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Efficient Approximation Methods for the Global Long term Behavior of Dynamical Systems Book PDF Summary
Fur die Analyse des Langzeitverhaltens dynamischer Systeme werden in dieser Dissertation drei neue Ansatze, basierend auf Transferoperator-Methoden, zur Entwicklung effizienter Algorithmen vorgestellt. Zuerst leiten wir eine Diskretisierung auf dunnen Gittern her, um den Fluch der Dimension in den Griff zu bekommen. Die zweite Methode behandelt den infinitesimalen Generator der Transferoperator-Halbgruppe fur zeit-kontinuierliche Systeme. Als Drittes benutzen wir mean-field-Theorie, um die Dynamik von Subsystemen zu beschreiben, wobei besonderes Augenmerk auf die Konformationsanalyse in der Molekuldynamik gerichtet wird. Des Weiteren werden Bedingungen hergeleitet, unter welchen die Galerkin-Projektion des Transferoperators mit einer kleinen zufalligen Storung des zugrunde liegenden Systems in Verbindung gebracht werden kann. In this thesis three new transfer operator based approaches are developed for the analysis of the long-term behavior of dynamical systems. First, a sparse grid discretization is derived in order to deal with the "curse of dimension". The second method considers the infinitesimal generator of the transfer operator semigroup for continuous-time systems. The third method uses mean field theory to describe the dynamics of subsystems; here the main attention is devoted to conformation analysis in molecular dynamics. Further, conditions are derived such that the Galerkin projection of the transfer operator can be related to a small random perturbation of the underlying system.
Detail Book of Efficient Approximation Methods for the Global Long term Behavior of Dynamical Systems PDF
- Author : Péter Koltai
- Release : 22 September 2024
- Publisher : Logos Verlag Berlin GmbH
- ISBN : 9783832527525
- Genre : Uncategoriezed
- Total Page : 162 pages
- Language : English
- PDF File Size : 12,6 Mb
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