Multiple Time Scale Dynamics
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Multiple Time Scale Dynamics
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Author : Christian Kuehn
language : en
Publisher: Springer
Release Date : 2015-02-25
Multiple Time Scale Dynamics written by Christian Kuehn and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-25 with Mathematics categories.
This book provides an introduction to dynamical systems with multiple time scales. The approach it takes is to provide an overview of key areas, particularly topics that are less available in the introductory form. The broad range of topics included makes it accessible for students and researchers new to the field to gain a quick and thorough overview. The first of its kind, this book merges a wide variety of different mathematical techniques into a more unified framework. The book is highly illustrated with many examples and exercises and an extensive bibliography. The target audience of this book are senior undergraduates, graduate students as well as researchers interested in using the multiple time scale dynamics theory in nonlinear science, either from a theoretical or a mathematical modeling perspective.
Multiple Time Scale Dynamical Systems
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Author : Christopher K.R.T. Jones
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Multiple Time Scale Dynamical Systems written by Christopher K.R.T. Jones and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Systems with sub-processes evolving on many different time scales are ubiquitous in applications: chemical reactions, electro-optical and neuro-biological systems, to name just a few. This volume contains papers that expose the state of the art in mathematical techniques for analyzing such systems. Recently developed geometric ideas are highlighted in this work that includes a theory of relaxation-oscillation phenomena in higher dimensional phase spaces. Subtle exponentially small effects result from singular perturbations implicit in certain multiple time scale systems. Their role in the slow motion of fronts, bifurcations, and jumping between invariant tori are all explored here. Neurobiology has played a particularly stimulating role in the development of these techniques and one paper is directed specifically at applying geometric singular perturbation theory to reveal the synchrony in networks of neural oscillators.
Multiple Time Scales
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Author : Jeremiah U. Brackbill
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Multiple Time Scales written by Jeremiah U. Brackbill and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Multiple Time Scales presents various numerical methods for solving multiple-time-scale problems. The selection first elaborates on considerations on solving problems with multiple scales; problems with different time scales; and nonlinear normal-mode initialization of numerical weather prediction models. Discussions focus on analysis of observations, nonlinear analysis, systems of ordinary differential equations, and numerical methods for problems with multiple scales. The text then examines the diffusion-synthetic acceleration of transport iterations, with application to a radiation hydrodynamics problem and implicit methods in combustion and chemical kinetics modeling. The publication ponders on molecular dynamics and Monte Carlo simulations of rare events; direct implicit plasma simulation; orbit averaging and subcycling in particle simulation of plasmas; and hybrid and collisional implicit plasma simulation models. Topics include basic moment method, electron subcycling, gyroaveraged particle simulation, and the electromagnetic direct implicit method. The selection is a valuable reference for researchers interested in pursuing further research on the use of numerical methods in solving multiple-time-scale problems.
Multi Scale Dynamics Modeling Of Brain Physiological Functions And Pathological Mechanisms
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Author : Ying Wu
language : en
Publisher: Frontiers Media SA
Release Date : 2023-10-09
Multi Scale Dynamics Modeling Of Brain Physiological Functions And Pathological Mechanisms written by Ying Wu and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-09 with Science categories.
The mechanisms of brain physiological functions and pathological mechanisms are crucial for us to understand how the brain works in the normal function such as memory, information processing and attentional perception, or in pathological conditions such as epilepsy, Parkinson's disease, and Alzheimer's diseases. These brain physiological functions and pathological mechanisms generally involve multiple spatial scales of brains, ranging from micro molecules, cellular channels, and meso-scale neuronal networks to the brain regions. To comprehensively understand the neural mechanisms of brain physiological functions and pathological mechanisms, multiple-scale investigations are essential to carry, involving neuronal circuit modeling, neural field modeling, large-scale modeling, data-driven complex network modeling, etc.
Multiplicity Of Time Scales In Complex Systems
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Author : Bernhelm Booß-Bavnbek
language : en
Publisher: Springer Nature
Release Date :
Multiplicity Of Time Scales In Complex Systems written by Bernhelm Booß-Bavnbek and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Nonlinear Dynamics And Chaos
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Author : J Hogan
language : en
Publisher: CRC Press
Release Date : 2002-08-01
Nonlinear Dynamics And Chaos written by J Hogan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-08-01 with Science categories.
Nonlinear dynamics has been successful in explaining complicated phenomena in well-defined low-dimensional systems. Now it is time to focus on real-life problems that are high-dimensional or ill-defined, for example, due to delay, spatial extent, stochasticity, or the limited nature of available data. How can one understand the dynamics of such systems? Written by international experts, Nonlinear Dynamics and Chaos: Where Do We Go from Here? assesses what the future holds for dynamics and chaos. The chapters address one or more of the broad and interconnected main themes: neural and biological systems, spatially extended systems, and experimentation in the physical sciences. The contributors offer suggestions as to what they see as the way forward, often in the form of open questions for future research.
Model Reduction And Coarse Graining Approaches For Multiscale Phenomena
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Author : Alexander N. Gorban
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-22
Model Reduction And Coarse Graining Approaches For Multiscale Phenomena written by Alexander N. Gorban and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-22 with Science categories.
Model reduction and coarse-graining are important in many areas of science and engineering. How does a system with many degrees of freedom become one with fewer? How can a reversible micro-description be adapted to the dissipative macroscopic model? These crucial questions, as well as many other related problems, are discussed in this book. All contributions are by experts whose specialities span a wide range of fields within science and engineering.
Nonlinear Time Scale Systems In Standard And Nonstandard Forms
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Author : Anshu Narang-Siddarth
language : en
Publisher: SIAM
Release Date : 2014-04-22
Nonlinear Time Scale Systems In Standard And Nonstandard Forms written by Anshu Narang-Siddarth and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-22 with Mathematics categories.
This book introduces key concepts for systematically controlling engineering systems that possess interacting phenomena occurring at widely different speeds. The aim is to present the reader with control techniques that extend the benefits of model reduction of singular perturbation theory to a larger class of nonlinear dynamical systems. New results and relevant background are presented through insightful examples that cover a wide range of applications from different branches of engineering. This book is unique because it presents a new perspective on existing control methods and thus broadens their application to a larger class of nonlinear dynamical systems. It also discusses general rather than problem-specific developments to certain applications or disciplines in order to provide control engineers with useful analytical tools, and it addresses new control problems using singular perturbation methods, including closed-form results for control of nonminimum phase systems.
Nonlinear Model Reduction And Control Of Multiple Time Scale Chemical Processes
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Author : Nishith Pramod Vora
language : en
Publisher:
Release Date : 2000
Nonlinear Model Reduction And Control Of Multiple Time Scale Chemical Processes written by Nishith Pramod Vora and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.
Dynamics And Nonlinear Control Of Integrated Process Systems
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Author : Michael Baldea
language : en
Publisher: Cambridge University Press
Release Date : 2012-08-02
Dynamics And Nonlinear Control Of Integrated Process Systems written by Michael Baldea and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-02 with Technology & Engineering categories.
Presenting a systematic model reduction and hierarchical controller design framework for broad classes of integrated process systems encountered in practice, this book first studies process systems with large material recycle and/or with small purge streams, followed by systems with energy integration. Step-by-step model reduction procedures are developed to derive nonlinear reduced models of the dynamics in each time scale. Hierarchical control architectures consisting of coordinated levels of control action in different time scales are proposed for each class of process systems considered to enforce stability, tracking performance and disturbance rejection. Numerous process applications are discussed in detail to illustrate the application of the methods and their potential to improve process operations. MATLAB codes are also presented to guide further application of the methods developed and facilitate practical implementations.