Journal ArticleDOI
The Huygens' Principle and Doppler Effect in the Presence of Time-Dependent Surfaces
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In this paper, a general formulation and discussion of simple examples are given for the surface integral representation for the solution of the scalar and vector wave equations, for harmonic and arbitrary time dependence, and its validity is discussed.Abstract:
Kirchhoff's surface integral representation for the solution of the wave equation, also commonly referred to as the Huygens' principle, is presently considered for the case of time dependent (i.e., moving) surfaces. This is motivated by problems involving moving sources and scatterers prescribed on moving surfaces. A general formulation and discussion of simple examples are given here. The surface integral representation for the solution of the scalar and vector wave equations, for harmonic and arbitrary time dependence, are used as a starting point. The extension of these integrals to the case of time dependent surfaces and its validity are discussed. In general one can always extend the representations to arbitrarily moving surfaces, but the explicit integration with respect to the retarded time relevant to the sources on the moving surface cannot be performed in general. In the special case of motion of surface elements in the direction of the normal, it is shown that the integration is feasible. The r...read more
Citations
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Quasi Doppler Effects Associated With Spatio-Temporal Translatory, Moving, and Active Boundaries
TL;DR: In this article, a model for generalized situations involving translatory and moving surfaces on which certain boundary or source conditions are prescribed is introduced, in which the role of physics, e.g., in the form of Einstein's Special Relativity theory, is considered.
Journal ArticleDOI
Huygens' Principle geometric derivation and elimination of the wake and backward wave.
TL;DR: In this article, a geometrical interpretation of the Huygens' principle of wave propagation is presented, which shows that the wavelets that exist outside of the new wave front do not form a wake, except where they contact their common tangent surfaces.
References
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Journal ArticleDOI
Some equivalence theorems of electromagnetics and their application to radiation problems
TL;DR: In this article, a review of the general aspects of the classical electromagnetic theory several equivalence theorems are established and illustrated with a number of examples from the diffraction theory.
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On the theory of electromagnetic wave diffraction by an aperture in an infinite plane conducting screen
TL;DR: In this article, a defect in the Kirchhoff procedure is revealed by its failure to duplicate the assumed boundary values at the conducting screen, leading to a lack of self-consistency.
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Multiple Scattering of Electromagnetic Waves by Arbitrary Configurations
TL;DR: In this article, a vector-dyadic formalism was introduced for vector electromagnetic scattering problems, and analogous integral equations which specify the multiple-scattering amplitudes for many objects in terms of the corresponding functions for isolated scatterers were derived.
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Theory of the Doppler effect: Fact, fiction and approximation
TL;DR: The theory of the generalized Doppler effect, concerning the scattering of waves from arbitrary time-varying objects, is still a vide open class of problems as mentioned in this paper, and several approximate methods have been devised.