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Fri, 23 Jun 2000 00:00:00 +0200Fri, 23 Jun 2000 00:00:00 +0200An Overview of the Method of Smoothed Particle Hydrodynamics
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/585
This report is intended to provide an introduction to the method of SmoothedParticle 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.J.P. Morrispreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/585Fri, 23 Jun 2000 00:00:00 +0200Direct Coupling of Fluid and Kinetic Equations: I
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/556
J. Schneiderpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/556Wed, 07 Jun 2000 00:00:00 +0200A Model for the Cloudiness of Fabrics
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/562
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.Joachim Weickertarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/562Wed, 07 Jun 2000 00:00:00 +0200Locally Supported Kernels for Spherical Spline Interpolation
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/572
By the use of locally supported basis functions for spherical spline interpolation the applicability of this approximation method is spread out since the resulting interpolation matrix is sparse and thus efficient solvers can be used. In this paper we study locally supported kernels in detail. Investigations on the Legendre coefficients allow a characterization of the underlying Hilbert space structure. We show now spherical spline interpolation with polynomial precision can be managed with locally supported kernels, thus giving the possibility to combine approximation techniques based on spherical harmonic expansions with those based on locally supported kernels.Michael Schreinerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/572Wed, 07 Jun 2000 00:00:00 +0200On a New Condition for Strictly Positive Definite Functions on Spheres
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/573
Recently, Xu and Cheney (1992) have proved that if all the Legendre coefficients of a zonal function defined on a sphere are positive then the function is strictly positive definite. It will be shown in this paper, that even if finitely many of the Legendre coefficients are zero, the strict positive definiteness can be assured. The results are based on approximation properties of singular integrals, and provide also a completely different proof of the results ofXu and Cheney.Michael Schreinerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/573Wed, 07 Jun 2000 00:00:00 +0200Learning and Replication of Periodic Signals in Neural-Like Networks
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/575
The paper describes the concepts and background theory for the analysis of a neural-like network for learning and replication of periodic signals containing a finite number of distinct frequency components. The approach is based on the combination of ideas from dynamic neural networks and systems and control theory where concepts of dynamics, adaptive control and tracking of specified time signals are fundamental. The proposed procedure is a two stage process consisting of a learning phase when the network is driven by the required signal followed by a replication phase where the network operates in an autonomous feedback mode whilst continuing to generate the required signal to a desired acccuracy for a specified time. The analysis draws on currently available control theory and, in particular, on concepts from model reference adaptive control.R. Reinke; D.H. Owens; D. Prätzel-Wolterspreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/575Wed, 07 Jun 2000 00:00:00 +0200Lectures on the Problem of Space and Time in Einstein" s Theory of Gravitation
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/578
C. Müllerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/578Wed, 07 Jun 2000 00:00:00 +0200The Solution of Linear Inverse Problems in Satellite Geodesy by Means of Spherical Spline Approximation
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/581
In this paper we consider a certain class of geodetic linear inverse problems LambdaF=G in a reproducing kernel Hilbert space setting to obtain a bounded generalized inverse operator Lambda. For a numerical realization we assume G to be given at a finite number of discrete points to which we employ a spherical spline interpolation method adapted to the Hilbertspaces. By applying Lambda to the obtained spline interpolant we get an approximation of the solution F. Finally our main task is to show some properties of the approximated solution and to prove convergence results if the data set increases.F. Schneiderpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/581Wed, 07 Jun 2000 00:00:00 +0200The Mathematical Simulation of an Electrolytic Cell for Aluminium Production
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/583
A. Buikis; H. Kalispreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/583Wed, 07 Jun 2000 00:00:00 +0200Periodic Signals in Neural-Like Networks - an Averaging Analysis
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/587
The paper describes the concepts and background theory of the analysis of a neural-like network for the learning and replication of periodic signals containing a finite number of distinct frequency components. The approach is based on a two stage process consisting of a learning phase when the network is driven by the required signal followed by a replication phase where the network operates in an autonomous feedback mode whilst continuing to generate the required signal to a desired accuracy for a specified time. The analysis focusses on stability properties of a model reference adaptive control based learning scheme via the averaging method. The averaging analysis provides fast adaptive algorithms with proven convergence properties.R. Reinke; D. Prätzel-Wolterspreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/587Wed, 07 Jun 2000 00:00:00 +0200Holomorphie und Laplace Transformation banachraumwertiger Funktionen
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/480
Peter Vietendoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/480Mon, 03 Apr 2000 00:00:00 +0200A: New Wavelet Methods for Approximating Harmonic Functions; B: Satellite Gradiometry - from Mathematical and Numerical Point of View
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/537
Some new approximation methods are described for harmonic functions corresponding to boundary values on the (unit) sphere. Starting from the usual Fourier (orthogonal) series approach, we propose here nonorthogonal expansions, i.e. series expansions in terms of overcomplete systems consisting of localizing functions. In detail, we are concerned with the so-called Gabor, Toeplitz, and wavelet expansions. Essential tools are modulations, rotations, and dilations of a mother wavelet. The Abel-Poisson kernel turns out to be the appropriate mother wavelet in approximation of harmonic functions from potential values on a spherical boundary.Willi Freeden; Michael Schreinerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/537Mon, 03 Apr 2000 00:00:00 +0200Second Order Scheme for the Spatially Homogeneous Boltzmann Equation with Maxwellian Molecules
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/557
In the standard approach, particle methods for the Boltzmann equation are obtained using an explicit time discretization of the spatially homogeneous Boltzmann equation. This kind of discretization leads to a restriction of the discretization parameter as well as on the differential cross section in the case of the general Boltzmann equation. Recently, it was shown, how to construct an implicit particle scheme for the Boltzmann equation with Maxwellian molecules. The present paper combines both approaches using a linear combination of explicit and implicit discretizations. It is shown that the new method leads to a second order particle method, when using an equiweighting of explicit and implicit discretization.Jens Struckmeier; Konrad Steinerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/557Mon, 03 Apr 2000 00:00:00 +0200Numerical Simulation of the Stationary One-Dimensional Boltzmann Equation by Particle Methods
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/558
The paper presents a numerical simulation technique - based on the well-known particle methods - for the stationary, one-dimensional Boltzmann equation for Maxwellian molecules. In contrast to the standard splitting methods, where one works with the instationary equation, the current approach simulates the direct solution of the stationary problem. The model problem investigated is the heat transfer between two parallel plates in the rarefied gas regime. An iteration process is introduced which leads to the stationary solution of the exact - space discretized - Boltzmann equation, in the sense of weak convergence.Jens Struckmeier; A.V. Bobylevpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/558Mon, 03 Apr 2000 00:00:00 +0200Normalized Coprime Factorizations in Continuous and Discrete Time - A Joint State-Space Approach
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/559
Based on state-space formulas for coprime factorizations over ... and an algebraic characterization of J-inner functions, normalized doubly-coprime factorizations for different classes of continuous- and discrete-time transfer functions are derived by using a single general construction method. The parametrization of the factors is in terms of the stabilizing solutions of general degenerate continuous- respectively discrete-time Riccati equations, which are obtained by examining state-space representations of J-normalized factor matrices.Jörg Hoffmannpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/559Mon, 03 Apr 2000 00:00:00 +0200Wavelet Thresholding: Beyond the Gaussian I.I.D. Situation
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/564
With this article we first like to give a brief review on wavelet thresholding methods in non-Gaussian and non-i.i.d. situations, respectively. Many of these applications are based on Gaussian approximations of the empirical coefficients. For regression and density estimation with independent observations, we establish joint asymptotic normality of the empirical coefficients by means of strong approximations. Then we describe how one can prove asymptotic normality under mixing conditions on the observations by cumulant techniques.; In the second part, we apply these non-linear adaptive shrinking schemes to spectral estimation problems for both a stationary and a non-stationary time series setup. For the latter one, in a model of Dahlhaus on the evolutionary spectrum of a locally stationary time series, we present two different approaches. Moreover, we show that in classes of anisotropic function spaces an appropriately chosen wavelet basis automatically adapts to possibly different degrees of regularity for the different directions. The resulting fully-adaptive spectral estimator attains the rate that is optimal in the idealized Gaussian white noise model up to a logarithmic factor.Michael H. Neumann; Rainer von Sachsarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/564Mon, 03 Apr 2000 00:00:00 +0200Stochastic Reconstruction of Loading Histories from a Rainflow Matrix
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/565
This paper is devoted to the mathematica l description of the solution of the so-called rainflow reconstruction problem, i.e. the problem of constructing a time series with an a priori given rainflow m atrix. The algorithm we present is mathematically exact in the sense that no app roximations or heuristics are involved. Furthermore it generates a uniform distr ibution of all possible reconstructions and thus an optimal randomization of the reconstructed series. The algorithm is a genuine on-line scheme. It is easy adj ustable to all variants of rainflow such as sysmmetric and asymmetric versions a nd different residue techniques.Klaus Dreßler; Michael Hack; Wilhelm Krügerarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/565Mon, 03 Apr 2000 00:00:00 +0200Fatigue Lifetime Estimation Based on Rainflow Counted Data Using the Local Strain Approach
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/566
In the automotive industry both the loca l strain approach and rainflow counting are well known and approved tools in the numerical estimation of the lifetime of a new developed part especially in the automotive industry. This paper is devoted to the combination of both tools and a new algorithm is given that takes advantage of the inner structure of the most used damage parameters.Klaus Dreßler; Michael Hackarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/566Mon, 03 Apr 2000 00:00:00 +0200Asymptotic-Induced Domain Decomposition Methods for Kinetic and Drift Diffusion Semiconductor Equations
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/568
This paper deals with domain decomposition methods for kinetic and drift diffusion semiconductor equations. In particular accurate coupling conditions at the interface between the kinetic and drift diffusion domain are given. The cases of slight and strong nonequilibrium situations at the interface are considered and some numerical examples are shown.Axel Klarpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/568Mon, 03 Apr 2000 00:00:00 +0200A Kinetic Model for Vehicular Traffic Derived from a Stochastic Microscopic Model
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/569
A way to derive consistently kinetic models for vehicular traffic from microscopic follow the leader models is presented. The obtained class of kinetic equations is investigated. Explicit examples for kinetic models are developed with a particular emphasis on obtaining models, that give realistic results. For space homogeneous traffic flow situations numerical examples are given including stationary distributions and fundamental diagrams.R. Wegener; Axel Klarpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/569Mon, 03 Apr 2000 00:00:00 +0200Multiscale Texture Enhancement
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/570
The ideas of texture analysis by means of the structure tensor are combined with the scale-space concept of anisotropic diffusion filtering. In contrast to many other nonlinear diffusion techniques, the proposed one uses a diffusion tensor instead of a scalar diffusivity. This allows true anisotropic behaviour. The preferred diffusion direction is determined according to the phase angle of the structure tensor. The diffusivity in this direction is increasing with the local coherence of the signal. This filter is constructed in such a way that it gives a mathematically well-funded scale-space representation of the original image. Experiments demonstrate its usefulness for the processing of interrupted one-dimensional structures such as fingerprint and fabric images.Joachim Weickertarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/570Mon, 03 Apr 2000 00:00:00 +0200Equidistribution on the Sphere
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/574
A concept of generalized discrepancy, which involves pseudodifferential operators to give a criterion of equidistributed pointsets, is developed on the sphere. A simply structured formula in terms of elementary functions is established for the computation of the generalized discrepancy. With the help of this formula five kinds of point systems on the sphere, namely lattices in polar coordinates, transformed 2-dimensional sequences, rotations on the sphere, triangulation, and sum of three squares sequence, are investigated. Quantitative tests are done, and the results are compared with each other. Our calculations exhibit different orders of convergence of the generalized discrepancy for different types of point systems.Willi Freeden; J. Cuipreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/574Mon, 03 Apr 2000 00:00:00 +0200Combined Spherical Harmonic and Wavelet Expansion - a Future Concepts in Earth" s Gravitational Determination
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/576
The basic theory of spherical singular integrals is recapitulated. Criteria are given for measuring the space-frequency localization of functions on the sphere. The trade off between space localization on the sphere and frequency localization in terms of spherical harmonics is described in form of an uncertainty principle. A continuous version of spherical multiresolution is introduced, starting from continuous wavelet transform corresponding to spherical wavelets with vanishing moments up to a certain order. The wavelet transform is characterized by least-squares properties. Scale discretization enables us to construct spherical counterparts of wavelet packets and scale discrete Daubechies" wavelets. It is shown that singular integral operators forming a semigroup of contraction operators of class (Co) (like Abel-Poisson or Gauß-Weierstraß operators) lead in canonical way to pyramyd algorithms. Fully discretized wavelet transforms are obtained via approximate integration rules on the sphere. Finally applications to (geo-)physical reality are discussed in more detail. A combined method is proposed for approximating the low frequency parts of a physical quantity by spherical harmonics and the high frequency parts by spherical wavelets. The particular significance of this combined concept is motivated for the situation of today" s physical geodesy, viz. the determination of the high frequency parts of the earth" s gravitational potential under explicit knowledge of the lower order part in terms of a spherical harmonic expansion.Willi Freeden; U. Windheuserpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/576Mon, 03 Apr 2000 00:00:00 +0200Statistische Mechanik und kinetische Gleichungen auf quantenmechanischer Grundlage
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/579
R. Wegenerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/579Mon, 03 Apr 2000 00:00:00 +0200Simulation of Boundary Value Problems for the Boltzmann Equation
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/580
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.Jens Struckmeierpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/580Mon, 03 Apr 2000 00:00:00 +0200