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Numerical analysis of invariant manifolds characterized by quasi-periodic oscillations of nonlinear systems
(kassel university press, 2021)
Quasi-periodic motions systematically occur, when a system is subjected to multiple unrelated excitation mechanisms. Since unrelated mechanisms generically exhibit in dependent frequencies, the resulting motion is characterized by multiple fundamental frequencies. Consequently, the resulting motion is not periodic, but, due to the inde pendent frequencies, sort of periodic, namely quasi-periodic. Not being able to identify one unique fundamental frequency, established methods for the identification of periodic ...
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Fomento de la Educación-STEM y la Modelización Matemática para profesores
(kassel university press, 2021)
Este libro, como otros en el área de la educación matemática, procura mostrar diversas formas que los profesores pueden utilizar para que sus estudiantes aprecien el rol de la matemática en sus vidas y la sepan utilizar y valorar cuando la requieran. Este libro es tambien un presente de los autores a los profesores de Matemáticas de Chile. En el libro han colaborado principalmente especialistas de Chile que se han destacado en la educación matemática y especialmente en la modelación y los campos STEM, entre ellos hay ...
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Denkstile als Herausforderung im Mathematikunterricht
(kassel university press, 2019)
In der Sekundarstufe I polarisiert insbesondere das Fach Mathematik wie kein zweites (vgl. Henn/ Kaiser 2001). Schülerinnen und Schüler lieben es oder sie hassen es, eher selten findet sich eine neutrale Einstellung. Eine mögliche Erklärung könnte hierbei die Theorie der mathematischen Denkstile liefern, die Personen Präferenzen für eine bestimmte Art und Weise mathematische Inhalte zu verstehen zuschreibt (vgl. Borromeo Ferri 2004).In diesem Zusammenhang wurde in dieser Arbeit anhand von Mathematikaufgaben untersucht, ...
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Control of Stochastic Hybrid Systems based on Probabilistic Reachable Set Computation
(kassel university press, 2018)
This thesis proposes an algorithmic controller synthesis based on the computation of probabilistic reachable sets for stochastic hybrid systems. Hybrid systems consist in general of a composition of discrete and continuous valued dynamics, and are able to capture a wide range of physical phenomena. The stochasticity is considered in form of normally distributed initial continuous states and normally distributed disturbances, resulting in stochastic hybrid systems.The reachable sets describe all states, which are ...
Buch
Mixed-mode cohesive cracks and complex potentials of linear elastic fracture mechanics: new theoretical aspects and numerical applications
(kassel university press, 2023)
The J-integral is a powerful tool to determine crack tip loading, where the J-integral vector also allows for the quantification of crack deflection applying the J-integral vector criterion. Although originally formulated for sharp cracks with a crack tip singularity, the J-integral vector can also be derived for cracks with cohesive zones. The relation and proof of equivalency of the first coordinate of the vector and the crack tip opening displacement, typically associated with the cohesive zone model, has been ...
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Distributed Model Predictive Control with Event-Based Communication
(kassel university press, 2015)
In this thesis, several algorithms for distributed model predictive control over digital communication networks with parallel computation are developed and analyzed. Distributed control aims at efficiently controlling large scale dynamical systems which consist of interconnected dynamical systems by means of communicating local controllers. Such distributed control problems arise in applications such as chemical processes, formation control, and control of power grids. In distributed model predictive control the ...
Buch
Quantum Technology using Cold Diatomic Molecular Ions: Interferometry and Cooling
(kassel university press, 2023)
Atoms and atomic ions have proved to be useful as quantum technological systems, where atomic clocks are one of the more famous implementations. Molecules, with more degrees of freedom (vibrations and rotations) are considered as natural extensions to atomic systems. In particular, we study cold molecular diatomic ions as systems for implementation in quantum technology and in particular the rotational degree of freedom of such molecular ions. Quantum effects manifest themselves at very cold temperatures. To reach ...
Buch
Ein diskontinuierliches Galerkin-Verfahren hoher Ordnung auf Dreiecksgittern mit modaler Filterung zur Lösung hyperbolischer Erhaltungsgleichungen
(kassel university press, 2012)
Die vorliegende Arbeit beschäftigt sich mit der Anwendung diskontinuierlicher Galerkin-Verfahren zur numerischen Lösung hyperbolischer Erhaltungsgleichungen. Diese Klasse zeitabhängiger partieller Differentialgleichungen stellt besondere Anforderungen an ein zur approximativen Berechnung ihrer L¨osungen ausgew¨ahltes numerisches Verfahren, da die Theorie hyperbolischer Erhaltungsgleichungen abweichend vom klassischen Lösungsbegriff unstetige Lösungen zulässt. Hinzu kommt, dass die Eindeutigkeit dieser Lösungen im ...
Buch
A Methodology for the Cryptanalysis of Classical Ciphers with Search Metaheuristics
(kassel university press, 2018)
Cryptography, the art and science of creating secret codes, and cryptanalysis, the art and science of breaking secret codes, underwent a similar and parallel course during history. Both fields evolved from manual encryption methods and manual codebreaking techniques, to cipher machines and codebreaking machines in the first half of the 20th century, and finally to computerbased encryption and cryptanalysis from the second half of the 20th century. However, despite the advent of modern computing technology, some of ...