Rogue and Shock Waves in Nonlinear Dispersive Media

Rogue and Shock Waves in Nonlinear Dispersive Media
Author: Miguel Onorato
Publisher: Springer
Total Pages: 376
Release: 2016-09-19
Genre: Science
ISBN: 331939214X

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This self-contained set of lectures addresses a gap in the literature by providing a systematic link between the theoretical foundations of the subject matter and cutting-edge applications in both geophysical fluid dynamics and nonlinear optics. Rogue and shock waves are phenomena that may occur in the propagation of waves in any nonlinear dispersive medium. Accordingly, they have been observed in disparate settings – as ocean waves, in nonlinear optics, in Bose-Einstein condensates, and in plasmas. Rogue and dispersive shock waves are both characterized by the development of extremes: for the former, the wave amplitude becomes unusually large, while for the latter, gradients reach extreme values. Both aspects strongly influence the statistical properties of the wave propagation and are thus considered together here in terms of their underlying theoretical treatment. This book offers a self-contained graduate-level text intended as both an introduction and reference guide for a new generation of scientists working on rogue and shock wave phenomena across a broad range of fields in applied physics and geophysics.

Rogue Waves

Rogue Waves
Author: Boling Guo
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 230
Release: 2017-06-26
Genre: Mathematics
ISBN: 3110469693

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This book gives an overview of the theoretical research on rogue waves and discusses solutions to rogue wave formation via the Darboux and bilinear transformations, algebro-geometric reduction, and inverse scattering and similarity transformations. Studies on nonlinear optics are included, making the book a comprehensive reference for researchers in applied mathematics, optical physics, geophysics, and ocean engineering. Contents The Research Process for Rogue Waves Construction of Rogue Wave Solution by the Generalized Darboux Transformation Construction of Rogue Wave Solution by Hirota Bilinear Method, Algebro-geometric Approach and Inverse Scattering Method The Rogue Wave Solution and Parameters Managing in Nonautonomous Physical Model

Shock Waves

Shock Waves
Author: Tai-Ping Liu
Publisher: American Mathematical Soc.
Total Pages: 437
Release: 2021-10-12
Genre: Education
ISBN: 1470465671

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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.

Shock Waves and Reaction—Diffusion Equations

Shock Waves and Reaction—Diffusion Equations
Author: Joel Smoller
Publisher: Springer Science & Business Media
Total Pages: 650
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461208734

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For this edition, a number of typographical errors and minor slip-ups have been corrected. In addition, following the persistent encouragement of Olga Oleinik, I have added a new chapter, Chapter 25, which I titled "Recent Results." This chapter is divided into four sections, and in these I have discussed what I consider to be some of the important developments which have come about since the writing of the first edition. Section I deals with reaction-diffusion equations, and in it are described both the work of C. Jones, on the stability of the travelling wave for the Fitz-Hugh-Nagumo equations, and symmetry-breaking bifurcations. Section II deals with some recent results in shock-wave theory. The main topics considered are L. Tartar's notion of compensated compactness, together with its application to pairs of conservation laws, and T.-P. Liu's work on the stability of viscous profiles for shock waves. In the next section, Conley's connection index and connection matrix are described; these general notions are useful in con structing travelling waves for systems of nonlinear equations. The final sec tion, Section IV, is devoted to the very recent results of C. Jones and R. Gardner, whereby they construct a general theory enabling them to locate the point spectrum of a wide class of linear operators which arise in stability problems for travelling waves. Their theory is general enough to be applica ble to many interesting reaction-diffusion systems.

Propagation and Reflection of Shock Waves

Propagation and Reflection of Shock Waves
Author: Fedor Vasil?evich Shugaev
Publisher: World Scientific
Total Pages: 264
Release: 1998
Genre: Science
ISBN: 9789810230104

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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.

Shock Waves in Condensed Matter

Shock Waves in Condensed Matter
Author: Y. M. Gupta
Publisher: Springer Science & Business Media
Total Pages: 922
Release: 2012-12-06
Genre: Science
ISBN: 1461322073

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The Fourth American Physical Society Topical Conference on Shock Waves in Condensed Matter was held in Spokane, Washington, July 22-25, 1985. Two hundred and fifty scientists and engineers representing thirteen countries registered at the conference. The countries represented included the United States of America, Australia, Canada, The People's Repub lic of China, France, India, Israel, Japan, Republic of China (Taiwan), United Kingdom, U. S. S. R, Switzerland and West Germany. One hundred and sixty-two technical papers, cov ering recent developments in shock wave and high pressure physics, were presented. All of the abstracts have been published in the September 1985 issue of the Bulletin of the American Physical Society. The topical conferences, held every two years since 1979, have become the principal forum for shock wave studies in condensed materials. Both formal and informal technical discussions regarding recent developments conveyed a sense of excitement. Consistent with the past conferences, the purpose of this conference was to bring together scientists and engineers studying the response of condensed matter to dynamic high pressures and temperatures. Papers covering experimental, theoretical, and numerical studies of con densed matter properties were presented. A noteworthy feature of this conference was the participation by several leading scientists engaged in static high pressure research. Donald Curran served as the Master of Ceremonies at the conference banquet, which was at tended by two hundred and seventy-five conference participants and guests including Dr. Samuel Smith, the new President of Washington State University. Dr.

Shock Wave Science and Technology Reference Library, Vol. 3

Shock Wave Science and Technology Reference Library, Vol. 3
Author: Yasuyuki Horie
Publisher: Springer Science & Business Media
Total Pages: 294
Release: 2008-09-18
Genre: Science
ISBN: 3540770801

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This book is the second volume of Solids Volumes in theShockWaveScience and Technology Reference Library. These volumes are primarily concerned with high-pressure shock waves in solid media, including detonation and hi- velocity impact and penetration events. This volume contains four articles. The ?rst two describe the reactive behavior of condensed-phase explosives, and the remaining two discuss the inert, mechanical response of solid materials. The articles are each se- contained, and can be read independently of each other. They o?er a timely reference, for beginners as well as professional scientists and engineers, cov- ing the foundations and the latest progress, and include burgeoning devel- ment as well as challenging unsolved problems. The ?rst chapter, by S. She?eld and R. Engelke, discusses the shock initiation and detonation phenomena of solids explosives. The article is an outgrowth of two previous review articles: “Explosives” in vol. 6 of En- clopedia of Applied Physics (VCH, 1993) and “Initiation and Propagation of Detonation in Condensed-Phase High Explosives” in High-Pressure Shock Compression of Solids III (Springer, 1998). This article is not only an - dated review, but also o?ers a concise heuristic introduction to shock waves and condensed-phase detonation. The authors emphasize the point that d- onation is not an uncontrollable, chaotic event, but that it is an orderly event that is governed by and is describable in terms of the conservation of mass, momentum, energy and certain material-speci?c properties of the explosive.

Handbook of Shock Waves, Three Volume Set

Handbook of Shock Waves, Three Volume Set
Author: Gabi Ben-Dor
Publisher: Elsevier
Total Pages: 2188
Release: 2000-10-18
Genre: Science
ISBN: 0080533728

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The Handbook of Shock Waves contains a comprehensive, structured coverage of research topics related to shock wave phenomena including shock waves in gases, liquids, solids, and space. Shock waves represent an extremely important physical phenomena which appears to be of special practical importance in three major fields: compressible flow (aerodynamics), materials science, and astrophysics. Shock waves comprise a phenomenon that occurs when pressure builds to force a reaction, i.e. sonic boom that occurs when a jet breaks the speed of sound.This Handbook contains experimental, theoretical, and numerical results which never before appeared under one cover; the first handbook of its kind.The Handbook of Shock Waves is intended for researchers and engineers active in shock wave related fields. Additionally, R&D establishments, applied science & research laboratories and scientific and engineering libraries both in universities and government institutions. As well as, undergraduate and graduate students in fluid mechanics, gas dynamics, and physics. Key Features* Ben-Dor is known as one of the founders of the field of shock waves* Covers a broad spectrum of shock wave research topics* Provides a comprehensive description of various shock wave related subjects* First handbook ever to include under one separate cover: experimental, theoretical, and numerical results