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Multiforms, Dyadics, and Electromagnetic Media [Kietas viršelis]

(Helsinki University of Technology)
  • Formatas: Hardback, 416 pages, aukštis x plotis x storis: 243x165x31 mm, weight: 826 g
  • Serija: IEEE Press Series on Electromagnetic Wave Theory
  • Išleidimo metai: 19-May-2015
  • Leidėjas: Wiley-IEEE Press
  • ISBN-10: 1118989333
  • ISBN-13: 9781118989333
Kitos knygos pagal šią temą:
Multiforms, Dyadics, and Electromagnetic MediaDidesnis paveikslėlis
  • Formatas: Hardback, 416 pages, aukštis x plotis x storis: 243x165x31 mm, weight: 826 g
  • Serija: IEEE Press Series on Electromagnetic Wave Theory
  • Išleidimo metai: 19-May-2015
  • Leidėjas: Wiley-IEEE Press
  • ISBN-10: 1118989333
  • ISBN-13: 9781118989333
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781118989333.html
Raktažodžiai:
This book applies the four-dimensional formalism with an extended toolbox of operation rules, allowing readers to define more general classes of electromagnetic media and to analyze EM waves that can exist in them





End-of-chapter exercises





Formalism allows readers to find novel classes of media





Covers various properties of electromagnetic media in terms of which they can be set in different classes
Preface xi
1 Multivectors and Multiforms 1(20)
1.1 Vectors and One-Forms,
1(2)
1.1.1 Bar Product |
1(1)
1.1.2 Basis Expansions
2(1)
1.2 Bivectors and Two-Forms,
3(5)
1.2.1 Wedge Product ^
3(1)
1.2.2 Basis Expansions
4(1)
1.2.3 Bar Product
5(1)
1.2.4 Contraction Products right floor apldownstyle and left floor apldownstyle
6(2)
1.2.5 Decomposition of Vectors and One-Forms
8(1)
1.3 Multivectors and Multiforms,
8(8)
1.3.1 Basis of Multivectors
9(1)
1.3.2 Bar Product of Multivectors and Multiforms
10(1)
1.3.3 Contraction of Trivectors and Three-Forms
11(1)
1.3.4 Contraction of Quadrivectors and Four-Forms
12(1)
1.3.5 Construction of Reciprocal Basis
13(1)
1.3.6 Contraction of Quintivector
14(1)
1.3.7 Generalized Bac-Cab Rules
14(2)
1.4 Some Properties of Bivectors and Two-Forms,
16(2)
1.4.1 Bivector Invariant
16(1)
1.4.2 Natural Dot Product
17(1)
1.4.3 Bivector as Mapping
17(1)
Problems,
18(3)
2 Dyadics 21(32)
2.1 Mapping Vectors and One-Forms,
21(4)
2.1.1 Dyadics
21(2)
2.1.2 Double-Bar Product ||
23(1)
2.1.3 Metric Dyadics
24(1)
2.2 Mapping Multivectors and Multiforms
25(7)
2.2.1 Bidyadics
25(1)
2.2.2 Double-Wedge Product ^
25(3)
2.2.3 Double-Wedge Powers ^
28(2)
2.2.4 Double Contractions right floor apldownstyle ight floor apldownstyle and left floor apldownstyle left floor apldownstyle
30(1)
2.2.5 Natural Dot Product for Bidyadics
31(1)
2.3 Dyadic Identities,
32(7)
2.3.1 Contraction Identities
32(1)
2.3.2 Special Cases
33(2)
2.3.3 More General Rules
35(1)
2.3.4 Cayley-Hamilton Equation
36(1)
2.3.5 Inverse Dyadics
36(3)
2.4 Rank of Dyadics,
39(2)
2.5 Eigenproblems,
41(4)
2.5.1 Eigenvectors and Eigen One-Forms
41(1)
2.5.2 Reduced Cayley-Hamilton Equations
42(1)
2.5.3 Construction of Eigenvectors
43(2)
2.6 Metric Dyadics,
45(4)
2.6.1 Symmetric Dyadics
46(1)
2.6.2 Antisymmetric Dyadics
47(1)
2.6.3 Inverse Rules for Metric Dyadics
48(1)
Problems,
49(4)
3 Bidyadics 53(26)
3.1 Cayley-Hamilton Equation,
54(4)
3.1.1 Coefficient Functions
55(2)
3.1.2 Determinant of a Bidyadic
57(1)
3.1.3 Antisymmetric Bidyadic
57(1)
3.2 Bidyadic Eigenproblem,
58(3)
3.2.1 Eigenbidyadic C_
60(1)
3.2.2 Eigenbidyadic C+
60(1)
3.3 Hehl-Obukhov Decomposition,
61(3)
3.4 Example: Simple Antisymmetric Bidyadic,
64(2)
3.5 Inverse Rules for Bidyadics,
66(8)
3.5.1 Skewon Bidyadic
67(3)
3.5.2 Extended Bidyadics
70(3)
3.5.3 3D Expansions
73(1)
Problems,
74(5)
4 Special Dyadics and Bidyadics 79(22)
4.1 Orthogonality Conditions,
79(2)
4.1.1 Orthogonality of Dyadics
79(2)
4.1.2 Orthogonality of Bidyadics
81(1)
4.2 Nilpotent Dyadics and Bidyadics,
81(2)
4.3 Projection Dyadics and Bidyadics,
83(2)
4.4 Unipotent Dyadics and Bidyadics,
85(2)
4.5 Almost-Complex Dyadics,
87(4)
4.5.1 Two-Dimensional AC Dyadics
89(1)
4.5.2 Four-Dimensional AC Dyadics
89(2)
4.6 Almost-Complex Bidyadics,
91(2)
4.7 Modified Closure Relation,
93(5)
4.7.1 Equivalent Conditions
94(1)
4.7.2 Solutions
94(2)
4.7.3 Testing the Two Solutions
96(2)
Problems,
98(3)
5 Electromagnetic Fields 101(40)
5.1 Field Equations,
101(5)
5.1.1 Differentiation Operator
101(2)
5.1.2 Maxwell Equations
103(2)
5.1.3 Potential One-Form
105(1)
5.2 Medium Equations,
106(4)
5.2.1 Medium Bidyadics
106(1)
5.2.2 Potential Equation
107(1)
5.2.3 Expansions of Medium Bidyadics
107(2)
5.2.4 Gibbsian Representation
109(1)
5.3 Basic Classes of Media,
110(7)
5.3.1 Hehl-Obukhov Decomposition
110(2)
5.3.2 3D Expansions
112(2)
5.3.3 Simple Principal Medium
114(3)
5.4 Interfaces and Boundaries,
117(6)
5.4.1 Interface Conditions
117(2)
5.4.2 Boundary Conditions
119(4)
5.5 Power and Energy,
123(5)
5.5.1 Bilinear Invariants
123(2)
5.5.2 The Stress-Energy Dyadic
125(2)
5.5.3 Differentiation Rule
127(1)
5.6 Plane Waves,
128(8)
5.6.1 Basic Equations
128(2)
5.6.2 Dispersion Equation
130(2)
5.6.3 Special Cases
132(1)
5.6.4 Plane-Wave Fields
132(2)
5.6.5 Simple Principal Medium
134(1)
5.6.6 Handedness of Plane Wave
135(1)
Problems,
136(5)
6 Transformation of Fields and Media 141(28)
6.1 Affine Transformation,
141(4)
6.1.1 Transformation of Fields
141(1)
6.1.2 Transformation of Media
142(2)
6.1.3 Dispersion Equation
144(1)
6.1.4 Simple Principal Medium
145(1)
6.2 Duality Transformation,
145(5)
6.2.1 Transformation of Fields
146(1)
6.2.2 Involutionary Duality Transformation
147(2)
6.2.3 Transformation of Media
149(1)
6.3 Transformation of Boundary Conditions,
150(3)
6.3.1 Simple Principal Medium
152(1)
6.3.2 Plane Wave
152(1)
6.4 Reciprocity Transformation,
153(6)
6.4.1 Medium Transformation
153(2)
6.4.2 Reciprocity Conditions
155(2)
6.4.3 Field Relations
157(1)
6.4.4 Time-Harmonic Fields
158(1)
6.5 Conformal Transformation,
159(7)
6.5.1 Properties of the Conformal Transformation
160(4)
6.5.2 Field Transformation
164(1)
6.5.3 Medium Transformation
165(1)
Problems,
166(3)
7 Basic Classes of Electromagnetic Media 169(28)
7.1 Gibbsian Isotropy,
169(9)
7.1.1 Gibbsian Isotropic Medium
169(1)
7.1.2 Gibbsian Bi-isotropic Medium
170(1)
7.1.3 Decomposition of GBI Medium
171(2)
7.1.4 Affine Transformation
173(1)
7.1.5 Eigenfields in GBI Medium
174(2)
7.1.6 Plane Wave in GBI Medium
176(2)
7.2 The Axion Medium,
178(4)
7.2.1 Perfect Electromagnetic Conductor
179(1)
7.2.2 PEMC as Limiting Case of GBI Medium
180(1)
7.2.3 PEMC Boundary Problems
181(1)
7.3 Skewon-Axion Media,
182(10)
7.3.1 Plane Wave in Skewon-Axion Medium
184(1)
7.3.2 Gibbsian Representation
185(2)
7.3.3 Boundary Conditions
187(5)
7.4 Extended Skewon-Axion Media,
192(2)
Problems,
194(3)
8 Quadratic Media 197(28)
8.1 P Media and Q Media,
197(3)
8.2 Transformations,
200(1)
8.3 Spatial Expansions,
201(4)
8.3.1 Spatial Expansion of Q Media
201(2)
8.3.2 Spatial Expansion of P Media
203(1)
8.3.3 Relation Between P Media and Q Media
204(1)
8.4 Plane Waves,
205(4)
8.4.1 Plane Waves in Q Media
205(2)
8.4.2 Plane Waves in P Media
207(1)
8.4.3 P Medium as Boundary Material
208(1)
8.5 P-Axion and Q-Axion Media,
209(2)
8.6 Extended Q Media,
211(7)
8.6.1 Gibbsian Representation
211(3)
8.6.2 Field Decomposition
214(1)
8.6.3 Transformations
215(1)
8.6.4 Plane Waves in Extended Q Media
215(3)
8.7 Extended P Media,
218(3)
8.7.1 Medium Conditions
218(1)
8.7.2 Plane Waves in Extended P Media
219(1)
8.7.3 Field Conditions
220(1)
Problems,
221(4)
9 Media Defined by Bidyadic Equations 225(24)
9.1 Quadratic Equation,
226(9)
9.1.1 SD Media
227(1)
9.1.2 Eigenexpansions
228(1)
9.1.3 Duality Transformation
229(2)
9.1.4 3D Representations
231(3)
9.1.5 SDN Media
234(1)
9.2 Cubic Equation,
235(5)
9.2.1 CU Media
235(1)
9.2.2 Eigenexpansions
236(2)
9.2.3 Examples of CU Media
238(2)
9.3 Bi-Quadratic Equation,
240(6)
9.3.1 BQ Media
241(1)
9.3.2 Eigenexpansions
242(2)
9.3.3 3D Representation
244(1)
9.3.4 Special Case
245(1)
Problems,
246(3)
10 Media Defined by Plane-Wave Properties 249(24)
10.1 Media with No Dispersion Equation (NDE Media),
249(10)
10.1.1 Two Cases of Solutions
250(5)
10.1.2 Plane-Wave Fields in NDE Media
255(2)
10.1.3 Other Possible NDE Media
257(2)
10.2 Decomposable Media,
259(10)
10.2.1 Special Cases
259(4)
10.2.2 DC-Medium Subclasses
263(4)
10.2.3 Plane-Wave Properties
267(2)
Problems,
269(4)
Appendix A Solutions to Problems 273(96)
Appendix B Transformation to Gibbsian Formalism 369(6)
Appendix C Multivector and Dyadic Identities 375(14)
References 389(6)
Index 395
Ismo V. Lindell is a Professor Emeritus in the Department of Radio Science and Engineering, in the School of Electrical Engineering at the Aalto University, Finland. Dr. Lindell has received many honors in the course of his career, including his recognition as an IEEE Fellow in 1990 for his contributions to electromagnetic theory and for the development of education in electromagnetics in Finland. Dr. Lindell has authored or co-authored 3 books in English, authored or co-authored 10 books in Finnish, and published several hundred articles in professional journals, conference proceedings, and contributed chapters to other books.