A scattering matrix approach is proposed to avoid numerical instabilities arising with the classical transfer matrix method when analyzing the propagation of plane surface acoustic waves in piezoelectric multilayers. The method is stable whatever the thickness of the layers, and the frequency or the slowness of the waves. The computation of the Green’s function and of the effective permittivity...

An analytic expression of transmittance based on the Airy wavefunctions approach has been derived for an electron through an anisotropic heterostructure with an applied voltage to the barrier of the heterostructure. The Si(110)|Si0.5Ge0.5|Si(110) heterostructure was used to examine the analytic expression. In order to evaluate the Airy wavefunctions approach, the transfer matrix method, which i...

in this paper, buckling of simply supported column with an edge crack is investigated numerically and analytically. four different scenarios of damage severities are applied to a column, open crack assumption and the effect of closing crack in stability of the column which depends on position and size of cracks, are numerically compared. crack surfaces contact is modeled with gap element using ...

Counting the number of words which contain a set of given strings as substrings a certain number of times is a classical problem in combinatorics. This problem can, for example, be attacked using the transfer matrix method (see [20, Section 4.7]). In particular, it is a well-known fact that the generating function of such words is always rational. For example, in [20, Example 4.7.5] it is shown...

We have previously discussed the classical diffusive system of the bounded one-dimensional multitrap using the transfer-matrix method which is generally applied for studying the energy spectrum of the unbounded quantum Kronig-Penney multibarrier. It was shown, by this method, that for certain values of the relevant parameters the bounded multitrap array have unity transmission and a double-peak...

We analyze the transmission of light through coupled-resonator optical waveguides in the form of evanescently coupled Fabry–Perot resonator arrays. We develop a transfer matrix method to calculate the amplitude and phase responses of the arrays. We also discuss the inclusion of optical gain in the system to compensate for losses in these structures. Owing to the compact length along the propaga...

An efŽ cient method has been developed for analyzing the three-dimensional electromechanical deformations of a monoclinic piezoelectric laminate subjected to surface tractions and electric displacements on the top and bottom surfaces. The procedure combines the transfer matrix method with the asymptotic expansion technique. The electromechanical coupled formulation is reduced to a hierarchy of ...

We study the combinatorics of addition using balanced digits, deriving an analog of Holte’s “amazing matrix” for carries in usual addition. The eigenvalues of this matrix for base b balanced addition of n numbers are found to be 1, 1/b, · · · , 1/b, and formulas are given for its left and right eigenvectors. It is shown that the left eigenvectors can be identified with hyperoctahedral Foulkes c...