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Caustics Catastrophes And Wave Fields
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Book Synopsis Caustics, Catastrophes and Wave Fields by : Yu.A. Kravtsov
Download or read book Caustics, Catastrophes and Wave Fields written by Yu.A. Kravtsov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: Caustics, Catastrophes and Wave Fields in a sense continues the treatment of the earlier volume 6 "Geometrical Optics of Inhomogeneous Media" in the present book series, by analysing caustics and their fields on the basis of modern catastrophe theory. This volume covers the key generalisations of geometrical optics related to caustic asymptotic expansions: The Lewis-Kravtsov method of standard functions, Maslov's method of caonical operators, Orlov's method of interference integrals, as well as their modifications for penumbra, space-time, random and other types of caustics. All the methods are amply illustrated by worked problems concerning relevant wave-field applications.
Book Synopsis Caustics, Catastrophes and Wave Fields by : Yu.A. Kravtsov
Download or read book Caustics, Catastrophes and Wave Fields written by Yu.A. Kravtsov and published by Springer. This book was released on 1993-11-24 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Caustics, Catastrophes and Wave Fields in a sense continues the treatment of the earlier volume 6 "Geometrical Optics of Inhomogeneous Media" by analysing caustics and their fields on the basis of modern catastrophe theory. The present volume covers local and uniform caustic asymptotic expansions: The Lewis-Kravtsov method of standard functions, Maslov's method of canonical operators , Orlov's method of interference integrals, as well as their modifications for penumbra, space-time, random and other types of caustics. All the methods are amply illustrated by worked problems concerning relevant wave-field applications.
Author :Iı̐Uı̐Łrii Aleksandrovich Kravtı̐sı̐Łov Publisher :Springer Series on Wave Phenomena ISBN 13 : Total Pages :236 pages Book Rating :4.F/5 ( download)
Book Synopsis Caustics, Catastrophes and Wave Fields by : Iı̐Uı̐Łrii Aleksandrovich Kravtı̐sı̐Łov
Download or read book Caustics, Catastrophes and Wave Fields written by Iı̐Uı̐Łrii Aleksandrovich Kravtı̐sı̐Łov and published by Springer Series on Wave Phenomena. This book was released on 1999 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of Histological Typing of Salivary Gland Tumours is more extensive and detailed than the previous edition. New technical methods haveincreased our understanding of many tumours. The various types of carcinomas are categorized separately and the inclusion of the TNM Classification of salivary gland tumours and the more detailed description of the lesions will contribute to a better understanding.
Book Synopsis The Transient Wave Fields in the Vicinity of the Cuspoid Caustics by : Michael G. Brown
Download or read book The Transient Wave Fields in the Vicinity of the Cuspoid Caustics written by Michael G. Brown and published by . This book was released on 1986 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general formalism is presented for the study of the transient wave fields in the vicinity of caustics of arbitrary complexity. The caustics are classified using catastrophe theory. A general introduction to the subject is presented and explicit results (numerical and analytical) for the cuspoid family of catastrophes which show the smooth variation of the acoustic field as the control parameters are independently varied. These results vividly demonstrate the phenomenon of ray focusing, showing the number of rays which converge at each catastrophe, the resulting phase shifts they undergo, as well as their decay in shadow regions. Analytical results are given which describe the time-dependent acoustic field on and at large distances away from each of the cuspoid catastrophes. Four sets of numbers are introduced which describe the behavior of the wave field in the vicinity of each catastrophe. These are: (1) an exponent which describes the temporal decay of the acoustic field on the most singular point of each catastrophe; (2) a number which describes the asymmetry of the time-dependent acoustic field on the most singular point of each catastrophe; (3) an exponent which describes the time separation as a function of control parameter between individual ray arrivals as each of the control parameters are independently varied; and (4) an exponent which describes the asymptotic decay as a function of control parameter of each constituent ray arrival. Sets (1) and (3) are shown to be simply related to the singularity and fringe indices. It is argued that many features of the frequency domain representation of the acoustic field in the vicinity of the catastrophes are most easily understood by examining the time domain representation.
Book Synopsis The Transient Wave Fields in the Vicinity of the Elliptic, Hyperbolic, and Parabolic Umbilic Caustics by : Michael G. Brown
Download or read book The Transient Wave Fields in the Vicinity of the Elliptic, Hyperbolic, and Parabolic Umbilic Caustics written by Michael G. Brown and published by . This book was released on 1986 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: The caustics of high-frequency wave propagation may be classified using catastrophe theory. This paper examines the transient wave fields in the vicinity of the elliptic, hyperbolic, and parabolic umbilic catastrophes. Analytical results are presented which describes the time-dependent wave field due to an impulsive source on and at large distances in each control direction away from the most singular point of each of these transient wave fields as each control parameter is independently varied. These results are compared to previously derived results on the transient wave fields in the vicinity of the cuspoid catastrophes (the cuspoid and umbilic catastrophes have coranks 1 and 2, respectively). The transient wave fields in the vicinity of the cuspoid and umbilic catastrophes differ with regard to the temporal structure of the wave field on the most singular point of each catastrophe, the manner in which these temporal structures unfold, and the phase shifts which individual rays undergo as a result of touching one of the catastrophes.
Book Synopsis Caustic Light in Nonlinear Photonic Media by : Alessandro Zannotti
Download or read book Caustic Light in Nonlinear Photonic Media written by Alessandro Zannotti and published by Springer. This book was released on 2021-09-28 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Caustics are natural phenomena, forming light patterns in rainbows or through drinking glasses, and creating light networks at the bottom of swimming pools. Only in recent years have scientists started to artificially create simple caustics with laser light. However, these realizations have already contributed to progress in advanced imaging, lithography, and micro-manipulation. In this book, Alessandro Zannotti pioneers caustics in many ways, establishing the field of artificial caustic optics. He employs caustic design to customize high-intensity laser light. This is of great relevance for laser-based machining, sensing, microscopy, and secure communication. The author also solves a long standing problem concerning the origin of rogue waves which appear naturally in the sea and can have disastrous consequences. By means of a far-reaching optical analogy, he identifies scattering of caustics in random media as the origin of rogue waves, and shows how nonlinear light-matter interaction increases their probability.
Book Synopsis Causality, Caustics, and the Structure of Transient Wave Fields by : Michael G. Brown
Download or read book Causality, Caustics, and the Structure of Transient Wave Fields written by Michael G. Brown and published by . This book was released on 1986 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transient acoustic wave fields in the vicinity of some possible caustics, the time history of the wave field due to an impulsive source includes a precursor. This noncausal behavior is reconciled with the physical principle of causality by requiring that such caustics be a part of certain higher dimensional caustics. With this constraint all noncausal arrivals are preceded by a causal arrival and the total time history is causal. This constraint is used to derive some simple general properties of transient wave fields in the short wave limit, e.g., the number of arrivals must be an odd number.
Book Synopsis Catastrophe Theory by : Vladimir I. Arnol'd
Download or read book Catastrophe Theory written by Vladimir I. Arnol'd and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new edition of this non-mathematical review of catastrophe theory contains updated results and many new or expanded topics including delayed loss of stability, shock waves, and interior scattering. Three new sections offer the history of singularity and its applications from da Vinci to today, a discussion of perestroika in terms of the theory of metamorphosis, and a list of 93 problems touching on most of the subject matter in the book.
Book Synopsis Caustics and Catastrophes by : P. A. Jones
Download or read book Caustics and Catastrophes written by P. A. Jones and published by . This book was released on 1977 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Caustics and Catastrophes by : R. E. Duncan
Download or read book Caustics and Catastrophes written by R. E. Duncan and published by . This book was released on 1977 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Catastrophe Theory by : V. I. Arnol'd
Download or read book Catastrophe Theory written by V. I. Arnol'd and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: Singularity theory is growing very fast and many new results have been discovered since the Russian edition appeared: for instance the relation of the icosahedron to the problem of by passing a generic obstacle. The reader can find more details about this in the articles "Singularities of ray systems" and "Singularities in the calculus of variations" listed in the bi bliography of the present edition. Moscow, September 1983 v. I. Arnold Preface to the Russian Edition "Experts discuss forecasting disasters" said a New York Times report on catastrophe theory in November 1977. The London Times declared Catastrophe Theory to be the "main intellectual movement of the century" while an article on catastrophe theory in Science was headed "The emperor has no clothes". This booklet explains what catastrophe theory is about and why it arouses such controversy. It also contains non-con troversial results from the mathematical theories of singulari ties and bifurcation. The author has tried to explain the essence of the fundamen tal results and applications to readers having minimal mathe matical background but the reader is assumed to have an in quiring mind. Moscow 1981 v. I. Arnold Contents Chapter 1. Singularities, Bifurcations, and Catastrophe Theories ............... 1 Chapter 2. Whitney's Singularity Theory ... 3 Chapter 3. Applications of Whitney's Theory 7 Chapter 4. A Catastrophe Machine ...... 10 Chapter 5. Bifurcations of Equilibrium States 14 Chapter 6. Loss of Stability of Equilibrium and the Generation of Auto-Oscillations . . . . . . 20 .
Book Synopsis Caustics and Catastrophes in Two and Three Dimensions by : P. N. Kesterton
Download or read book Caustics and Catastrophes in Two and Three Dimensions written by P. N. Kesterton and published by . This book was released on 1978 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Singularities of Functions, Wave Fronts, Caustics and Multidimensional Integrals by : Vladimir Igorevich Arnolʹd
Download or read book Singularities of Functions, Wave Fronts, Caustics and Multidimensional Integrals written by Vladimir Igorevich Arnolʹd and published by . This book was released on 2012 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic paper is an introduction to some difficult contemporary fields of study in mathematics known under the rubric of Catastrophe Theory, which encompasses the theory of typical singularities of functions and mappings. The authors discuss the basic ideas, concepts and methods of the theory of singularities. The survey is presented in three sections: Section 1: Singularities of Functions, Caustics and Wave Fronts. Section 2: Integrals of the Stationary Phase Method. Section 3: The Geometry of Fomulas. The survey provides a useful source of reference for students, postgraduates and researchers in these areas of mathematics.
Book Synopsis Caustics and Catastrophes by : David B. White
Download or read book Caustics and Catastrophes written by David B. White and published by . This book was released on 1978 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Caustics and Catastrophes by : Klaus Jänich
Download or read book Caustics and Catastrophes written by Klaus Jänich and published by . This book was released on 1973 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mat-report written by and published by . This book was released on 1981 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Catastrophe Theory by : Vladimir Igorevich Arnolʹd
Download or read book Catastrophe Theory written by Vladimir Igorevich Arnolʹd and published by Springer. This book was released on 1984 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt:
