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Author: Yu.A. Kravtsov
Publisher: Springer Science & Business Media
ISBN: 3642598870
Category : Science
Languages : en
Pages : 229
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Book Description
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.
Author: Yu.A. Kravtsov
Publisher: Springer Science & Business Media
ISBN: 3642598870
Category : Science
Languages : en
Pages : 229
Get Book Here
Book Description
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.
Author: Yu.A. Kravtsov
Publisher: Springer
ISBN: 9783540565871
Category : Science
Languages : en
Pages : 210
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Book Description
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:
Category : Mathematics
Languages : en
Pages : 236
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Book Description
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.
Author: Michael G. Brown
Publisher:
ISBN:
Category :
Languages : en
Pages : 18
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Book Description
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.
Author: Michael G. Brown
Publisher:
ISBN:
Category :
Languages : en
Pages : 17
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Book Description
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.
Author: Alessandro Zannotti
Publisher: Springer Nature
ISBN: 3030530884
Category : Science
Languages : en
Pages : 180
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Book Description
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.
Author: Michael G. Brown
Publisher:
ISBN:
Category :
Languages : en
Pages : 5
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Book Description
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.
Author: AA Fuki
Publisher: Routledge
ISBN: 1351445308
Category : Technology & Engineering
Languages : en
Pages : 182
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Book Description
Until recently, there was no effective method for describing waves in weakly anisotropic inhomogeneous media. The method of quasi-isotropic approximation (QIA) of geometrical optics was developed to overcome this problem. The QIA approach bridges the gap between geometrical optics of isotropic media (Rytov method) and that of anisotropic media (Courant-Lax approach). thus providing a complete picture of the geometrical optics of inhomogeneous media. The book explores recent developments in QIA and describes the application of the theory to different branches of wave physics, from plasma physics. quantum physics and ionospheric radio wave propagation to acoustics, optics and astrophysics. The authors present some modifications and generalisations of QIA equations, and look at electromagnetic waves and optical and acoustic effects in weakly anisotropic media, as well as geometrical optics of 3D inhomogeneous media. The book closes with some quantum mechanical analogies. This is an up-to-the minute exposition of the latest developments in an important new area, written by authors of outstanding international reputation. A rich source of both theoretical methods and practical applications, this book covers a wide range of problems of general physical significance and will be of interest to those working in optics, acoustics, electrical engineering, radio engineering and wave propagation through plasma.
Author: Eberhard Zeidler
Publisher: Springer Science & Business Media
ISBN: 3540853774
Category : Mathematics
Languages : en
Pages : 1125
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Book Description
And God said, Let there be light; and there was light. Genesis 1,3 Light is not only the basis of our biological existence, but also an essential source of our knowledge about the physical laws of nature, ranging from the seventeenth century geometrical optics up to the twentieth century theory of general relativity and quantum electrodynamics. Folklore Don’t give us numbers: give us insight! A contemporary natural scientist to a mathematician The present book is the second volume of a comprehensive introduction to themathematicalandphysicalaspectsofmodernquantum?eldtheorywhich comprehends the following six volumes: Volume I: Basics in Mathematics and Physics Volume II: Quantum Electrodynamics Volume III: Gauge Theory Volume IV: Quantum Mathematics Volume V: The Physics of the Standard Model Volume VI: Quantum Gravitation and String Theory. It is our goal to build a bridge between mathematicians and physicists based on the challenging question about the fundamental forces in • macrocosmos (the universe) and • microcosmos (the world of elementary particles). The six volumes address a broad audience of readers, including both und- graduate and graduate students, as well as experienced scientists who want to become familiar with quantum ?eld theory, which is a fascinating topic in modern mathematics and physics.
Author: J.F Nye
Publisher: CRC Press
ISBN: 9780750306102
Category : Technology & Engineering
Languages : en
Pages : 354
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Book Description
A new kind of optics has grown up during the last 25 years. Geometrical optics has been studied for centuries (the law of reflection was known to the ancient Greeks) and wave optics (heralded by Huygens' Treatise on Light) has been studied for more than 300 years. But in the mid 1970s it began to be understood that when natural processes focus light, as when sunlight is reflected from the sea at sunset, the light caustics that are produced have a systematic behavior previously unrecognized. Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations provides a definitive account of how classical optics has been reconstructed in a modern way by emphasizing the hierarchy of singularities that exists in light fields. The book discusses the singularities of geometrical optics and their systematization by catastrophe theory. It explores the diffraction patterns associated with caustics that are dominated by wave dislocations, line singularities of the phase, and analogous to crystal dislocations. The book is a perfect blend of mathematics and physics, combining theory, computer simulation, and beautiful experimental photographs of the phenomena studied.
