Download or read book Multiscale Analysis and Nonlinear Dynamics written by Misha Meyer Pesenson and published by John Wiley & Sons. This book was released on 2013-09-13 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since modeling multiscale phenomena in systems biology and neuroscience is a highly interdisciplinary task, the editor of the book invited experts in bio-engineering, chemistry, cardiology, neuroscience, computer science, and applied mathematics, to provide their perspectives. Each chapter is a window into the current state of the art in the areas of research discussed and the book is intended for advanced researchers interested in recent developments in these fields. While multiscale analysis is the major integrating theme of the book, its subtitle does not call for bridging the scales from genes to behavior, but rather stresses the unifying perspective offered by the concepts referred to in the title. It is believed that the interdisciplinary approach adopted here will be beneficial for all the above mentioned fields.

Download or read book Information Theory and Stochastics for Multiscale Nonlinear Systems written by Andrew Majda and published by American Mathematical Soc.. This book was released on with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces mathematicians to the fascinating mathematical interplay between ideas from stochastics and information theory and practical issues in studying complex multiscale nonlinear systems. It emphasizes the serendipity between modern applied mathematics and applications where rigorous analysis, the development of qualitative and/or asymptotic models, and numerical modeling all interact to explain complex phenomena. After a brief introduction to the emerging issues in multiscale modeling, the book has three main chapters. The first chapter is an introduction to information theory with novel applications to statistical mechanics, predictability, and Jupiter's Red Spot for geophysical flows. The second chapter discusses new mathematical issues regarding fluctuation-dissipation theorems for complex nonlinear systems including information flow, various approximations, and illustrates applications to various mathematical models. The third chapter discusses stochastic modeling of complex nonlinear systems. After a general discussion, a new elementary model, motivated by issues in climate dynamics, is utilized to develop a self-contained example of stochastic mode reduction. Based on A. Majda's Aisenstadt lectures at the University of Montreal, the book is appropriate for both pure and applied mathematics graduate students, postdocs and faculty, as well as interested researchers in other scientific disciplines. No background in geophysical flows is required. About the authors: Andrew Majda is a member of the National Academy of Sciences and has received numerous honors and awards, including the National Academy of Science Prize in Applied Mathematics, the John von Neumann Prize of the Society of Industrial and Applied Mathematics, the Gibbs Prize of the American Mathematical Society, and the Medal of the College de France. In the past several years at the Courant Institute, Majda and a multi-disciplinary faculty have created the Center for Atmosphere Ocean Science to promote cross-disciplinary research with modern applied mathematics in climate modeling and prediction. R.V. Abramov is a young researcher; he received his PhD in 2002. M. J. Grote received his Ph.D. under Joseph B. Keller at Stanford University in 1995.

Download or read book Multivariate Multiscale Analysis of Natural and Engineered Dynamical Systems written by David B. Segala and published by . This book was released on 2011 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Information Theory and Stochastics for Multiscale Nonlinear Systems written by Andrew Majda and published by American Mathematical Soc.. This book was released on 2005 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces mathematicians to the fascinating mathematical interplay between ideas from stochastics and information theory and practical issues in studying complex multiscale nonlinear systems. It emphasizes the serendipity between modern applied mathematics and applications where rigorous analysis, the development of qualitative and/or asymptotic models, and numerical modeling all interact to explain complex phenomena. After a brief introduction to the emerging issues in multiscale modeling, the book has three main chapters. The first chapter is an introduction to information theory with novel applications to statistical mechanics, predictability, and Jupiter's Red Spot for geophysical flows. The second chapter discusses new mathematical issues regarding fluctuation-dissipation theorems for complex nonlinear systems including information flow, various approximations, and illustrates applications to various mathematical models. The third chapter discusses stochastic modeling of complex nonlinear systems. After a general discussion, a new elementary model, motivated by issues in climate dynamics, is utilized to develop a self-contained example of stochastic mode reduction. Based on A. Majda's Aisenstadt lectures at the University of Montreal, the book is appropriate for both pure and applied mathematics graduate students, postdocs and faculty, as well as interested researchers in other scientific disciplines. No background in geophysical flows is required. About the authors: Andrew Majda is a member of the National Academy of Sciences and has received numerous honors and awards, including the National Academy of Science Prize in Applied Mathematics, the John von Neumann Prize of the Society of Industrial and Applied Mathematics, the Gibbs Prize of the American Mathematical Society, and the Medal of the College de France. In the past several years at the Courant Institute, Majda and a multi-disciplinary faculty have created the Center for Atmosphere Ocean Science to promote cross-disciplinary research with modern applied mathematics in climate modeling and prediction. R.V. Abramov is a young researcher; he received his PhD in 2002. M. J. Grote received his Ph.D. under Joseph B. Keller at Stanford University in 1995.

Download or read book Analysis Modeling and Simulation of Multiscale Problems written by Alexander Mielke and published by Springer Science & Business Media. This book was released on 2006-10-14 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reports recent mathematical developments in the Programme "Analysis, Modeling and Simulation of Multiscale Problems", which started as a German research initiative in 2006. Multiscale problems occur in many fields of science, such as microstructures in materials, sharp-interface models, many-particle systems and motions on different spatial and temporal scales in quantum mechanics or in molecular dynamics. The book presents current mathematical foundations of modeling, and proposes efficient numerical treatment.

Download or read book Multiscale Analysis of Nonlinear Systems Using Computational Homology written by and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collaborative project between the principal investigators. However, as is to be expected, different PIs have greater focus on different aspects of the project. This report lists these major directions of research which were pursued during the funding period: (1) Computational Homology in Fluids - For the computational homology effort in thermal convection, the focus of the work during the first two years of the funding period included: (1) A clear demonstration that homology can sensitively detect the presence or absence of an important flow symmetry, (2) An investigation of homology as a probe for flow dynamics, and (3) The construction of a new convection apparatus for probing the effects of large-aspect-ratio. (2) Computational Homology in Cardiac Dynamics - We have initiated an effort to test the use of homology in characterizing data from both laboratory experiments and numerical simulations of arrhythmia in the heart. Recently, the use of high speed, high sensitivity digital imaging in conjunction with voltage sensitive fluorescent dyes has enabled researchers to visualize electrical activity on the surface of cardiac tissue, both in vitro and in vivo. (3) Magnetohydrodynamics - A new research direction is to use computational homology to analyze results of large scale simulations of 2D turbulence in the presence of magnetic fields. Such simulations are relevant to the dynamics of black hole accretion disks. The complex flow patterns from simulations exhibit strong qualitative changes as a function of magnetic field strength. Efforts to characterize the pattern changes using Fourier methods and wavelet analysis have been unsuccessful. (4) Granular Flow - two experts in the area of granular media are studying 2D model experiments of earthquake dynamics where the stress fields can be measured; these stress fields from complex patterns of 'force chains' that may be amenable to analysis using computational homology. (5) Microstructure Characterization - We extended our previous work on studying the time evolution of patterns associated with phase separation in conserved concentration fields. (6) Probabilistic Homology Validation - work on microstructure characterization is based on numerically studying the homology of certain sublevel sets of a function, whose evolution is described by deterministic or stochastic evolution equations. (7) Computational Homology and Dynamics - Topological methods can be used to rigorously describe the dynamics of nonlinear systems. We are approaching this problem from several perspectives and through a variety of systems. (8) Stress Networks in Polycrystals - we have characterized stress networks in polycrystals. This part of the project is aimed at developing homological metrics which can aid in distinguishing not only microstructures, but also derived mechanical response fields. (9) Microstructure-Controlled Drug Release - This part of the project is concerned with the development of topological metrics in the context of controlled drug delivery systems, such as drug-eluting stents. We are particularly interested in developing metrics which can be used to link the processing stage to the resulting microstructure, and ultimately to the achieved system response in terms of drug release profiles. (10) Microstructure of Fuel Cells - we have been using our computational homology software to analyze the topological structure of the void, metal and ceramic components of a Solid Oxide Fuel Cell.

Download or read book Multiscale Multibody Dynamics written by Jielong Wang and published by Springer Nature. This book was released on 2023-03-24 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a novel theory of multibody dynamics with distinct features, including unified continuum theory, multiscale modeling technology of multibody system, and motion formalism implementation. All these features together with the introductions of fundamental concepts of vector, dual vector, tensor, dual tensor, recursive descriptions of joints, and the higher-order implicit solvers formulate the scope of the book’s content. In this book, a multibody system is defined as a set consisted of flexible and rigid bodies which are connected by any kinds of joints or constraints to achieve the desired motion. Generally, the motion of multibody system includes the translation and rotation; it is more efficient to describe the motion by using the dual vector or dual tensor directly instead of defining two types of variables, the translation and rotation separately. Furthermore, this book addresses the detail of motion formalism and its finite element implementation of the solid, shell-like, and beam-like structures. It also introduces the fundamental concepts of mechanics, such as the definition of vector, dual vector, tensor, and dual tensor, briefly. Without following the Einstein summation convention, the first- and second-order tensor operations in this book are depicted by linear algebraic operation symbols of row array, column array, and two-dimensional matrix, making these operations easier to understand. In addition, for the integral of governing equations of motion, a set of ordinary differential equations for the finite element-based discrete system, the book discussed the implementation of implicit solvers in detail and introduced the well-developed RADAU IIA algorithms based on post-error estimation to make the contents of the book complete. The intended readers of this book are senior engineers and graduate students in related engineering fields.

Download or read book Multiscale Analysis of Deformation and Failure of Materials written by Jinghong Fan and published by John Wiley & Sons. This book was released on 2011-06-28 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting cutting-edge research and development within multiscale modeling techniques and frameworks, Multiscale Analysis of Deformation and Failure of Materials systematically describes the background, principles and methods within this exciting new & interdisciplinary field. The author’s approach emphasizes the principles and methods of atomistic simulation and its transition to the nano and sub-micron scale of a continuum, which is technically important for nanotechnology and biotechnology. He also pays close attention to multiscale analysis across the micro/meso/macroscopy of a continuum, which has a broad scope of applications encompassing different disciplines and practices, and is an essential extension of mesomechanics. Of equal interest to engineers, scientists, academics and students, Multiscale Analysis of Deformation and Failure of Materials is a multidisciplinary text relevant to those working in the areas of materials science, solid and computational mechanics, bioengineering and biomaterials, and aerospace, automotive, civil, and environmental engineering. Provides a deep understanding of multiscale analysis and its implementation Shows in detail how multiscale models can be developed from practical problems and how to use the multiscale methods and software to carry out simulations Discusses two interlinked categories of multiscale analysis; analysis spanning from the atomistic to the micro-continuum scales, and analysis across the micro/meso/macro scale of continuum.

Download or read book Multicomponent and Multiscale Systems written by Juergen Geiser and published by Springer. This book was released on 2015-08-21 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the latest research results from combined multi-component and multi-scale explorations. It provides theory, considers underlying numerical methods and presents brilliant computational experimentation. Engineering computations featured in this monograph further offer particular interest to many researchers, engineers and computational scientists working in frontier modeling and applications of multicomponent and multiscale problems. Professor Geiser gives specific attention to the aspects of decomposing and splitting delicate structures and controlling decomposition and the rationale behind many important applications of multi-component and multi-scale analysis. Multicomponent and Multiscale Systems: Theory, Methods and Applications in Engineering also considers the question of why iterative methods can be powerful and more appropriate for well-balanced multiscale and multicomponent coupled nonlinear problems. The book is ideal for engineers and scientists working in theoretical and applied areas.

Download or read book Dynamics of Nonlinear Systems written by Vladimir Hlavacek and published by CRC Press. This book was released on 1986 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Global Analysis of Nonlinear Dynamics written by Jian-Qiao Sun and published by Springer Science & Business Media. This book was released on 2012-05-01 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Global Analysis of Nonlinear Dynamics collects chapters on recent developments in global analysis of non-linear dynamical systems with a particular emphasis on cell mapping methods developed by Professor C.S. Hsu of the University of California, Berkeley. This collection of contributions prepared by a diverse group of internationally recognized researchers is intended to stimulate interests in global analysis of complex and high-dimensional nonlinear dynamical systems, whose global properties are largely unexplored at this time.

Download or read book Nonlinear Dynamics Volume 1 written by Gaetan Kerschen and published by Springer. This book was released on 2016-04-22 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Dynamics, Volume 1. Proceedings of the 34th IMAC, A Conference and Exposition on Dynamics of Multiphysical Systems: From Active Materials to Vibroacoustics, 2016, the fi rst volume of ten from the Conference, brings together contributions to this important area of research and engineering. Th e collection presents early fi ndings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: • Nonlinear Oscillations • Nonlinear Modal Analysis • Nonlinear System Identifi cation • Nonlinear Modeling & Simulation • Nonlinearity in Practice • Nonlinearity in Multi-Physics Systems • Nonlinear Modes and Modal Interactions

Download or read book Principles of Multiscale Modeling written by Weinan E and published by Cambridge University Press. This book was released on 2011-07-07 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic discussion of the fundamental principles, written by a leading contributor to the field.

Download or read book Multiscale Analysis of Complex Time Series written by Jianbo Gao and published by John Wiley & Sons. This book was released on 2007-12-04 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: The only integrative approach to chaos and random fractal theory Chaos and random fractal theory are two of the most important theories developed for data analysis. Until now, there has been no single book that encompasses all of the basic concepts necessary for researchers to fully understand the ever-expanding literature and apply novel methods to effectively solve their signal processing problems. Multiscale Analysis of Complex Time Series fills this pressing need by presenting chaos and random fractal theory in a unified manner. Adopting a data-driven approach, the book covers: DNA sequence analysis EEG analysis Heart rate variability analysis Neural information processing Network traffic modeling Economic time series analysis And more Additionally, the book illustrates almost every concept presented through applications and a dedicated Web site is available with source codes written in various languages, including Java, Fortran, C, and MATLAB, together with some simulated and experimental data. The only modern treatment of signal processing with chaos and random fractals unified, this is an essential book for researchers and graduate students in electrical engineering, computer science, bioengineering, and many other fields.

Download or read book Applications of Nonlinear Dynamics written by Visarath In and published by Springer Science & Business Media. This book was released on 2009-02-11 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ?eld of applied nonlinear dynamics has attracted scientists and engineers across many different disciplines to develop innovative ideas and methods to study c- plex behavior exhibited by relatively simple systems. Examples include: population dynamics, ?uidization processes, applied optics, stochastic resonance, ?ocking and ?ightformations,lasers,andmechanicalandelectricaloscillators. Acommontheme among these and many other examples is the underlying universal laws of nonl- ear science that govern the behavior, in space and time, of a given system. These laws are universal in the sense that they transcend the model-speci?c features of a system and so they can be readily applied to explain and predict the behavior of a wide ranging phenomena, natural and arti?cial ones. Thus the emphasis in the past decades has been in explaining nonlinear phenomena with signi?cantly less att- tion paid to exploiting the rich behavior of nonlinear systems to design and fabricate new devices that can operate more ef?ciently. Recently, there has been a series of meetings on topics such as Experimental Chaos, Neural Coding, and Stochastic Resonance, which have brought together many researchers in the ?eld of nonlinear dynamics to discuss, mainly, theoretical ideas that may have the potential for further implementation. In contrast, the goal of the 2007 ICAND (International Conference on Applied Nonlinear Dynamics) was focused more sharply on the implementation of theoretical ideas into actual - vices and systems.

Download or read book Data Driven Science and Engineering written by Steven L. Brunton and published by Cambridge University Press. This book was released on 2022-05-05 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook covering data-science and machine learning methods for modelling and control in engineering and science, with Python and MATLAB®.

Download or read book Medical Diagnostic Techniques and Procedures written by M. R. S. Reddy and published by Alpha Science Int'l Ltd.. This book was released on 2000-01-30 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on important and evolving aspects of medical diagnostic techniques and procedures such as bioelectric phenomenon, medical imaging, biomedical signal processing, biomechanical techniques, microcirculatory techniques, optical techniques and modelling, and biomedical instrumentation covering sophisticated to low cost ideally suited for mass screening in rural areas.