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The Mathematics Of Shock Reflection Diffraction And Von Neumanns Conjectures
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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 The Mathematics of Shock Reflection-diffraction and Von Neumann's Conjectures by : Gui-Qiang Chen
Download or read book The Mathematics of Shock Reflection-diffraction and Von Neumann's Conjectures written by Gui-Qiang Chen and published by . This book was released on 2018 with total page 814 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 829 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 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 Complex Analysis and Dynamical Systems IV by : Mark Lʹvovich Agranovskiĭ
Download or read book Complex Analysis and Dynamical Systems IV written by Mark Lʹvovich Agranovskiĭ and published by American Mathematical Soc.. This book was released on 2011 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume cover a wide variety of topics in differential geometry, general relativity, and partial differential equations. In addition, there are several articles dealing with various aspects of Lie groups and mathematics physics. Taken together, the articles provide the reader with a panorama of activity in general relativity and partial differential equations, drawn by a number of leading figures in the field. The companion volume (Contemporary Mathematics, Volume 553) is devoted to function theory and optimization.
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 Industrial Mathematics and Complex Systems by : Pammy Manchanda
Download or read book Industrial Mathematics and Complex Systems written by Pammy Manchanda and published by Springer. This book was released on 2017-10-18 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book discusses essential topics in industrial and applied mathematics such as image processing with a special focus on medical imaging, biometrics and tomography. Applications of mathematical concepts to areas like national security, homeland security and law enforcement, enterprise and e-government services, personal information and business transactions, and brain-like computers are also highlighted. These contributions – all prepared by respected academicians, scientists and researchers from across the globe – are based on papers presented at the international conference organized on the occasion of the Silver Jubilee of the Indian Society of Industrial and Applied Mathematics (ISIAM) held from 29 to 31 January 2016 at Sharda University, Greater Noida, India. The book will help young scientists and engineers grasp systematic developments in those areas of mathematics that are essential to properly understand challenging contemporary problems.
Book Synopsis Nonlinear Conservation Laws and Applications by : Alberto Bressan
Download or read book Nonlinear Conservation Laws and Applications written by Alberto Bressan and published by Springer Science & Business Media. This book was released on 2011-04-19 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Summer Program on Nonlinear Conservation Laws and Applications held at the IMA on July 13--31, 2009. Hyperbolic conservation laws is a classical subject, which has experienced vigorous growth in recent years. The present collection provides a timely survey of the state of the art in this exciting field, and a comprehensive outlook on open problems. Contributions of more theoretical nature cover the following topics: global existence and uniqueness theory of one-dimensional systems, multidimensional conservation laws in several space variables and approximations of their solutions, mathematical analysis of fluid motion, stability and dynamics of viscous shock waves, singular limits for viscous systems, basic principles in the modeling of turbulent mixing, transonic flows past an obstacle and a fluid dynamic approach for isometric embedding in geometry, models of nonlinear elasticity, the Monge problem, and transport equations with rough coefficients. In addition, there are a number of papers devoted to applications. These include: models of blood flow, self-gravitating compressible fluids, granular flow, charge transport in fluids, and the modeling and control of traffic flow on networks.
Book Synopsis Nonlinear Partial Differential Equations by : Helge Holden
Download or read book Nonlinear Partial Differential Equations written by Helge Holden and published by Springer Science & Business Media. This book was released on 2012-01-14 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topic of the 2010 Abel Symposium, hosted at the Norwegian Academy of Science and Letters, Oslo, was Nonlinear Partial Differential Equations, the study of which is of fundamental importance in mathematics and in almost all of natural sciences, economics, and engineering. This area of mathematics is currently in the midst of an unprecedented development worldwide. Differential equations are used to model phenomena of increasing complexity, and in areas that have traditionally been outside the realm of mathematics. New analytical tools and numerical methods are dramatically improving our understanding of nonlinear models. Nonlinearity gives rise to novel effects reflected in the appearance of shock waves, turbulence, material defects, etc., and offers challenging mathematical problems. On the other hand, new mathematical developments provide new insight in many applications. These proceedings present a selection of the latest exciting results by world leading researchers.
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 . This book was released on 2020 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 Princeton Companion to Applied Mathematics by : Nicholas J. Higham
Download or read book The Princeton Companion to Applied Mathematics written by Nicholas J. Higham and published by Princeton University Press. This book was released on 2015-09-15 with total page 1016 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more. Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics. Features nearly 200 entries organized thematically and written by an international team of distinguished contributors Presents the major ideas and branches of applied mathematics in a clear and accessible way Explains important mathematical concepts, methods, equations, and applications Introduces the language of applied mathematics and the goals of applied mathematical research Gives a wide range of examples of mathematical modeling Covers continuum mechanics, dynamical systems, numerical analysis, discrete and combinatorial mathematics, mathematical physics, and much more Explores the connections between applied mathematics and other disciplines Includes suggestions for further reading, cross-references, and a comprehensive index
Book Synopsis Hyperbolic Problems: Theory, Numerics and Applications by : Eitan Tadmor
Download or read book Hyperbolic Problems: Theory, Numerics and Applications written by Eitan Tadmor and published by American Mathematical Soc.. This book was released on 2009 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 'HYP2008', was held at the University of Maryland from June 9-13, 2008. This book, the first in a two-part volume, contains nineteen papers based on plenary and invited talks presented at the conference.
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 Hyperbolic Problems by : Eitan Tadmor
Download or read book Hyperbolic Problems written by Eitan Tadmor and published by American Mathematical Society(RI). This book was released on 2009 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'The International Conference on Hyperbolic Problems: Theory, Numerics and Applications', 'HYP2008', was held at the University of Maryland from June 9-14, 2008. This title contains articles that cover a range of multi-disciplinary topics addressing theoretical, modeling and computational issues arising under the umbrella of 'hyperbolic PDEs'.
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 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 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 2007-08-28 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive state-of-the-knowledge summation of shock wave reflection phenomena from a phenomenological point of view. It includes a thorough introduction to oblique shock wave reflections, dealing with both regular and Mach types. It also covers in detail the corresponding two- and three-shock theories. The book moves on to describe reflection phenomena in a variety of flow types, as well as providing the resolution of the Neumann paradox.
