This book is a multifaceted approach to understanding, calculating, and managing electromagnetic discontinuities.
Presenting new, innovative approaches alongside basic results, this text helps readers better understand, calculate, and manage the discontinuities that occur within the electromagnetic field. Among the electromagnetic discontinuities explored in this volume are:
- Bounded jump discontinuities at the interfaces between two media or on the material sheets that model very thin layers.
- Unbounded values at the edges of wedge-type structures.
- Unbounded values at the tips of conical structures.
The text examines all the key issues related to the bodies that carry the interfaces, edges, or tips, whether these bodies are at rest or in motion with respect to an observer. In addition to its clear explanations, the text offers plenty of step-by-step examples to clarify complex theory and calculations. Moreover, readers are encouraged to fine-tune their skills and knowledge by solving the text's problem sets.
Three fundamental, classical theories serve as the foundation for this text: distributions, confluence, and the special theory of relativity. The text sets forth the fundamentals of all three of these theories for readers who are not fully familiar with them. Moreover, the author demonstrates how to solve electromagnetic discontinuity problems by seamlessly combining all three theories into a single approach.
With this text as their guide, readers can apply a unique philosophy and approach to the investigation and development of structures that have the potential to enhance the capabilities of electronics, antennas, microwaves, acoustics, medicine, and many more application areas.
Contents
1. Introduction
2. Distributions and Derivatives in the Sense of Distribution
- 2.1 Functions and Distributions,
- 2.2 Test Functions. The Space C∞ 0 ,
- 2.3 Convergence in D,
- 2.4 Distribution,
- 2.5 Some Simple Operations in D,
- 2.6 Order of a Distribution,
- 2.7 The Support of a Distribution,
- 2.8 Some Generalizations,
3. Maxwell Equations in the Sense of Distribution
- 3.1 Maxwell Equations Reduced into the Vacuum,
- 3.2 Universal Boundary Conditions and Compatibility Relations,
- 3.3 The Concept of Material Sheet,
- 3.4 The Case of Monochromatic Fields,
- Simple Media that Are at Rest,
4. Boundary Conditions on Material Sheets at Rest
- 4.1 Universal Boundary Conditions and Compatibility Relations for a Fixed Material Sheet,
- 4.2 Some General Results,
- 4.3 Some Particular Cases,
5. Discontinuities on a Moving Sheet
- 5.1 Special Theory of Relativity,
- 5.2 Discontinuities on a Uniformly Moving Surface,
- 5.3 Discontinuities on a Nonuniformly Moving Sheet,
6. Edge Singularities on Material Wedges Bounded by Plane Boundaries
- 6.1 Introduction,
- 6.2 Singularities at the Edges of Material Wedges,
- 6.3 The Wedge with Penetrable Boundaries,
- 6.4 The Wedge with Impenetrable Boundaries,
- 6.5 Examples. Application to Half-Planes,
- 6.6 Edge Conditions for the Induced Surface Currents,
7. Tip Singularities at the Apex of a Material Cone
- 7.1 Introduction,
- 7.2 Algebraic Singularities of an H-Type Field,
- 7.3 Algebraic Singularities of an E-Type Field,
- 7.4 The Case of Impenetrable Cones,
- 7.5 Confluence and Logarithmic Singularities,
- 7.6 Application to some Widely used Actual Boundary Conditions,
- 7.7 Numerical Solutions of the Transcendental Equations Satisfied by the Minimal Index,
8. Temporal Discontinuities
- 8.1 Universal Initial Conditions,
- 8.2 Linear Mediums in the Generalized Sense,
- 8.3 An Illustrative Example,
- References
Index
About the Author
- M. Mithat Idemen, PhD, is Professor in the Mathematics Department of Yeditepe University (Istanbul, Turkey) and honorary member of the Turkish Academy of Sciences (TüBA). He has served as editor and associate editor for various scientific journals, including the International Series of Monographs on Advanced Electromagnetics.
Product Details
- Hardcover: 240 pages
- Publisher: Wiley-IEEE Press; 1 edition (2011)
- Language: English
- ISBN-10: 1118034155
- ISBN-13: 978-1118034156
- Product Dimensions: 6.3 x 0.7 x 9.5 inches
List Price: $110.00