Multiple Time Scales

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Publisher : Academic Press
ISBN 13 : 1483257568
Total Pages : 457 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Multiple Time Scales by : Jeremiah U. Brackbill

Download or read book Multiple Time Scales written by Jeremiah U. Brackbill and published by Academic Press. This book was released on 2014-05-10 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Multiple Time Scale Dynamics

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Publisher : Springer
ISBN 13 : 3319123165
Total Pages : 816 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Multiple Time Scale Dynamics by : Christian Kuehn

Download or read book Multiple Time Scale Dynamics written by Christian Kuehn and published by Springer. This book was released on 2015-02-25 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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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Publisher : Springer Science & Business Media
ISBN 13 : 1461301173
Total Pages : 278 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Multiple-Time-Scale Dynamical Systems by : Christopher K.R.T. Jones

Download or read book Multiple-Time-Scale Dynamical Systems written by Christopher K.R.T. Jones and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Dynamic Equations on Time Scales

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Publisher : Springer Science & Business Media
ISBN 13 : 1461202019
Total Pages : 365 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Dynamic Equations on Time Scales by : Martin Bohner

Download or read book Dynamic Equations on Time Scales written by Martin Bohner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: On becoming familiar with difference equations and their close re lation to differential equations, I was in hopes that the theory of difference equations could be brought completely abreast with that for ordinary differential equations. [HUGH L. TURRITTIN, My Mathematical Expectations, Springer Lecture Notes 312 (page 10), 1973] A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both. [E. T. BELL, Men of Mathematics, Simon and Schuster, New York (page 13/14), 1937] The theory of time scales, which has recently received a lot of attention, was introduced by Stefan Hilger in his PhD thesis [159] in 1988 (supervised by Bernd Aulbach) in order to unify continuous and discrete analysis. This book is an intro duction to the study of dynamic equations on time scales. Many results concerning differential equations carryover quite easily to corresponding results for difference equations, while other results seem to be completely different in nature from their continuous counterparts. The study of dynamic equations on time scales reveals such discrepancies, and helps avoid proving results twice, once for differential equa tions and once for difference equations. The general idea is to prove a result for a dynamic equation where the domain of the unknown function is a so-called time scale, which is an arbitrary nonempty closed subset of the reals.

Dynamic Inequalities On Time Scales

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Publisher : Springer
ISBN 13 : 3319110020
Total Pages : 264 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Dynamic Inequalities On Time Scales by : Ravi Agarwal

Download or read book Dynamic Inequalities On Time Scales written by Ravi Agarwal and published by Springer. This book was released on 2014-10-30 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a monograph devoted to recent research and results on dynamic inequalities on time scales. The study of dynamic inequalities on time scales has been covered extensively in the literature in recent years and has now become a major sub-field in pure and applied mathematics. In particular, this book will cover recent results on integral inequalities, including Young's inequality, Jensen's inequality, Holder's inequality, Minkowski's inequality, Steffensen's inequality, Hermite-Hadamard inequality and Čebyšv's inequality. Opial type inequalities on time scales and their extensions with weighted functions, Lyapunov type inequalities, Halanay type inequalities for dynamic equations on time scales, and Wirtinger type inequalities on time scales and their extensions will also be discussed here in detail.

Multiple Scale and Singular Perturbation Methods

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Publisher : Springer Science & Business Media
ISBN 13 : 1461239680
Total Pages : 642 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Multiple Scale and Singular Perturbation Methods by : J.K. Kevorkian

Download or read book Multiple Scale and Singular Perturbation Methods written by J.K. Kevorkian and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a revised and updated version, including a substantial portion of new material, of our text Perturbation Methods in Applied Mathematics (Springer Verlag, 1981). We present the material at a level that assumes some familiarity with the basics of ordinary and partial differential equations. Some of the more advanced ideas are reviewed as needed; therefore this book can serve as a text in either an advanced undergraduate course or a graduate-level course on the subject. Perturbation methods, first used by astronomers to predict the effects of small disturbances on the nominal motions of celestial bodies, have now become widely used analytical tools in virtually all branches of science. A problem lends itself to perturbation analysis if it is "close" to a simpler problem that can be solved exactly. Typically, this closeness is measured by the occurrence of a small dimensionless parameter, E, in the governing system (consisting of differential equations and boundary conditions) so that for E = 0 the resulting system is exactly solvable. The main mathematical tool used is asymptotic expansion with respect to a suitable asymptotic sequence of functions of E. In a regular perturbation problem, a straightforward procedure leads to a system of differential equations and boundary conditions for each term in the asymptotic expansion. This system can be solved recursively, and the accuracy of the result improves as E gets smaller, for all values of the independent variables throughout the domain of interest. We discuss regular perturbation problems in the first chapter.

The Proper Generalized Decomposition for Advanced Numerical Simulations

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Publisher : Springer Science & Business Media
ISBN 13 : 3319028650
Total Pages : 127 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis The Proper Generalized Decomposition for Advanced Numerical Simulations by : Francisco Chinesta

Download or read book The Proper Generalized Decomposition for Advanced Numerical Simulations written by Francisco Chinesta and published by Springer Science & Business Media. This book was released on 2013-10-08 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in scientific computing are intractable with classical numerical techniques. These fail, for example, in the solution of high-dimensional models due to the exponential increase of the number of degrees of freedom. Recently, the authors of this book and their collaborators have developed a novel technique, called Proper Generalized Decomposition (PGD) that has proven to be a significant step forward. The PGD builds by means of a successive enrichment strategy a numerical approximation of the unknown fields in a separated form. Although first introduced and successfully demonstrated in the context of high-dimensional problems, the PGD allows for a completely new approach for addressing more standard problems in science and engineering. Indeed, many challenging problems can be efficiently cast into a multi-dimensional framework, thus opening entirely new solution strategies in the PGD framework. For instance, the material parameters and boundary conditions appearing in a particular mathematical model can be regarded as extra-coordinates of the problem in addition to the usual coordinates such as space and time. In the PGD framework, this enriched model is solved only once to yield a parametric solution that includes all particular solutions for specific values of the parameters. The PGD has now attracted the attention of a large number of research groups worldwide. The present text is the first available book describing the PGD. It provides a very readable and practical introduction that allows the reader to quickly grasp the main features of the method. Throughout the book, the PGD is applied to problems of increasing complexity, and the methodology is illustrated by means of carefully selected numerical examples. Moreover, the reader has free access to the Matlab© software used to generate these examples.

Multiplicity of Time Scales in Complex Systems

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Publisher : Springer Nature
ISBN 13 : 3031280490
Total Pages : 477 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Multiplicity of Time Scales in Complex Systems by : Bernhelm Booss

Download or read book Multiplicity of Time Scales in Complex Systems written by Bernhelm Booss and published by Springer Nature. This book was released on 2024 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: Zusammenfassung: 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 world around 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

Asymptotic Multiple Scale Method in Time Domain

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Publisher : CRC Press
ISBN 13 : 100058125X
Total Pages : 411 pages
Book Rating : 4.0/5 (5 download)

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Book Synopsis Asymptotic Multiple Scale Method in Time Domain by : Jan Awrejcewicz

Download or read book Asymptotic Multiple Scale Method in Time Domain written by Jan Awrejcewicz and published by CRC Press. This book was released on 2022-05-10 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers up novel research which uses analytical approaches to explore nonlinear features exhibited by various dynamic processes. Relevant to disciplines across engineering and physics, the asymptotic method combined with the multiple scale method is shown to be an efficient and intuitive way to approach mechanics. Beginning with new material on the development of cutting-edge asymptotic methods and multiple scale methods, the book introduces this method in time domain and provides examples of vibrations of systems. Clearly written throughout, it uses innovative graphics to exemplify complex concepts such as nonlinear stationary and nonstationary processes, various resonances and jump pull-in phenomena. It also demonstrates the simplification of problems through using mathematical modelling, by employing the use of limiting phase trajectories to quantify nonlinear phenomena. Particularly relevant to structural mechanics, in rods, cables, beams, plates and shells, as well as mechanical objects commonly found in everyday devices such as mobile phones and cameras, the book shows how each system is modelled, and how it behaves under various conditions. It will be of interest to engineers and professionals in mechanical engineering and structural engineering, alongside those interested in vibrations and dynamics. It will also be useful to those studying engineering maths and physics.

On the Application of the Method of Multiple Time Scales to Problems in the Theory of Optimal Control

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Publisher :
ISBN 13 :
Total Pages : 420 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis On the Application of the Method of Multiple Time Scales to Problems in the Theory of Optimal Control by : Raymond Paul Gogolewski

Download or read book On the Application of the Method of Multiple Time Scales to Problems in the Theory of Optimal Control written by Raymond Paul Gogolewski and published by . This book was released on 1970 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Time Scale Systems in Standard and Nonstandard Forms

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Publisher : SIAM
ISBN 13 : 1611973333
Total Pages : 231 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Nonlinear Time Scale Systems in Standard and Nonstandard Forms by : Anshu Narang-Siddarth

Download or read book Nonlinear Time Scale Systems in Standard and Nonstandard Forms written by Anshu Narang-Siddarth and published by SIAM. This book was released on 2014-04-22 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Methods and Applications of Singular Perturbations

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Publisher : Springer Science & Business Media
ISBN 13 : 0387283137
Total Pages : 328 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Methods and Applications of Singular Perturbations by : Ferdinand Verhulst

Download or read book Methods and Applications of Singular Perturbations written by Ferdinand Verhulst and published by Springer Science & Business Media. This book was released on 2006-06-04 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains well-chosen examples and exercises A student-friendly introduction that follows a workbook type approach

Nonlinear Model Reduction and Control of Multiple Time Scale Chemical Processes

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Publisher :
ISBN 13 :
Total Pages : 432 pages
Book Rating : 4.:/5 (319 download)

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Book Synopsis Nonlinear Model Reduction and Control of Multiple Time Scale Chemical Processes by : Nishith Pramod Vora

Download or read book Nonlinear Model Reduction and Control of Multiple Time Scale Chemical Processes written by Nishith Pramod Vora and published by . This book was released on 2000 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Boundary Value Problems on Time Scales, Volume I

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Publisher : CRC Press
ISBN 13 : 100042989X
Total Pages : 324 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis Boundary Value Problems on Time Scales, Volume I by : Svetlin G. Georgiev

Download or read book Boundary Value Problems on Time Scales, Volume I written by Svetlin G. Georgiev and published by CRC Press. This book was released on 2021-10-15 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boundary Value Problems on Time Scales, Volume I is devoted to the qualitative theory of boundary value problems on time scales. Summarizing the most recent contributions in this area, it addresses a wide audience of specialists such as mathematicians, physicists, engineers and biologists. It can be used as a textbook at the graduate level and as a reference book for several disciplines. The text contains two volumes, both published by Chapman & Hall/CRC Press. Volume I presents boundary value problems for first- and second-order dynamic equations on time scales. Volume II investigates boundary value problems for three, four, and higher-order dynamic equations on time scales. Many results to differential equations carry over easily to corresponding results for difference equations, while other results seem to be totally different in nature. Because of these reasons, the theory of dynamic equations is an active area of research. The time-scale calculus can be applied to any field in which dynamic processes are described by discrete or continuous time models. The calculus of time scales has various applications involving noncontinuous domains such as certain bug populations, phytoremediation of metals, wound healing, maximization problems in economics, and traffic problems. Boundary value problems on time scales have been extensively investigated in simulating processes and the phenomena subject to short-time perturbations during their evolution. The material in this book is presented in highly readable, mathematically solid format. Many practical problems are illustrated displaying a wide variety of solution techniques. AUTHORS Svetlin G. Georgiev is a mathematician who has worked in various areas of the study. He currently focuses on harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, integral equations, and dynamic calculus on time scales. Khaled Zennir earned his PhD in mathematics in 2013 from Sidi Bel Abbès University, Algeria. In 2015, he received his highest diploma in Habilitation in mathematics from Constantine University, Algeria. He is currently assistant professor at Qassim University in the Kingdom of Saudi Arabia. His research interests lie in the subjects of nonlinear hyperbolic partial differential equations: global existence, blowup, and long-time behavior.

Multiple-time-scale Order Reduction for Stochastic Kinetics and Molecular Simluation of Crystallization

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Publisher :
ISBN 13 :
Total Pages : 226 pages
Book Rating : 4.:/5 (89 download)

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Book Synopsis Multiple-time-scale Order Reduction for Stochastic Kinetics and Molecular Simluation of Crystallization by : Ethan Allen Sturman Mastny

Download or read book Multiple-time-scale Order Reduction for Stochastic Kinetics and Molecular Simluation of Crystallization written by Ethan Allen Sturman Mastny and published by . This book was released on 2007 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Selected Statistical Papers of Sir David Cox: Volume 1, Design of Investigations, Statistical Methods and Applications

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Publisher : Cambridge University Press
ISBN 13 : 9780521849395
Total Pages : 620 pages
Book Rating : 4.8/5 (493 download)

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Book Synopsis Selected Statistical Papers of Sir David Cox: Volume 1, Design of Investigations, Statistical Methods and Applications by : David Roxbee Cox

Download or read book Selected Statistical Papers of Sir David Cox: Volume 1, Design of Investigations, Statistical Methods and Applications written by David Roxbee Cox and published by Cambridge University Press. This book was released on 2005 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sir David Cox's most important papers, each the subject of a new commentary by Professor Cox.

Neuronal Dynamics

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Publisher : Cambridge University Press
ISBN 13 : 1107060834
Total Pages : 591 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Neuronal Dynamics by : Wulfram Gerstner

Download or read book Neuronal Dynamics written by Wulfram Gerstner and published by Cambridge University Press. This book was released on 2014-07-24 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: This solid introduction uses the principles of physics and the tools of mathematics to approach fundamental questions of neuroscience.