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...

We research on the possible orientations patterns of a grid graph G, and propose a method for counting certain combinatorial structures over the class of orientations of G. For example, our method can be applied for counting sink-free orientations of G, as well as it can be applied for solving the #2SAT problem for grid Boolean formulas. Our proposal extends the classical transfer matrix method...

The most general nonuniform reaction-diffusion models on a one-dimensional lattice with boundaries, for which the time evolution equations of correlation functions are closed, are considered. A transfer matrix method is used to find the static solution. It is seen that this transfer matrix can be obtained in a closed form, if the reaction rates satisfy certain conditions. We call such models su...

Using transfer matrix method to solve 3D Ising model is generalized straightforwardly from 2D case. We follow the B.Kaufman's approach. No approximation is made except the largest eigenvalue cannot be identified. This problem comes from the fact that we follow the choice of directions of 2-dimensional rotations in direct product space of 2D Ising model such that all eigenvalue equations reduce ...