Nonlinear Hyperbolic Waves In Multidimensions
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Nonlinear Hyperbolic Waves In Multidimensions
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Author : Phoolan Prasad
language : en
Publisher: CRC Press
Release Date : 2001-05-18
Nonlinear Hyperbolic Waves In Multidimensions written by Phoolan Prasad and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-05-18 with Mathematics categories.
The propagation of curved, nonlinear wavefronts and shock fronts are very complex phenomena. Since the 1993 publication of his work Propagation of a Curved Shock and Nonlinear Ray Theory, author Phoolan Prasad and his research group have made significant advances in the underlying theory of these phenomena. This volume presents their results and pr
Nonlinear Hyperbolic Waves In Multi Dimensions
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Author : Phoolan Prasad
language : en
Publisher:
Release Date : 1999-05
Nonlinear Hyperbolic Waves In Multi Dimensions written by Phoolan Prasad and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-05 with categories.
The propagation of curved, nonlinear wavefronts and shock fronts is a very complex phenomena. This book provides a self-contained account an d gradual development of mathematical methods for studying successive positions of these fronts. It includes an introduction to shock fronts, derives the ray theory for a nonlinear wavefront, discusses kink phe nomena, develops a new theory for plane and curved shock propagation, and contains Huygens' method of wavefronts construction and an extensi on of Fermat's principle. The book also has approximate equations to d iscuss stability of steady transonic flows. The author includes a num ber of examples of the theory to converging wavefronts in gasdynamics and demonstrates numerical computations. All of the results presented are new and were developed by the author and his research group.
Propagation Of Multidimensional Nonlinear Waves And Kinematical Conservation Laws
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Author : Phoolan Prasad
language : en
Publisher: Springer
Release Date : 2018-03-06
Propagation Of Multidimensional Nonlinear Waves And Kinematical Conservation Laws written by Phoolan Prasad and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-06 with Mathematics categories.
This book formulates the kinematical conservation laws (KCL), analyses them and presents their applications to various problems in physics. Finally, it addresses one of the most challenging problems in fluid dynamics: finding successive positions of a curved shock front. The topics discussed are the outcome of collaborative work that was carried out mainly at the Indian Institute of Science, Bengaluru, India. The theory presented in the book is supported by referring to extensive numerical results. The book is organised into ten chapters. Chapters 1–4 offer a summary of and briefly discuss the theory of hyperbolic partial differential equations and conservation laws. Formulation of equations of a weakly nonlinear wavefront and those of a shock front are briefly explained in Chapter 5, while Chapter 6 addresses KCL theory in space of arbitrary dimensions. The remaining chapters examine various analyses and applications of KCL equations ending in the ultimate goal-propagation of a three-dimensional curved shock front and formation, propagation and interaction of kink lines on it.
Multidimensional Hyperbolic Problems And Computations
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Author : James Glimm
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Multidimensional Hyperbolic Problems And Computations written by James Glimm 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.
This IMA Volume in Mathematics and its Applications MULTIDIMENSIONAL HYPERBOLIC PROBLEMS AND COMPUTATIONS is based on the proceedings of a workshop which was an integral part ofthe 1988-89 IMA program on NONLINEAR WAVES. We are grateful to the Scientific Commit tee: James Glimm, Daniel Joseph, Barbara Keyfitz, Andrew Majda, Alan Newell, Peter Olver, David Sattinger and David Schaeffer for planning and implementing an exciting and stimulating year-long program. We especially thank the Work shop Organizers, Andrew Majda and James Glimm, for bringing together many of the major figures in a variety of research fields connected with multidimensional hyperbolic problems. A vner Friedman Willard Miller PREFACE A primary goal of the IMA workshop on Multidimensional Hyperbolic Problems and Computations from April 3-14, 1989 was to emphasize the interdisciplinary nature of contemporary research in this field involving the combination of ideas from the theory of nonlinear partial differential equations, asymptotic methods, numerical computation, and experiments. The twenty-six papers in this volume span a wide cross-section of this research including some papers on the kinetic theory of gases and vortex sheets for incompressible flow in addition to many papers on systems of hyperbolic conservation laws. This volume includes several papers on asymptotic methods such as nonlinear geometric optics, a number of articles applying numerical algorithms such as higher order Godunov methods and front tracking to physical problems along with comparison to experimental data, and also several interesting papers on the rigorous mathematical theory of shock waves.
Nonlinear Partial Differential Equations And Hyperbolic Wave Phenomena
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Author : Norske videnskaps-akademi. Research Program on Nonlinear Partial Differential Equations
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-10-01
Nonlinear Partial Differential Equations And Hyperbolic Wave Phenomena written by Norske videnskaps-akademi. Research Program on Nonlinear Partial Differential Equations and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-01 with Mathematics categories.
This volume presents the state of the art in several directions of research conducted by renowned mathematicians who participated in the research program on Nonlinear Partial Differential Equations at the Centre for Advanced Study at the Norwegian Academy of Science and Letters, Oslo, Norway, during the academic year 2008-09. The main theme of the volume is nonlinear partial differential equations that model a wide variety of wave phenomena. Topics discussed include systems of conservation laws, compressible Navier-Stokes equations, Navier-Stokes-Korteweg type systems in models for phase transitions, nonlinear evolution equations, degenerate/mixed type equations in fluid mechanics and differential geometry, nonlinear dispersive wave equations (Korteweg-de Vries, Camassa-Holm type, etc.), and Poisson interface problems and level set formulations.
Hyperbolic Problems Theory Numerics Applications
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Author : Michael Fey
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-04-01
Hyperbolic Problems Theory Numerics Applications written by Michael Fey 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 1999-04-01 with Mathematics categories.
[Infotext]((Kurztext))These are the proceedings of the 7th International Conference on Hyperbolic Problems, held in Zürich in February 1998. The speakers and contributors have been rigorously selected and present the state of the art in this field. The articles, both theoretical and numerical, encompass a wide range of applications, such as nonlinear waves in solids, various computational fluid dynamics from small-scale combustion to relativistic astrophysical problems, multiphase phenomena and geometrical optics. ((Volltext))These proceedings contain, in two volumes, approximately one hundred papers presented at the conference on hyperbolic problems, which has focused to a large extent on the laws of nonlinear hyperbolic conservation. Two-fifths of the papers are devoted to mathematical aspects such as global existence, uniqueness, asymptotic behavior such as large time stability, stability and instabilities of waves and structures, various limits of the solution, the Riemann problem and so on. Roughly the same number of articles are devoted to numerical analysis, for example stability and convergence of numerical schemes, as well as schemes with special desired properties such as shock capturing, interface fitting and high-order approximations to multidimensional systems. The results in these contributions, both theoretical and numerical, encompass a wide range of applications such as nonlinear waves in solids, various computational fluid dynamics from small-scale combustion to relativistic astrophysical problems, multiphase phenomena and geometrical optics.
Analytical Approaches To Multidimensional Balance Laws
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Author : Olga S. Rozanova
language : en
Publisher: Nova Publishers
Release Date : 2006
Analytical Approaches To Multidimensional Balance Laws written by Olga S. Rozanova and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Science categories.
It is difficult to overestimate the importance of mathematical investigation of balance laws. They arise in many areas of physics, mechanics, chemistry, biology, social sciences. In this collective book we concentrate in particular on the equations of continuous medium and related to them. As a rule, they are very complicated in their primitive form. An important feature of such equations is a possible formation of singularities even in initially smooth solution within a finite time. The structure of the singularities can be very complex. A natural step in the approach to this problem is the transition, despite the three-dimensionality of our world, to spatially one-dimensional model. Significant progress has been achieved in this direction. Unfortunately, the methods of the one-dimensional theory, as usual, cannot be adapted to a case of many spatial variables. However, there are many attempts to deal with multidimensional problems. We would like to present some of them. All of the papers are written by outstanding experts, representing various schools in mathematics and mechanics. Each paper is organised as follows: it contains an elementary (as far as it is possible) introduction to a problem, a brief review of previously published results, and then original results of the authors are presented.
Geometric Optics For Surface Waves In Nonlinear Elasticity
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Author : Jean-François Coulombel
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-04-03
Geometric Optics For Surface Waves In Nonlinear Elasticity written by Jean-François Coulombel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-03 with Education categories.
This work is devoted to the analysis of high frequency solutions to the equations of nonlinear elasticity in a half-space. The authors consider surface waves (or more precisely, Rayleigh waves) arising in the general class of isotropic hyperelastic models, which includes in particular the Saint Venant-Kirchhoff system. Work has been done by a number of authors since the 1980s on the formulation and well-posedness of a nonlinear evolution equation whose (exact) solution gives the leading term of an approximate Rayleigh wave solution to the underlying elasticity equations. This evolution equation, which is referred to as “the amplitude equation”, is an integrodifferential equation of nonlocal Burgers type. The authors begin by reviewing and providing some extensions of the theory of the amplitude equation. The remainder of the paper is devoted to a rigorous proof in 2D that exact, highly oscillatory, Rayleigh wave solutions uε to the nonlinear elasticity equations exist on a fixed time interval independent of the wavelength ε, and that the approximate Rayleigh wave solution provided by the analysis of the amplitude equation is indeed close in a precise sense to uε on a time interval independent of ε. This paper focuses mainly on the case of Rayleigh waves that are pulses, which have profiles with continuous Fourier spectrum, but the authors' method applies equally well to the case of wavetrains, whose Fourier spectrum is discrete.
Analysis And Numerics For Conservation Laws
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Author : Gerald Warnecke
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-05
Analysis And Numerics For Conservation Laws written by Gerald Warnecke 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 2005-12-05 with Mathematics categories.
Whatdoasupernovaexplosioninouterspace,?owaroundanairfoil and knocking in combustion engines have in common? The physical and chemical mechanisms as well as the sizes of these processes are quite di?erent. So are the motivations for studying them scienti?cally. The super- 8 nova is a thermo-nuclear explosion on a scale of 10 cm. Astrophysicists try to understand them in order to get insight into fundamental properties of the universe. In ?ows around airfoils of commercial airliners at the scale of 3 10 cm shock waves occur that in?uence the stability of the wings as well as fuel consumption in ?ight. This requires appropriate design of the shape and structure of airfoils by engineers. Knocking occurs in combustion, a chemical 1 process, and must be avoided since it damages motors. The scale is 10 cm and these processes must be optimized for e?ciency and environmental conside- tions. The common thread is that the underlying ?uid ?ows may at a certain scale of observation be described by basically the same type of hyperbolic s- tems of partial di?erential equations in divergence form, called conservation laws. Astrophysicists, engineers and mathematicians share a common interest in scienti?c progress on theory for these equations and the development of computational methods for solutions of the equations. Due to their wide applicability in modeling of continua, partial di?erential equationsareamajor?eldofresearchinmathematics. Asubstantialportionof mathematical research is related to the analysis and numerical approximation of solutions to such equations. Hyperbolic conservation laws in two or more spacedimensionsstillposeoneofthemainchallengestomodernmathematics.
Iutam Symposium Transsonicum Iv
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Author : H. Sobieczky
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Iutam Symposium Transsonicum Iv written by H. Sobieczky 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 Technology & Engineering categories.
"Symposium Transsonicum" was founded by Klaus Oswatitsch four decades ago when there was clearly a need for a systematic treatment of flow problems in the higher speed regime in aeronautics. The first conference in 1962 brought together scientists concerned with fundamental problems involving the sonic flow speed regime. Results of the conference provided an understanding of some basic tran sonic phenomena by proposing mathematical methods that allowed for the de velopment of practical calculations. The "Transonic Controversy" (about shock free flows) was still an open issue after this meeting. In 1975 the second symposium was held, by then there was much understanding in how to avoid shocks in a steady plane flow to be designed, but still very little was known in unsteady phenomena due to a lack of elucidating experiments. A third meeting in 1988 reflected the availability oflarger computers which allowed the numerical analysis of flows with shocks to a reasonable accuracy. Because we are trying to keep Oswatitsch's heritage in science alive especially in Gottingen, we were asked by the aerospace research community to organize another symposium. Much had been achieved already in the knowledge, techno logy and applications in transonics, so IUT AM had to be convinced that a fourth meeting would not just be a reunion of old friends reminiscing some scientific past. The scientific committee greatly supported my efforts to invite scientists ac tively working in transonic problems which still pose substantial difficulties to ae rospace and turbomachinery industry.