be viewed as generalizations of the well-known Strichartz-Pecher inequalities.

     

Spectral properties of dissipative chaotic quantum maps

I examine spectral properties of a dissipative chaotic quantum map with the help of a recently discovered semiclassical trace formula. I show that in the presence of a small amount of dissipation the traces of any finite power of the propagator of the reduced density matrix, and traces of its classical counterpart, the Frobenius-Perron operator, are identical in the limit of variant Planck's over 2pi -->0. Numerically I find that even for finite variant Planck's over 2pi the agreement can be very good. This holds in particular if the classical phase space contains a strange attractor, as long as one stays clear of bifurcations. Traces of the quantum propagator for iterations of the map agree well with the corresponding traces of the Frobenius-Perron operator if the classical dynamics is dominated by a strong point attractor. (c) 1999 American Institute of Physics.     

Nanocomposite Mullite/Mullite Powders by Spray Pyrolysis

A mullite/mullite nanocomposite powder has been synthesized, composed of nanometer-size 3Al₂O₃·2SiO₂ (3/2) mullite precipitates within a matrix of the high alumina 2Al₂O₃·SiO₂ (2:1) mullite. Historically, the transition from the metastable high-alumina phase to the thermodynamically stable 3:2 phase of mullite has been thought to be a continuous process, involving a continuous solid solution between the two forms of mullite. In contradiction to this widely held view, our high resolution transmission electron microscopic characterization confirms that a first order phase transition between two distinct mullites occurs. The high degree of interface coherence between the precipitates and the matrix allows us to speculate that the mechanical properties of the matrix could be enhanced by a process similar to the precipitation hardening of metals.