A real orthogonal matrix R is a matrix whose elements are real numbers and satisfies R−1 = R (or equivalently, RR = I, where I is the 3 × 3 identity matrix). Taking the determinant of the equation RR = I and using the fact that det(R) = det R, it follows that (det R) = 1, which implies that either detR = 1 or detR = −1. A real orthogonal matrix with detR = 1 provides a matrix representation of ...

the effect of single and double-layer anti-reflective coatings on efficiency enhancement of silicon solar cells was investigated. the reflectance of different anti-reflection structures were calculated using the transfer matrix method and then to predict the performance of solar cells coated by these structures, the weighted average reflectance curves were used as an input of a pc1d simulation....

We interpret magnetic billiards as Finsler ones and describe an analog of the string construction for magnetic billiards. Finsler billiards for which the law “angle of incidence equals angle of reflection” are described. We characterize the Finsler metrics in the plane whose geodesics are circles of a fixed radius. This is a magnetic analog of Hilbert’s fourth problem asking to describe the Fin...

We discuss the integrable boundary conditions for the one-dimensional (1D) Hubbard Model in the framework of the Quantum Inverse Scattering Method (QISM). We use the fermionic R-matrix proposed by Olmedilla et al. to treat the twisted periodic boundary condition and the open boundary condition. We determine the most general form of the integrable twisted periodic boundary condition by consideri...

In this paper, the wave propagation approach is presented to analyze the vibration and wave power reflection in FG rectangular plates based on the first order shear deformation plate theory. The wave propagation is one of the useful methods for analyzing the vibration of structures. This method gives the reflection and propagation matrices that are valuable for the analysis of mechanical energy...

Dispersing nanoparticles in a polymer matrix is intrinsically challenging due to unfavorable entropic interactions between the matrix and the nanoparticle. In this research dispersion of nanoparticles in polymer matrix was studied and the effect of dispersion on properties was investigated. The properties of polymer composite depend on the type, size, shape, concentration of nanoparticles, and ...

In this paper, ultrasonic wave propagation in three phases (3P) of composite materials was investigated. The simulation was conducted by PZFlex analysis code, a time domain finite element program. The reflection and transmission characteristics with different shapes of middle layer between glass fiber and epoxy resin are investigated in order to understand basic ultrasonic behavior of energy di...

Observing and measuring the weld pool surface is a key to developing next-generation intelligent welding machines and to understanding the welding process better. In this paper, a dot-matrix pattern is used to project a commercially-available low power continuous laser onto the weld pool surface and the reflection of the laser is intercepted by an image plane which is placed with a distance fro...

A new boundary condition is introduced to calculate the effective impedance matrix of semi-infinite periodic structures such as photonic crystals and metamaterials, which leads to a reduction of the solution space. The obtained effective impedance matrix allows one to relate a matrix to a PC, which includes all of its properties in terms of reflection from its interface. For one-dimensional pho...