A fast direct solver for elliptic problems with a divergence constraint

A fast direct solution method for a discretized vector‐valued elliptic partial differential equation with a divergence constraint is considered. Such problems are typical in many disciplines such as fluid dynamics, elasticity and electromagnetics. The method requires the problem to be posed in a rectangle and boundary conditions to be either periodic boundary conditions or the so‐called slip boundary conditions in one co‐ordinate direction. The arising saddle‐point matrix has a separable form when bilinear finite elements are used in the discretization. Based on a result for so‐called p‐circulant matrices, the saddle‐point matrix can be transformed into a block‐diagonal form by fast Fourier transformations. Thus, the fast direct solver has the same structure as methods for scalar‐valued problems which are based on Fourier analysis and, therefore, it has the same computational cost ??(N log N). Numerical experiments demonstrate the good efficiency and accuracy of the proposed method. Copyright © 2002 John Wiley & Sons, Ltd.     

Detailed investigation of the β-decay of the 9/2+ ground state of 99Nb to levels in 99Mo

The decay of ⁹⁹Nb to ⁹⁹Mo has been investigated. The use of the ion-guide technique for on-line mass separation and of a Ge-array for γ-ray detection have allowed the observation of decay branchings lower than 10^?3. Mediumspin levels, some already known from reaction studies and new ones at high energy, are populated. The β-feeding patterns of the decays of the 9/2⁺ states in ⁹⁹Nb and in its isotones ⁹⁷Y, and ¹⁰¹Tc are qualitatively reproduced by QRPA calculations.     

Numerical valuation of options under Kou's model

Numerical methods are developed for pricing European and American options under Kou's jump-diffusion model which assumes the price of the underlying asset to behave like a geometrical Brownian motion with a drift and jumps whose size is log-double-exponentially distributed. The price of a European option is given by a partial integro-differential equation (PIDE) while American options lead to a linear complementarity problem (LCP) with the same operator. Spatial differential operators are discretized using finite differences on nonuniform grids and time stepping is performed using the implicit Rannacher scheme. For the evaluation of the integral term easy to implement recursion formulas are derived which have optimal computational cost. When pricing European options the resulting dense linear systems are solved using a stationary iteration. Also for pricing American options similar iterations can be employed. A numerical experiment demonstrates that the described method is very efficient as accurate option prices can be computed in a few milliseconds on a PC. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Variations in the chemical composition within pine (Pinus sylvestris) trunks determined by diffuse reflectance infrared spectroscopy and chemometrics

The feasibility of using DRIFT (diffuse reflectance infrared Fourier transform) spectroscopy combined with a multivariate analysis method (a PLS (projection to latent structures), regression) for predicting the distribution of the main organic constituents (cellulose, glucomannan, xylan, lignin, and extractives) within the Scots pine (Pinus sylvestris) stemwood was examined. PLS calibrations were carried out to establish a mathematical correlation between the data sets of conventional (“wet-chemistry-based”) wood analysis and the DRIFT spectra of the corresponding wood samples. Based on this approach, different surface maps on variations in the content of the main organic constituents within the stemwood matrix were shown.     

Nuclear shell model applied to metallic clusters

We apply the nuclear shell model to jellium clusters of up to twenty-one Na atoms. Binding energies, ionization potentials, and photoabsorption cross sections are calculated and compared with mean-field results.     

Theoretical LSP detection rates for dark-matter detectors

Low-energy structure of the dark-matter detector nuclei ⁷¹Ga, ⁷³Ge and ¹²⁷I has been studied by using the nuclear shell model. The calculations have been done in realistic model spaces by using renormalized microscopic two-body interactions. The resulting ground states have been used to calculate theoretical predictions for detection rates of the lightest supersymmetric particle (LSP) in experiments studying elastic scattering of the LSP’s from atomic nuclei. Presented by T.S. Kosmas at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’05), Corfu, Greece, September 26–29, 2005.     

Theoretical LSP detection rates for <Superscript>71</Superscript>Ga, <Superscript>73</Superscript>Ge,and <Superscript>127</Superscript>I dark-matter detectors

The low-energy structure of the dark-matter detector nuclei ⁷¹Ga, ⁷³Ge, and ¹²⁷I has been studied by using the microscopic quasiparticle-phonon model. The resulting ground states have been used to calculate theoretical predictions for detection rates of the lightest supersymmetric particle (LSP) in experiments studying elastic scattering of an LSP from an atomic nucleus. The highest rate, approximately 0.27 yr^?1kg^?1, among all the adopted SUSY parameters and renormalization schemes was provided by ¹²⁷I at the zero limit of the detector energy threshold.     

Characterisation of optical detectors using high-accuracy instruments

The facilities of the Metrology Research Institute at the Helsinki University of Technology, and methods for characterisation of optical detectors for spectral radiant intensity and irradiance responsivity, are described. The instrumentation for such characterisations includes a reference spectrometer with a number of auxiliary set-ups, and equipment for the spectral irradiance measurements with a filter radiometer based on a trap detector. The methods of realising the spectral responsivity scales based on an absolute cryogenic radiometer in house are addressed. The procedures and results of characterisation of a multipoint measuring system of photosynthetically active radiation, by employing the available facilities, are briefly described. The absolute irradiance responsivity of the device is determined by using a photometric lamp, whose spectral irradiance has been measured with the filter radiometer. The combined standard uncertainty of this set of calibrations is 3.6% at the 1σ level. The uncertainty is caused almost completely by the multipoint measuring system.     

Optimal shape design in a fibre orientation model

We study a 2D model of the orientation distribution of fibres in a paper machine headbox. The goal is to control the orientation of fibres at the outlet by shape variations. The mathematical formulation leads to an optimization problem with control in coefficients of a linear convection-diffusion equation as the state problem. Existence of solutions both to the state and the optimization problem is analyzed and sensitivity analysis is performed. Further, discretization is done and a numerical example is shown. This research was supported by the Charles University Grant Agency under Contract 6/2005/R, MSM 0021620839 (MŠMT ČR), and the Academy of Finland, Grant #204741.