软X射线超光滑表面传输特性的初步研究

本文给出了软Ｘ射线超光滑表面散射的一级近似的一般理论推导，从中给出软Ｘ射线的散射传输特性。通过实验测量了λ＝２４．３ｎｍ、２５．６ｎｍ时具有超光滑表面的Ｍｏ、Ｓｉ样品的反射率和λ＝４．４６ｎｍ时熔石英超光滑样品的反射单。对４．４６ｎｍ进行了了散射测量，可以明显观察到软Ｘ射线的非正常反射现象。     

Ultrasonic propagation in slurries

Experimental measurements have been made of the ultrasonic velocity and attenuation in some simple suspensions of, mainly, silicon carbide in water and in ethylene glycol. These are compared with theoretical predictions based on a novel hydrodynamic model. Predicted ultrasonic velocities are in excellent agreement with the measured values. Predicted and measured ultrasonic attenuations do not agree as well. However, the suspensions give rise to excess attenuations rising to a few hundred nepers per metre and special experimental techniques were needed to measure ultrasonic properties. To predict attenuations to within, say, 20% for mixtures such as these is a major achievement.     

Analysis of femtosecond optical pulse propagation in one-dimensional nonlinear photonic crystals using finite-difference time-domain method

In this paper, we have used the finite-difference time-domain (FDTD) method to analyze the optical pulse propagation in a nonlinear, one-dimensional photonic crystal (1DPC). Hyperbolic secant pulses with various carrier wavelengths are utilized in this study. In a nonlinear regime, a 1DPC introduces a photonic band-gap whose central wavelength and width depend on the input pulse intensity. In the present work, three different cases are considered. These correspond to the carrier wavelengths of the incident pulses being out of, near to, and partially in the band-gap. For each case, the effect of nonlinearity on pulse propagation is investigated. Also, we have analyzed the two-frequency regime, in which each of the two pulses has a different carrier frequency (wavelength). This kind of study can be done directly with FDTD without any further computational burden but it is somewhat complicated using nonlinear coupled-mode equations (NLCME) and nonlinear Schrödinger equation (NLSE), which require separate treatments for each carrier wavelength.     

Performance of Dispersion-Compensated Optical Transmission Systems Based on Different Electrical Drivers

In this article, the simulation results have been presented for dispersive optical communication with different electrical drivers. The length of single-mode fiber has been put in a run that is compensated by dispersion-compensated fiber. The results have been presented and it is observed that of all the electrical drivers, the NRZ rectangular is best suited for dispersive optical communication systems. For this electrical driver, the parameters like BER remain constant and low. For other drivers, the BER decreases more for RZ super-Gaussian. Similarly, the Q factor increases with runs for all types of drivers except for NRZ rectangular, for which it decreases. For all the drivers, it is clear that as the runs are varied, the eye opening penalty increases, that is, there is less eye opening as the length of single-mode fiber is increased. It is also seen that the dispersion-compensated fiber compensates for the dispersion very effectively irrespective of the type of driver. Of the two formats, return to zero (RZ) and non-return to zero (NRZ), the earlier has more eye-opening penalty as the distortion is more and is clearly visible in all the rectangular, super-Gaussian, and raised cosine RZ formats. Of the three RZ formats, it is observed that RZ rectangular has the least eye-opening penalty. The non-return to zero format has less distortion and, of the two rectangular and raised cosine, the NRZ rectangular has less eye-opening penalty.     

Ti∶LiNbO_3二维渐变折射率光波导传播常数的计算

从Ti∶LiNbO3波导截面折射率分布的特点出发，得出一套计算传播常数简单而精确的方法。文中对该法进行了分析，并应用该方法计算了钛扩散波导的色散关系。该方法为钛扩散光波导集成光学器件的设计提供了一种较可靠的理论手段。     

The Beam Propagation Factor of Nonparaxial Truncated Flattened Gaussian Beams

By using the second-order moment of the power density, the beam width, far-field divergence angle and M² factor of nonparaxial truncated flattened Gaussian (FG) beams are derived analytically. It is shown that the M² factor of nonparaxial truncated FG beams depends not only on the truncation parameter δ and beam order N, but also on the initial waist-width to wavelength ratio w₀/λ. The far-field divergence angle approaches an asymptotic value of θ_max=63.435° when the truncation parameter δ → 0. For the special cases of N = 0 and δ → ∞ our results reduce to those of nonparaxial truncated Gaussian beams and nonparaxial untruncated FG beams, respectively.     

等价分布源方法新发展

本文以广义Lighthill方程和广义Green函数为基础给出任意截面管道声传播计算模型,同时应用等价分布源方法建立了包含声衬影响的声传播模型,该方法避开了复杂的管道特征值计算,并在此基础上以积分变换发展了等价分布源方法,免去了声源及观察点匹配时产生的奇异性,使该方法大大简化,易于工程实际计算.此外,本文还给出了特殊截面管的算例.     

用含时波包理论处理HD＋H→H＋DH,D＋H2反应

用含时波包（ＴＤＷＰ）理论计算了具有两个不同产物道的反应ＨＤ＋Ｈ→Ｈ＋ＤＨ，Ｄ＋Ｈ２的初态确定的反应几率及生咸物的分支比。在利用分解算符法进行波包传播的过程中，采取了分立变量表象（ＤＶＲ）及分立交量－有限基表象（ＤＶＲ—ＦＢＲ）变换，这一方法降低了传播过程中需保存大变换矩阵的要求。通过应用能量投影法，可从单一波包中抽出许多能量确定的动力学信息。为了避免因所选取的格点范围有限而引起的波函数在边界点附近的反射，传播过程中还采用了光学势以吸收反射波函。     

非线性波动方程解的Blow up

本文证明了非线性波动方程的一类小初值问题，当初始能量小于或等于零时，解在有限时间内Ｂｌｏｗｕｐ．并给出当解有有限扩散速度时解的生命区间的上界估计。     

A stochastic approach to global error estimation in ODE multistep numerical integration

In order to assess the quality of approximate solutions obtained in the numerical integration of ordinary differential equations related to initial-value problems, there are available procedures which lead to deterministic estimates of global errors. The aim of this paper is to propose a stochastic approach to estimate the global errors, especially in the situations of integration which are often met in flight mechanics and control problems. Treating the global errors in terms of their orders of magnitude, the proposed procedure models the errors through the distribution of zero-mean random variables belonging to stochastic sequences, which take into account the influence of both local truncation and round-off errors. The dispersions of these random variables, in terms of their variances, are assumed to give an estimation of the errors. The error estimation procedure is developed for Adams-Bashforth-Moulton type of multistep methods. The computational effort in integrating the variational equations to propagate the error covariance matrix associated with error magnitudes and correlations is minimized by employing a low-order (first or second) Euler method. The diagonal variances of the covariance matrix, derived using the stochastic approach developed in this paper, are found to furnish reasonably precise measures of the orders of magnitude of accumulated global errors in short-term as well as long-term orbit propagations.