回旋管谐振腔本征模式计算的新算法

基于龙格库塔理论,提出了一种计算回旋管谐振腔本征模式的新方法.不同于传统计算方法,新算法只需要通过对含有本征模式谐振频率和Q值,两个变量的目标函数进行最小值优化,就能够确定出回旋管谐振腔本征模式的所有特性.通过实例的具体计算,可以证明新算法的计算效率,相对于传统计算方法有了本质上的提高. 关键词： 回旋管 算法 本征模式 计算效率     

表象变换和久期微扰理论在耦合杜芬方程中的应用

本文通过对耦合杜芬方程线性项的表象变换及非线性项的久期微扰理论的应用,将耦合杜芬方程转化为简正表象下的退耦合形式,由此可以很方便地得出耦合杜芬方程的解.为了验证该方法的正确性,设计了音叉耦合实验,观测到了振幅谱谱峰的劈裂以及"振滞回线"现象,这些实验结果都可以和之前所得的理论结果符合得很好.本文求解耦合非线性方程的方法,为灵活运用非线性理论提供一种方案,同时可以推广到光、电等耦合体系,对理解耦合体系的动力学行为具有一定的指导意义.     

The Method of Fundamental Solutions for Solving Convection-Diffusion Equations with Variable Coefficients

A meshless method based on the method of fundamental solutions (MFS) is proposed to solve the time-dependent partial differential equations with variable coefficients. The proposed method combines the time discretization and the one-stage MFS for spatial discretization. In contrast to the traditional two-stage process, the one-stage MFS approach is capable of solving a broad spectrum of partial differential equations. The numerical implementation is simple since both closed-form approximate particular solution and fundamental solution are easier to find than the traditional approach. The numerical results show that the one-stage approach is robust and stable.     

Reduced scattering-matrix algorithm for high-density plasmonic structures

We describe a method to compute S-matrix interface terms using a selection of eigenmodes. When solving the modal equation, the computation of left and right eigenvectors leads to rectangular eigenmodes matrices. Expressions of S-matrix interface terms are then expressed so as to allow for a significant reduction of the computation cost. The reduction is even further decreased in the case of the B-spline modal method, which deals with sparse matrices. Its convergence is illustrated on a high-density plasmonic structure and compared to a full modal method.     

Research on camera calibration using new optimization strategy

An important task for stereo vision is camera calibration, whose goal is to obtain the intrinsic and extrinsic parameters of each camera. This paper proposes a new accurate calibration method with multilevel process of camera parameters. In order to improve the calibration accuracy, a sub-pixel corner detection method is presented. We start with several views of a planar calibration to obtain some intrinsic camera parameters and to build an accurate model with lens distortion on a planar calibration target. Flexibly making use of geometry imaging theory, our algorithm obtains all the parameters through logical organization of solving order, accordingly avoids obtaining possible local optimized problem when solving the non-linear equation, gets over the relativity influence of every unknown parameters of traditional calibration way, and makes the error distributed among the constraint relation of parameters. Experiments with real images are carried out to verify the image correction effect and numerical robustness of our results. Compared with classical calibration techniques, that use expensive equipment and complicated mathematical computation, the proposed technique, which was verified by experiment, achieves high accuracy and reliable parameters.     

单谐振腔束团长度监测器的设计与仿真

提出了一种利用单个谐振腔测量直线加速器束团长度的新方法。不同于传统的双谐振腔束团长度监测器，该方法仅需要使用单个谐振腔，省去了用于辅助测量的参考腔，从而简化了装置结构，节省了空间。针对国家同步辐射实验室基于可调谐红外激光的能源化学研究大型实验装置进行了监测器的物理设计。通过设定同轴探针的插入位置，解决了双模信号互相干扰的问题，利用微扰金属改变调节工作频率，克服了双模难以同时谐振的困难。利用CST软件进行建模和仿真。仿真结果表明，该监测器可实现2～5 ps束团长度的诊断，测量误差小于5%。     

Spin remagnetization excitations in semiconductors with Rashba and Dresselhaus spin–orbit coupling

Spin remagnetization modes in paramagnetic materials with Rashba and Dresselhaus spin–orbit interaction are studied by analytically solving the kinetic equations for the spin-density matrix. These eigenmodes, which are induced by an in-plane electric field, lead to a rotation of the spin magnetic moment. The specific character of the spin remagnetization modes depends on the details of the excitation mechanism. By applying the approach to another system, namely to a model for graphene, pseudospin excitations are identified.     

Coupled-Mode Analysis of an NRD-Guide Coupler Based on Singular Perturbation Technique

A coupled-mode formulation for an NRD-guide coupler is presented using the singular perturbation technique. The first-order and second-order perturbations are taken into account in the analysis and the coupled-mode equations based on the eigenmodes of each waveguide in isolation are derived. The propagation constants obtained by these equations are compared with those by the exact theory, conventional coupled-mode theory, and improved coupled-mode theory. The numerical results of present formulation are in good agreement with the exact theory and superior to those of the other formulations.     

Transparent boundary conditions for the Helmholtz equation in some ramified domains with a fractal boundary

The paper addresses a class of boundary value problems in some self-similar ramified domains, with the Laplace or Helmholtz equations. Much stress is placed on transparent boundary conditions which allow the solutions to be computed in subdomains. A self similar finite element method is proposed and tested. It can be used for numerically computing the spectrum of the Laplace operator with Neumann boundary conditions, as well as the eigenmodes. The eigenmodes are normalized by means of a perturbation method and the spectral decomposition of a compactly supported function is carried out. Finally, a numerical method for the wave equation is addressed.     

长基线声学定位系统跟踪解算优化方法

针对现有长基线定位解算算法忽略阵型标定误差的问题,本文提出了一种结合声信标的标定误差和测距误差的待定目标解算方法。该方法利用观测数据的先验误差将观测数据连同带求解量一并构建平差解算模型,可以对待定目标位置解算进行优化求解。采用该方法对现有测量船只的跟踪定位实验进行数据处理,得到的跟踪定位轨迹平滑连续,和传统方法相比更接近于GPS输出结果,在深水环境下效果提升明显。理论分析和实验结果表明采用该方法能够获得更优化的位置估计结果及全局误差,能够应用于高精度长基线定位系统中。      

用改进的准静态方法求解反应堆三维瞬态方程

本文介绍了三维中子瞬态方程的改进准静态求解方法。给出了两个瞬态问题计算结果的比较;TWIGL结果与基准直接数值结果比较,其功率最大偏差为1.57%;CANDU堆模型,在功率上升达到最大值时的热中子通量与参考解的偏差为0.88%。因此,用改进的准静态方法求解三维中子瞬变问题,其结果是满意的,大大节省了计算时间。     

Direct Minimization of the least-squares spectral element functional – Part I: Direct solver

This paper describes an equivalent but improved least-squares formulation for the numerical approximation of the solution of partial differential equations. Instead of using variational analysis to impose the conditions for minimizing the residual, the residuals are minimized directly, thus leading to a method we will denote by Direct Minimization (DM). DM circumvents setting up the normal equations which consists of matrix–matrix multiplications. Matrix–matrix multiplications are expensive, may lead to loss of accuracy and destroy the sparsity pattern present in the original system. The condition number of the DM formulation is the square root of the condition number which would be obtained if variational analysis was employed. An element-by-element procedure will be presented which allows for parallelization of DM. A computational comparison between DM and the conventional least-squares formulation based on variational analysis will be presented.     

Time-dependent integral equations of neutron transport for calculating the kinetics of nuclear reactors by the Monte Carlo method

Integral equations for the shape functions in the adiabatic, quasi-static, and improved quasi-static approximations are presented. The approach to solving these equations by the Monte Carlo method is described.     

宽波段太阳辐照度仪光谱定标方法研究

宽波段太阳辐照度仪采用fèry棱镜分光,利用线阵CCD反馈控制光谱扫描,波长覆盖范围为400~2 500nm.为实现该仪器的高准确度光谱定标,在实验室内利用单波长激光器和OPO激光器分别作为光源.通过光谱扫描,得出定标波长与CCD像元的对应关系.根据棱镜参量和光路设计参量推导出全波段内光谱定标方程,实现全波段光谱定标.通过与其他特征波长比较,分析得出光谱定标合成不确定度优于0.5nm.用定标好的仪器进行室外测量,将测量结果与大气辐射传输软件modtran4模拟结果相比对,可得实际测量的大气吸收峰与模拟结果一致.将该方法在红外波长区域定标结果与传统的多项式拟合光谱定标方法对比,显示该定标结果优于传统多项式拟合方法.证明该定标方法的正确性和仪器设计的合理性.     

Use of a generalized method of eigenmodes in the theory of lasers

An analysis is made of the application a generalized method of eigenmodes, which is used in steady-state diffraction problems to the theory of lasers. In the study of open laser cavities the use of this method makes it possible to avoid difficulties associated with the exponential growth of the field at infinity. The generalized method developed previously for solving steady-state diffraction problems is extended to the case of non-steady-state narrow-band processes to construct in the ordinary way the equations describing the operation of the laser. The only difference is that the field is expanded in the eigenfunctions that are orthogonal in the region occupied by the active medium. This eliminates the difficulties associated with the behavior of the mode field at infinity. In addition, in a number of cases the generalized eigenfunctions (modes) correspond considerably better to the field distribution in the operating laser. Zh. Tekh. Fiz. 67, 46–49 (June 1997)     

多光谱高温计有效波长标定方法研究

针对光纤式多光谱高温计波长标定中由于光纤耦合导致信号太弱而无法获得有效波长的问题,基于普朗克定律,充分结合不同标定温度点的标定值的比值,提出了一种由温度标定数据来确定有效波长的方法。相比于传统的有效波长标定方法,新方法避免了耗时复杂的波长标定过程可以快速获取有效波长。分别采用仿真和实验两种手段来验证新方法的可行性和有效性。仿真结果表明所提出的新方法可行并且具有一定的抗随机误差能力,所得有效波长计算的真温值与实际值的相对误差小于0.7%。实验结果表明提出的新方法能够得到各个通道的有效波长值,进一步验证了该方法的有效性。所提出的新方法也可应用于其他多光谱高温计,为多光谱高温计的研制和应用提供了理论基础。     

长基线定位系统高精度阵型标定方法

为解决长基线定位系统传统标定方法中受垂直方向声速变化剧烈而导致的标定精度差、逐个声信标交汇标定效率低、跟踪定位阶段采用不同声信标基准对目标解算不一致的问题,本文提出了一种高精度相对阵型标定方法,通过水下声信标的互测距信息构建观测模型改进了传统标定方式。理论分析表明,采用该方法水平方向上能够获得与测距等量级的标定精度,有效地提高了标定效率,采用不同的声信标基准目标解算结果一致,在深海作业中优势明显。通过浅水试验结果可以看出该方法水平方向上的标定精度能达到和测距等量级的毫米量级精度,和传统标定方法相比提高了一个数量级,在提高标定精度的同时降低了作业复杂度,采用本文的标定结果获得的目标定位结果更接近于GPS输出,具有良好的工程应用价值。      

Convergence criteria for the Hartree iterative solution of the general self-consistent field equations

The traditional Hartree method of solving the Hartree-Fock equations, by repeated diagonalization and recalculation of the single-particle Hamiltonian, is expressed in terms of repeated unitary transformations and shown to be applicable to the general SCF (self-consistent field) equations. The necessary and sufficient conditions for convergence to a unique local SCF solution are derived and it is shown that only a small class of solutions are obtainable by this method.     

Birkhoff系统的离散最优控制及其在航天器交会对接中的应用

由于非线性,最优控制问题通常依赖于数值求解,即通过离散目标泛函和受控运动方程转化为一有限维的非线性最优化问题.最优控制问题中的受控运动方程在表示为受控Birkhoff方程的形式之后,可以利用受控Birkhoff方程的离散变分差分格式进行离散.与按照传统差分格式近似受控运动方程相比,此途径可以诱导更加真实可靠的非线性最优化问题,进而也会诱导更加精确有效的离散最优控制.应用于航天器交会对接问题,该种数值求解最优控制问题的方法在较大时间步长的情况下仍然求得了一个有效实现交会对接的离散最优控制.模拟结果验证了该方法的有效性.     

Homogenization of 3D finite photonic crystals with heterogeneous permittivity and permeability

We consider a heterogeneous magneto-dielectric photonic crystal and derive the so-called ‘homogenized Maxwell system’ via the multi-scale method and provide ad hoc proofs for the convergence of the electromagnetic field towards the homogeneous one using the notion of two-scale convergence. The homogenized medium is described by anisotropic matrices of permittivity and permeability, deduced from the resolution of two annex problems of electrostatic type on a periodic cell. Noteworthily, this asymptotic analysis also covers the case of photonic crystals with non-cuboidal periodic cells. We solve numerically the associated system of partial differential equations with a method of fictitious charges and a finite element method (FEM) in order to exhibit the matrices of effective permittivity and permeability for given magneto-dielectric periodic composites. We then compare our results in the 2D case against some Fourier expansion approach and provide duality relations in the case of magneto-dielectric checkerboards. We further compute some low-frequency eigenmodes of a photonic crystal fiber with metallic outer boundary and compare them with the eigenmodes of a corresponding effective anisotropic waveguide, thanks to the FEM. Finally, we derive the effective properties of a 3D photonic crystal both through classical homogenization (solving numerically two decoupled annex problems) and Bloch wave homogenization. In the case of spherical inclusions, the latter approach amounts to evaluating the slope of the first band around the origin on a Bloch diagram which we compute using finite edge elements.