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Author: Jiu Ding
Publisher: Springer Science & Business Media
ISBN: 3540853677
Category : Mathematics
Languages : en
Pages : 248
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Book Description
Part of Tsinghua University Texts, "Statistical Properties of Deterministic Systems" discusses the fundamental theory and computational methods of the statistical properties of deterministic discrete dynamical systems. After introducing some basic results from ergodic theory, two problems related to the dynamical system are studied: first the existence of absolute continuous invariant measures, and then their computation. They correspond to the functional analysis and numerical analysis of the Frobenius-Perron operator associated with the dynamical system. The book can be used as a text for graduate students in applied mathematics and in computational mathematics; it can also serve as a reference book for researchers in the physical sciences, life sciences, and engineering. Dr. Jiu Ding is a professor at the Department of Mathematics of the University of Southern Mississippi; Dr. Aihui Zhou is a professor at the Academy of Mathematics and Systems Science of the Chinese Academy of Sciences.
Author: Jiu Ding
Publisher: Springer Science & Business Media
ISBN: 3540853677
Category : Mathematics
Languages : en
Pages : 248
Get Book Here
Book Description
Part of Tsinghua University Texts, "Statistical Properties of Deterministic Systems" discusses the fundamental theory and computational methods of the statistical properties of deterministic discrete dynamical systems. After introducing some basic results from ergodic theory, two problems related to the dynamical system are studied: first the existence of absolute continuous invariant measures, and then their computation. They correspond to the functional analysis and numerical analysis of the Frobenius-Perron operator associated with the dynamical system. The book can be used as a text for graduate students in applied mathematics and in computational mathematics; it can also serve as a reference book for researchers in the physical sciences, life sciences, and engineering. Dr. Jiu Ding is a professor at the Department of Mathematics of the University of Southern Mississippi; Dr. Aihui Zhou is a professor at the Academy of Mathematics and Systems Science of the Chinese Academy of Sciences.
Author: Péter Koltai
Publisher: Logos Verlag Berlin GmbH
ISBN: 3832527524
Category :
Languages : en
Pages : 162
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Book Description
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.
Author: Arkady Tsinober
Publisher: Springer Science & Business Media
ISBN: 9400771800
Category : Technology & Engineering
Languages : en
Pages : 171
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Book Description
This book critically reexamines what turbulence really is, from a fundamental point of view and based on observations from nature, laboratories, and direct numerical simulations. It includes critical assessments and a comparative analysis of the key developments, their evolution and failures, along with key misconceptions and outdated paradigms. The main emphasis is on conceptual and problematic aspects, physical phenomena, observations, misconceptions and unresolved issues rather than on conventional formalistic aspects, models, etc. Apart from the obvious fundamental importance of turbulent flows, this emphasis stems from the basic premise that without corresponding progress in fundamental aspects there is little chance for progress in applications such as drag reduction, mixing, control and modeling of turbulence. More generally, there is also a desperate need to grasp the physical fundamentals of the technological processes in which turbulence plays a central role.
Author: W. Q. Zhu
Publisher: CRC Press
ISBN: 0203492951
Category : Technology & Engineering
Languages : en
Pages : 626
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Book Description
Collection of technical papers presented at the 5th International Conference on Stochastic Structural Dynamics (SSD03) in Hangzhou, China during May 26-28, 2003. Topics include direct transfer substructure method for random response analysis, generation of bounded stochastic processes, and sample path behavior of Gaussian processes.
Author: Andrzej Lasota
Publisher: Cambridge University Press
ISBN: 9780521090964
Category : Mathematics
Languages : en
Pages : 376
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Book Description
This book shows how densities arise in simple deterministic systems. There has been explosive growth in interest in physical, biological and economic systems that can be profitably studied using densities. Due to the inaccessibility of the mathematical literature there has been little diffusion of the applicable mathematics into the study of these 'chaotic' systems. This book will help to bridge that gap. The authors give a unified treatment of a variety of mathematical systems generating densities, ranging from one-dimensional discrete time transformations through continuous time systems described by integro-partial differential equations. They have drawn examples from many scientific fields to illustrate the utility of the techniques presented. The book assumes a knowledge of advanced calculus and differential equations, but basic concepts from measure theory, ergodic theory, the geometry of manifolds, partial differential equations, probability theory and Markov processes, and stochastic integrals and differential equations are introduced as needed.
Author: Valerio Lucarini
Publisher: John Wiley & Sons
ISBN: 111863229X
Category : Mathematics
Languages : en
Pages : 314
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Book Description
Written by a team of international experts, Extremes and Recurrence in Dynamical Systems presents a unique point of view on the mathematical theory of extremes and on its applications in the natural and social sciences. Featuring an interdisciplinary approach to new concepts in pure and applied mathematical research, the book skillfully combines the areas of statistical mechanics, probability theory, measure theory, dynamical systems, statistical inference, geophysics, and software application. Emphasizing the statistical mechanical point of view, the book introduces robust theoretical embedding for the application of extreme value theory in dynamical systems. Extremes and Recurrence in Dynamical Systems also features: • A careful examination of how a dynamical system can serve as a generator of stochastic processes • Discussions on the applications of statistical inference in the theoretical and heuristic use of extremes • Several examples of analysis of extremes in a physical and geophysical context • A final summary of the main results presented along with a guide to future research projects • An appendix with software in Matlab® programming language to help readers to develop further understanding of the presented concepts Extremes and Recurrence in Dynamical Systems is ideal for academics and practitioners in pure and applied mathematics, probability theory, statistics, chaos, theoretical and applied dynamical systems, statistical mechanics, geophysical fluid dynamics, geosciences and complexity science. VALERIO LUCARINI, PhD, is Professor of Theoretical Meteorology at the University of Hamburg, Germany and Professor of Statistical Mechanics at the University of Reading, UK. DAVIDE FARANDA, PhD, is Researcher at the Laboratoire des science du climat et de l’environnement, IPSL, CEA Saclay, Université Paris-Saclay, Gif-sur-Yvette, France. ANA CRISTINA GOMES MONTEIRO MOREIRA DE FREITAS, PhD, is Assistant Professor in the Faculty of Economics at the University of Porto, Portugal. JORGE MIGUEL MILHAZES DE FREITAS, PhD, is Assistant Professor in the Department of Mathematics of the Faculty of Sciences at the University of Porto, Portugal. MARK HOLLAND, PhD, is Senior Lecturer in Applied Mathematics in the College of Engineering, Mathematics and Physical Sciences at the University of Exeter, UK. TOBIAS KUNA, PhD, is Associate Professor in the Department of Mathematics and Statistics at the University of Reading, UK. MATTHEW NICOL, PhD, is Professor of Mathematics at the University of Houston, USA. MIKE TODD, PhD, is Lecturer in the School of Mathematics and Statistics at the University of St. Andrews, Scotland. SANDRO VAIENTI, PhD, is Professor of Mathematics at the University of Toulon and Researcher at the Centre de Physique Théorique, France.
Author: Gijs Bosman
Publisher: World Scientific
ISBN: 9812811168
Category : Electronic noise
Languages : en
Pages : 850
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Book Description
The International Conference on Noise in Physical Systems and 1/f Fluctuations brings together physicists and engineers interested in all aspects of noise and fluctuations in materials, devices, circuits, and physical and biological systems. The experimental research on novel devices and systems and the theoretical studies included in this volume provide the reader with a comprehensive, in-depth treatment of present noise research activities worldwide. Contents: Noise in Nanoscale Devices (S Bandyopadhyay et al.); 1/f Voltage Noise Induced by Magnetic Flux Flow in Granular Superconductors (O V Gerashchenko); Low Frequency Noise Analysis of Different Types of Polysilicon Resistors (A Penarier et al.); Low Frequency Noise in CMOS Transistors: An Experimental and Comparative Study on Different Technologies (P Fantini et al.); Modeling of Current Transport and 1/f Noise in GaN Based HBTs (H Unlu); Low Frequency Noise in CdSe Thin Film Transistors (M J Deen & S Rumyanstsev); NIST Program on Relative Intensity Noise Standards for Optical Fiber Sources Near 1550 nm (G Obarski); Physical Model of the Current Noise Spectral Density Versus Dark Current in CdTe Detectors (A Imad et al.); Time and Frequency Study of RTS in Bipolar Transistors (A Penarier et al.); Neural Network Based Adaptive Processing of Electrogastrogram (S Selvan); Shot Noise as a Test of Entanglement and Nonlocality of Electrons in Mesoscopic Systems (E V Sukhorukov et al.); The Readout of Time, Continued Fractions and 1/f Noise (M Planat & J Cresson); Longitudinal and Transverse Noise of Hot Electrons in 2DEG Channels (J Liberis et al.); 1/f Noise, Intermittency and Clustering Poisson Process (F Gruneis); Noise Modeling for PDE Based Device Simulations (F Bonani & G Ghione); Methods of Slope Estimation of Noise Power Spectral Density (J Smulko); and other papers. Readership: Researchers, academics and graduate students in electrical and electronic engineering, biophysics, nanoscience, applied physics, statistical physics and semiconductor science.
Author: Michael Ruzhansky
Publisher: World Scientific
ISBN: 9814464708
Category : Mathematics
Languages : en
Pages : 668
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Book Description
The International Society for Analysis, its Applications and Computation (ISAAC) has held its international congresses biennially since 1997. This proceedings volume reports on the progress in analysis, applications and computation in recent years as covered and discussed at the 7th ISAAC Congress. This volume includes papers on partial differential equations, function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, stochastic analysis, inverse problems, homogenization, continuum mechanics, mathematical biology and medicine. With over 500 participants from almost 60 countries attending the congress, the book comprises a broad selection of contributions in different topics.
Author: Yong Bai
Publisher: John Wiley & Sons
ISBN: 1119605814
Category : Technology & Engineering
Languages : en
Pages : 395
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Book Description
Written by two experts across multiple disciplines, this is the perfect reference on structural dynamics for veteran engineers and introduction to the field for engineering students. Across many disciplines of engineering, dynamic problems of structures are a primary concern. Civil engineers, mechanical engineers, aircraft engineers, ocean engineers, and engineering students encounter these problems every day, and it is up to them systematically to grasp the basic concepts, calculation principles and calculation methods of structural dynamics. This book focuses on the basic theories and concepts, as well as the application and background of theories and concepts in engineering. Since the basic principles and methods of dynamics are applied to other various engineering fields, this book can also be used as a reference for practicing engineers in the field across many multiple disciplines and for undergraduate and graduate students in other majors as well. The main contents include basic theory of dynamics, establishment of equation of motion, single degree of freedom systems, multi-degree of freedom systems, distributed-parameter systems, stochastic structural vibrations, research projects of structural dynamics, and structural dynamics of marine pipeline and risers. Whether for the veteran engineer or student, this is a must-have for any scientific or engineering library. Useful for students and veteran engineers and scientists alike, this is the only book covering these important issues facing anyone working with coastal models and ocean, coastal, and civil engineering in this area.
Author: Shyam Wuppuluri
Publisher: Springer Nature
ISBN: 3030921921
Category : Science
Languages : en
Pages : 886
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Book Description
This highly interdisciplinary book, covering more than six fields, from philosophy and sciences all the way up to the humanities and with contributions from eminent authors, addresses the interplay between content and context, reductionism and holism and their meeting point: the notion of emergence. Much of today’s science is reductionist (bottom-up); in other words, behaviour on one level is explained by reducing it to components on a lower level. Chemistry is reduced to atoms, ecosystems are explained in terms of DNA and proteins, etc. This approach fails quickly since we can’t cannot extrapolate to the properties of atoms solely from Schrödinger's equation, nor figure out protein folding from an amino acid sequence or obtain the phenotype of an organism from its genotype. An alternative approach to this is holism (top-down). Consider an ecosystem or an organism as a whole: seek patterns on the same scale. Model a galaxy not as 400 billion-point masses (stars) but as an object in its own right with its own properties (spiral, elliptic). Or a hurricane as a structured form of moist air and water vapour. Reductionism is largely about content, whereas holistic models are more attuned to context. Reductionism (content) and holism (context) are not opposing philosophies — in fact, they work best in tandem. Join us on a journey to understand the multifaceted dialectic concerning this duo and how they shape the foundations of sciences and humanities, our thoughts and, the very nature of reality itself.
