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.     

New source of dense, cryogenic positron plasmas

We have developed a new method, based on the ballistic transfer of preaccumulated plasmas, to obtain large and dense positron plasmas in a cryogenic environment. The method involves transferring plasmas emanating from a region with a low magnetic field (0.14 T) and relatively high pressure (10(-9) mbar) into a 15 K Penning-Malmberg trap immersed in a 3 T magnetic field with a base pressure better than 10(-13) mbar. The achieved positron accumulation rate in the high field cryogenic trap is more than one and a half orders of magnitude higher than the previous most efficient UHV compatible scheme. Subsequent stacking resulted in a plasma containing more than 1.2 x 10(9) positrons, which is a factor 4 higher than previously reported. Using a rotating wall electric field, plasmas containing about 20 x 10(6) positrons were compressed to a density of 2.6 x 10(10) cm(-3). This is a factor of 6 improvement over earlier measurements.     

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.     

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.     

Uniqueness of travelling waves for nonlocal monostable equations

We consider a nonlocal analogue of the Fisher-KPP equation

0 ~{\rm on}~(0,1),\end{displaymath}">

and its discrete counterpart , , and show that travelling wave solutions of these equations that are bounded between and are unique up to translation. Our proof requires finding exact a priori asymptotics of a travelling wave. This we accomplish with the help of Ikehara's Theorem (which is a Tauberian theorem for Laplace transforms).

     

Wavelength dependence of laser-induced damage: determining the damage initiation mechanisms

A novel experimental approach is employed to understand the mechanisms of laser induced damage. Using an OPO (optical parametric oscillator) laser, we have measured the damage thresholds of deuterated potassium dihydrogen phosphate (DKDP) from the near ultraviolet into the visible. Distinct steps, whose width is of the order of k(B)T, are observed in the damage threshold at photon energies associated with the number of photons (3-->2 or 4-->3) needed to promote a ground state electron across the energy gap. The wavelength dependence of the damage threshold suggests that a primary mechanism for damage initiation in DKDP is a multiphoton process in which the order is reduced through excited defect state absorption.