Wavefronts And Rays As Characteristics And Asymptotics (Third Edition)
Wavefronts And Rays As Characteristics And Asymptotics (Third Edition)

Author: Andrej Bona

Publisher: World Scientific

Published: 2020-09-24

Total Pages: 357

ISBN-13: 9811226482

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Characteristics and asymptotics of partial differential equations play an important role in mathematical physics since they lead to insightful solutions of complex problems that might not be solvable otherwise. They constitute, however, a difficult subject, and the purpose of this book, with its additions and refinements that led to its third edition, is to present this subject in an accessible manner, without decreasing the rigor. As any method, characteristics and asymptotics have their limitations. This important issue is addressed in the last chapter, where we discuss caustics, which must be understood in applications of the method, and which constitute a fertile ground for further mathematical research.The book is both a research reference and a textbook. Its careful and explanatory style, which includes numerous exercises with detailed solutions, makes it an excellent textbook for senior undergraduate and graduate courses, as well as for independent studies. Six appendices are provided, which form a self-contained course on applied mathematics and can be used as a textbook on its own.

Waves And Rays In Seismology: Answers To Unasked Questions (Third Edition)
Waves And Rays In Seismology: Answers To Unasked Questions (Third Edition)

Author: Michael A Slawinski

Publisher: World Scientific

Published: 2020-11-20

Total Pages: 654

ISBN-13: 9811226458

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This is a book on seismology dealing with advanced aspects of wave propagation in complex media. It can also be viewed as a book on mathematical modelling, wherein the accuracy of describing seismic phenomena exemplifies the modelling itself. The book gives an insight into the power of abstractness by applying the same mathematical methods and strategies to solve a variety of different physical problems. This book covers a broad range of topics in an advanced yet accessible manner. Each chapter is accompanied by a number of solved exercises, which render the book convenient for a lecturer and facilitate its use for an independent study. The details of mathematical methods are discussed in the appendices, which form a substantial portion of the book.

Waves And Rays In Elastic Continua (3rd Edition)
Waves And Rays In Elastic Continua (3rd Edition)

Author: Michael A Slawinski

Publisher: World Scientific Publishing Company

Published: 2014-12-15

Total Pages: 654

ISBN-13: 9814644218

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The present book — which is the third, significantly revised edition of the textbook originally published by Elsevier Science — emphasizes the interdependence of mathematical formulation and physical meaning in the description of seismic phenomena. Herein, we use aspects of continuum mechanics, wave theory and ray theory to explain phenomena resulting from the propagation of seismic waves.The book is divided into three main sections: Elastic Continua, Waves and Rays and Variational Formulation of Rays. There is also a fourth part, which consists of appendices.In Elastic Continua, we use continuum mechanics to describe the material through which seismic waves propagate, and to formulate a system of equations to study the behaviour of such a material. In Waves and Rays, we use these equations to identify the types of body waves propagating in elastic continua as well as to express their velocities and displacements in terms of the properties of these continua. To solve the equations of motion in anisotropic inhomogeneous continua, we invoke the concept of a ray. In Variational Formulation of Rays, we show that, in elastic continua, a ray is tantamount to a trajectory along which a seismic signal propagates in accordance with the variational principle of stationary traveltime. Consequently, many seismic problems in elastic continua can be conveniently formulated and solved using the calculus of variations. In the Appendices, we describe two mathematical concepts that are used in the book; namely, homogeneity of a function and Legendre's transformation. This section also contains a list of symbols.

Waves And Rays In Elastic Continua (Fourth Edition)
Waves And Rays In Elastic Continua (Fourth Edition)

Author: Michael A Slawinski

Publisher: World Scientific

Published: 2020-09-24

Total Pages: 680

ISBN-13: 9811226423

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Seismology, as a branch of mathematical physics, is an active subject of both research and development. Its reliance on computational and technological advances continuously motivates the developments of its underlying theory. The fourth edition of Waves and Rays in Elastic Continua responds to these needs.The book is both a research reference and a textbook. Its careful and explanatory style, which includes numerous exercises with detailed solutions, makes it an excellent textbook for the senior undergraduate and graduate courses, as well as for an independent study. Used in its entirety, the book could serve as a sole textbook for a year-long course in quantitative seismology. Its parts, however, are designed to be used independently for shorter courses with different emphases. The book is not limited to quantitive seismology; it can serve as a textbook for courses in mathematical physics or applied mathematics.

Waves And Rays In Seismology: Answers To Unasked Questions (Second Edition)
Waves And Rays In Seismology: Answers To Unasked Questions (Second Edition)

Author: Michael A Slawinski

Publisher: World Scientific

Published: 2018-05-04

Total Pages: 577

ISBN-13: 9813239891

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'In summary, Professor Slawinski has written an engaging volume covering an unfamiliar topic in a highly accessible fashion. Non-specialists will gain a significant appreciation of the unique complexities associated with seismology.'Contemporary PhysicsThe author dedicates this book to readers who are concerned with finding out the status of concepts, statements and hypotheses, and with clarifying and rearranging them in a logical order. It is thus not intended to teach tools and techniques of the trade, but to discuss the foundations on which seismology — and in a larger sense, the theory of wave propagation in solids — is built. A key question is: why and to what degree can a theory developed for an elastic continuum be used to investigate the propagation of waves in the Earth, which is neither a continuum nor fully elastic. But the scrutiny of the foundations goes much deeper: material symmetry, effective tensors, equivalent media; the influence (or, rather, the lack thereof) of gravitational and thermal effects and the rotation of the Earth, are discussed ab initio. The variational principles of Fermat and Hamilton and their consequences for the propagation of elastic waves, causality, Noether's theorem and its consequences on conservation of energy and conservation of linear momentum are but a few topics that are investigated in the process to establish seismology as a science and to investigate its relation to subjects like realism and empiricism in natural sciences, to the nature of explanations and predictions, and to experimental verification and refutation.In the second edition, new sections, figures, examples, exercises and remarks are added. Most importantly, however, four new appendices of about one-hundred pages are included, which can serve as a self-contained continuum-mechanics course on finite elasticity. Also, they broaden the scope of elasticity theory commonly considered in seismology.

Analytical Fluid Dynamics, Third Edition
Analytical Fluid Dynamics, Third Edition

Author: George Emanuel

Publisher: CRC Press

Published: 2017-09-18

Total Pages: 651

ISBN-13: 1351374591

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New Edition Now Covers Shock-Wave Analysis An in-depth presentation of analytical methods and physical foundations, Analytical Fluid Dynamics, Third Edition breaks down the "how" and "why" of fluid dynamics. While continuing to cover the most fundamental topics in fluid mechanics, this latest work emphasizes advanced analytical approaches to aid in the analytical process and corresponding physical interpretation. It also addresses the need for a more flexible mathematical language (utilizing vector and tensor analysis and transformation theory) to cover the growing complexity of fluid dynamics. Revised and updated, the text centers on shock-wave structure, shock-wave derivatives, and shock-produced vorticity; supersonic diffusers; thrust and lift from an asymmetric nozzle; and outlines operator methods and laminar boundary-layer theory. In addition, the discussion introduces pertinent assumptions, reasons for studying a particular topic, background discussion, illustrative examples, and numerous end-of-chapter problems. Utilizing a wide variety of topics on inviscid and viscous fluid dynamics, the author covers material that includes: Viscous dissipation The second law of thermodynamics Calorically imperfect gas flows Aerodynamic sweep Shock-wave interference Unsteady one-dimensional flow Internal ballistics Force and momentum balance The Substitution Principle Rarefaction shock waves A comprehensive treatment of flow property derivatives just downstream of an unsteady three-dimensional shock Shock-generated vorticity Triple points An extended version of the Navier‒Stokes equations Shock-free supersonic diffusers Lift and thrust from an asymmetric nozzle Analytical Fluid Dynamics, Third Edition outlines the basics of analytical fluid mechanics while emphasizing analytical approaches to fluid dynamics. Covering the material in-depth, this book provides an authoritative interpretation of formulations and procedures in analytical fluid dynamics, and offers analytical solutions to fluid dynamic problems.

Ocean Surface Waves: Their Physics And Prediction (Third Edition)
Ocean Surface Waves: Their Physics And Prediction (Third Edition)

Author: Stanislaw Ryszard Massel

Publisher: World Scientific

Published: 2017-09-28

Total Pages: 801

ISBN-13: 9813228393

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This book is an extended and substantially updated edition of the previous book editions published in 1996 and 2013 under the same title. The 3rd edition is a one-volume, modern and comprehensive overview of the current knowledge of regular and random ocean surface waves in deep waters and in coastal zones.Since the previous editions many new theoretical advances have been made in the physical understanding and analytical and numerical treatment of various ocean wave problems. The revisions and supplements demanded by these advances have been substantial, therefore the scope of the book has been extended by adding a new chapter and substantially supplementing others.All chapters of the book have been rewritten to include and describe in detail many new discoveries made since the completion of the previous editions. In this 3rd edition a comprehensive and updated overview of the fundamentals of the regular wave mechanics, as well as the spectral and statistical properties of random waves are given. Except for the updated chapters dedicated to tsunami and extreme waves, a new chapter dealing with other types of impulsive waves starting from rest, are also included.The air-sea interaction processes as well as the last improvements in ocean wave modelling and presently available wave prediction models (WAM, WAVEWATCH III, UMWM, NEMO) are thoroughly discussed and their applications are demonstrated. The review of the present ocean observation methods encompasses the modern sea-truthing, as well as applications of data from presently operating marine satellites.In this revised edition, chapters on the behavior of surface waves in the vegetated environments such as coral reef, mangrove forest, seaweed and seagrass areas are substantially extended and updated to include the last discoveries.The explanations in the book are self-contained and detailed enough to capture the interest of the potential readers and to prompt them to explore the research literature. The list of rapidly growing number of the recent papers on the ocean waves has been extended substantially, up to about 900 titles.

Twenty-Third Symposium on Naval Hydrodynamics
Twenty-Third Symposium on Naval Hydrodynamics

Author: National Research Council

Publisher: National Academies Press

Published: 2002-01-01

Total Pages: 1024

ISBN-13: 0309254671

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"Vive la Revolution!" was the theme of the Twenty-Third Symposium on Naval Hydrodynamics held in Val de Reuil, France, from September 17-22, 2000 as more than 140 experts in ship design, construction, and operation came together to exchange naval research developments. The forum encouraged both formal and informal discussion of presented papers, and the occasion provides an opportunity for direct communication between international peers. This book includes sixty-three papers presented at the symposium which was organized jointly by the Office of Naval Research, the National Research Council (Naval Studies Board), and the Bassin d'Essais des Carènes. This book includes the ten topical areas discussed at the symposium: wave-induced motions and loads, hydrodynamics in ship design, propulsor hydrodynamics and hydroacoustics, CFD validation, viscous ship hydrodynamics, cavitation and bubbly flow, wave hydrodynamics, wake dynamics, shallow water hydrodynamics, and fluid dynamics in the naval context.

Beyond Einstein
Beyond Einstein

Author: David E. Rowe

Publisher: Birkhäuser

Published: 2018-06-18

Total Pages: 500

ISBN-13: 1493977083

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Beyond Einstein: Perspectives on Geometry, Gravitation, and Cosmology explores the rich interplay between mathematical and physical ideas by studying the interactions of major actors and the roles of important research communities over the course of the last century.