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In 1907 Lord Rayleigh published a paper on the dynamic theory of gratings. In this paper he presented a rigorous approach for solving plane wave scattering on periodic surfaces. Moreover he derived explicit expressions for a perfectly conducting sinusoidal surface, and for perpendicular incidence of the electromagnetic plane wave. This paper was criticized by Lippmann in 1953 for he assumed Rayleigh’s approach to be incomplete. Since this time there have been published several arguments, proofs, and discussions concerning the correctness and the range of validity of Rayleigh’s approach not only for plane wave scattering on gratings but also for light scattering on nonspherical structures, in general. In the paper at hand we will discuss the different point of views on what is called “Rayleigh’s hypothesis” as well as the relevance of a found theoretical limit for its validity. Furthermore we present a numerical treatment of the original scattering problem of a p-polarized plane wave perpendicularly incident on a perfectly conducting sinusoidal surface (i.e., the scalar Dirichlet problem). In doing so we emphasizes the near-field solution especially within the grooves of the grating up to points on the surface, and below the surface. Two different Green’s function formulations of Huygens’ principle are used as starting points. One of this formulation results in the general T-matrix approach which is considered to be affected by Rayleigh’s hypothesis especially for near-field calculations. The other formulation provides a conventional boundary integral equation which is in accordance with Lippmann’s point of view and free of problems with Rayleigh’s hypothesis. But the obtained results show that Lippmann’s argumentation do not withstand a critical numerical analysis, and that the independence of least-squares approaches from Rayleigh’s hypothesis, as understood and proven by Millar, seems to hold also for certain methods which does not fit into such an approach. 相似文献
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The present note is concerned with the numerical simulation of two-dimensional homogeneous decaying turbulence. We employ a Galerkin-type discretization in an adaptive basis of orthogonal wavelets. Therewith the solution is represented by means of a reduced basis being adapted at each time step. This is one of the first times that wavelet decomposition of a turbulent flow field has been used not only for a posteriori analysis but directly for the computation of the flow in a reduced basis. A classical Fourier method furnishesa suitable reference solution. 相似文献
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Mixtures of a calix[4]arene and a naphthyridine derivative dissolved in 1,2-dichlorobenzene form thermoreversible aggregates. The aggregation process was followed by means of time-resolved multiangle light scattering at two different mixing ratios, 1:3 and 1:4, yielding a detailed record of the relative mass, the radius of gyration, and the particle scattering function of the growing aggregates. On the basis of these data, a conclusive model of the structure is presented for the developing aggregates: monomers aggregate to wormlike filaments which form branching points. Formation of branching points proceeds in a frequency and distribution which is similar to the polycondensation of ABC monomers toward non-randomly branched macromolecules (Burchard, W. Macromolecules 1977, 10, 919-927). Thus, aggregation results in hyperbranched-like particles with striking analogies to the polymerization of glucose to amylopectin. 相似文献