The application of centre manifolds to amplitude expansions. I. Ordinary differential equations

The theory of centre manifolds for a system of ordinary differential equations is summarized and its relationship to amplitude expansions based upon multiple time scales is discussed. Emphasis is placed upon the practical computational aspects of applying centre manifold theory to near-critical problems, and, in particular, to the computation of the centre manifold. The calculations are illustrated by a detailed analysis of two problems in fluid mechanics.     

Spectroscopic analysis of electrically polarized polyacrylonitrile

Electrically polarized and unpolarized films of polyacrylonitrile (PAN) have been investigated by both infrared attenuated total reflection (ATR) and thermally stimulated discharge (TSD). ATR analysis of PAN films has been aimed at explaining the molecular origin of thermally stimulated currents, and consequently that of phenomena contributing to electrical polarization in this material. Preferred orientation of nitrile dipoles along the thickness direction (applied electric field direction) has been detected by ATR in both polarized and unpolarized films. It is suggested that dipolar alignment in unpolarized solvent-cast films could result from internal electric fields associated with space charges. The observed orientational anisotropy is found to disappear gradually as films (both polarized and unpolarized) are heated from ambient temperature to 100°C and rotational motion in the backbone is thermally activated. TSD currents observed in this thermal range are thus associated with randomization of molecular dipoles. TSD currents observed above 100°C are suggested to originate from drift of space charges, since both an isotropic orientation of dipoles and onset of considerable diffusion are detected by ATR in this temperature range. PAN films polarized by high-intensity electric fields (5 × 10⁵Vcm^?1, as opposed to 5 × 10⁴Vcm^?1) are found to retain orientational anisotropy above 100°C, and this is believed to be associated with a structural rearrangement induced by electrical polarization.     

A prism reflector of anti-resonant ring configuration

Two identical prisms are combined to form an anti-resonant ring reflector, giving total reflection without the use of coatings or roof edges. When used as the total reflector in a Q-switched NdYAG laser this device has shown a damage threshold twice that of a multilayer reflector.     

High harmonic XUV spectral phase interferometry for direct electric-field reconstruction

We demonstrate the first experimental complete temporal characterization of high-harmonic XUV pulses by spectral phase interferometry, with an all-optical setup. This method allows us to perform single-shot measurements of the harmonic temporal profile and phase, revealing a remarkable shot-to-shot stability. We characterize harmonics generated in argon by a 50 fs 800 nm laser pulse. The 11th harmonic is found to be 22 fs long with a negative chirp rate of -4.8 x 10(27) s(-2). This duration can be reduced to 13 fs by modulating the polarization of the generating laser. The technique is easy to implement and could be routinely used in femtosecond XUV pump-probe experiments with harmonics.     

Multiwavelength investigation of laser-damage performance in potassium dihydrogen phosphate after laser annealing

The laser-induced damage performance of potassium dihydrogen phosphate and deuterated potassium dihydrogen phosphate nonlinear optical crystals after pre-exposure to lower-energy laser pulses (laser annealing, also known as laser conditioning) is investigated as a function of wavelength for both the damaging and conditioning pulses. We obtain a quantitative evaluation of the bulk damage performance of these materials by measuring the density of damage events as a function of laser parameters. This new method allows for a detailed assessment of the improvement of material performance from laser conditioning and reveals the key parameters for optimizing performance depending on the operational wavelength.     

Orthomodular lattices from 3-dimensional quadratic spaces

If E is a vector space over a field K, then any regular symmetric bilinear form on E induces a polarity on the lattice of all subspaces of E. In the particular case where E is 3-dimensional, the set of all subspaces M of E such that both M and are not N-subspaces (which, in most cases, is equivalent to saying that M is nonisotropic), ordered by inclusion and endowed with the restriction of the above polarity, is an orthomodular lattice T(E, ). We show that if K is a proper subfield of K, with K F₂, and E a 3-dimensional K -subspace of E such that the restriction of to E × E is, up to multiplicative constant, a bilinear form on the K -space E , then T(E , ) is isomorphic to an irreducible 3-homogeneous proper subalgebra of T(E, ). Our main result is a structure theorem stating that, when K is not of characteristic 3, the converse is true, i.e., any irreducible 3-homogeneous proper subalgebra of T(E, ) is of this form. As a corollary, we construct infinitely many finite orthomodular lattices which are minimal in the sense that all their proper subalgebras are modular. In fact, this last result was our initial aim in this paper.Received June 4, 2003; accepted in final form May 18, 2004.     

Parity-violating electron deuteron scattering and the proton's neutral weak axial vector form factor

We report on a new measurement of the parity-violating asymmetry in quasielastic electron scattering from the deuteron at backward angles at Q2=0.038 (GeV/c)2. This quantity provides a determination of the neutral weak axial vector form factor of the nucleon, which can potentially receive large electroweak corrections. The measured asymmetry A=-3.51+/-0.57 (stat)+/-0.58 (syst) ppm is consistent with theoretical predictions. We also report on updated results of the previous experiment at Q2=0.091 (GeV/c)2, which are also consistent with theoretical predictions.     

Part I. Chromatography using ultra-stable metal oxide-based stationary phases for HPLC

The first part of the review contrasts the main drawbacks of silica-based packings such as their relative thermal and chemical instability with excellent stability of metal oxides. The paper concerns mainly ZrO2, TiO2 and Al2O3. Methods of preparation of spherical particles for HPLC are described. Surface chemistry of the oxides is, however, very different from that of silica. Ability of the oxides to ion- and ligand exchange is discussed from a chromatographic point of view.