Two Scale Approach To Oscillatory Singularly Perturbed Transport Equations

Author : Emmanuel Frénod
Publisher : Springer
Page : 126 pages
File Size : 43,8 Mb
Release : 2017-10-05
Category : Mathematics
ISBN : 9783319646688

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Two-Scale Approach to Oscillatory Singularly Perturbed Transport Equations by Emmanuel Frénod Pdf

This book presents the classical results of the two-scale convergence theory and explains – using several figures – why it works. It then shows how to use this theory to homogenize ordinary differential equations with oscillating coefficients as well as oscillatory singularly perturbed ordinary differential equations. In addition, it explores the homogenization of hyperbolic partial differential equations with oscillating coefficients and linear oscillatory singularly perturbed hyperbolic partial differential equations. Further, it introduces readers to the two-scale numerical methods that can be built from the previous approaches to solve oscillatory singularly perturbed transport equations (ODE and hyperbolic PDE) and demonstrates how they can be used efficiently. This book appeals to master’s and PhD students interested in homogenization and numerics, as well as to the Iter community.

Author : Christian Kuehn
Publisher : Springer
Page : 814 pages
File Size : 43,8 Mb
Release : 2015-02-25
Category : Mathematics
ISBN : 9783319123165

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Multiple Time Scale Dynamics by Christian Kuehn Pdf

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.

Author : Oualid Hamdaoui,Kaouther Kerboua
Publisher : Elsevier
Page : 390 pages
File Size : 51,6 Mb
Release : 2022-08-06
Category : Science
ISBN : 9780323984904

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Energy Aspects of Acoustic Cavitation and Sonochemistry by Oualid Hamdaoui,Kaouther Kerboua Pdf

Energy Aspects of Acoustic Cavitation and Sonochemistry: Fundamentals and Engineering covers topics ranging from fundamental modeling to up-scaled experiments. The book relates acoustic cavitation and its intrinsic energy balance to macroscopic physical and chemical events that are analyzed from an energetic perspective. Outcomes are directly projected into practical applications and technological assessments covering energy consumption, thermal dissipation, and energy efficiency of a diverse set of applications in mixed phase synthesis, environmental remediation and materials chemistry. Special interest is dedicated to the sonochemical production of hydrogen and its energetic dimensions. Due to the sensitive energy balance that governs this process, this is seen as a "green process" for the production of future energy carriers. Provides a concise and detailed description of energy conversion and exchange within the single acoustic cavitation bubble and bubble population, accompanying physical and chemical effects Features a comprehensive approach that is supported by experiments and the modeling of energy concentration within the sonochemical reactor, jointly with energy dissipation and damping phenomenon Gives a clear definition of energy efficiency metrics of industrial sono-processes and their application to the main emergent industrial fields harnessing acoustic cavitation and sonochemistry, notably for the production of hydrogen

Author : Martin Wechselberger
Publisher : Springer Nature
Page : 143 pages
File Size : 55,6 Mb
Release : 2020-02-21
Category : Mathematics
ISBN : 9783030363994

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Geometric Singular Perturbation Theory Beyond the Standard Form by Martin Wechselberger Pdf

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.

Author : J.K. Kevorkian,J.D. Cole
Publisher : Springer Science & Business Media
Page : 642 pages
File Size : 46,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461239680

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Multiple Scale and Singular Perturbation Methods by J.K. Kevorkian,J.D. Cole Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 704 pages
File Size : 47,7 Mb
Release : 1995
Category : Aeronautics
ISBN : UIUC:30112050127304

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Scientific and Technical Aerospace Reports by Anonim Pdf

Author : Jane Cronin
Publisher : American Mathematical Soc.
Page : 201 pages
File Size : 46,6 Mb
Release : 1999
Category : Differentiable dynamical systems
ISBN : 9780821809297

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Analyzing Multiscale Phenomena Using Singular Perturbation Methods by Jane Cronin Pdf

To understand multiscale phenomena, it is essential to employ asymptotic methods to construct approximate solutions and to design effective computational algorithms. This volume consists of articles based on the AMS Short Course in Singular Perturbations held at the annual Joint Mathematics Meetings in Baltimore (MD). Leading experts discussed the following topics which they expand upon in the book: boundary layer theory, matched expansions, multiple scales, geometric theory, computational techniques, and applications in physiology and dynamic metastability. Readers will find that this text offers an up-to-date survey of this important field with numerous references to the current literature, both pure and applied.

Author : Mark H. Holmes
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 55,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461253471

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Introduction to Perturbation Methods by Mark H. Holmes Pdf

This introductory graduate text is based on a graduate course the author has taught repeatedly over the last ten years to students in applied mathematics, engineering sciences, and physics. Each chapter begins with an introductory development involving ordinary differential equations, and goes on to cover such traditional topics as boundary layers and multiple scales. However, it also contains material arising from current research interest, including homogenisation, slender body theory, symbolic computing, and discrete equations. Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas.

Author : S R Shimjith,A P Tiwari,B Bandyopadhyay
Publisher : Springer
Page : 154 pages
File Size : 43,5 Mb
Release : 2012-08-10
Category : Technology & Engineering
ISBN : 9783642305894

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Modeling and Control of a Large Nuclear Reactor by S R Shimjith,A P Tiwari,B Bandyopadhyay Pdf

Control analysis and design of large nuclear reactors requires a suitable mathematical model representing the steady state and dynamic behavior of the reactor with reasonable accuracy. This task is, however, quite challenging because of several complex dynamic phenomena existing in a reactor. Quite often, the models developed would be of prohibitively large order, non-linear and of complex structure not readily amenable for control studies. Moreover, the existence of simultaneously occurring dynamic variations at different speeds makes the mathematical model susceptible to numerical ill-conditioning, inhibiting direct application of standard control techniques. This monograph introduces a technique for mathematical modeling of large nuclear reactors in the framework of multi-point kinetics, to obtain a comparatively smaller order model in standard state space form thus overcoming these difficulties. It further brings in innovative methods for controller design for systems exhibiting multi-time-scale property, with emphasis on three-time-scale systems.

Author : Michael P. Mortell
Publisher : Cambridge University Press
Page : 362 pages
File Size : 49,6 Mb
Release : 2005-06
Category : Computers
ISBN : 0898715970

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Singular Perturbation and Hysteresis by Michael P. Mortell Pdf

This book unifies many important recent developments in the analysis of singular perturbation and hysteresis phenomena in an accessible and comprehensive fashion. In April 2002 at University College Cork in Ireland, the editors conducted a workshop to provide a forum for experts to share their interests and knowledge. For this book, the editors have compiled research from those practitioners in areas such as reacting systems, semiconductor lasers, shock phenomena in economic modeling, and fluid mechanics, all with an emphasis on hysteresis and singular perturbations. A basic introduction to hysteresis and singular perturbation theory is included, with simple examples from both physics and mathematics. Later chapters address: applications of hysteresis to economics; various aspects of the asymptotic theory of singularly perturbed systems; typical problems of the asymptotic theory of contrast structures; and the geometrical approach to an investigation of models with singular perturbations and hysteresis.

Author : Anonim
Publisher : Unknown
Page : 986 pages
File Size : 53,7 Mb
Release : 1978
Category : Power resources
ISBN : MSU:31293010867319

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Energy Research Abstracts by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 520 pages
File Size : 49,9 Mb
Release : 1972
Category : Mechanics, Applied
ISBN : UCAL:C2682436

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Applied Mechanics Reviews by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 1884 pages
File Size : 51,5 Mb
Release : 2005
Category : Mathematics
ISBN : UVA:X006195258

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Mathematical Reviews by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 880 pages
File Size : 55,5 Mb
Release : 1978
Category : Power resources
ISBN : STANFORD:36105013133736

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Energy Research Abstracts by Anonim Pdf

Author : L. Gary Leal
Publisher : Cambridge University Press
Page : 7 pages
File Size : 45,8 Mb
Release : 2007-06-18
Category : Technology & Engineering
ISBN : 9781139462068

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Advanced Transport Phenomena by L. Gary Leal Pdf

Advanced Transport Phenomena is ideal as a graduate textbook. It contains a detailed discussion of modern analytic methods for the solution of fluid mechanics and heat and mass transfer problems, focusing on approximations based on scaling and asymptotic methods, beginning with the derivation of basic equations and boundary conditions and concluding with linear stability theory. Also covered are unidirectional flows, lubrication and thin-film theory, creeping flows, boundary layer theory, and convective heat and mass transport at high and low Reynolds numbers. The emphasis is on basic physics, scaling and nondimensionalization, and approximations that can be used to obtain solutions that are due either to geometric simplifications, or large or small values of dimensionless parameters. The author emphasizes setting up problems and extracting as much information as possible short of obtaining detailed solutions of differential equations. The book also focuses on the solutions of representative problems. This reflects the book's goal of teaching readers to think about the solution of transport problems.