Corrected Sum Rule, Generalized Virial Identity and Elementary Excitation Spectrum of Bose–Einstein Condensates at Any Trapped Atom Number

Using a corrected sum rule and a generalized virial identity, we study the analytical expression for entire modes of the collective elementary excitation spectrum in a trapped Bose–Einstein condensate at any atom number. Explicit analytical formulas for the spectrum are obtained for the harmonic traps with both spherical symmetry and axial symmetry using the gaussian approximation for the N-body ground-state wave function of the condensate. These formulas give the simple dependence of all energy levels on the atom numbers, their interaction strength and trap geometry parameters.     

Minimax estimation of deterministic parameters in linear models with a random model matrix

We consider the problem of estimating an unknown deterministic parameter vector in a linear model with a random model matrix, with known second-order statistics. We first seek the linear estimator that minimizes the worst-case mean-squared error (MSE) across all parameter vectors whose (possibly weighted) norm is bounded above. We show that the minimax MSE estimator can be found by solving a semidefinite programming problem and develop necessary and sufficient optimality conditions on the minimax MSE estimator. Using these conditions, we derive closed-form expressions for the minimax MSE estimator in some special cases. We then demonstrate, through examples, that the minimax MSE estimator can improve the performance over both a Baysian approach and a least-squares method. We then consider the case in which the norm of the parameter vector is also bounded below. Since the minimax MSE approach cannot account for a nonzero lower bound, we consider, in this case, a minimax regret method in which we seek the estimator that minimizes the worst-case difference between the MSE attainable using a linear estimator that does not know the parameter vector, and the optimal MSE attained using a linear estimator that knows the parameter vector. For analytical tractability, we restrict our attention to the scalar case and develop a closed-form expression for the minimax regret estimator.     

Second harmonic generation from a ferroelectric film

We derive an expression for transmittivity (T_SHG) of second harmonic generation (SHG) signals from a ferroelectric (FE) film. Intensities of up and down fields in the medium are investigated in relation to T_SHG. The derivations are made based on undepletion of input fields and nonlinear wave equation derived from the Maxwell equations. We present two cases: film without mirrors and with partial mirrors. Expressions for the newly derived nonlinear susceptibility coefficients of SHG for real crystal symmetry [J. Opt. Soc. Am. B 19 (2002) 2007] are used to get more realistic results. Variations in T_SHG with respect to film thickness are illustrated.     

The First Template‐Free Growth of Crystalline Silicon Microtubes

A simple template‐free high‐temperature evaporation method was developed for the growth of crystalline Si microtubes for the first time. As‐grown Si microtubes were characterized using X‐ray diffraction, scanning electron microscopy, transmission electron microscopy, and room‐temperature photoluminescence. The lengths of the Si tubes can reach several hundreds of micrometers; some of them have lengths on the order of millimeters. Each tube has a uniform outer diameter along its entire length, and the typical outer diameter is ≈ 2–3 μm. Most of the tubes have a wall thickness of ≈ 400–500 nm, though a considerable number of them exhibit a very thin wall thickness of ≈ 50 nm. Room‐temperature photoluminescence measurement shows the as‐synthesized Si microtubes have two strong emission peaks centered at ≈ 589 nm and ≈ 617 nm and a weak emission peak centered at ≈ 455 nm. A possible mechanism for the formation of these Si tubes is proposed. We believe that the present discovery of the crystalline Si microtubes will promote further experimental studies on their physical properties and smart applications.     

Electronic properties of magnetically doped nanotubes

Effect of doping of carbon nanotubes by magnetic transition metal atoms has been considered in this paper. In the case of semiconducting tubes, it was found that the system has zero magnetization, whereas in metallic tubes the valence electrons of the tube screen the magnetization of the dopants: the coupling to the tube is usually antiferromagnetic (except for Cr).     

Moving Least-Squares Differential Quadrature Method for Free Vibration of Antisymmetric Laminates

In this paper, the moving least-squares differential quadrature (MLSDQ) method is employed for free vibration of thick antisymmetric laminates based on the first-order shear deformation theory. The generalized displacements of the laminates are independently approximated with the centered moving least-squares (MLS) technique within each domain of influence. The MLS nodal shape functions and their partial derivatives are computed quickly through back-substitutions after only one LU decomposition. Subsequently, the weighting coefficients in the MLSDQ discretization are determined with the nodal partial derivatives of the MLS shape functions. The MLSDQ method combines the merits of both the differential quadrature and meshless methods which can be conveniently applied to complex domains and irregular discretizations without loss of implementation efficiency and numerical accuracy. The natural frequencies of the laminates with various edge conditions, ply angles, and shapes are calculated and compared with the existing solutions to study the numerical accuracy and stability of the MLSDQ method. Effects of support size, order of completeness of basis functions, and node irregularity on the numerical accuracy are investigated in detail.     

Low-temperature poly-SiGe alloy growth of high gain/speed pin infrared photosensor with gold-induced lateral crystallization (Au-ILC)

The hydrogenated poly-silicon germanium (poly-SiGe:H) epitaxial film has been investigated using gold-induced lateral crystallization (Au-ILC) technology on a-SiGe:H layers at 10-h 350/spl deg/C annealing temperature and 60-sccm hydrogen (H/sub 2/) content. Using this optimal condition, the growth rate of the induced Au was as large as 15.9 /spl mu/m/h. With a low annealing temperature (/spl les/400/spl deg/C) and large growth rate, this novel technology will be noticeably useful for poly-SiGe:H pin IR-sensing fabrication on a conventional precoated indium tin oxide (ITO)-glass substrate. Under a 1-/spl mu/W IR-LED incident light (with peak wave length at 710 nm) and at a 5-V biased voltage, the poly-SiGe:H pin IR sensor developed by the Au-ILC technology, i.e., an Al (anode)/n poly-SiGe:H/i poly-SiGe:H/p poly-SiGe:H/ITO (cathode)/glass-substrate structure allowed for maximum optical gain and response speed. The optical gains and the response speeds were almost 600 and 130%, respectively, better than that of a traditional pin type. Meanwhile, the FWHM of a poly-SiGe:H pin sensor with Au-ILC technology was reduced from 280 to 150 nm. This reveals excellent IR-sensing selectivity. These IR-sensing trials demonstrated again that the proposed Au-ILC technology has very useful application in the field of low cost integrated circuits on optoelectronic applications.