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Wavefronts and Rays as Characteristics and Asymptotics

Author: Andrej BÃ³na

Publisher: World Scientific Publishing Company

Published: 2014-12-30

Total Pages: 344

ISBN-13: 9814651559

This textbook — incorporated with many illuminating examples and exercises — is aimed at graduate students of physical sciences and engineering. The purpose is to provide a background of physics and underlying mathematics for the concept of rays, filling the gap between mathematics and physics textbooks for a coherent treatment of all topics. The authors' emphasis and extremely good presentation of the theory of characteristics, which defines the rays, accentuate the beauty and versatility of this theory. To this end, the rigour of the formulation — by a pure mathematician's standards — is downplayed to highlight the physical meaning and to make the subject accessible to a wider audience. The authors describe in detail the theory of characteristics for different types of differential equations, the applications to wave propagation in different types of media, and phenomena such as caustics.

Wavefronts and Rays as Characteristics and Asymptotics

Author: Andrej BÃ³na

Publisher: World Scientific Publishing Company

Published: 2011-05-09

Total Pages: 295

ISBN-13: 9813107820

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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.

The Optics of Rays, Wavefronts, and Caustics

Author: O Stavroudis

Publisher: Elsevier

Published: 2012-12-02

Total Pages: 333

ISBN-13: 0323155553

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The Optics of Rays, Wavefronts, and Caustics presents the fundamental principles of geometrical optics and its unique role in modern technology. It also discusses the procedures used in optical design, which are based on geometrical optics. Organized into 16 chapters, this volume begins with an overview of the underlying general mathematical facts, which constitute the substance of geometrical optics. It then presents the various techniques used to solve the ray and wavefront problems in general inhomogeneous medium. Other chapters consider the concept of ray tracing as a tool for calculating the principal curvatures of a wavefront as it propagates through a lens. In addition, the book tackles several topics, including the aspects of lens design, as well as a system of equations that are similar to the Maxwell equations. The last chapter deals with orthotomic systems of rays. Optical designers, optical physicists, theoretical physicists, and mathematicians will find the information and methods in this book extremely useful.

Fringe 2013

Author: Wolfgang Osten

Publisher: Springer Science & Business Media

Published: 2013-08-15

Total Pages: 975

ISBN-13: 3642363598

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In continuation of the FRINGE Workshop Series this Proceeding contains all contributions presented at the 7. International Workshop on Advanced Optical Imaging and Metrology. The FRINGE Workshop Series is dedicated to the presentation, discussion and dissemination of recent results in Optical Imaging and Metrology. Topics of particular interest for the 7. Workshop are: - New methods and tools for the generation, acquisition, processing, and evaluation of data in Optical Imaging and Metrology (digital wavefront engineering, computational imaging, model-based reconstruction, compressed sensing, inverse problems solution) - Application-driven technologies in Optical Imaging and Metrology (high-resolution, adaptive, active, robust, reliable, flexible, in-line, real-time) - High-dynamic range solutions in Optical Imaging and Metrology (from macro to nano) - Hybrid technologies in Optical Imaging and Metrology (hybrid optics, sensor and data fusion, model-based solutions, multimodality) - New optical sensors, imaging and measurement systems (integrated, miniaturized, in-line, real-time, traceable, remote) Special emphasis is put on new strategies, taking into account the active combination of physical modeling, computer aided simulation and experimental data acquisition. In particular attention is directed towards new approaches for the extension of existing resolution limits that open the gates to wide-scale metrology, ranging from macro to nano, by considering dynamic changes and using advanced optical imaging and sensor systems.

Wavefronts and Rays

Author: Andrej Bóna

Publisher:

Published: 2014

Total Pages: 342

ISBN-13: 9789814651547

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Rays, Waves, and Scattering

Author: John A. Adam

Publisher: Princeton University Press

Published: 2017-05-30

Total Pages: 616

ISBN-13: 140088540X

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This one-of-a-kind book presents many of the mathematical concepts, structures, and techniques used in the study of rays, waves, and scattering. Panoramic in scope, it includes discussions of how ocean waves are refracted around islands and underwater ridges, how seismic waves are refracted in the earth's interior, how atmospheric waves are scattered by mountains and ridges, how the scattering of light waves produces the blue sky, and meteorological phenomena such as rainbows and coronas. Rays, Waves, and Scattering is a valuable resource for practitioners, graduate students, and advanced undergraduates in applied mathematics, theoretical physics, and engineering. Bridging the gap between advanced treatments of the subject written for specialists and less mathematical books aimed at beginners, this unique mathematical compendium features problems and exercises throughout that are geared to various levels of sophistication, covering everything from Ptolemy's theorem to Airy integrals (as well as more technical material), and several informative appendixes. Provides a panoramic look at wave motion in many different contexts Features problems and exercises throughout Includes numerous appendixes, some on topics not often covered An ideal reference book for practitioners Can also serve as a supplemental text in classical applied mathematics, particularly wave theory and mathematical methods in physics and engineering Accessible to anyone with a strong background in ordinary differential equations, partial differential equations, and functions of a complex variable

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 Elastic Continua

Author: Michael A Slawinski

Publisher: World Scientific Publishing Company

Published: 2014-12-15

Total Pages: 656

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. Request Inspection Copy

Waves and Rays in Elastic Continua

Author: Michael A Slawinski

Publisher: World Scientific Publishing Company

Published: 2010-09-09

Total Pages: 616

ISBN-13: 9813107677

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The present book — which is the second, and significantly extended, 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.