Topological laws of the Rayleigh wave scattering on a statistical inhomogeneity of isotropic solid in the Rayleigh limit

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Abstract

Topological laws of the Rayleigh wave scattering on a statistical inhomogeneity of isotropic solid are obtained theoretically in the Rayleigh limit. They are completely defined by the inhomogeneity structure and include the Rayleigh law of scattering as a particular case. They violate the Rayleigh law in the case of a more general inhomogeneity topology, then the Rayleigh one. It enables first to construct theoretically arbitrary spectrum of scattering up to its oscillations and a strong angular anisotropy.

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About the authors

V. N. Chukov

Emanuel Institute of Biochemical Physics of the Russian Academy of Sciences

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Email: vchukov@mail.ru
Russian Federation, Moscow

References

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2. Fig. 1. Correlator (3), (14) - (23), (27) describing the ensemble of realisations of statistical inhomogeneity (a), averaging over which gives the angular distribution (9) under the deterministic structure of the disturbed layer F(x3) in the form (24) everywhere, satisfying the Rayleigh scattering law in accordance with the topological scattering laws in the Rayleigh limit (25), (26). NR = 0 (25); τm = τ / amax; N(r) = 1, (17), , m11 = 0, (17), . Poisson's ratio σ = 0.25, d / amax = 1, q1 = 1 (24) and (22) throughout. Rayleigh scattering law for the angular scattering distribution , where everywhere, unless otherwise specified, p0 = 0.1, with the correlator shown in Fig. 1a (b). The correlator (3), (14) to (23), (27), which gives a violation of the Rayleigh scattering law according to the topological laws (25), (26). NR = 6; N(r) = 1, , , , m11 = 3, , (c). Violation of the Rayleigh scattering law. for the correlator shown in Fig. 1c; p0 = 0.1 (d). The correlator (3), (14) - (23), (29), which gives scattering oscillations in the Rayleigh limit. N(r) = 1, , , , , , , , m11 = 1, m12 = 31, m13 = 25, , (e). Scattering oscillations in the Rayleigh limit. Violation of the Rayleigh scattering law presented in Fig. 1b. for the correlator presented in Fig. 1d; p0 = 0.015 (e)

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3. Fig. 2. The characteristic angular anisotropy of Rayleigh scattering (a) found in the present work due to the boundary conditions on the free inhomogeneous surface and the inhomogeneity structure (24) perpendicular to the surface, while preserving the Rayleigh frequency law of scattering for the correlation function presented in Fig. 1a. Fully angle isotropic Rayleigh scattering pattern (b) obtained by excluding the influence of boundary conditions and vertical arbitrary F(x3) (2) of the inhomogeneity structure on the Rayleigh wave scattering angular distribution (30), (31), while taking into account the correlator presented in Fig. 1a. everywhere unless otherwise specified

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4. Fig. 3. Correlator (3), (14) - (23), (29), which gives strong anisotropy and scattering zeros in the Rayleigh limit p << 1 determined by the new topological laws (25), (26) with obligatory violation of the Rayleigh frequency law for long-wavelength scattering (a). The parameter values are the same as for Fig. 1d, but m11 = 1; m12 = 2; m13 = 3 (17). Strong anisotropy and zeros of the angular distribution of Rayleigh wave scattering in the Rayleigh limit (b). Violation of both the pure Rayleigh [1, 5] isotropy of the angular distribution of scattering presented in Fig. 2b and the characteristic anisotropy of Rayleigh scattering in the form of a forward shifted isotropic circle of the angular distribution in polar coordinates presented in Fig. 2a, and the topological symmetry of laws (25), (26) as a whole

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