Stochastic Averaging

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Nonlinear Random Vibration

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Author : Cho W.S. To
language : en
Publisher: CRC Press
Release Date : 2000-01-01

Nonlinear Random Vibration written by Cho W.S. To and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-01 with Technology & Engineering categories.

This is a systematic presentation of several classes of analytical techniques in non-linear random vibration. The book also includes a concise treatment of Markovian and non-Markovian solutions of non-linear differential equations.

High Resolution Nmr In Solids Selective Averaging

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Author : Ulrich Haeberlen
language : en
Publisher: Elsevier
Release Date : 2012-12-02

High Resolution Nmr In Solids Selective Averaging written by Ulrich Haeberlen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Science categories.

High Resolution NMR in Solids: Selective Averaging presents the principles and applications of the four approaches to high resolution NMR in solids — magic-angle sample spinning, multiple-pulse, proton-enhanced nuclear induction, and indirect detection methods. Divided into six chapters, this book initially describes the tensorial properties of nuclear spin interactions in both ordinary and spin spaces. It then deals with the manifestations of nuclear magnetic shielding in NMR spectra of both single-crystal and powder samples, and then discusses the techniques for analyzing spectra and rotation patterns in terms of shielding tensors. A wide range of NMR phenomena that are result of intentional or natural, selective or unselective averaging processes and the average Hamiltonian theory that yields the inclusion of correction are covered. This book also provides a detailed discussion on multiple-pulse sequences intended for high resolution NMR in solids. The concluding chapter examines the applications of multiple-pulse techniques, with particular emphasis on measurements of 19F and 1H shielding tensors. Discussions on rotations of angular momentum operators; time ordering and the Magnus expansion; off-resonance averaging of the second-order dipolar Hamiltonian; and phase transients are covered in the supplemental texts.

Stochastic Averaging

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Author : Wei-Qiu Zhu
language : en
Publisher: Springer Nature
Release Date : 2025-06-19

Stochastic Averaging written by Wei-Qiu Zhu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-19 with Science categories.

The stochastic averaging methods are among the most effective and widely applied approximate methods for studying nonlinear stochastic dynamics. Upon an overview of global research on the subject, the book highlights a comprehensive summary of research results obtained by the group led by Professor Weiqiu Zhu at Zhejiang University in China and the group led by Professors Y. K. Lin and G. Q. Cai at Florida Atlantic University in the USA over the past three decades. The books are structured to progress logically from foundational principles to simple problems and then to increasingly complex applications. To facilitate understanding and mastery of the methods, the books offer essential preliminary knowledge and a wealth of examples. The book comprises two volumes. Volume 1 introduces the basic principles of stochastic averaging methods and their applications to single-degree-of-freedom systems under various random excitations. It also covers stochastic averaging methods for quasi-Hamiltonian systems subjected to different random excitations, including Gaussian white noise, combined Gaussian and Poisson white noises, and fractional Gaussian noise. Volume 2 explores stochastic averaging methods for quasi-integrable Hamiltonian systems under colored noise excitation, quasi-integrable Hamiltonian systems with genetic effects under Gaussian white noise and colored noise excitations, and quasi-generalized Hamiltonian systems under Gaussian white noise excitation. Additionally, it covers applications of these methods in ecosystems and some other natural science and engineering scenarios. These books serve as both introductory texts and valuable reference resources for readers in higher education and research institutions who are interested in or actively engaged in research involving nonlinear stochastic dynamics. The fields covered include mechanics, physics, chemistry, biology, ecology, astronautics and aeronautics, oceanography, civil engineering, mechanical engineering, and electrical engineering.

Nonlinear Random Vibration Second Edition

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Author : Cho W.S. To
language : en
Publisher: CRC Press
Release Date : 2011-08-10

Nonlinear Random Vibration Second Edition written by Cho W.S. To and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-10 with Technology & Engineering categories.

This second edition of the book, Nonlinear Random Vibration: Analytical Techniques and Applications, expands on the original edition with additional detailed steps in various places in the text. It is a first systematic presentation on the subject. Its features include: • a concise treatment of Markovian and non- Markovian solutions of nonlinear stochastic differential equations, • exact solutions of Fokker-Planck-Kolmogorov equations, • methods of statistical linearization, • statistical nonlinearization techniques, • methods of stochastic averaging, • truncated hierarchy techniques, and • an appendix on probability theory. A special feature is its incorporation of detailed steps in many examples of engineering applications. Targeted audience: Graduates, research scientists and engineers in mechanical, aerospace, civil and environmental (earthquake, wind and transportation), automobile, naval, architectural, and mining engineering.

Modeling Of Complex Dynamic Systems

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Author : Vladimir Stojanović
language : en
Publisher: Elsevier
Release Date : 2025-04-09

Modeling Of Complex Dynamic Systems written by Vladimir Stojanović and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-09 with Technology & Engineering categories.

Motion is the essence of any mechanical system. Analyzing a system's dynamical response to distinct motion parameters allows for increased understanding of its performance thresholds and can in turn provide clear data to inform improved system designs.Modeling of Complex Dynamic Systems: Fundamentals and Applications equips readers with significant insights into nonlinear vibration phenomenology through a combination of advanced mathematical fundamentals and worked-through modeling experiments. To guide them in determining novel stabilization characteristics for complex moving objects, coupled structures, as well as the stochastic stability of mechanical systems, the technical and methodological analysis is accompanied by industry-relevant practical examples, contributing much sought-after applicable knowledge.The book is intended for use by postgraduate students, academic researchers, and professional engineers alike. - Connects three areas of theoretical and applied mechanics – nonlinear vibrations, dynamics of moving objects, and stochastic stability of structures, while also reviewing literature - Compares classical dynamic models with the authors' proposed modeling methodologies to analyze mechanical systems affected by parametric instabilities - Discusses new technical solutions powered by AI and ML to introduce possible further research directions

Applied Mechanics Reviews

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Author :
language : en
Publisher:
Release Date : 1987

Applied Mechanics Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mechanics, Applied categories.

Parametric Random Vibration

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Author : Raouf A. Ibrahim
language : en
Publisher: Courier Dover Publications
Release Date : 2008-01-11

Parametric Random Vibration written by Raouf A. Ibrahim and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-11 with Science categories.

This systematic treatment examines linear and nonlinear dynamical systems subject to parametric random vibrations. It formulates stochastic stability theorems and analytical techniques for determining random response of nonlinear systems. 1985 edition.

Computation And Combinatorics In Dynamics Stochastics And Control

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Author : Elena Celledoni
language : en
Publisher: Springer
Release Date : 2019-01-13

Computation And Combinatorics In Dynamics Stochastics And Control written by Elena Celledoni and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-13 with Mathematics categories.

The Abel Symposia volume at hand contains a collection of high-quality articles written by the world’s leading experts, and addressing all mathematicians interested in advances in deterministic and stochastic dynamical systems, numerical analysis, and control theory. In recent years we have witnessed a remarkable convergence between individual mathematical disciplines that approach deterministic and stochastic dynamical systems from mathematical analysis, computational mathematics and control theoretical perspectives. Breakthrough developments in these fields now provide a common mathematical framework for attacking many different problems related to differential geometry, analysis and algorithms for stochastic and deterministic dynamics. In the Abel Symposium 2016, which took place from August 16-19 in Rosendal near Bergen, leading researchers in the fields of deterministic and stochastic differential equations, control theory, numerical analysis, algebra and random processes presented and discussed the current state of the art in these diverse fields. The current Abel Symposia volume may serve as a point of departure for exploring these related but diverse fields of research, as well as an indicator of important current and future developments in modern mathematics.

Stochastically Excited Nonlinear Ocean Structures

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Author : Michael F. Shlesinger
language : en
Publisher: World Scientific
Release Date : 1998

Stochastically Excited Nonlinear Ocean Structures written by Michael F. Shlesinger and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Technology & Engineering categories.

Ocean structures, including ships, boats, piers, docks, rigs and platforms, are subject to fair weather wind and waves, as well as violent storms. A scientific analysis of these structures, under varying conditions, requires a mix of civil engineering, physics and applied mathematics. Chapters by experts in these fields are presented which explore the nonlinear responses of ocean structures to stochastic forcing. Theoretical methods calculate aspects of time, frequency and phase space responses. Probabilities governed by stochastic differential equations arc investigated directly or through moment correlations, such as power spectra. Calculations can also involve level crossing statistics and first passage times. Tiffs book will help scientists study stochastic nonlinear equations and help engineers design for short term survivability of structures in storms and long life in the face of everyday fatigue.

Advances In Global Optimization

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Author : David Gao
language : en
Publisher: Springer
Release Date : 2014-11-11

Advances In Global Optimization written by David Gao and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-11 with Mathematics categories.

This proceedings volume addresses advances in global optimization—a multidisciplinary research field that deals with the analysis, characterization and computation of global minima and/or maxima of nonlinear, non-convex and nonsmooth functions in continuous or discrete forms. The volume contains selected papers from the third biannual World Congress on Global Optimization in Engineering & Science (WCGO), held in the Yellow Mountains, Anhui, China on July 8-12, 2013. The papers fall into eight topical sections: mathematical programming; combinatorial optimization; duality theory; topology optimization; variational inequalities and complementarity problems; numerical optimization; stochastic models and simulation and complex simulation and supply chain analysis.