Topic

# Dyadics

About: Dyadics is a research topic. Over the lifetime, 192 publications have been published within this topic receiving 3392 citations. The topic is also known as: dyadic tensor & tensor product.

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01 Feb 1980TL;DR: In this paper, a straightforward approach that does not involve delta-function techniques is used to rigorously derive a generalized electric dyadic Green's function which defines uniquely the electric field inside as well as outside the source region.

Abstract: A straightforward approach that does not involve delta-function techniques is used to rigorously derive a generalized electric dyadic Green's function which defines uniquely the electric field inside as well as outside the source region. The electric dyadic Green's function, unlike the magnetic Green's function and the impulse functions of linear circuit theory, requires the specification of two dyadics: the conventional dyadic G- e outside its singularity and a source dyadic L-which is determined solely from the geometry of the "principal volume" chosen to exclude the singularity of G- e . The source dyadic L-is characterized mathematically, interpreted physically as a generalized depolarizing dyadic, and evaluated for a number of principal volumes (self-cells) which are commonly used in numerical integration or solution schemes. Discrepancies at the source point among electric dyadic Green's functions derived by a number of authors are shown to be explainable and reconcilable merely through the proper choice of the principal volume. Moreover, the ordinary delta-function method, which by itself is shown to be inadequate to extract uniquely the proper electric dyadic Green's function in the source region, can be supplemented by a simple procedure to yield unambiguously the correct Green's function representation and associated fields.

498 citations

01 Jan 2007

TL;DR: In this article, physical limitations on bandwidth, realized gain, Q-factor and directivity for antennas of arbitrary shape were derived from the eigenvalues of the long-wavelength, high-contrast polarizability dyadics.

Abstract: In this paper, physical limitations on bandwidth, realized gain, Q-factor and directivity are derived for antennas of arbitrary shape. The product of bandwidth and realizable gain is shown to be bounded from above by the eigenvalues of the long-wavelength, high-contrast polarizability dyadics. These dyadics are proportional to the antenna volume and are easily determined for an arbitrary geometry. Ellipsoidal antenna volumes are analysed in detail, and numerical results for some generic geometries are presented. The theory is verified against the classical Chu limitations for spherical geometries and shown to yield sharper bounds for the ratio of the directivity and the Q-factor for non-spherical geometries.

259 citations

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TL;DR: In this article, physical limitations on bandwidth, realized gain, Q-factor and directivity for antennas of arbitrary shape were derived from the eigenvalues of the long-wavelength, high-contrast polarizability dyadics.

Abstract: In this paper, physical limitations on bandwidth, realized gain, Q-factor and directivity are derived for antennas of arbitrary shape. The product of bandwidth and realizable gain is shown to be bounded from above by the eigenvalues of the long-wavelength, high-contrast polarizability dyadics. These dyadics are proportional to the antenna volume and are easily determined for an arbitrary geometry. Ellipsoidal antenna volumes are analysed in detail, and numerical results for some generic geometries are presented. The theory is verified against the classical Chu limitations for spherical geometries and shown to yield sharper bounds for the ratio of the directivity and the Q-factor for non-spherical geometries.

165 citations

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01 Jan 2004

TL;DR: In this article, the Grassmann algebra was used to define the Dyadic Algebra and Dyadic Dyadics (DYADIA) in three dimensions and in four dimensions.

Abstract: Preface. 1 Multivectors. 1.1 The Grassmann algebra. 1.2 Vectors and dual vectors. 1.3 Bivectors. 1.4 Multivectors. 1.5 Geometric interpretation. 2 Dyadic Algebra. 2.1 Products of dyadics. 2.2 Dyadic identities. 2.3 Eigenproblems. 2.4 Inverse dyadic. 2.5 Metric dyadics. 2.6 Hodge dyadics. 3 Differential Forms. 3.1 Differentiation. 3.2 Differentiation theorems. 3.3 Integration. 3.4 Affine transformations. 4 Electromagnetic Fields and Sources. 4.1 Basic electromagnetic quantities. 4.2 Maxwell equations in three dimensions. 4.3 Maxwell equations in four dimensions. 4.4 Transformations. 4.5 Super forms. 5 Medium, Boundary, and Power Conditions. 5.1 Medium conditions. 5.2 Conditions on boundaries and interfaces. 5.3 Power conditions. 5.4 The Lorentz force law. 5.5 Stress dyadic. 6 Theorems and Transformations. 6.1 Duality transformation. 6.2 Reciprocity. 6.3 Equivalence of sources. 7 Electromagnetic Waves. 7.1 Wave equation for potentials. 7.2 Wave equation for fields. 7.3 Plane waves. 7.4 TE and TM polarized waves. 7.5 Green functions. References. Appendix A: Multivector and Dyadic Identities. Appendix B: Solutions to Selected Problems. Index. About the Author.

153 citations

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TL;DR: In this article, the second derivatives of the free space scalar Green's function are treated as generalized functions in the manner described by Gel'fand and Shilov, and a new formula is derived that regularizes a divergent convolution integral involving the second derivative of g.

Abstract: The free-space scalar Green's function g has an R^{-1} singularity, where R is the distance between the source and observation points. The second derivatives of g have R^{-3} singularities, which are not generally integrable over a volume. The derivatives of g are treated as generalized functions in the manner described by Gel'fand and Shilov, and a new formula is derived that regularizes a divergent convolution integral involving the second derivatives of g . When the formula is used in the dyadic Green's function formulation for calculating the E field, all previous results are recovered as special cases. Furthermore, it is demonstrated that the formula is particularly suitable for the numerical evaluation of the field at a source point, because it allows the exclusion of an arbitrary finite region around the singular point from the integration volume. This feature is not shared by any of the previous results on the dyadic Green's function.

120 citations