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Efficient Approximation Methods for the Global Long-term Behavior of Dynamical Systems

2011
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Release : 2011
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Book Rating : 524/5 ( reviews)

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Book Synopsis Efficient Approximation Methods for the Global Long-term Behavior of Dynamical Systems by : Péter Koltai

Download or read book Efficient Approximation Methods for the Global Long-term Behavior of Dynamical Systems written by Péter Koltai. This book was released on 2011. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Approximation of Large-Scale Dynamical Systems

2009-06-25 Mathematics
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Release : 2009-06-25
Genre : Mathematics
Kind : eBook
Book Rating : 586/5 ( reviews)

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Book Synopsis Approximation of Large-Scale Dynamical Systems by : Athanasios C. Antoulas

Download or read book Approximation of Large-Scale Dynamical Systems written by Athanasios C. Antoulas. This book was released on 2009-06-25. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical models are used to simulate, and sometimes control, the behavior of physical and artificial processes such as the weather and very large-scale integration (VLSI) circuits. The increasing need for accuracy has led to the development of highly complex models. However, in the presence of limited computational accuracy and storage capabilities model reduction (system approximation) is often necessary. Approximation of Large-Scale Dynamical Systems provides a comprehensive picture of model reduction, combining system theory with numerical linear algebra and computational considerations. It addresses the issue of model reduction and the resulting trade-offs between accuracy and complexity. Special attention is given to numerical aspects, simulation questions, and practical applications.

Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
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Book Rating : 891/5 ( reviews)

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Book Synopsis Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems by : Bernold Fiedler

Download or read book Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems written by Bernold Fiedler. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: Presenting very recent results in a major research area, this book is addressed to experts and non-experts in the mathematical community alike. The applied issues range from crystallization and dendrite growth to quantum chaos, conveying their significance far into the neighboring disciplines of science.

Novel Insights into the Circulation, Biogeochemistry, and Ecosystem Function of the Gulf of Mexico: A Perspective from Mexican Waters in Support of Oil Spill Preparedness

2023-12-11 Science
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Release : 2023-12-11
Genre : Science
Kind : eBook
Book Rating : 287/5 ( reviews)

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Book Synopsis Novel Insights into the Circulation, Biogeochemistry, and Ecosystem Function of the Gulf of Mexico: A Perspective from Mexican Waters in Support of Oil Spill Preparedness by : Maria Josefina Olascoaga

Download or read book Novel Insights into the Circulation, Biogeochemistry, and Ecosystem Function of the Gulf of Mexico: A Perspective from Mexican Waters in Support of Oil Spill Preparedness written by Maria Josefina Olascoaga. This book was released on 2023-12-11. Available in PDF, EPUB and Kindle. Book excerpt: In response to the Deepwater Horizon oil spill in the Gulf of Mexico (GoM), and given the increased activities of the offshore oil industry, an international multidisciplinary consortium - the CIGOM Consortium - was funded by Mexico's Energy Secretariat (SENER) and its National Council for Science and Technology (CONACyT). Spanning 2015-2022, CIGOM's goals were to establish an environmental baseline to characterize the southern GOM’s natural variability and contribute to the understanding of ecosystem function, use cutting-edge technologies to observe the ocean, couple physical circulation and biogeochemical models to gain understating of oceanographic processes, generate oil spill scenarios using model ensembles and statistical techniques and conducting vulnerability assessments. Over 300 researchers participated in the CIGOM consortium's efforts.

Analysis of Infinite Dimensional Dynamical Systems by Set-oriented Numerics

2018
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Release : 2018
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Book Synopsis Analysis of Infinite Dimensional Dynamical Systems by Set-oriented Numerics by : Adrian Ziessler

Download or read book Analysis of Infinite Dimensional Dynamical Systems by Set-oriented Numerics written by Adrian Ziessler. This book was released on 2018. Available in PDF, EPUB and Kindle. Book excerpt: One central goal in the analysis of dynamical systems is the characterization of long term behavior of the system state. To this end, the so-called global attractor is of interest, that is, an invariant set that attracts all the trajectories of the underlying dynamical system. Over the last 20 years so-called set-oriented numerical methods have been developed that allow to compute approximations of invariant sets. The basic idea is to cover the objects of interest, for instance attractors or unstable manifolds, by outer approximations which are created via subdivision techniques. However, the applicability of those techniques is restricted to finite dimensional dynamical systems, i.e., ordinary differential equations or discrete dynamical systems. In this thesis, we extend the set-oriented numerical methods to the infinite dimensional context. With those extensions we will be able to compute finite dimensional invariant sets for infinite dimensional dynamical systems, e.g., for delay and partial differential equations. The idea is to utilize infinite dimensional embedding techniques in our numerical treatment. This will allow us to construct a finite dimensional dynamical system, the core dynamical system (CDS), on an appropriately chosen observation space. Using the CDS, we then can approximate finite dimensional embedded attractors or embedded unstable manifolds. Furthermore, we will be able to compute approximations of the embedded invariant measure in the observation space which gives a statistical description of the dynamical behavior of the infinite dimensional dynamical system. We present numerical realizations of the CDS for delay and partial differential equations and illustrate the efficiency of our approach in several examples. Furthermore, we present modifications for the set-oriented subdivision and continuation method. ... ; eng

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