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- Kaiserslautern - Fachbereich Mathematik (608)
- Kaiserslautern - Fachbereich Informatik (346)
- Kaiserslautern - Fachbereich Physik (159)
- Fraunhofer (ITWM) (19)
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Mathematische Weiterbildung
(1984)
Ziel des Modellversuchs war es, zu untersuchen, welche Ergebnisse der mathematischen Forschung an Universitäten für den Praktiker besser zugänglich gemacht werden sollten und wie dies geschehen kann. Als Zielgruppen einer solchen Bildungsaufgabe waren insbesondere Ingenieure in den Forschungs- und Entwicklungsabteilungen der Industrie und Studenten der Mathematik und Technik (im Sinne einer mehr praxisbezogenen Ausbildung) vorgesehen; in organisatorischer Hinsicht war an ein Fernstudium gedacht.
Bei den bisherigen Untersuchungen auf dem Gebiet der passiven Solarnutzung mit speicherfähigen gemauerten Ziegelwänden stellte sich heraus, daß direkt im Strahlengang der Sonnenstrahlung liegende Wandbauteile keine ausreichende Speicherwirkung haben. Ausreichend heißt: Schnelle Wärmeabführung in eine Wärmesenke, ausreichende Speicherkapazität als Tagesspeicher. Abhilfe schaffen hier Latentspeicher oder großvolumige Wasserspeicher. In unserem konkreten Fall stand ein Texxor-Latentspeicher mit 2 l Inhalt und 100 Wh Kapazität bei 27oC in einem Poroton-Formstein zur Verfügung.
In diesem Projekt soll die Bildung von Wirbeln bei der Strömung eines Gases um eine Ecke numerisch untersucht werden. Dabei sollen verschiedene numerische Verfahren getestet und die Ergebnisse mit Versuchsdaten verglichen werden. Ferner soll untersucht werden, wie gut sich diese Verfahren vektorisieren lassen, da kompliziertere zweidimensionale und selbst einfache dreidimensionale Probleme der Strömungsdynamik auf den heute üblichen Universalrechnern nicht mit vertretbarem Zeitaufwand zu lösen sind, besonders, wenn, wie an der Universität Kaiserslautern, nur eine relativ langsame Anlage (Siemens 7551/7561) zur Verfügung steht. Die numerischen Rechnungen werden auf der CYBER 205 in Karlsruhe durchgeführt.
Fast reconstruction formulae in x-ray computerized tomography demand the directions, in which the measurements are taken, to be equally distributed over the whole circle. In many applications data can only be provided in a restricted range. Here the intrinsic difficulties are studied by giving a singular value decomposition of the Radon transform in a restricted range. Practical limitations are deduced.
The Trippstadt Problem
(1984)
Close to Kaiserslautern is the town of Trippstadt, which, together with five other small towns forms a local administration unit (Verbandsgemeinde) called Kaiserslautern-Süd. Trippstadt has its own beautiful public swimming pool, which causes problems though; the cost for the upkeep of the pool is higher than the income and thus has to be divided among the towns belonging to the Verbandsgemeinde. Because of this problem the administration wanted to find out which fraction of the total number of pool visitors came from the different towns. They planned to ask each pool guest where he came from. They did this for only three days though because the waiting lines at the cashiers became unbearably long and they could see that because of this the total number of guests would decrease. Then they wondered how to find a better method to get the same data and that was when I was asked to help with the solution of the problem.
Die Aufgabe dieses Projektes ist die Untersuchung des Schallfeldes, das sich in einem geschlossenen Quader bei Erregung durch eine punktförmige Schallquelle einstellt. Eine zentrale Rolle spielt hierbei die Wechselwirkung zwischen dem Schallfeld und den Quaderplatten, die zu Schwingungen angeregt werden und so dem Schallfeld Energie entziehen. Der Zweck dieser Untersuchung ist, Erkenntnisse für die Berechnung des Innendrucks zu Fahrzeugkarosserien zu gewinnen. Dies muß bei der Dimensionierung des Quaders und bei der Wahl des Plattenmaterials berücksichtigt werden. Numerische Berechnungen des Schalldrucks in einem Quader wurden beispielsweise in [1] durchgeführt. Das Ergebnis zeigt, daß zwei Arten von Resonanzen auftreten: Zum einen Strukturresonanzen, die durch Eigenschwingungen der Wände hervorgerufen werden und die von den Wandabmessungen und dem Plattenmaterial abhängen, zum anderen Hohlraumresonanzen, die auftreten, wenn die Luftwellenlänge in einem geeigneten Verhältnis zu den Abmessungen des Hohlraums steht. Es ist sehr zweifelhaft, welche Rückschlüsse gezogen werden können von den numerischen Resultaten in [1] auf kompliziertere Geometrien, wie sie bei Fahrzeugkarosserien vorliegen. Eine tiefere Einsicht in die Kopplung zwischen Schallfeld und Plattenschwingungen vor allem in den Resonanzbereichen ist nur zu erwarten, wenn die Berechnung dieser Wechselwirkung weitgehend analytisch durchgeführt wird. Eine solche analytische Berechnung ist das Ziel dieses Projektes.
In diesem Projekt soll die Bildung von Wirbeln bei der Strömung eines Gases um eine Ecke numerisch untersucht werden. Dabei sollen verschiedene numerische Verfahren getestet und die Ergebnisse mit Versuchsdaten verglichen werden. Ferner soll untersucht werden, wie gut sich diese Verfahren vektorisieren lassen, da komplizierte zweidimensionale und selbst einfache dreidimensionale Probleme der Strömungsdynamik auf den heute üblichen Universalrechnern nicht mit vertretbarem Zeitaufwand zu lösen sind. Die numerischen Berechnungen werden auf der CYBER 205 in Karlsruhe durchgeführt.
In these notes we will discuss some aspects of a problem arising in carindustry. For the sake of clarity we will set the problem into an extremely simplified scheme. Suppose that we have a body which is emitting sound, and that the sound is measured at a finite number of points around the body. We wish to determine the intensity of the sound at an observation point which is moving.
We report on the exchange bias effect as a function of the in-plane direction of the applied field in two-fold symmetric, epitaxial Ni80Fe20/Fe50Mn50 bilayers grown on Cu(110) single crystal substrates. An enhancement of the exchange bias field, Heb, up to a factor of two is observed if the external field is nearly, but not fully aligned perpendicular to the symmetry direction of the exchange bias field. From the measurement of the ex-change bias field as a function of the in-plane angle of the applied field, the unidirectional, uniaxial and four-fold anisotropy contributions are determined with high precision. The symmetry direction of the unidirec-tional anisotropy switches with increasing NiFe thickness from [110] to [001].
Zur Datenreduktion gemessener stochastischer Beanspruchungszeitfunktionen werden Zählverfahren eingesetzt. Mit den dabei entstehenden Beanspruchungskollektiven werden rechnerische Lebensdauerabschätzungen gemacht. Da diese mit großen Unsicherheiten behaftet sind, besteht der Wunsch, aus den Beanspruchungskollektiven on-line stochastische Beanspruchungszeitfunktionen zu rekonstruieren, damit ein experimenteller Lebensdauernachweis im Labor mit servohydraulischen Zylindern durchgeführt werden kann. In bezug auf die Lebensdauer der Bauteile unter stochastischer Beanspruchung wird heute dem zweiparametrigen Rainflow-Zählverfahren die größte Bedeutung beigemessen. Es werden ein gegenüber /1/ verbessertes Markov-Inversionsverfahren und ein Rekonstruktionsverfahren aus der symmetrischen und der unsymmetrischen Rainflow-Matrix vorgestellt. Anhand von Beispielen werden diese Inversionsverfahren, die jeweils unter allen Zeitfunktionen, die zu der betreffenden Matrix führen, mit gleicher Wahrscheinlichkeit eine auswählen, verglichen. Es zeigt sich dabei, daß im Hinblick auf die Lebensdauer von Bauteilen unter stochastischer Beanspruchung die Rainflow-Inversionen zu wesentlich besseren Ergebnissen führt als die Markov-Inversionen.
Bei einem von VDO entwickelten Navigationsgerät stehen unterschiedliche Verfahren zur Durchführung der Navigation zur Verfügung. Das Problem besteht darin, daß die von dem jeweiligen Verfahren erzielten Navigationsendpunkte von dem gewünschten Ziel mehr oder weniger stark abweichen. Diese Abweichungen hängen nicht nur von Anfangs- und Endpunkt der Testfahrt und vom Navigationsverfahren ab, sondern ändern sich auch bei der Wiederholung solcher Testfahrten. Ordnet man nun jedem Navigationsverfahren einen Parameter (vektor) zu und bezeichnet man die Menge aller betrachteten Parameter (werte) mit M (M kann zunächst endlich oder unendlich sein), so besteht das Ziel darin, den Parameter p*EM aufzufinden, für den das zugehörige Verfahren im Mittel am besten abschneidet. Hierzu ist es notwendig, zunächst ein Gütekriterium festzulegen.