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Mathematical Analysis Of Shock Wave Reflection
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Book Synopsis Mathematical Analysis of Shock Wave Reflection by : Shuxing Chen
Download or read book Mathematical Analysis of Shock Wave Reflection written by Shuxing Chen and published by Springer Nature. This book was released on 2020-09-04 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed to make careful analysis to various mathematical problems derived from shock reflection by using the theory of partial differential equations. The occurrence, propagation and reflection of shock waves are important phenomena in fluid dynamics. Comparing the plenty of studies of physical experiments and numerical simulations on this subject, this book makes main efforts to develop the related theory of mathematical analysis, which is rather incomplete so far. The book first introduces some basic knowledge on the system of compressible flow and shock waves, then presents the concept of shock polar and its properties, particularly the properties of the shock polar for potential flow equation, which are first systematically presented and proved in this book. Mathematical analysis of regular reflection and Mach reflection in steady and unsteady flow are the most essential parts of this book. To give challenges in future research, some long-standing open problems are listed in the end. This book is attractive to researchers in the fields of partial differential equations, system of conservation laws, fluid dynamics, and shock theory.
Book Synopsis The Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures by : Gui-Qiang G Chen
Download or read book The Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures written by Gui-Qiang G Chen and published by Princeton University Press. This book was released on 2018-02-27 with total page 832 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a survey of recent developments in the analysis of shock reflection-diffraction, a detailed presentation of original mathematical proofs of von Neumann's conjectures for potential flow, and a collection of related results and new techniques in the analysis of partial differential equations (PDEs), as well as a set of fundamental open problems for further development. Shock waves are fundamental in nature. They are governed by the Euler equations or their variants, generally in the form of nonlinear conservation laws—PDEs of divergence form. When a shock hits an obstacle, shock reflection-diffraction configurations take shape. To understand the fundamental issues involved, such as the structure and transition criteria of different configuration patterns, it is essential to establish the global existence, regularity, and structural stability of shock reflection-diffraction solutions. This involves dealing with several core difficulties in the analysis of nonlinear PDEs—mixed type, free boundaries, and corner singularities—that also arise in fundamental problems in diverse areas such as continuum mechanics, differential geometry, mathematical physics, and materials science. Presenting recently developed approaches and techniques, which will be useful for solving problems with similar difficulties, this book opens up new research opportunities.
Book Synopsis Supersonic Flow and Shock Waves by : Richard Courant
Download or read book Supersonic Flow and Shock Waves written by Richard Courant and published by Springer Science & Business Media. This book was released on 1999-02-11 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Courant and Friedrich's classical treatise was first published in 1948 and tThe basic research for it took place during World War II. However, many aspects make the book just as interesting as a text and a reference today. It treats the dynamics of compressible fluids in mathematical form, and attempts to present a systematic theory of nonlinear wave propagation, particularly in relation to gas dynamics. Written in the form of an advanced textbook, it should appeal to engineers, physicists and mathematicians alike.
Book Synopsis Propagation and Reflection of Shock Waves by : Fedor Vasil?evich Shugaev
Download or read book Propagation and Reflection of Shock Waves written by Fedor Vasil?evich Shugaev and published by World Scientific. This book was released on 1998 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with the propagation of three-dimensional shock waves and their reflection from curved walls. It is divided into two parts. The first part presents a ray method. This is based on the expansion of fluid properties in power series at an arbitrary point on the shock front. Continuous fractions are used. Results for shock propagation in non-uniform fluids are given.The second part discusses the shock reflection from a concave body. The important shock-focusing problem is included. The work is supported by both numerical and experimental results. Many interesting features, such as formation of a jet, vortices and the appearance of disturbances on the shock front, are discussed.Besides shock waves in gases, the distinctive features of shock propagation through a weakly ionized plasma are considered.
Book Synopsis Advances in the Theory of Shock Waves by : Heinrich Freistühler
Download or read book Advances in the Theory of Shock Waves written by Heinrich Freistühler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the field known as "the mathematical theory of shock waves," very exciting and unexpected developments have occurred in the last few years. Joel Smoller and Blake Temple have established classes of shock wave solutions to the Einstein Euler equations of general relativity; indeed, the mathematical and physical con sequences of these examples constitute a whole new area of research. The stability theory of "viscous" shock waves has received a new, geometric perspective due to the work of Kevin Zumbrun and collaborators, which offers a spectral approach to systems. Due to the intersection of point and essential spectrum, such an ap proach had for a long time seemed out of reach. The stability problem for "in viscid" shock waves has been given a novel, clear and concise treatment by Guy Metivier and coworkers through the use of paradifferential calculus. The L 1 semi group theory for systems of conservation laws, itself still a recent development, has been considerably condensed by the introduction of new distance functionals through Tai-Ping Liu and collaborators; these functionals compare solutions to different data by direct reference to their wave structure. The fundamental prop erties of systems with relaxation have found a systematic description through the papers of Wen-An Yong; for shock waves, this means a first general theorem on the existence of corresponding profiles. The five articles of this book reflect the above developments.
Book Synopsis Shock Waves and Reaction—Diffusion Equations by : Joel Smoller
Download or read book Shock Waves and Reaction—Diffusion Equations written by Joel Smoller and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: . . . the progress of physics will to a large extent depend on the progress of nonlinear mathe matics, of methods to solve nonlinear equations . . . and therefore we can learn by comparing different nonlinear problems. WERNER HEISENBERG I undertook to write this book for two reasons. First, I wanted to make easily available the basics of both the theory of hyperbolic conservation laws and the theory of systems of reaction-diffusion equations, including the generalized Morse theory as developed by C. Conley. These important subjects seem difficult to learn since the results are scattered throughout the research journals. 1 Second, I feel that there is a need to present the modern methods and ideas in these fields to a wider audience than just mathe maticians. Thus, the book has some rather sophisticated aspects to it, as well as certain textbook aspects. The latter serve to explain, somewhat, the reason that a book with the title Shock Waves and Reaction-Diffusion Equations has the first nine chapters devoted to linear partial differential equations. More precisely, I have found from my classroom experience that it is far easier to grasp the subtleties of nonlinear partial differential equations after one has an understanding of the basic notions in the linear theory. This book is divided into four main parts: linear theory, reaction diffusion equations, shock wave theory, and the Conley index, in that order. Thus, the text begins with a discussion of ill-posed problems.
Book Synopsis Shock Wave Reflection Phenomena by : Gabi Ben-Dor
Download or read book Shock Wave Reflection Phenomena written by Gabi Ben-Dor and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: The phenomenon of shock wave reflection was first reported by the distinguished philosopher Ernst Mach in 1878. Its study was then abandoned for a period of about 60 years until its investigation was initiated in the early 1940s by Professor John von Neumann and Professor Bleakney. Under their supervision, 15 years of intensive research related to various aspects of the reflection of shock waves in pseudo-steady flows were carried out. It was during this period that the four basic shock wave reflection configurations were discovered. Then, for a period of about 10 years from the mid 1950s until the mid 1960s, investigation of the reflection phenomenon of shock waves was kept on a low flame all over the world (e. g. Australia, Japan, Canada, U. S. A. , U. S. S. R. , etc. ) until Professor Bazhenova from the U. S. S. R. , Professor Irvine Glass from Canada, and Professor Roy Henderson from Australia re initiated the study of this and related phenomena. Under their scientific supervision and leadership, numerous findings related to this phenomenon were reported. Probably the most productive research group in the mid 1970s was that led by Professor Irvine Glass in the Institute of Aerospace Studies of the University of Toronto. In 1978, exactly 100 years after Ernst Mach first reported his discovery of the reflection phenomenon, I published my Ph. D. thesis in which, for the first time, analytical transition criteria between the various shock wave reflection configurations were established.
Book Synopsis Shock Wave Reflection Phenomena by : Gabi Ben-Dor
Download or read book Shock Wave Reflection Phenomena written by Gabi Ben-Dor and published by . This book was released on 1992 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Shock Waves @ Marseille IV by : Raymond Brun
Download or read book Shock Waves @ Marseille IV written by Raymond Brun and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently, there have been significant advances in the fields of high-enthalpy hypersonic flows, high-temperature gas physics, and chemistry shock propagation in various media, industrial and medical applications of shock waves, and shock-tube technology. This series contains all the papers and lectures of the 19th International Symposium on Shock Waves held in Marseille in 1993. They are published in four topical volumes, each containing papers on related topics, and preceded by an overview written by a leading international expert. The volumes may be purchased independently.
Book Synopsis Shock Wave Interactions by : Konstantinos Kontis
Download or read book Shock Wave Interactions written by Konstantinos Kontis and published by Springer. This book was released on 2018-03-28 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited monograph contains the proceedings of the International Shock Interaction Symposium, which emerged as an heir to both the Mach Reflection and Shock Vortex Interaction Symposia. These scientific biannual meetings provide an ideal platform to expose new developments and discuss recent challenges in the field of shock wave interaction phenomena. The goal of the symposia is to offer a forum for international interaction between young and established scientists in the field of shock and blast wave interaction phenomena. The target audience of this book comprises primarily researchers and experts in the field of shock waves, but the book may also be beneficial for young scientists and graduate students alike.
Download or read book Technical Abstract Bulletin written by and published by . This book was released on with total page 912 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis U.S. Government Research Reports by :
Download or read book U.S. Government Research Reports written by and published by . This book was released on 1962 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Supersonic Flow and Shock Waves by : R. Courant
Download or read book Supersonic Flow and Shock Waves written by R. Courant and published by Trieste Publishing. This book was released on 2017-10-04 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Trieste Publishing has a massive catalogue of classic book titles. Our aim is to provide readers with the highest quality reproductions of fiction and non-fiction literature that has stood the test of time. The many thousands of books in our collection have been sourced from libraries and private collections around the world.The titles that Trieste Publishing has chosen to be part of the collection have been scanned to simulate the original. Our readers see the books the same way that their first readers did decades or a hundred or more years ago. Books from that period are often spoiled by imperfections that did not exist in the original. Imperfections could be in the form of blurred text, photographs, or missing pages. It is highly unlikely that this would occur with one of our books. Our extensive quality control ensures that the readers of Trieste Publishing's books will be delighted with their purchase. Our staff has thoroughly reviewed every page of all the books in the collection, repairing, or if necessary, rejecting titles that are not of the highest quality. This process ensures that the reader of one of Trieste Publishing's titles receives a volume that faithfully reproduces the original, and to the maximum degree possible, gives them the experience of owning the original work.We pride ourselves on not only creating a pathway to an extensive reservoir of books of the finest quality, but also providing value to every one of our readers. Generally, Trieste books are purchased singly - on demand, however they may also be purchased in bulk. Readers interested in bulk purchases are invited to contact us directly to enquire about our tailored bulk rates.
Download or read book Shock Waves written by Tai-Ping Liu and published by American Mathematical Soc.. This book was released on 2021-10-12 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the fundamentals of the shock wave theory. The first part of the book, Chapters 1 through 5, covers the basic elements of the shock wave theory by analyzing the scalar conservation laws. The main focus of the analysis is on the explicit solution behavior. This first part of the book requires only a course in multi-variable calculus, and can be used as a text for an undergraduate topics course. In the second part of the book, Chapters 6 through 9, this general theory is used to study systems of hyperbolic conservation laws. This is a most significant well-posedness theory for weak solutions of quasilinear evolutionary partial differential equations. The final part of the book, Chapters 10 through 14, returns to the original subject of the shock wave theory by focusing on specific physical models. Potentially interesting questions and research directions are also raised in these chapters. The book can serve as an introductory text for advanced undergraduate students and for graduate students in mathematics, engineering, and physical sciences. Each chapter ends with suggestions for further reading and exercises for students.
Book Synopsis Supersonic Flow and Shock Waves by : Richard Courant
Download or read book Supersonic Flow and Shock Waves written by Richard Courant and published by Forgotten Books. This book was released on 2016-09-13 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Supersonic Flow and Shock Waves: A Manual on the Mathematical Theory of Non-Linear Wave Motion For obvious reasons, detailed references to classified material and specific applications are not provided, and thus the table of contents may convey an impression of overemphasis on theoretical aspects. The fol lowing comments may, therefore, be made. Chapter I contains classical facts underlying any mathematical treatment of compressible flow. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1973 with total page 1040 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Book Synopsis Shock Wave Dynamics by : George Emanuel
Download or read book Shock Wave Dynamics written by George Emanuel and published by CRC Press. This book was released on 2012-12-18 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: Working knowledge of the relations of various quantities and their derivatives across a shock wave is useful for any advanced research involving shock waves. Although these relations can be derived in principle by any diligent student of the subject, the derivations are often not trivial, and once derived, neither the approach nor the result can be confidently verified. Comprehensive and analytical, Shock Wave Dynamics: Derivatives and Related Topics includes not only the final results but also the methods, which are of great practical value as examples of mathematical procedure in this field. The book focuses on shock wave derivatives under various conditions and extensively covers shock-generated vorticity, including a novel analysis of triple points. Special care is given to the presentation of assumptions, implementation requirements, and the illustrative examples included for partial verification of the preceding analysis. Designed both as a research monograph and for self study, Shock Wave Dynamics is a complete discussion of shock wave dynamics. An analytical exploration of shock wave phenomena, it will be interesting reading for experts in the field of high-speed gas dynamics. Given today's emphasis on numerical simulation, it will also be of interest to computational engineers as a source for code verification and validation.
