عنوان
پدید آورنده
موضوع
رده
کتابخانه
محل استقرار
3642974910
9783642974915
b576737
Caustics, Catastrophes and Wave Fields
[Book]
by Yu. A. Kravtsov, Yu. I. Orlov.
Berlin, Heidelberg
Springer Berlin Heidelberg
1993
(59 illustrations)
Springer series on wave phenomena, 15.
1 Introduction --; 1.1 Caustic Fields in Physical Problems --; 1.2 The Geometrical Aspect of the Caustic Problem --; 1.3 The Wave Aspect of the Caustic Problem --; 2 Rays and Caustics --; 2.1 Equations of Geometrical Optics --; 2.2 The Role of Rays in the Method of Geometrical Optics --; 2.3 Physical Characteristics of Caustics --; 2.4 Complex Rays --; 3 Caustics as Catastrophes --; 3.1 Mappings Induced by Rays --; 3.2 Classification of Typical Caustics --; 4 Typical Integrals of Catastrophe Theory --; 4.1 Standard Caustic Integrals --; 4.2 The Airy Integral --; 4.3 The Pearsey Integral --; 4.4 Other Typical Integrals --; 5 Uniform Caustic Asymptotics Derived with Standard Integrals --; 5.1 Uniform Airy Asymptotic of a Scalar Field --; 5.2 Uniform Caustic Asymptotics Based on General Standard Integrals --; 5.3 Illustrative Examples --; 6 Maslov's Method of the Canonical Operator --; 6.1 Principal Relationships --; 6.2 Specific Problems --; 7 Method of Interference Integrals --; 7.1 Ray Type Integrals --; 7.2 Caustic Integrals --; 7.3 Additional Topics and Generalizations --; 8 Penumbra Caustics --; 8.1 Broken Penumbra Caustics --; 8.2 Penumbra Caustics of Diffraction Rays --; 8.3 Penumbral Caustics and Edge Catastrophes --; 9 Modifications and Generalizations of Standard Integrals and Functions --; 9.1 Nonpolynomial Phase Standard Integrals --; 9.2 Structurally Unstable Caustics --; 9.3 Standard Integrals with Amplitude Correction --; 9.4 Reflection from a Barrier and Oscillations in a Potential Well --; 9.5 Standard Functions Induced by Ordinary Differential Equations --; 10 Caustics Revisited --; 10.1 Caustics in Dispersive Media --; 10.2 Caustics in Anisotropic Media --; 10.3 Complex Caustics --; 10.4 Random Caustics --; 10.5 Caustics in Quantum Mechanical Problems --; 10.6 Concluding Remarks --; References --; List of Symbols.
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.
Engineering.
Physical geography.
Physics.
by Yu. A. Kravtsov, Yu. I. Orlov.
Yu A Kravtsov
Yu I Orlov
مطالعه متن کتاب [Book]
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