Download or read book Efficient Approximation Methods for the Global Long term Behavior of Dynamical Systems written by Péter Koltai and published by Logos Verlag Berlin GmbH. This book was released on 2011 with total page 162 pages. 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.
Download or read book Approximation of Large Scale Dynamical Systems written by Athanasios C. Antoulas and published by SIAM. This book was released on 2009-06-25 with total page 489 pages. 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.
Download or read book Ergodic Theory Analysis and Efficient Simulation of Dynamical Systems written by Bernold Fiedler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 816 pages. 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.
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 and published by Frontiers Media SA. This book was released on 2023-12-11 with total page 259 pages. 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.
Download or read book Analysis of Infinite Dimensional Dynamical Systems by Set oriented Numerics written by Adrian Ziessler and published by . This book was released on 2018 with total page 0 pages. 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
Download or read book Multi Resolution Methods for Modeling and Control of Dynamical Systems written by Puneet Singla and published by CRC Press. This book was released on 2008-08-01 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unifying the most important methodology in this field, Multi-Resolution Methods for Modeling and Control of Dynamical Systems explores existing approximation methods as well as develops new ones for the approximate solution of large-scale dynamical system problems. It brings together a wide set of material from classical orthogonal function
Download or read book Advances in Dynamics Optimization and Computation written by Oliver Junge and published by Springer Nature. This book was released on 2020-07-20 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of papers on recent advances in problems concerning dynamics, optimal control and optimization. In many chapters, computational techniques play a central role. Set-oriented techniques feature prominently throughout the book, yielding state-of-the-art algorithms for computing general invariant sets, constructing globally optimal controllers and solving multi-objective optimization problems.
Download or read book Dynamics and Fault Diagnosis of Nonlinear Rotors and Impellers written by Jiazhong Zhang and published by Springer Nature. This book was released on 2022-04-28 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume presents recent developments in nonlinear dynamics applied to engineering. Specifically, the authors address stability and bifurcation in large-scale, complex rotor dynamic systems; periodic motions and their bifurcations in nonlinear circuit systems, fault diagnosis of complex engineering systems with nonlinear approaches, singularities in fluid-machinery and bifurcation analysis, nonlinear behaviors in rotor dynamic system with multi-mistuned blades, mode localization induced by mistuning in impellers with periodical and cyclic symmetry, and nonlinear behaviors in fluid-structure interaction and their control. These new results will maximize reader understand on the recent progress in nonlinear dynamics applied to large-scale, engineering systems in general and nonlinear rotors and impellers in particular.
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1993 with total page 768 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advances in Dynamical Systems Theory Models Algorithms and Applications written by Bruno Carpentieri and published by BoD – Books on Demand. This book was released on 2021-07-28 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of modern dynamical systems dates back to 1890 with studies by Poincaré on celestial mechanics. The tradition was continued by Birkhoff in the United States with his pivotal work on periodic orbits, and by the Moscow School in Russia (Liapunov, Andronov, Pontryagin). In the 1960s the field was revived by the emergence of the theory of chaotic attractors, and in modern years by accurate computer simulations. This book provides an overview of recent developments in the theory of dynamical systems, presenting some significant advances in the definition of new models, computer algorithms, and applications. Researchers, engineers and graduate students in both pure and applied mathematics will benefit from the chapters collected in this volume.
Download or read book Mathematical Reviews written by and published by . This book was released on 2008 with total page 866 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Exploiting the Use of Strong Nonlinearity in Dynamics and Acoustics written by Oleg V. Gendelman and published by Springer Nature. This book was released on with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dynamical Systems on Networks written by Mason Porter and published by Springer. This book was released on 2016-03-31 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a tutorial for the study of dynamical systems on networks. It discusses both methodology and models, including spreading models for social and biological contagions. The authors focus especially on “simple” situations that are analytically tractable, because they are insightful and provide useful springboards for the study of more complicated scenarios. This tutorial, which also includes key pointers to the literature, should be helpful for junior and senior undergraduate students, graduate students, and researchers from mathematics, physics, and engineering who seek to study dynamical systems on networks but who may not have prior experience with graph theory or networks. Mason A. Porter is Professor of Nonlinear and Complex Systems at the Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, UK. He is also a member of the CABDyN Complexity Centre and a Tutorial Fellow of Somerville College. James P. Gleeson is Professor of Industrial and Applied Mathematics, and co-Director of MACSI, at the University of Limerick, Ireland.
Download or read book Featured Reviews in Mathematical Reviews 1995 1996 written by Donald G. Babbitt and published by American Mathematical Soc.. This book was released on with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of reprinted 'Featured Reviews' published in Mathematical Reviews (MR) in 1995 and 1996 makes widely available informed reviews of some of the best mathematics published recently. 'Featured Reviews' were introduced in MR at the beginning of 1995 in part to provide some guidance to the current research-level literature. With the exponential growth of publications in mathematical research in the first half-century of MR, it had become essentially impossible for users of MR to identify the most important new research-level books and papers, especially in fields outside of the users' own expertise. This work identifies some of the "best" new publications, papers, and books that are expected to have a significant impact on the area of pure or applied mathematics with which researchers are concerned. All of the papers reviewed here contain interesting new ideas or applications, a deep synthesis of existing ideas, or any combination of these. The volume is intended to lead the user to important new research across all fields covered by MR.
Download or read book Differential Equations and Dynamical Systems written by Lawrence Perko and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence bf interest in the modern as well as the clas sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mat!!ematics (TAM). The development of new courses is a natural consequence of a high level of excitement oil the research frontier as newer techniques, such as numerical and symbolic cotnputer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Math ematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface to the Second Edition This book covers those topics necessary for a clear understanding of the qualitative theory of ordinary differential equations and the concept of a dynamical system. It is written for advanced undergraduates and for beginning graduate students. It begins with a study of linear systems of ordinary differential equations, a topic already familiar to the student who has completed a first course in differential equations.
Download or read book Proxy Simulations for Efficient Dynamics written by Okan Arikan and published by . This book was released on 2001 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advanced Dynamic Modeling of Economic and Social Systems written by Araceli N. Proto and published by Springer. This book was released on 2012-09-18 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume recent advances in the use of modern quantitative models for the analysis of various problems related to the dynamics of social and economic systems are presented. The majority chapters describe tools and techniques of broadly perceived computational intelligence, notably fuzzy logic, evolutionary computation, neural networks and some non-standard probabilistic and statistical analyses. Due to the high complexity of the systems and problems considered, in many situations it is necessary to consider at the same time analytic, topological and statistical aspects and apply appropriate procedures and algorithms. This volume is a direct result of vivid discussions held during the Fifth International Workshop on Dynamics of Social and Economical Systems (DYSES) which was held at Benevento, Italy September 20-25, 2010, as well as a couple of post-workshop meetings and consultations.
