固体火箭发动机喷管气固两相流动的数值模拟

对颗粒相采用颗粒轨道模型,气相求解可压缩N-S方程组,计算方法采用显式Runge-Kutta时间推进法与有总变差衰减(TVD)性质的高精度MUSCL-Roe格式;自主开发了曲线坐标系下二维轴对称可压缩N-S方程组的解算器Solve2D,研究了固体火箭发动机喷管中颗粒相对流场的影响以及不同尺寸颗粒运动规律.结果表明:颗粒相对流场的影响主要表现在喷管喉部以及扩张段,和单相流场相比,沿轴线马赫数减小,且颗粒尺寸越小减少得越多;沿轴线气相温度升高,且颗粒尺寸越小温度升高越多;颗粒尺寸越小,无粒子区越小;颗粒越大与收缩段壁面碰撞越剧烈,无粒子区越大.

双掺杂LiNbO3晶体中光栅均匀性的优化研究

研究了非挥发全息记录中南于紫外光的强吸收而引起的光栅非均匀性，分析了这种非均匀性对光栅衍射效率的影响。结果显示，非均匀性致使光折变光栅的平均强度减弱，衍射效率降低。提出了采用两束等光强的敏化紫外光由晶体两侧入射的优化方案以改善光栅的均匀性，提高光栅的衍射效率。通过联立两中心带输运物质方程和双光束耦合波方程，进行了相应的理论模拟，并给出实验验证。结果表明双侧紫外光照射能够实现均匀性较好的光栅，是提高衍射效率的有效途径之一。

Effect of microcosmic optical parameters of dopants on the signal-to-noise ratio in doubly doped LiNbO3 crystals

We propose a united theory that describes the two-center recording system by taking scattering noise into account. The temporal evolution of the signal-to-noise ratio in doubly doped photorefractive crystals is described based on jointly solving material equations and coupled-wave equations with the fourth-order Runge-Kutta method. Roles of microcosmic optical parameters of dopants on the signal-to-noise ratio are discussed in detail. The theoretical results can confirm and predict experimental results. (c) 2005 Elsevier GmbH. All rights reserved.

A highly efficient beam propagation method for modeling step-index waveguides with tilt interface

Based on a new finite-difference scheme and Runge-Kutta method together with transparent boundary conditions (TBCs), a novel beam propagation method to model step-index waveguides with tilt interfaces is presented. The modified scheme provides an precies description of the tilt interface of the nonrectangular waveguide structure, showing a much better efficiency and accuracy comparing with the previously presented formulas.

Fast and effective analysis methods for fiber Raman amplifiers

A series of new single-step methods and their corresponding algorithms with automatic step size adjustment for model equations of fiber Raman amplifiers are proposed and compared in this paper. On the basis of the Newton-Raphson method, multiple shooting algorithms for the two-point boundary value problems involved in solving Raman amplifier propagation equations are constructed. A verified example shows that, compared with the traditional Runge-Kutta methods, the proposed methods can increase the accuracy by more than two orders of magnitude under the same conditions. The simulations for Raman amplifier propagation equations demonstrate that our methods can increase the computing speed by more than 5 times, extend the step size significantly, and improve the stability in comparison with the Dormand-Prince method. The numerical results show that the combination of the multiple shooting algorithms and the proposed methods has the capacity to rapidly and effectively solve the model equations of multipump Raman amplifiers under various conditions such as co-, counter- and bi-directionally pumped schemes, as well as dual-order pumped schemes.

关于半导体电极上极化成份的分解和电极反应动力学参数的确定

电极动力学在金属电极上已经发展得比较成熟，对半导体来说，由于电极反应的复杂性，还有不少问题比较模糊。其中之一是怎样根据表观的极化测量求得反映界面电荷转移的动力学参数。目前有关这方面的工作不多，还没有见到具体对极化成份进行分解以求解半导体电极反应的动力学系统的报导。本工作从一定的电极物理模型出发，在电化学测量的基础上结合电子计算技术，对这方面问题的研究提出了测量计算方法。本文提出的半导体电极的物理模型如图A所示。I，I_J, I_S, I_D, I_H均取阴极性电流方向为正，η则按电极电势的方向取阳极过电热为正，阴极过电势为负。模型中的J反映空间电荷层的Schottky结特性，其数学描述可概括（对n-型半导体）为：I_J = I_0[exp(-n_s/a)-1] I_0： 结的反向饱和电流。（a:k_T）/q或（RT）/F D反映界面电荷转移反应的特性，其数学描述适用Butler-Volmer方程：I_D = i~0[exp(-(1-β)n η_H)/a) - exp(βη-η_H/a)] i~0:交换电流。β：阳极传递系数 C_s，C_H分别表示空间电荷层和Helmholtz层的电容。R_B和R_l分别为半导体体内和溶液电阻。由于J，D二者特性不同，可以通过极化测量利用电子计算机加以鉴别。实验上针对电路主要是串联结构的特点，采用恒电流极化，利用恒电流恒电位仪实现一系列的电流阶跃（I_(K-1) I_K K = 1, 2, 3 ……）记录相应的电位随时间变化的响应曲线如图B所示。根据曲线各段的特点，利用电子计算机曲线拟合，分别求解有关参数。（1）在t = 0时，找出一系列不同I下的φ（I_K, t = 0）值，根据φ（I_K, t = 0) = φ(I = 0)-I_KR拟合求解φ（I = 0）， R。（2）找出一系列不同I下的稳态极化数据φ（I_K,t →∞），推导出电位随电流变化关系式，拟合求解I_0, j~0, β。（3）利用暂态过程的φ（I_K, t = 0) ～ t曲线，拟合求解每阶电位变化区间的C_s，C_H。由于在我们的电极模型中，D采取的是完整的Butler-Volmer表达式，没有作任何简化或近似，因而在数据处理和计算时，涉及隐式超越代数方程和隐式超越微分方程，无法通过一般解析法求解。为此我们把牛顿迭代法和Runge-Kutta法引入相应的曲线拟合计算程序中。这样做虽然计算上比较复杂困难，但方法的通用性更广泛。无论Helmholtz层处于线性极化，弱极化，或强极化区部同样适用。我们用BASIC语言编写了梯度法，线性化法联合使用的曲线拟合源程序及牛顿迭代法和Runge-Kutta法于程序。利用上述研究方法，对不同掺杂浓度的n-型GaAs电极在S~(2-)/S_x~(2-)体系中的电化学行为进行了研究。求解的电荷转移反应的动力学参数I_0, i~0, β分别在7.27 * 10~(-8) - 4.66 * 10~(-1) A/cm~2, 2.08 * 10~(-6)-4.62 * 10~(-6)A/cm~2, 0.70 - 0.78的范围之内。并于Pt电极连同一体系中的i~0，β进行了比较。i_（半导体）~0 < i_（导体）~0。但β在二种材料上差别不大。将半导体电极极化分解为空间电荷层极化和Helmholtz层极化两部分。测量了空间电荷层电学及Helmholtz层电容与电极电位的关系。从实际测量中证明，本文提出的电极模型比较恰当的反映了半导体电极的特性，本工作的测量和拟合计算方法对研究半导体电极行为是一种可行的方法。

A Numerical Method for Calculating Transmission Coefficients Across Arbitrary Potential Barriers with High Accuracy

We report a new method for calculating transmission coefficients across arbitrary potential barriers based on the Runge-Kutta method. A numerical solution of the Schrodinger equation is calculated using the Runge-Kutta method,and a new model is established to analyze the numerical results to find the transmission coefficient. This technique is applied to various cases, such as parabolic potential barrier and double-barrier structures. Transmission probability with high precision is obtained and discussed. The tunnelling current density through a MOS structure is also explored and the result coincides with the Fowler-Nordheim model,which indicates the applicability of our method.

一种模拟倾斜折射率界面光波导的新方法

针对传统离散格式下，束传播方法（BPM）模拟倾斜折射率界面出现的问题，提出了一种简明且易于编程实现的改进方案．在横向上，通过坐标系变换和插值处理，以新颖的7点差分格式代替传统的5点差分方式；在纵向上，以四阶显式Runge-Kutta方法（RKBPM）代替二阶Crank-Nicholson算法（CNBPM），避免了求解不规则矩阵方程，从而使计算效率显著提高．

Methanol synthesis from CO2 using a silicone rubber/ceramic composite membrane reactor

A one-dimensional isothermal pseudo-homogeneous parallel flow model was developed for the methanol synthesis from CO2 in a silicone rubber/ceramic composite membrane reactor. The fourth-order Runge-Kutta method was adopted to simulate the process behaviors in the membrane reactor. How those parameters affect the reaction behaviors in the membrane reactor, such as Damkohler number Da, pressure ratio p(r), reaction temperature T, membrane separation factor alpha, membrane permeation parameter phi , as well as the non-uniform parameter of membrane permeation L-1, were discussed in detail. Parts of the theoretical results were tested and verified; the experimental results showed that the conversion of the main reaction in the membrane reactor increased by 22% against traditional fixed bed reactor, and the optimal non-uniform parameter of membrane permeation rate, L-1.opt ,does exist. (C) 2003 Elsevier B.V All rights reserved.

便携式移动机器人姿态解算方法

本文根据便携式移动机器人的特点,采用四元数法解算机器人导航系统的姿态,避免了在机器人运动角度较大时出现奇异点的问题。文中应用改进的四阶龙格-库塔算法解算四元数微分方程,经仿真实验,精度完全能够达到要求。给出了合理的变换公式,在机器人运动范围内,满足了四元数与欧拉角之间转换的一一对应。

旋转轴对称弱各向异性介质模型的射线追踪方法

Ray tracing is a rapid and effective method for wave field calculation. Not only in the field of seismic-wave theory, but also in the field of seismic inversion and migration imaging,the seismic ray tracing method has become one of the most important methods. In anisotropic media, group velocity and phase velocity have different propagation directions. The seismic wave propagates along the direction of group velocity , it does not depend on the direction of phase velocity. Ray angle is a complex function with respect to phase angle, it is difficult to measure and calculate. But most rocks are weak anisotropic, so the expression of phase velocity can be simplified greatly. Based on the approximate expression of phase velocity this thesis for rotating axisymmetric weak anisotropic media deduces an expression of the partial derivative of phase velocity and an expression of group velocity with the method of linear approximation. This paper uses the fourth order Runge-Kutta method together with the two-dimensional interpolation and linear interpolation to obtain the parameters of the physical locations. At last the paths of seismic wave in rotating axisymmetric weak anisotropic media are computed. According to the analysis of the computational results, it indicates that the method developed in this paper has strong adaptability, high computational efficiency and high accuracy for rotating axisymmetric weak anisotropic media.

VSP克希霍夫法多波联合成像

Geophones being inside the well, VSP can record upgoing and downgoing P waves, upgoing and downgoing S waves simultaneously.Aiming at overcoming the shortages of the known VSP velocity tomography , attenuation tomography , inverse Q filtering and VSP image method , this article mainly do the following jobs:CD; I do the common-source-point raytracing by soving the raytracing equations with Runge-Kutta method, which can provide traveltime , raypath and amplitude for VSP velocity tomography , attenuation tomography and VSP multiwave migration.(D. The velocity distribution can be inversed from the difference between the computed traveltime and the observed traveltime of the VSP downgoing waves. I put forward two methods: A. VSP building-velocity tomography method that doesn't lie on the layered model from which we can derive the slowness of the grids' crunodes . B. deformable layer tomography method from which we can get the location of the interface if the layer's velocity is known..(3). On the basis of the velocity tomography , using the attenuation information shown by the VSP seismic wave , we can derive the attenuation distribution of the subsurface. I also present an algorithm to solve the inverse Q filtering problem directly and accurately from the Q modeling equation . Numerical results presented have shown that our algorithm gives reliable results . ?. According to the theory that the transformed point is the point where the four kinds of wave come into being , and where the stacked energy will be the largest than at other points . This article presents a VSP multiwave Kirchhoff migration method . Application on synthetic examples and field seismic records have shown that the algorithm gives reliable results . (5). When the location of the interface is determined and the velocity of the P wave and S wave is known , we can obtain the transmittivity and reflection coefficient 5 thereby we can gain the elastic parameters . This method is also put into use derive good result.Above all, application on models and field seismic records show that the method mentioned above is efficient and accurate .

高斯束偏移的方法及应用

Gaussian beam is the asymptotic solution of wave equation concentred at the central ray. The Gaussian beam ray tracing method has many advantages over ray tracing method. Because of the prevalence of multipath and caustics in complex media, Kirchhoff migration usually can not get satisfactory images, but Gaussian beam migration can get better results.The Runge-Kutta method is used to carry out the raytracing, and the wavefront construction method is used to calculate the multipath wavefield. In this thesis, a new method to determine the starting point and initial direction of a new ray is proposed take advantage of the radius of curvature calculated by dynamic ray tracing method.The propagation characters of Gaussian beam in complex media are investigated. When Gaussian beam is used to calculate the Green function, the wave field near the source was decomposed in Gaussian beam in different direction, then the wave field at a point is the superposition of individual Gaussian beams.Migration aperture is the key factor for Kirchhoff migration. In this thesis, the criterion for the choice of optimum aperture is discussed taking advantage of stationary phase analysis. Two equivalent methods are proposed, but the second is more preferable.Gaussian beam migration based on dip scanning and its procedure are developed. Take advantage of the travel time, amplitude, and takeoff angle calculated by Gaussian beam method, the migration is accomplished.Using the proposed migration method, I carry out the numerical calculation of simple theoretical model, Marmousi model and field data, and compare the results with that of Kirchhoff migration. The comparison shows that the new Gaussian beam migration method can get a better result over Kirchhoff migration, with fewer migration noise and clearer image at complex structures.