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.
Topics In Multiple Time Scale Dynamics
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Author : Maximilian Engel
language : en
Publisher: American Mathematical Society
Release Date : 2024-10-21
Topics In Multiple Time Scale Dynamics written by Maximilian Engel and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-21 with Mathematics categories.
This volume contains the proceedings of the BIRS Workshop "Topics in Multiple Time Scale Dynamics," held from November 27? December 2, 2022, at the Banff International Research Station, Banff, Alberta, Canada. The area of multiple-scale dynamics is rapidly evolving, marked by significant theoretical breakthroughs and practical applications. The workshop facilitated a convergence of experts from various sub-disciplines, encompassing topics like blow-up techniques for ordinary differential equations (ODEs), singular perturbation theory for stochastic differential equations (SDE), homogenization and averaging, slow-fast maps, numerical approaches, and network dynamics, including their applications in neuroscience and climate science. This volume provides a wide-ranging perspective on the current challenging subjects being explored in the field, including themes such as novel approaches to blowing-up and canard theory in unique contexts, complex multi-scale challenges in PDEs, and the role of stochasticity in multiple-scale systems.
Methods And Applications Of Singular Perturbations
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Author : Ferdinand Verhulst
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-04
Methods And Applications Of Singular Perturbations written by Ferdinand Verhulst 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 2006-06-04 with Mathematics categories.
Contains well-chosen examples and exercises A student-friendly introduction that follows a workbook type approach
Multiplicity Of Time Scales In Complex Systems
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Author : Bernhelm Booß-Bavnbek
language : en
Publisher: Springer Nature
Release Date : 2024-03-04
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 2024-03-04 with Science categories.
This highly interdisciplinary volume brings together a carefully curated set of case studies examining complex systems with multiple time scales (MTS) across a variety of fields: materials science, epidemiology, cell physiology, mathematics, climatology, energy transition planning, ecology, economics, sociology, history, and cultural studies. The book addresses the vast diversity of interacting processes underlying the behaviour of different complex systems, highlighting the multiplicity of characteristic time scales that are a common feature of many and showcases a rich variety of methodologies across disciplinary boundaries. Self-organizing, out-of-equilibrium, ever-evolving systems are ubiquitous in the natural and social world. Examples include the climate, ecosystems, living cells, epidemics, the human brain, and many socio-economic systems across history. Their dynamical behaviour poses great challenges in the pressing context of the climate crisis, since they may involve nonlinearities, feedback loops, and the emergence of spatial-temporal patterns, portrayed by resilience or instability, plasticity or rigidity; bifurcations, thresholds and tipping points; burst-in excitation or slow relaxation, and worlds of other asymptotic behaviour, hysteresis, and resistance to change. Chapters can be read individually by the reader with special interest in such behaviours of particular complex systems or in specific disciplinary perspectives. Read together, however, the case studies, opinion pieces, and meta-studies on MTS systems presented and analysed here combine to give the reader insights that are more than the sum of the book’s individual chapters, as surprising similarities become apparent in seemingly disparate and unconnected systems. MTS systems call into question naïve perceptions of time and complexity, moving beyond conventional ways of description, analysis, understanding, modelling, numerical prediction, and prescription of the worldaround us. This edited collection presents new ways of forecasting, introduces new means of control, and – perhaps as the most demanding task – it singles out a sustainable description of an MTS system under observation, offering a more nuanced interpretation of the floods of quantitative data and images made available by high- and low-frequency measurement tools in our unprecedented era of information flows. Chapter “Multiplicity of Time Scales in Blood Cell Formation and Leukemia” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
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.
Geometric Singular Perturbation Theory Beyond The Standard Form
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Author : Martin Wechselberger
language : en
Publisher: Springer Nature
Release Date : 2020-02-21
Geometric Singular Perturbation Theory Beyond The Standard Form written by Martin Wechselberger and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-21 with Mathematics categories.
This volume provides a comprehensive review of multiple-scale dynamical systems. Mathematical models of such multiple-scale systems are considered singular perturbation problems, and this volume focuses on the geometric approach known as Geometric Singular Perturbation Theory (GSPT). It is the first of its kind that introduces the GSPT in a coordinate-independent manner. This is motivated by specific examples of biochemical reaction networks, electronic circuit and mechanic oscillator models and advection-reaction-diffusion models, all with an inherent non-uniform scale splitting, which identifies these examples as singular perturbation problems beyond the standard form. The contents cover a general framework for this GSPT beyond the standard form including canard theory, concrete applications, and instructive qualitative models. It contains many illustrations and key pointers to the existing literature. The target audience are senior undergraduates, graduate students and researchers interested in using the GSPT toolbox in nonlinear science, either from a theoretical or an application point of view. Martin Wechselberger is Professor at the School of Mathematics & Statistics, University of Sydney, Australia. He received the J.D. Crawford Prize in 2017 by the Society for Industrial and Applied Mathematics (SIAM) for achievements in the field of dynamical systems with multiple time-scales.
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.
Transient Characteristics Modelling And Stability Analysis Of Microgrid
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Author : Zhikang Shuai
language : en
Publisher: Springer Nature
Release Date : 2020-10-31
Transient Characteristics Modelling And Stability Analysis Of Microgrid written by Zhikang Shuai and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-31 with Technology & Engineering categories.
The book focuses on the transient modelling, stability analysis and control of power electronic systems, since these systems face severe safe operation problems the during transient period. It discusses both theoretical analysis and practical applications, highlighting the transient characteristics of converters with different control strategies, and proposes transient modelling and model reduction methods. Furthermore, it classifies the transient stability problems of the system to help the readers gain an understanding of the basic theoretical methods for analysing the power electronic system, at the same time providing sufficient detail to enable engineers to design such systems. Comprehensively describing theoretical analyses, ranging from system modelling and stability analysis to transient control, the book is a valuable resource for researchers, engineers and graduate students in fields of transient modelling, stability analysis and control of power electronic systems.
Advances In Complex Societal Environmental And Engineered Systems
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Author : Mohamed Nemiche
language : en
Publisher: Springer
Release Date : 2016-12-20
Advances In Complex Societal Environmental And Engineered Systems written by Mohamed Nemiche and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-20 with Technology & Engineering categories.
This book addresses recent technological progress that has led to an increased complexity in many natural and artificial systems. The resulting complexity research due to the emergence of new properties and spatio-temporal interactions among a large number of system elements - and between the system and its environment - is the primary focus of this text. This volume is divided into three parts: Part one focuses on societal and ecological systems, Part two deals with approaches for understanding, modeling, predicting and mastering socio-technical systems, and Part three includes real-life examples. Each chapter has its own special features; it is a self-contained contribution of distinguished experts working on different fields of science and technology relevant to the study of complex systems. Advances in Complex Systems of Contemporary Reality: Societal, Environmental and Engineered Systems will provide postgraduate students, researchers and managers with qualitative and quantitative methods for handling the many features of complex contemporary reality.
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.