Article history: Received 20 September 2016 Received in revised form 11 May 2017 Accepted 14 May 2017 Available online 10 June 2017 In this paper, free longitudinal vibration of nanorods is investigated from the wave viewpoint. The Eringen’s nonlocal elasticity theory is used for nanorods modelling. Wave propagation in a medium has a similar formulation as vibrations and thus, it can be used to...

We present a theoretical analysis of a remarkable phenomenon evinced by a periodic structurally chiral material—for example, a chiral sculptured thin film (STF) or a chiral liquid crystal—with a central 908-twist defect illuminated with normally incident, circularly polarized light. Based on the coupled-wave theory (CWT), an approximate but closed-form solution of the relevant boundary-value pr...

Reduction of a matrix to triangular form plays a crucial role in the solution of linear equations. In this chapter, I analyze a pipeline algorithm for Householder reduction (Brinch Hansen 1990). The pipeline is folded several times across an array of processors to achieve approximate load balancing. The pipeline inputs, transforms, and outputs a matrix, column by column. During the computation,...

the matrix functions appear in several applications in engineering and sciences. the computation of these functions almost involved complicated theory. thus, improving the concept theoretically seems unavoidable to obtain some new relations and algorithms for evaluating these functions. the aim of this paper is proposing some new reciprocal for the function of block anti diagonal matrices. more...

In this work, an anti-reflection coating was prepared in the region (400-1000) nm of wavelength, with a double layer silicon dioxide (SiO2) as inner and second mixture titanium (TiO2) certain ratios, outer using chemical spraying method number 6 sprays SiO2 12 - TiO2. Using deposited on glass substrate different SiO2, fixed TiO2-SiO2. The optical structural properties were determined UV-Vis spe...

Asymptotic expressions for the reflected, transmitted, and internal scattered radiation field in optically thick, vertically homogeneous, plane-parallel media are derived from first principles by using the discrete ordinates method of radiative transfer. Compact matrix equations are derived for computing the escape function, diffusion pattern, diffusion exponent, and the reflection function of ...

using adaptive beam forming, " [J. Abstract Abstract: Harrison [J. Acoust. Soc. Am. 125, 3511– 3513 (2009)] presented a mathematical explanation for a sign-inversion induced to the passive fathometer response by minimum variance distortionless response (MVDR) beamforming. Here a concise mathematical formulation is offered, which decomposes the cross-spectral density matrix into coherent and inc...

This work presents an acoustic field simulation method derived from the Green’s functions based monochromatic solutions of the wave equation in homogeneous media. Following this approach, for a given emitting aperture and for an arbitrary set of target points, it is possible to define a spatial monochromatic transfer matrix (MTM). The amplitude and phase of the acoustic field at the target poin...

We study the one-point and two-point Green’s functions in a complex random matrix model to sub-leading orders in the large N limit. We take this complex matrix model as a model for the two-state scattering problem, as applied to spin dependent scattering of impurities in quantum Hall fluids. The density of state shows a singularity at the band center due to reflection symmetry. We also compute ...

A simple design of one dimensional gradual stacked photonic crystal has been proposed. This structure exhibits a periodic array of alternate layers of Graphene and Silica. These are the materials of low and high refractive indices respectively. Here the structure considered has three stacks .Each stack has five alternate layers of Graphene and silica. The transfer matrix method has been used fo...