Conductance calculation of a long tube with equilateral triangle cross section

Using the stratified gas flow model for calculating the conductance of long tubes with constant cross section, an analytical expression for calculating the conductance of along tube with equilateral triangle cross section has been derived. The formula given is applicable to the full pressure range. A minimum in the conductance in the intermediate flow state is shown. 2002 American vacuum Society.

Far-field intensity distribution and M-2 factor of hollow Gaussian beams

The far-field intensity distribution of hollow Gaussian beams was investigated based on scalar diffraction theory. An analytical expression of the M-2 factor of the beams was derived on the basis of the second-order moments. Moreover, numerical examples to illustrate our analytical results are given. (c) 2005 Optical Society of America.

Level-oscillation-induced pump effect in a quantum dot with asymmetric constrictions

We have investigated the pump effect induced by the level oscillation in a quantum dot with asymmetric constrictions. The curve of pumped current versus the frequency of level oscillation undulates at zero temperature. The oscillation of the pumped current can be smeared by increasing the temperature and the coupling strength between the quantum dot and the leads. Either the temperature increase or the coupling strength enhancement can lead to a positive or negative effect on the pumped current, depending on the parameters of the quantum dot system. A larger level-oscillation magnitude results in a larger pumped current, especially in the low-frequency case. An analytical expression of the pumped current is obtained in the regime far from adiabatic. A convenient physical picture based on our analytic result is proposed, with which we can explain all the features of the pumped current curves.

Rashba spin splitting in biased semiconductor quantum wells

Rashba spin splitting (RSS) in biased semiconductor quantum wells is investigated theoretically based on eight-band k center dot p theory. We find that at large wave vectors, RSS is both nonmonotonic and anisotropic as a function of in-plane wave vector, in contrast to the widely used isotropic linear model. We derive an analytical expression for RSS, which can qualitatively reproduce such nonmonotonic behavior at large wave vectors. We also investigate numerically the dependence of RSS on the various band parameters and find that RSS increases with decreasing band gap and subband index, increasing valence band offset, external electric field, and well width. All these dependences can be qualitatively described by our analytical model.

Interplay between partial incoherence, partial inelasticity, resonance, and heterogeneity in long-range electron transfer and transport

A generalized scattering matrix formalism is constructed to elucidate the interplay of electron resonance, coherence, dephasing, inelastic scattering, and heterogeneity, which play important roles in the physics of long-range electron transfer/transport. The theory consists of an extension of the standard Buttiker phase-breaking model and an analytical expression of the electron transmission coefficient for donor-bridge-acceptor systems with arbitrary length and sequence. The theory incorporates the following features: Dephasing-assisted off-resonance enhancement, inelasticity-induced turnover, resonance enhancement and its dephasing-induced suppression, dephasing-induced smooth superexchange-hopping transition, and heterogeneity effects. (C) 2002 American Institute of Physics.

Signal bandwidth of general N x N multimode interference couplers

Analytical expression of signal bandwidth of general straight and tapered N x N multimode interference (MMI) couplers is presented. The signal bandwidth is characterized as a function of mode relative energy, mode propagation delay time, and mode pulse broadening in the multimode section of MMI coupler. The model is used to evaluate the signal bandwidth of specific couplers. Results indicate that the signal bandwidth decreases seriously with the increase of channel number and channel guide space. Compared with the straight MMI coupler, the tapered MMI coupler has an improved signal bandwidth.

马蹄形过水断面临界水深的直接计算法

马蹄形过水断面是无压隧洞较常采用的断面形式之一,水力计算中临界水深的求解无显函数公式,传统的试算法或查图法不仅计算过程繁琐复杂,而且计算精度不高。该文通过对马蹄形断面临界流方程的数学变换,并对本文引入的无量纲参数与相对临界水深的关系分析及数值计算,应用逐步优化拟合原理,得到标准Ⅰ、Ⅱ型马蹄形断面临界水深的直接计算式。实例计算及误差分析表明:在工程实用范围内该公式最大相对误差仅为0.8%,且该式物理概念清晰明确、公式形式简捷,为工程设计及水工设计手册的编制提供有益的参考。

SOME ASPECTS ON INTERFACE MODES AND LO EIGENMODES IN GAAS/ALAS QUANTUM-WELLS

The interface modes and LO phonon modes in GaAs/AlAs quantum wells is investigated within the isotropic dispersionless dielectric continuum with nodes in displacement u at the interfaces as boundary condition. The interface modes are found to be purely interface polarization charge effect while LO eigenmodes induce only bulk polarization charges. Analytical expression is determined for LO eigenmodes and is found in good agreement with realistic model calculation, and its labeling index is interpreted as the helicity of electric field as it travels from one side to the other side of the slab.

An Ameliorated Phase Generated Carrier Demodulation Algorithm With Low Harmonic Distortion and High Stability

A novel ameliorated phase generated carrier (PGC) demodulation algorithm based on arctangent function and differential-self-multiplying (DSM) is proposed in this paper. The harmonic distortion due to nonlinearity and the stability with light intensity disturbance (LID) are investigated both theoretically and experimentally. The nonlinearity of the PGC demodulation algorithm has been analyzed and an analytical expression of the total-harmonic-distortion (THD) has been derived. Experimental results have confirmed the low harmonic distortion of the ameliorated PGC algorithm as expected by the theoretical analysis. Compared with the traditional PGC-arctan and PGC-DCM algorithm, the ameliorated PGC algorithm has a much lower THD as well as a better signal-to-noise-and-distortion (SINAD). A THD of below 0.1% and a SINAD of 60 dB have been achieved with PGC modulation depth (value) ranges from 1.5 to 3.5 rad. The stability performance with LID has also been studied. The ameliorated PGC algorithm has a much higher stability than the PGC-DCM algorithm. It can keep stable operations with LID depth as large as 26.5 dB and LID frequency as high as 1 kHz. The system employing the ameliorated PGC demodulation algorithm has a minimum detectable phase shift of 5 mu rad/root Hz @ 1 kHz, a large dynamic range of 120 dB @ 100 Hz, and a high linearity of better than 99.99%.

Theoretical analysis of the relationships between hardness, elastic modulus, and the work of indentation for work-hardening materials

In our previous paper, the expanding cavity model (ECM) and Lame solution were used to obtain an analytical expression for the scale ratio between hardness (H) to reduced modulus (E-r) and unloading work (W-u) to total work (W-t) of indentation for elastic-perfectly plastic materials. In this paper, the more general work-hardening (linear and power-law) materials are studied. Our previous conclusions that this ratio depends mainly on the conical angle of indenter, holds not only for elastic perfectly-plastic materials, but also for work-hardening materials. These results were also verified by numerical simulations.

The analytical description and experiments of the optical bottle generated by an axicon and a lens

Based on the interferential theory, we deduce a new type of analytic expression suitable for describing the evolutions of the optical bottle beam generated from the axicon-lens optical system illuminated by the Gaussian beam for the first time. The theory does not use much approximation in the process of mathematical analysis and can better illustrate the optical bottle beam evolutions at any positions. With the derived expression, the three-dimensional (3D) longitudinal and transverse intensity profiles of the optical bottle beam are simulated numerically. The numerical calculations have been confirmed by the experimental results.

An Analytical Solution for Three-Dimensional Diffraction of Plane P-Waves by a Hemispherical Alluvial Valley with Saturated Soil Deposits

An analytical solution for the three-dimensional scattering and diffraction of plane P-waves by a hemispherical alluvial valley with saturated soil deposits is developed by employing Fourier-Bessel series expansion technique. Unlike previous studies, in which the saturated soil deposits were simulated with the single-phase elastic theory, in this paper, they are simulated with Biot's dynamic theory for saturated porous media, and the half space is assumed as a single-phase elastic medium. The effects of the dimensionless frequency, the incidence angle of P-wave and the porosity of soil deposits on the surface displacement magnifications of the hemispherical alluvial valley are investigated. Numerical results show that the existence of a saturated hemispherical alluvial valley has much influence on the surface displacement magnifications. It is more reasonable to simulate soil deposits with Biot's dynamic theory when evaluating the displacement responses of a hemispherical alluvial valley with an incidence of P-waves.

Analytical Interaction of the Acoustic Wave and Turbulent Flame

A modified resonance model of a weakly turbulent flame in a high-frequency acoustic wave is derived analytically. Under the mechanism of Darrieus-Landau instability, the amplitude of flame wrinkles, which is as functions of the expansion coefficient and the perturbation wave number, increases greatly independent of the 'stationary' turbulence. The high perturbation wave number makes the resonance easier to be triggered but weakened with respect to the extra acoustic wave. In a closed burning chamber with the acoustic wave induced by the flame itself, the high perturbation wave number is to restrain the resonance for a realistic flame.

Numerical and Analytical Study on the Pull-in Instability of Micro-Structure under Electrostatic Loading

The one-mode analysis method on the pull-in instability of micro-structure under electrostatic loading is presented. Taylor series are used to expand the electrostatic loading term in the one-mode analysis method, which makes analytical solution available. The one-mode analysis is the combination of Galerkin method and Cardan solution of cubic equation. The one-mode analysis offers a direct computation method on the pull-in voltage and displacement. In low axial loading range, it shows little difference with the established multi-mode analysis on predicting the pull-in voltages for three different structures (cantilever, clamped-clamped beams and the plate with four edges simply-supported) studied here. For numerical multi-mode analysis, we also show that using the structural symmetry to select the symmetric mode can greatly reduce both the computation effort and the numerical fluctuation.