Wavelet smoothing of evolutionary spectra by non-linear thresholding

We consider wavelet estimation of the time-dependent (evolutionary) power spectrum of a locally stationary time series in a model which was recently introduced by Dahlhaus. Allowing for departures from stationarity proves useful for modelling, e.g., transient phenomena, quasi-oscillating behavior or spectrum modulation. In contrast to classical parametric and nonparametric (linear) approaches we use nonlinear thresholding of the empirical wavelet coefficients of the evolutionary spectrum. We show how these techniques allow for both adaptively reconstructing the local structure in the time-frequency plane and for denoising the resulting estimates. To this end a threshold choice is derived which is motivated by minimax properties w.r.t. the integrated mean squared error. Our approach is based on a 2-d orthogonal wavelet transform modified by using a cardinal Lagrange interpolation function on the finest scale. As an example, we apply our procedure to a time-varying spectrum motivated from mobile radio propagation. (orig.)SIGLEAvailable from TIB Hannover: RO 5810(106)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

An overview of the method of smoothed particle hydrodynamics

The numerical method, SPH, was first developed to model astrophysical problems. It has since been successfully applied to a vast range of problems, including elastic-plastic flow, MHD, incompressible flow and pyroclastic flow, to name a few. SPH is an extremely versatile method, however, the errors in results can sometimes be substantially larger than those obtained using methods specifically tailored for a given problem. There are many problems, though, which can only be practically handled by SPH. Problems where the geometry is highly irregular, or even dynamic, for example, are quite readily handled by SPH. It is hoped that this report will give the reader some insight into the potential of SPH and its limitations. This report is intended to provide an introduction to the method of Smoothed Particle Hydrodynamics or SPH. SPH is a very versatile, fully Lagrangian, particle based code for solving fluid dynamical problems. Many technical aspects of the method are explained which can then be employed to extend the application of SPH to new problems. (orig.)Available from TIB Hannover: RO 5810(152)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

On the cohomology of nilpotent Lie algebras

SIGLECopy held by FIZ Karlsruhe; available from UB/TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

A model for the cloudiness of fabrics

Cloudy inhomogenities in artificial fabrics are graded by a fast method which is based on a Laplacian pyramid decomposition of the fabric image. This band-pass representation takes into account the scale character of the cloudiness. A quality measure of the entire cloudiness is obtained as a weighted mean over the variances of all scales. (orig.)Available from TIB Hannover: RO 5810(131)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Weighted particle methods solving kinetic equations for dilute ionized gases

SIGLEAvailable from TIB Hannover: RO 5810(155)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Convergence of alternating domain decomposition schemes for kinetic and aerodynamic equations

A domain decomposition scheme linking linearized kinetic and aerodynamic equations is considered. Convergence of the alternating scheme is shown. Moreover the physical correctness of the obtained coupled solutions is discussed. (orig.)Available from TIB Hannover: RO 5810(117)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Simulation of boundary value problems for the Boltzmann equation

The paper presents numerical results on the simulation of boundary value problems for the Boltzmann equation in one and two dimensions. In the one-dimensional case, we use prescribed fluxes at the left and diffusive conditions on the right end of a slab to study the resulting steady state solution. Moreover, we compute the numerical density function in velocity space and compare the result with the Chapman-Enskog distribution obtained in the limit for continuous media. The aim of the two-dimensional simulations is to investigate the possibility of a symmetry break in the numerical solution. (orig.)Available from TIB Hannover: RO 5810(148)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Line bundles and syzygies of trigonal curves

SIGLECopy held by FIZ Karlsruhe; available from UB/TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Quasistationary solutions of the Boltzmann equation

Equations of quasistationary hydrodynamics are derived from the Boltzmann equation by using the modified Hilbert approach. The physical and mathematical meaning of quasistationary solutions are discussed in detail. (orig.)Available from TIB Hannover: RO 5810(124)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Generation of random variates using asymptotic expansions

Monte-Carlo methods are widely used numerical tools in various fields of application, like rarefied gas dynamics, vacuum technology, stellar dynamics or nuclear physics. A central part in all applications is the generation of random variates according to a given probability law. Fundamental techniques to generate non-uniform random variates are the inversion principle or the acceptance-rejection method. Both procedures can be quite time-consuming if the given probability law has a complicated structure. In this paper we consider probability laws depending on a small parameter and investigate the use of asymptotic expansions to generate random variates. The results given in the paper are restricted to first order expansions. We show error estimates for the discrepancy as well as for the bounded Lipschitz distance of the asymptotic expansion. Furthermore the integration error for some special classes of functions is given. The efficiency of the method is proofed by a numerical example from rarefied gas flows. (orig.)Available from TIB Hannover: RO 5810(107)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman