Symmetric polynomials in the transfer matrix scaling

Belyayev, Yuriy N.

doi:10.1109/dd.2013.6712796

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Scaling Exponent1

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Cited by 5 publications

(2 citation statements)

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“…It is not difficult to notice that the elementary symmetric polynomials of matrix (22) satisfy the condition (8) if S 14 = S 15 = S 24 = S 25 = S 34 = S 35 = S 46 = S 56 = 0. These equalities hold in particular for cubic, tetragonal and orthorhombic crystal systems (there is also S 45 = 0) [9].…”

Section: Analytical Solutionsmentioning

confidence: 98%

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Transfer matrix of the sixth order

Belyayev

2014

Proceedings of the International Conference Days on Diffraction 2014

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Method of the transfer matrix is used to describe the six-wave diffraction in layered media. The system of differential equations that determine the 6-order transfer matrix is solved by the scaling method with the aid of 6-th order symmetric polynomials. This method is applied to the elastic waves in anisotropic media. Influence of layer thickness and frequency of the wave on the scaling parameter is found. Analytic solutions describing the transfer of thermoelastic waves in isotropic media and elastic stresses in the crystalline layers of the cubic, tetragonal and orthorhombic systems are obtained.

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Section: Analytical Solutionsmentioning

confidence: 98%

“…The number N terms in the last formula and evaluation of the relative truncation error can be found by analogy with the article [8]. Eigenvalues λ j of the matrix W x 3 /m have a simple physical meaning, namely…”

Section: Scaling Exponentmentioning

confidence: 99%