The application of Transfer matrix method TMM ranges from linear/nonlinear vibration, composite structure, and multibody system to calculating static deformation, natural vibration, dynamical response, and damage identification. Generally TMM has two characteristics: 1 the TMM formulae share similarity to the chain mechanics model in terms of topology structure; then TMM often is selected as a ...

This is the third part of the five-part saga on the umbral transfermatrix method, based on Gian-Carlo Rota’s seminal notion of the umbra. In this article we describe the Maple package ZOO that for any specific k, automatically constructs an umbral scheme for enumerating “k-board” lattice animals (polyominoes) on the two-dimensional square lattice. Such umbral schemes enable counting these impor...

A hybrid transfer-matrix finite-difference time-domain (FDTD) method is proposed for modeling the optical properties of finite-width planar periodic structures. This method can also be applied for calculation of the photonic bands in infinite photonic crystals. We describe the procedure of evaluating the transfer-matrix elements by a special numerical FDTD simulation. The accuracy of the new me...

We present a new method of calculation of partition function for the layered systems with the arbitrary spin-modulated structure in the linear cluster approximation. The thermodynamic description of the system in question is based on the Bogolyubov variational principle (inequality). The transfer matrix technique is used to determine the partition function, finally the free energy of the system...

Mufflers are widely used for exhaust noise attenuation in vehicles and machinery. Recent advances in modeling procedures for accurate performance prediction have led to the development of modeling methods for practical muffler components in commercial design. Muffler designers need simple and fast modeling tools, especially in the preliminary design evaluation stages. Finite Element and Boundar...

In recent years there has been a growing focus on reducing the suction noise from hermetic household compressors. One approach is to reduce the transmitted sound power through the suction muffler at particular frequencies. In order to better control the acoustic performance of the muffler, a large variety of muffler designs have emerged. Most notably is the appearance of mufflers with two or mo...

We propose a new algorithm which works effectively in global updates in Monte Carlo study. We apply it to the quantum spin chain with next-nearest-neighbor interactions. We observe that Monte Carlo results are in excellent agreement with numerically exact ones obtained by the transfer matrix method.