A parallel version of the preconditioned conjugate gradient method for boundary element equations

The parallel version of precondition techniques is developed for matrices arising from the Galerkin boundary element method for two-dimensional domains with Dirichlet boundary conditions. Results were obtained for implementations on a transputer network as well as on an nCUBE-2 parallel computer showing that iterative solution methods are very well suited for a MIMD computer. A comparison of numerical results for iterative and direct solution methods is presented and underlines the superiority of iterative methods for large systems.     

The role of the pion cloud in the interpretation of the valence light-cone wavefunction of the nucleon

The pion cloud renormalises the light-cone wavefunction of the nucleon which is measured in hard, exclusive photon-nucleon reactions. We discuss the leading twist contributions to high-energy exclusive reactions taking into account both the pion cloud and perturbative QCD physics. The nucleon’s electromagnetic form-factor at high Q² is proportional to the bare nucleon probability Z and the cross-sections for hard (real at large angle or deeply virtual) Compton scattering are proportional to Z². Our present knowledge of the pion-nucleon system is consistent with Z = 0.7 ± 0.2. If we apply just perturbative QCD to extract a light-cone wavefunction directly from these hard exclusive cross-sections, then the light-cone wavefunction that we extract measures the three valence quarks partially screened by the pion cloud of the nucleon. We discuss how this pion cloud renormalisation effect might be understood at the quark level in terms of the (in-)stability of the perturbative Dirac vacuum in low energy QCD.     

Intra-cavity spectroscopy with diode lasers

A multi-mode diode laser with an external cavity is studied experimentally and theoretically for its application to intra-cavity spectroscopy. One facet of a typical Ga_0.89Al_0.11As laser diode was antireflection-coated by deposition of HfO₂ such that 10^–3 residual reflectivity was left over. This diode was placed in an external optical cavity. The emission spectrum of this diode laser is highly sensitive to any frequency-dependent loss in the cavity, and the detectivity of such a loss grows with the pump rate. Even close to threshold, the absorption at 780 nm of Rb atoms with a density of 5×10¹⁰ cm^–3 has been detected. An adequate model for diode lasers based on rate equations and including frequency-dependent gain saturation is developed and applied to the calculations of output spectra. The sensitivity of these spectra to intra-cavity absorption is determined by the overall cavity loss — which is rather high — and the fraction of spontaneous emission in the total emission, in contrast with dye lasers where it is limited by nonlinear mode coupling. Various criteria for the sensitivity are suggested. The smallest detectable absorption with a perfectly antireflection-coated laser is 10^–6 cm^–1. Improvement of the characteristics of the laser diode would increase the sensitivity.     

Bivariate Free Knot Splines

We consider the least squares approximation of gridded 2D data by tensor product splines with free knots. The smoothing functional to be minimized—a generalization of the univariate Schoenberg functional—is chosen in such a way that the solution of the bivariate problem separates into the solution of a sequence of univariate problems in case of fixed knots. The resulting optimization problem is a constrained separable least squares problem with tensor product structure. Based on some ideas developed by the authors for the univariate case, an efficient method for solving the specially structured 2D problem is proposed, analyzed and tested on hand of some examples from the literature.     

Monstrous Branes

 We study D-branes in the bosonic closed string theory whose automorphism group is the Bimonster group (the wreath product of the Monster simple group with ℤ₂). We give a complete classification of D-branes preserving the chiral subalgebra of Monster invariants and show that they transform in a representation of the Bimonster. Our results apply more generally to self-dual conformal field theories which admit the action of a compact Lie group on both the left- and right-moving sectors. Received: 20 February 2002 / Accepted: 17 August 2002 Published online: 19 December 2002 Communicated by R.H. Dijkgraaf     

Realisation and metrological characterisation of thickness standards below 100 nm

High-accuracy film thickness measurements in the range below 100 nm can be made by various complex methods like spectral ellipsometry (SE), scanning force microscopy (SFM), grazing incidence X-ray reflectometry (GIXR), or X-ray fluorescence analysis (XRF). The measurement results achieved with these methods are based on different interactions between the film and the probe. A key question in nanotechnology is how to achieve consistent results on a level of uncertainty below one nanometre with different techniques.Two different types of thickness standards are realised. Metal film standards for X-ray techniques in the thickness range 10 to 50 nm are calibrated by GIXR with monochromatised synchrotron radiation of 8048 eV. The results obtained at four different facilities show excellent agreement. SiO₂ on Si standards for SE and SFM in the thickness range 6 to 1000 nm are calibrated by GIXR with monochromatised synchrotron radiation of 1841 eV and with a metrological SFM. Consistent results within the combined uncertainties are obtained with the two methods. Surfaces and interfaces of both types of standards are additionally investigated by transmission electron microscopy (TEM). PACS 61.10.Kw; 68.55.Jk; 06.20.Fn; 06.60.Mr; 07.79.Lh     

Effective-field theory and the nuclear many-body problem

We review many-body calculations of the equation of state of dilute neutron matter in the context of effective-field theories of the nucleon-nucleon interaction.