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Author: Gui-Qiang G Chen Publisher: Princeton University Press ISBN: 1400885434 Category : Mathematics Languages : en Pages : 832
Book Description
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.
Author: Gui-Qiang G Chen Publisher: Princeton University Press ISBN: 1400885434 Category : Mathematics Languages : en Pages : 832
Book Description
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.
Author: Hans G Hornung Publisher: World Scientific ISBN: 9814548022 Category : Languages : en Pages : 1740
Book Description
The symposia take place every two years. They are the forum at which scientists concerned with shock waves present their research. They USE shock waves for chemical kinetics studies, for materials studies, and smashing kidney stones; they STUDY the phenomena associated with flows involving shock waves, such as supersonic flow, explosions, detonations, volcanic eruptions, and, in this symposium, even such with-it topics as impact of Shoemaker-Levy on Jupiter and blast waves in the World Trade Center. They also discover new, bigger and better ways of generating flows at hypervelocity speeds and develop their technological tools further.The international exchange of information is documented in the proceedings volumes, which have become a storehouse of information on the subject, documenting the history of this peculiar branch of science that involves chemists, physicists, engineers, geophysicists, material scientists and biologists.
Author: S. Friedlander Publisher: Elsevier ISBN: 0080478301 Category : Science Languages : en Pages : 725
Book Description
This is the fourth volume in a series of survey articles covering many aspects of mathematical fluid dynamics, a vital source of open mathematical problems and exciting physics.
Author: Peter O. K. Krehl Publisher: Springer Science & Business Media ISBN: 3540304215 Category : Science Languages : en Pages : 1298
Book Description
This unique and encyclopedic reference work describes the evolution of the physics of modern shock wave and detonation from the earlier and classical percussion. The history of this complex process is first reviewed in a general survey. Subsequently, the subject is treated in more detail and the book is richly illustrated in the form of a picture gallery. This book is ideal for everyone professionally interested in shock wave phenomena.
Author: Roland Glowinski Publisher: Springer Science & Business Media ISBN: 1402087586 Category : Science Languages : en Pages : 294
Book Description
For more than 250 years partial di?erential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural at ?rst and then those originating from - man activity and technological development. Mechanics, physics and their engineering applications were the ?rst to bene?t from the impact of partial di?erential equations on modeling and design, but a little less than a century ago the Schr ̈ odinger equation was the key opening the door to the application of partial di?erential equations to quantum chemistry, for small atomic and molecular systems at ?rst, but then for systems of fast growing complexity. The place of partial di?erential equations in mathematics is a very particular one: initially, the partial di?erential equations modeling natural phenomena were derived by combining calculus with physical reasoning in order to - press conservation laws and principles in partial di?erential equation form, leading to the wave equation, the heat equation, the equations of elasticity, the Euler and Navier–Stokes equations for ?uids, the Maxwell equations of electro-magnetics, etc. It is in order to solve ‘constructively’ the heat equation that Fourier developed the series bearing his name in the early 19th century; Fourier series (and later integrals) have played (and still play) a fundamental roleinbothpureandappliedmathematics,includingmanyareasquiteremote from partial di?erential equations. On the other hand, several areas of mathematics such as di?erential ge- etry have bene?ted from their interactions with partial di?erential equations.
Author: Steve Armfield Publisher: Springer Science & Business Media ISBN: 3642593348 Category : Science Languages : en Pages : 837
Book Description
We are pleased to present the Proceedings of the Second International Conference on Computational Fluid Dynamics held at the University of Sydney, Australia, from July 15 to 19, 2002. The conference was a productive meeting of scientists, mathematicians and engineers involved in the computation of fluid flow. Keynote lectures were presented in the areas of optimisation, algorithms, turbulence and bio-fluid mechanics. Two hundred and fifty abstracts from many countries were received for con sideration. The executive committee, consisting of A. Lerat, M. Napolitano, J.J. Chattot, N. Satofuka and myself, were responsible for the selection of papers. Each of the members had a separate subcommittee to carry out the evaluation. One hundred and seventy papers were selected of which one hundred and fifty two were presented at the conference. All papers that appear in the proceedings have been peer reviewed by a panel of experts (with a minimum of two for every paper) before publication. The conference was attended by 160 delegates with a minimum of late with drawals. The informal and friendly atmosphere provided by the university sur roundings was highly appreciated, and the technical aspects of the conference were stimulating. It is appropriate here to thank Alain Lerat, the retiring secretary of the international scientific committee of the conference. We also wish to welcome J. J. Chattot who is the incoming secretary.
Author: Walter Gautschi Publisher: American Mathematical Soc. ISBN: 0821802917 Category : Mathematics Languages : en Pages : 669
Book Description
Proceedings of an International Conference held in Vancouver, B.C., August 1993, to commemorate the 50th anniversary of the founding of the journal Mathematics of Computation. It consisted of a Symposium on Numerical Analysis and a Minisymposium of Computational Number Theory. This proceedings contains 14 invited papers, including two not presented at the conference--an historical essay on integer factorization, and a paper on componentwise perturbation bounds in linear algebra. The invited papers present surveys on the various subdisciplines covered by Mathematics of Computation, in a historical perspective and in a language accessible to a wide audience. The 46 contributed papers address contemporary specialized work. Annotation copyright by Book News, Inc., Portland, OR
Author: Mark I. Freidlin Publisher: Springer Science & Business Media ISBN: 1461519918 Category : Mathematics Languages : en Pages : 297
Book Description
Volume 2 offers three in-depth articles covering significant areas in applied mathematics research. Chapters feature numerous illustrations, extensive background material and technical details, and abundant examples. The authors analyze nonlinear front propagation for a large class of semilinear partial differential equations using probabilistic methods; examine wave localization phenomena in one-dimensional random media; and offer an extensive introduction to certain model equations for nonlinear wave phenomena.
Author: James Glimm Publisher: World Scientific ISBN: 9814548588 Category : Languages : en Pages : 510
Book Description
The intellectual center of this proceedings volume is the subject of conservation laws. Conservation laws are the most basic model of many continuum processes, and for this reason they govern the motion of fluids, solids, and plasma. They are basic to the understanding of more complex modeling issues, such as multiphase flow, chemically reacting flow, and non-equilibrium thermodynamics. Equations of this type also arise in novel and unexpected areas, such as the pattern recognition and image processing problem of edge enhancement and detection. The articles in this volume address the entire range of the study of conservation laws, including the fundamental mathematical theory, familiar and novel applications, and the numerical problem of finding effective computational algorithms for the solution of these problems.
Author: Gui-Qiang G Chen
Author: Gui-Qiang G Chen
Author: Hans G Hornung
Author: S. Friedlander
Author: Peter O. K. Krehl
Author: Roland Glowinski
Author: Steve Armfield
Author: Walter Gautschi
Author: Allen Mark Tesdall
Author: Mark I. Freidlin
Author: James Glimm