Analysis and improvement of Laguerre-Gaussian beam position estimation using quadrant detectors

Laguerre-Gaussian beams have become increasingly important in areas like optical manipulation and quantum communications. A good understanding of the accuracy and sensitivity of their displacement measurements are required for these applications. In this Letter, we present a method to analyze and compare the performance of these measurements, and an estimation technique is proposed to improve their measurement accuracies. The effectiveness of our methods is verified by simulation studies.     

Growth and annealing of zinc-blende CdSe thin films on GaAs (0 0 1) by molecular beam epitaxy

CdSe thin films have been grown on GaAs (0 0 1) substrates by molecular beam epitaxy (MBE). The effects of substrate temperature and annealing treatment on the structural properties of CdSe layers were investigated. The growth rate slightly decreases due to the accelerated desorption of Cd from CdSe surface with an increase in the temperature. The sample grown at 260 °C shows a polycrystalline structure with rough surface. As the temperature increases over 300 °C, crystalline CdSe (0 0 1) epilayers with zinc-blende structure are achieved and the structural quality is improved remarkably. The epilayer grown at 340 °C displays the narrowest full-width at half-maximum (FWHM) from (0 0 4) reflection in double-crystal X-ray rocking curve (DCXRC) and the smallest root-mean-square (RMS) roughness of 0.816 nm. Additionally, samples fabricated at 320 °C were annealed in air for 30 min to study the films’ thermal stability. X-ray diffraction (XRD) results indicate that the zinc-blende structure remains unchanged when the annealing temperature is elevated to 460 °C, meaning a good thermal stability of the cubic CdSe epilayers.     

Reliability measures for two-part partition of states for aggregated Markov repairable systems

Three models for the aggregated stochastic processes based on an underlying continuous-time Markov repairable system are developed in which two-part partition of states is used. Several availability measures such as interval availability, instantaneous availability and steady-state availability are presented. Some of these availabilities are derived by using Laplace transforms, which are more compact and concise. Other reliability-distributions for these three models are given as well.     

Uniqueness of weak solution to the generalized magneto-hydrodynamic system

We study uniqueness of weak solution for the generalized incompressible magneto-hydrodynamic (GMHD) system with suitable \(\beta \) , and we prove that the weak solutions are unique in the class \(L^{\frac{2\beta }{2\beta -1+r}}(0,T;B^{r}_{\infty ,\infty })\) with \(r\in (1-2\beta ,1]\) .     

A simple method to synthesize α-Si3N4, β-SiC and SiO2 nanowires by carbothermal route

α-Si₃N₄ nanowires, β-SiC nanowires and SiO₂ amorphous nanowires are synthesized via the direct current arc discharge method with a mixture of silicon, activated carbon and silicon dioxide as the precursor. The α-Si₃N₄ nanowires, β-SiC nanowires and SiO₂ amorphous nanowires are about 50–200 nm in stem diameter and 10–100 μm in length. α-Si₃N₄ nanowires and β-SiC nanowires consist of a solid single-crystalline core along the [0 0 1] and [1 1 1] directions, respectively, wrapped within an amorphous SiO_x layer. The direct current arc plasma-assisted self-catalytic vapor–solid and/or vapor–liquid–solid (VLS) growth processes are proposed as the growth mechanism of the nanowires.     

Optimization of Extension-Shear Coupled Laminates Based on the Differential Evolution Algorithm

Mechanics of Composite Materials - The buckling strength is an important index in the design process of composite extension-shear coupled laminates. In this paper, the differential evolution...     

Fixed point theorems for a class of nonlinear operators in Hilbert spaces and applications

We discuss the existence of fixed point for a class of nonlinear operators by a combination of topological and variational method. The theoretical results are applied to second order dynamic equation with homogeneous Dirichlet boundary conditions.     

DDT Theorem over square-free numbers in short interval

We study the Ces`aro means related to the divisor function. We show that the DDT theorem holds over square-free numbers in short interval, which generalizes some results established by Deshouillers-Dress-Tenenbaum and by Cui-Wu.