Mathematical Modeling in Diffraction Theory - 1st Edition - ISBN: 9780128037287, 9780128037485

Mathematical Modeling in Diffraction Theory

1st Edition

Based on A Priori Information on the Analytical Properties of the Solution

Authors: Alexander Kyurkchan Nadezhda Smirnova
eBook ISBN: 9780128037485
Paperback ISBN: 9780128037287
Imprint: Elsevier
Published Date: 21st September 2015
Page Count: 280
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Description

Mathematical Modeling in Diffraction Theory: Based on A Priori Information on the Analytical Properties of the Solution provides the fundamental physical concepts behind the theory of wave diffraction and scattered wave fields as well as its application in radio physics, acoustics, optics, radio astronomy, biophysics, geophysics, and astrophysics.

This book provides a coherent discussion of several advanced topics that have the potential to push forward progress in this field. It begins with examples illustrating the importance of taking a priori information into account when developing algorithms for solving diffraction problems, with subsequent chapters discussing the basic analytical representations of wave fields, the auxiliary current and source methods for solving the problems of diffraction at compact scatterers, the null field and matrix methods that are widely used to solve problems in radio-physics, radio-astronomy, and biophysics, and the continued boundary condition and pattern equation method.

Key Features

  • Provides ideas and techniques for obtaining a priori information on analytical properties of wave fields and provides methods for solving diffraction problems
  • Includes numerous concrete examples of localization of singularities of analytical continuation of wave fields
  • Presents a qualitative explanation of the formation of visions of objects
  • Formulates the concept of “invisible” objects
  • Supplies appropriate computer programs for all presented methods

Readership

Researchers, scientists and graduate students in the field of radio physics, acoustics, optics, radio astronomy, biophysics, geophysics, astrophysics, and mathematical physics

Table of Contents

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  • Introduction
  • Chapter 1: Analytic Properties of Wave Fields
    • Abstract
    • 1.1 Derivation of Basic Analytic Representations of Wave Fields
    • 1.2 Analytic Properties of the Wave Field Pattern and the Domains of Existence of Analytic Representations
  • Chapter 2: Methods of Auxiliary Currents and Method of Discrete Sources
    • Abstract
    • 2.1 Existence and Uniqueness Theorems
    • 2.2 Solution of the MAC Integral Equation and the MDS
    • 2.3 Rigorous Solution of the Diffraction Problem by MAC [9, 16]
    • 2.4 Modified MDS
  • Chapter 3: Null Field and T-Matrix Methods
    • Abstract
    • 3.1 NFM for Scalar Diffraction Problems
    • 3.2 NFM for Vector Diffraction Problems
    • 3.3 Results of Numerical Studies
    • 3.4 T-Matrix Method
  • Chapter 4: Method of Continued Boundary Conditions
    • Abstract
    • 4.1 Method of Continued Boundary Conditions for Scalar Diffraction Problems
    • 4.2 Method of Continued Boundary Conditions for Vector Problems of Diffraction
    • 4.3 Results of Numerical Investigations
    • 4.4 Modified Method of Continued Boundary Conditions
  • Chapter 5: Pattern Equation Method
    • Abstract
    • 5.1 Solution of Two-Dimensional Problem of Diffraction at a Compact Scatterer Using the Pattern Equation Method
    • 5.2 Wave Diffraction at a Group of Bodies
    • 5.3 Wave Diffraction at Periodic Gratings
    • 5.4 Solution of the Three-Dimensional Acoustic Problem of Diffraction at a Compact Scatterer
    • 5.5 Plane Wave Scattering at a Periodic Interface Between Media
    • 5.6 Calculation of the Reflection and Transmission Coefficients in a Plane Dielectric Waveguide with Foreign Objects Near It
  • References
  • Index

Details

No. of pages:
280
Language:
English
Copyright:
© Elsevier 2016
Published:
Imprint:
Elsevier
eBook ISBN:
9780128037485
Paperback ISBN:
9780128037287

About the Author

Alexander Kyurkchan

Professor A.G. Kyurkchan is the head of the Department of Probability Theory and Applied Mathematics of the Moscow Technical University of Communication and Informatics, and he is a leading researcher at the Institute of Radio Engineering and Electronics, the Russian Academy of Sciences, Fryazino Branch. His research area is mathematical modelling in diffraction theory. Since 1994 he has been the project manager on grants of the Russian Fund of Basic Researches. He has published 137 articles in international scientific journals. His monograph "Analytical Properties of Wave Fields" was published in 1990.

Affiliations and Expertise

Department of Probability Theory and Applied Mathematics, Moscow Technical University of Communication and Informatics, Moscow, Russia

Nadezhda Smirnova

N.I. Smirnova is an associate professor in the Department of Probability Theory and Applied Mathematics at the Moscow Technical University of Communication and Informatics. Her research area is mathematical modeling in diffraction theory. She has published 10 articles in international scientific journals.

Affiliations and Expertise

Department of Probability Theory and Applied Mathematics, Moscow Technical University of Communication and Informatics, Moscow, Russia