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Behaviour of Electromagnetic Waves in Different Media and Structures Part 2

Tham khảo tài liệu 'behaviour of electromagnetic waves in different media and structures part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 18 Behaviour of Electromagnetic Waves in Different Media and Structures increase the degree of a surface calibration the picture becomes complicated the greatest intensity of a scattering wave is observed in a mirror direction there are other direction in which the bursts of intensity are observed. 2. Fractal model for two-dimensional rough surfaces At theoretical research of processes of electromagnetic waves scattering selfsimilar heterogeneous objects by rough surfaces is a necessity to use the mathematical models of dispersive objects. As a basic dispersive object we will choose a rough surface. As is generally known she is described by the function z x y of rejections z of points of M of surface from a supporting plane x y fig.l and requires the direct task of relief to the surface. Fig. 1. Schematic image of rough surface There are different modifications of Weierstrass-Mandelbrot function in the modern models of rough surface are used. For a design a rough surface we is used the Weierstrass limited to the stripe function 3 4 N-1 M . 1 c 2 sill Kq n 0 m l 2mn 2mn . cos 1 sin M M 1 where cw is a constant which ensures that 1V . 1 has a unit perturbation amplitude q q 1 is the fundamental spatial frequency D 2 D 3 is the fractal dimension K is the Features of Electromagnetic Waves Scattering by Surface Fractal Structures 19 fundamental wave number N and M are number of tones and p is a phase term that has a uniform distribution over the interval -h h . The above function is a combination of both deterministic periodic and random structures. This function is anisotropic in the two directions if M and N are not too large. It has a large derivative and is self similar. It is a multi-scale surface that has same roughness down to some fine scales. Since natural surfaces are generally neither purely random nor purely periodic and often anisotropic the above proposed function is a good candidate for modeling natural surfaces. The phases cp m can be chosen determinedly