M. Mithat Idemen
Discontinuities in the Electromagnetic Field
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M. Mithat Idemen
Discontinuities in the Electromagnetic Field
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Filled with new approaches and basic results connected with the discontinuities of the electromagnetic field, this new book offers an important resource for graduate and undergraduate students. The discontinuities in question may be one of three things: The bounded jump discontinuities on the interfaces between two media or on the material sheets which model very thin layers or; Unbounded values at the edge of wedge type structures; Unbounded values at the tips of conical structures. The book contains many examples as well as problems and exercises that challenge the readers.
Filled with new approaches and basic results connected with the discontinuities of the electromagnetic field, this new book offers an important resource for graduate and undergraduate students. The discontinuities in question may be one of three things: The bounded jump discontinuities on the interfaces between two media or on the material sheets which model very thin layers or; Unbounded values at the edge of wedge type structures; Unbounded values at the tips of conical structures. The book contains many examples as well as problems and exercises that challenge the readers.
Produktdetails
- Produktdetails
- IEEE/OUP Series on Electromagnetic Wave Theory
- Verlag: Wiley & Sons
- 1. Auflage
- Seitenzahl: 240
- Erscheinungstermin: 27. September 2011
- Englisch
- Abmessung: 240mm x 161mm x 18mm
- Gewicht: 498g
- ISBN-13: 9781118034156
- ISBN-10: 1118034155
- Artikelnr.: 33271818
- IEEE/OUP Series on Electromagnetic Wave Theory
- Verlag: Wiley & Sons
- 1. Auflage
- Seitenzahl: 240
- Erscheinungstermin: 27. September 2011
- Englisch
- Abmessung: 240mm x 161mm x 18mm
- Gewicht: 498g
- ISBN-13: 9781118034156
- ISBN-10: 1118034155
- Artikelnr.: 33271818
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.
Preface ix 1. Introduction 1 2. Distributions and Derivatives in the Sense of Distribution 7 2.1 Functions and Distributions
7 2.2 Test Functions. The Space C infinity 0
9 2.3 Convergence in D
14 2.4 Distribution
16 2.5 Some Simple Operations in D
21 2.5.1 Multiplication by a Real Number or a Function
21 2.5.2 Translation and Rescaling
21 2.5.3 Derivation of a Distribution
22 2.6 Order of a Distribution
26 2.7 The Support of a Distribution
31 2.8 Some Generalizations
33 2.8.1 Distributions on Multidimensional Spaces
33 2.8.2 Vector-Valued Distributions
38 3. Maxwell Equations in the Sense of Distribution 49 3.1 Maxwell Equations Reduced into the Vacuum
49 3.1.1 Some Simple Examples
53 3.2 Universal Boundary Conditions and Compatibility Relations
54 3.2.1 An Example. Discontinuities on a Combined Sheet
57 3.3 The Concept of Material Sheet
59 3.4 The Case of Monochromatic Fields
62 3.4.1 Discontinuities on the Interface Between Two Simple Media that Are at Rest
64 4. Boundary Conditions on Material Sheets at Rest 67 4.1 Universal Boundary Conditions and Compatibility Relations for a Fixed Material Sheet
67 4.2 Some General Results
69 4.3 Some Particular Cases
70 4.3.1 Planar Material Sheet Between Two Simple Media
70 4.3.2 Cylindrically or Spherically Curved Material Sheet Located Between Two Simple Media
91 4.3.3 Conical Material Sheet Located Between Two Simple Media
93 5. Discontinuities on a Moving Sheet 109 5.1 Special Theory of Relativity
110 5.1.1 The Field Created by a Uniformly Moving Point Charge
112 5.1.2 The Expressions of the Field in a Reference System Attached to the Charged Particle
114 5.1.3 Lorentz Transformation Formulas
115 5.1.4 Transformation of the Electromagnetic Field
118 5.2 Discontinuities on a Uniformly Moving Surface
120 5.2.1 Transformation of the Universal Boundary Conditions
123 5.2.2 Transformation of the Compatibility Relations
126 5.2.3 Some Simple Examples
126 5.3 Discontinuities on a Nonuniformly Moving Sheet
138 5.3.1 Boundary Conditions on a Plane that Moves in a Direction Normal to Itself
139 5.3.2 Boundary Conditions on the Interface of Two Simple Media
143 6. Edge Singularities on Material Wedges Bounded by Plane Boundaries 149 6.1 Introduction
149 6.2 Singularities at the Edges of Material Wedges
153 6.3 The Wedge with Penetrable Boundaries
154 6.3.1 The H Case
156 6.3.2 The E Case
171 6.4 The Wedge with Impenetrable Boundaries
174 6.5 Examples. Application to Half-Planes
175 6.6 Edge Conditions for the Induced Surface Currents
176 7. Tip Singularities at the Apex of a Material Cone 179 7.1 Introduction
179 7.2 Algebraic Singularities of an H-Type Field
185 7.2.1 Contribution of the Energy Restriction
185 7.2.2 Contribution of the Boundary Conditions
186 7.3 Algebraic Singularities of an E-Type Field
191 7.4 The Case of Impenetrable Cones
193 7.5 Confluence and Logarithmic Singularities
195 7.6 Application to some Widely used Actual Boundary Conditions
197 7.7 Numerical Solutions of the Transcendental Equations Satisfied by the Minimal Index
200 7.7.1 The Case of Very Sharp Tip
200 7.7.2 The Case of Real-Valued Minimal v
201 7.7.3 A Function-Theoretic Method to Determine Numerically the Minimal v
203 8. Temporal Discontinuities 209 8.1 Universal Initial Conditions
209 8.2 Linear Mediums in the Generalized Sense
211 8.3 An Illustrative Example
212 References 215 Index 219 IEEE Press Series on Electromagnetic Wave Theory
7 2.2 Test Functions. The Space C infinity 0
9 2.3 Convergence in D
14 2.4 Distribution
16 2.5 Some Simple Operations in D
21 2.5.1 Multiplication by a Real Number or a Function
21 2.5.2 Translation and Rescaling
21 2.5.3 Derivation of a Distribution
22 2.6 Order of a Distribution
26 2.7 The Support of a Distribution
31 2.8 Some Generalizations
33 2.8.1 Distributions on Multidimensional Spaces
33 2.8.2 Vector-Valued Distributions
38 3. Maxwell Equations in the Sense of Distribution 49 3.1 Maxwell Equations Reduced into the Vacuum
49 3.1.1 Some Simple Examples
53 3.2 Universal Boundary Conditions and Compatibility Relations
54 3.2.1 An Example. Discontinuities on a Combined Sheet
57 3.3 The Concept of Material Sheet
59 3.4 The Case of Monochromatic Fields
62 3.4.1 Discontinuities on the Interface Between Two Simple Media that Are at Rest
64 4. Boundary Conditions on Material Sheets at Rest 67 4.1 Universal Boundary Conditions and Compatibility Relations for a Fixed Material Sheet
67 4.2 Some General Results
69 4.3 Some Particular Cases
70 4.3.1 Planar Material Sheet Between Two Simple Media
70 4.3.2 Cylindrically or Spherically Curved Material Sheet Located Between Two Simple Media
91 4.3.3 Conical Material Sheet Located Between Two Simple Media
93 5. Discontinuities on a Moving Sheet 109 5.1 Special Theory of Relativity
110 5.1.1 The Field Created by a Uniformly Moving Point Charge
112 5.1.2 The Expressions of the Field in a Reference System Attached to the Charged Particle
114 5.1.3 Lorentz Transformation Formulas
115 5.1.4 Transformation of the Electromagnetic Field
118 5.2 Discontinuities on a Uniformly Moving Surface
120 5.2.1 Transformation of the Universal Boundary Conditions
123 5.2.2 Transformation of the Compatibility Relations
126 5.2.3 Some Simple Examples
126 5.3 Discontinuities on a Nonuniformly Moving Sheet
138 5.3.1 Boundary Conditions on a Plane that Moves in a Direction Normal to Itself
139 5.3.2 Boundary Conditions on the Interface of Two Simple Media
143 6. Edge Singularities on Material Wedges Bounded by Plane Boundaries 149 6.1 Introduction
149 6.2 Singularities at the Edges of Material Wedges
153 6.3 The Wedge with Penetrable Boundaries
154 6.3.1 The H Case
156 6.3.2 The E Case
171 6.4 The Wedge with Impenetrable Boundaries
174 6.5 Examples. Application to Half-Planes
175 6.6 Edge Conditions for the Induced Surface Currents
176 7. Tip Singularities at the Apex of a Material Cone 179 7.1 Introduction
179 7.2 Algebraic Singularities of an H-Type Field
185 7.2.1 Contribution of the Energy Restriction
185 7.2.2 Contribution of the Boundary Conditions
186 7.3 Algebraic Singularities of an E-Type Field
191 7.4 The Case of Impenetrable Cones
193 7.5 Confluence and Logarithmic Singularities
195 7.6 Application to some Widely used Actual Boundary Conditions
197 7.7 Numerical Solutions of the Transcendental Equations Satisfied by the Minimal Index
200 7.7.1 The Case of Very Sharp Tip
200 7.7.2 The Case of Real-Valued Minimal v
201 7.7.3 A Function-Theoretic Method to Determine Numerically the Minimal v
203 8. Temporal Discontinuities 209 8.1 Universal Initial Conditions
209 8.2 Linear Mediums in the Generalized Sense
211 8.3 An Illustrative Example
212 References 215 Index 219 IEEE Press Series on Electromagnetic Wave Theory
Preface ix 1. Introduction 1 2. Distributions and Derivatives in the Sense of Distribution 7 2.1 Functions and Distributions
7 2.2 Test Functions. The Space C infinity 0
9 2.3 Convergence in D
14 2.4 Distribution
16 2.5 Some Simple Operations in D
21 2.5.1 Multiplication by a Real Number or a Function
21 2.5.2 Translation and Rescaling
21 2.5.3 Derivation of a Distribution
22 2.6 Order of a Distribution
26 2.7 The Support of a Distribution
31 2.8 Some Generalizations
33 2.8.1 Distributions on Multidimensional Spaces
33 2.8.2 Vector-Valued Distributions
38 3. Maxwell Equations in the Sense of Distribution 49 3.1 Maxwell Equations Reduced into the Vacuum
49 3.1.1 Some Simple Examples
53 3.2 Universal Boundary Conditions and Compatibility Relations
54 3.2.1 An Example. Discontinuities on a Combined Sheet
57 3.3 The Concept of Material Sheet
59 3.4 The Case of Monochromatic Fields
62 3.4.1 Discontinuities on the Interface Between Two Simple Media that Are at Rest
64 4. Boundary Conditions on Material Sheets at Rest 67 4.1 Universal Boundary Conditions and Compatibility Relations for a Fixed Material Sheet
67 4.2 Some General Results
69 4.3 Some Particular Cases
70 4.3.1 Planar Material Sheet Between Two Simple Media
70 4.3.2 Cylindrically or Spherically Curved Material Sheet Located Between Two Simple Media
91 4.3.3 Conical Material Sheet Located Between Two Simple Media
93 5. Discontinuities on a Moving Sheet 109 5.1 Special Theory of Relativity
110 5.1.1 The Field Created by a Uniformly Moving Point Charge
112 5.1.2 The Expressions of the Field in a Reference System Attached to the Charged Particle
114 5.1.3 Lorentz Transformation Formulas
115 5.1.4 Transformation of the Electromagnetic Field
118 5.2 Discontinuities on a Uniformly Moving Surface
120 5.2.1 Transformation of the Universal Boundary Conditions
123 5.2.2 Transformation of the Compatibility Relations
126 5.2.3 Some Simple Examples
126 5.3 Discontinuities on a Nonuniformly Moving Sheet
138 5.3.1 Boundary Conditions on a Plane that Moves in a Direction Normal to Itself
139 5.3.2 Boundary Conditions on the Interface of Two Simple Media
143 6. Edge Singularities on Material Wedges Bounded by Plane Boundaries 149 6.1 Introduction
149 6.2 Singularities at the Edges of Material Wedges
153 6.3 The Wedge with Penetrable Boundaries
154 6.3.1 The H Case
156 6.3.2 The E Case
171 6.4 The Wedge with Impenetrable Boundaries
174 6.5 Examples. Application to Half-Planes
175 6.6 Edge Conditions for the Induced Surface Currents
176 7. Tip Singularities at the Apex of a Material Cone 179 7.1 Introduction
179 7.2 Algebraic Singularities of an H-Type Field
185 7.2.1 Contribution of the Energy Restriction
185 7.2.2 Contribution of the Boundary Conditions
186 7.3 Algebraic Singularities of an E-Type Field
191 7.4 The Case of Impenetrable Cones
193 7.5 Confluence and Logarithmic Singularities
195 7.6 Application to some Widely used Actual Boundary Conditions
197 7.7 Numerical Solutions of the Transcendental Equations Satisfied by the Minimal Index
200 7.7.1 The Case of Very Sharp Tip
200 7.7.2 The Case of Real-Valued Minimal v
201 7.7.3 A Function-Theoretic Method to Determine Numerically the Minimal v
203 8. Temporal Discontinuities 209 8.1 Universal Initial Conditions
209 8.2 Linear Mediums in the Generalized Sense
211 8.3 An Illustrative Example
212 References 215 Index 219 IEEE Press Series on Electromagnetic Wave Theory
7 2.2 Test Functions. The Space C infinity 0
9 2.3 Convergence in D
14 2.4 Distribution
16 2.5 Some Simple Operations in D
21 2.5.1 Multiplication by a Real Number or a Function
21 2.5.2 Translation and Rescaling
21 2.5.3 Derivation of a Distribution
22 2.6 Order of a Distribution
26 2.7 The Support of a Distribution
31 2.8 Some Generalizations
33 2.8.1 Distributions on Multidimensional Spaces
33 2.8.2 Vector-Valued Distributions
38 3. Maxwell Equations in the Sense of Distribution 49 3.1 Maxwell Equations Reduced into the Vacuum
49 3.1.1 Some Simple Examples
53 3.2 Universal Boundary Conditions and Compatibility Relations
54 3.2.1 An Example. Discontinuities on a Combined Sheet
57 3.3 The Concept of Material Sheet
59 3.4 The Case of Monochromatic Fields
62 3.4.1 Discontinuities on the Interface Between Two Simple Media that Are at Rest
64 4. Boundary Conditions on Material Sheets at Rest 67 4.1 Universal Boundary Conditions and Compatibility Relations for a Fixed Material Sheet
67 4.2 Some General Results
69 4.3 Some Particular Cases
70 4.3.1 Planar Material Sheet Between Two Simple Media
70 4.3.2 Cylindrically or Spherically Curved Material Sheet Located Between Two Simple Media
91 4.3.3 Conical Material Sheet Located Between Two Simple Media
93 5. Discontinuities on a Moving Sheet 109 5.1 Special Theory of Relativity
110 5.1.1 The Field Created by a Uniformly Moving Point Charge
112 5.1.2 The Expressions of the Field in a Reference System Attached to the Charged Particle
114 5.1.3 Lorentz Transformation Formulas
115 5.1.4 Transformation of the Electromagnetic Field
118 5.2 Discontinuities on a Uniformly Moving Surface
120 5.2.1 Transformation of the Universal Boundary Conditions
123 5.2.2 Transformation of the Compatibility Relations
126 5.2.3 Some Simple Examples
126 5.3 Discontinuities on a Nonuniformly Moving Sheet
138 5.3.1 Boundary Conditions on a Plane that Moves in a Direction Normal to Itself
139 5.3.2 Boundary Conditions on the Interface of Two Simple Media
143 6. Edge Singularities on Material Wedges Bounded by Plane Boundaries 149 6.1 Introduction
149 6.2 Singularities at the Edges of Material Wedges
153 6.3 The Wedge with Penetrable Boundaries
154 6.3.1 The H Case
156 6.3.2 The E Case
171 6.4 The Wedge with Impenetrable Boundaries
174 6.5 Examples. Application to Half-Planes
175 6.6 Edge Conditions for the Induced Surface Currents
176 7. Tip Singularities at the Apex of a Material Cone 179 7.1 Introduction
179 7.2 Algebraic Singularities of an H-Type Field
185 7.2.1 Contribution of the Energy Restriction
185 7.2.2 Contribution of the Boundary Conditions
186 7.3 Algebraic Singularities of an E-Type Field
191 7.4 The Case of Impenetrable Cones
193 7.5 Confluence and Logarithmic Singularities
195 7.6 Application to some Widely used Actual Boundary Conditions
197 7.7 Numerical Solutions of the Transcendental Equations Satisfied by the Minimal Index
200 7.7.1 The Case of Very Sharp Tip
200 7.7.2 The Case of Real-Valued Minimal v
201 7.7.3 A Function-Theoretic Method to Determine Numerically the Minimal v
203 8. Temporal Discontinuities 209 8.1 Universal Initial Conditions
209 8.2 Linear Mediums in the Generalized Sense
211 8.3 An Illustrative Example
212 References 215 Index 219 IEEE Press Series on Electromagnetic Wave Theory