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    Longitudinal dynamics of semiconductor lasers
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2001) Philip, Jan
    We investigate the longitudinal dynamics of semiconductor lasers using a model which couples a hyperbolic linear system of partial differential equations nonlinearly with ordinary differential equations. We prove the global existence and uniqueness of solutions using the theory of strongly continuous semigroups. Subsequently, we analyse the long-time behavior of the solutions in two steps. First, we find attracting invariant manifolds of low dimension benefitting from the fact that the system is singularly perturbed, i. e., the optical and the electronic variables operate on differente time-scales. The flow on these manifolds can be approximated by the so-called mode approximations. The dimension of these mode approximations depends on the number of critical eigenvalues of the linear hyperbolic operator. Next, we perform a detailed numerical and analytic bifurcation analysis for the two most common constellations. Starting from known results for the single-mode approximation, we investigate the two-mode approximation in the special case of a rapidly rotating phase difference between the two optical components. In this case, the first-order averaged model unveils the mechanisms for various phenomena observed in simulations of the complete system. Moreover, it predicts the existence of a more complex spatio-temporal behavior. In the scope of the averaged model, this is a bursting regime.
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    TetGen : a quality tetrahedral mesh generator and three-dimensional delaunay triangulator version 1.3 user's manual
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2004) Si, Hang
    TetGen is a quality tetrahedral mesh generator and 3-dimensional Delaunay triangulator. Based on the the-state-of-the-art algorithms for Delaunay tetrahedralization and mesh generation, this program has been specifically designed to fulfill the task of automatically generating high quality tetrahedral meshes, which are suitable for scientific computing using numerical methods such as finite element and finite volume methods. The purpose of this document is to give a brief explanation of the problems solved by TetGen and to provide a detailed user's documentation. In this document, the user will learn how to create tetrahedral meshes using TetGen's input files and command line switches. In the following section, the programming interface of TetGen for calling TetGen from another program is explained. Various examples are given to simplify the ``getting started''.
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    Simulation der Strahlhärtung von Stahl mit WIAS-SHarP
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2002) Buchwalder, A.; Hömberg, D.; Jurke, Th.; Spies, H.-J.; Weiss, W.
    Die Software WIAS-SHarP zur Simulation der Oberflaechenhaertung von Stahl mit Laser- und Elektronenstrahl wurde im Rahmen eines zweijaehrigen interdisziplinaeren Forschungsprojektes entwickelt. Das zugrunde liegende mathematische Modell besteht aus einem System gewoehnlicher Differentialgleichungen zur Beschreibung der Gefuegeumwandlungen, gekoppelt mit einer nichtlinearen Waermeleitungsgleichung sowie Komponenten zur Beschreibung der Energieeinkopplung. Um eine moeglichst breite Anwendbarkeit der Software zu gewaehrleisten, wurden werkstoffspezifische Kennwerte zum Umwandlungsverhalten fuer eine grosse Anzahl praxisrelevanter Staehle bereitgestellt. Zur Modellverifikation wurden experimentelle Untersuchungen bei beteiligten Industriepartnern durchgefuehrt und mit den entsprechenden Simulationsrechnungen verglichen.
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    3D-Simulation von Halbleiterdetektoren : Schlussbericht
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2001) Gajewski, Herbert
    [no abstract available]
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    Analysing fMRI experiments with the fmri package in R. version 1.0 : a user's guide
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Polzehl, Jörg; Tabelow, Karsten
    This document describes the usage of the R package fmri to analyse functional Magnetic Resonance Imaging (fMRI) data with structure adaptive smoothing procedures (Propagation-Separation (PS) approach) as described in [7].
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    Classification and clustering: models, software and applications
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Mucha, Hans-Joachim; Ritter, Gunter
    We are pleased to present the report on the 30th Fall Meeting of the working group ``Data Analysis and Numerical Classification'' (AG-DANK) of the German Classification Society. The meeting took place at the Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin, from Friday Nov. 14 till Saturday Nov. 15, 2008. Already 12 years ago, WIAS had hosted a traditional Fall Meeting with special focus on classification and multivariate graphics (Mucha and Bock, 1996). This time, the special topics were stability of clustering and classification, mixture decomposition, visualization, and statistical software.
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    TetGen : a 3D Delaunay tetrahedral mesh generator version 1.2 user's manual
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2002) Si, Hang
    This technical report describes the main features and the using of TetGen, a 3D Delaunay tetrahedral mesh generator. Based on the most recent developments in mesh generation algorithms, this program has been specifically designed to fulfill the task of automatically generating high quality tetrahedral meshes, which are suitable for scientific computing using numerical methods such as finite element and finite volume methods. In this document, the user will learn how to create 3D tetrahedral meshes using TetGen's input files and command line switches. Various examples were given for better understanding. This document describes the features of the version 1.2.
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    Effiziente Methoden zur Bestimmung von Risikomaßen : Schlussbericht ; Projekt des BMBF-Förderprogramm "Neue Mathematische Verfahren in Industrie und Dienstleistungen"
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2004) Schoenmakers, John; Spokoiny, Vladimir; Reiß, Oliver; Zacherias-Langhans, Johan-Hinrich
    [no abstract available]
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    Algebraische Modellierung von Tonsystemen : Musiktheorie mit mathematischen Mitteln
    (Mühltal : Verl. Allgemeine Wissenschaft, 2009) Winkler, Jan Thomas
    Das vorliegende Buch stellt Möglichkeiten einer algebraischen Modellierung von Tonsystemen vor. Dazu wird zunächst die von Rudolf Wille und Wilfried Neumaier formulierte extensionale Standardsprache der Musiktheorie aufbereitet und ein breites Spektrum musiktheoretischer Begriffe mathematisch gefasst. Diese Begriffe werden in ihrem Bezug zu Tonsystemen dargestellt und ausführlich analysiert. Zum Abschluss des Buches wird eine Interpretation von Tonsystemen in der Kategorientheorie formuliert und eine einfache Möglichkeit vorgestellt, strukturerhaltende Abbildungen zwischen Tonsystem-Kategorien zu konstruieren.
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