Retarded treatment of substrate-related effects on granular films I. Polarizability of a single sphere

A multipolar treatment of the retarded fields radiated by a metal sphere on a dielectric substrate under the influence of an incident plane wave described. Unlike previous treatments, the present one allows boundary conditions, both on the spherical surface and on the substrate interface, to be matched by simply solving an adequate number of linear equations. The problem is thus reduced to inverting three complex matrices, whose sizes depend on the number of multipoles included in the field forms. The solutions, which represent the object and image multipoles (both in the incidence and in the transmission media) associated with the polarized sphere, are given the form of linear combinations of the multipoles associated with the unperturbed field (incident and reflected waves).     

中波红外8通道微型集成滤光片的研制

利用组合刻蚀法布里珀罗（F－P）干涉滤光片的谐振腔间隔层的方法,制备了集成在一个基片上的8通道中波红外（λ₀=2.8 μm）窄带滤光片,通道线宽为0.7 mm,光谱通道定位精度优于1%,各通道相对半峰宽为1%,此法有效提高了成品率,并可满足实现通道数更多,集成度更高的滤光器件发展的需求,     

Identification of Elastic Orthotropic Material Parameters by the Singular Boundary Method

This article addresses the resolution of the inverse problem for the parameter identification in orthotropic materials with a number of measurements merely on the boundaries. The inverse problem is formulated as an optimization problem of a residual functional which evaluates the differences between the experimental and predicted displacements. The singular boundary method, an integration-free, mathematically simple and boundary-only meshless method, is employed to numerically determine the predicted displacements. The residual functional is minimized by the Levenberg-Marquardt method. Three numerical examples are carried out to illustrate the robustness, efficiency, and accuracy of the proposed scheme. In addition, different levels of noise are added into the boundary conditions to verify the stability of the present methodology.     

Determination of an Extremal in Two-Dimensional Variational Problems Based on the RBF Collocation Method

This paper introduces a direct method derived from the global radial basis function (RBF) interpolation over arbitrary collocation nodes occurring in variational problems involving functionals that depend on functions of a number of independent variables. This technique parameterizes solutions with an arbitrary RBF and transforms the two-dimensional variational problem (2DVP) into a constrained optimization problem via arbitrary collocation nodes. The advantage of this method lies in its flexibility in selecting between different RBFs for the interpolation and parameterizing a wide range of arbitrary nodal points. Arbitrary collocation points for the center of the RBFs are applied in order to reduce the constrained variation problem into one of a constrained optimization. The Lagrange multiplier technique is used to transform the optimization problem into an algebraic equation system. Three numerical examples indicate the high efficiency and accuracy of the proposed technique.     

Optimized local basis set for Kohn–Sham density functional theory

We develop a technique for generating a set of optimized local basis functions to solve models in the Kohn–Sham density functional theory for both insulating and metallic systems. The optimized local basis functions are obtained by solving a minimization problem in an admissible set determined by a large number of primitive basis functions. Using the optimized local basis set, the electron energy and the atomic force can be calculated accurately with a small number of basis functions. The Pulay force is systematically controlled and is not required to be calculated, which makes the optimized local basis set an ideal tool for ab initio molecular dynamics and structure optimization. We also propose a preconditioned Newton–GMRES method to obtain the optimized local basis functions in practice. The optimized local basis set is able to achieve high accuracy with a small number of basis functions per atom when applied to a one dimensional model problem.     

阵列波导光栅线性系统理论分析及优化设计

运用线性系统理论分析了阵列波导光栅的模场特性 ,导出器件传输的数学模型即光栅方程。提出了设计阵列波导光栅阵列波导数M的新方法 ,该方法综合考虑了降低器件串扰以及收集发散光场的能力 ,与文献 [1 ]的方法相比简单且准确。分析了造成器件衍射损耗的原因 ,提出了降低器件衍射损耗的方法。给出了 8× 0 .8nm ,中心波长为 1 550nm的阵列波导光栅波分复用器的设计实例 ,并进行了数值模拟计算验证了文中所提方法的准确性。     

非平整基底上受热液膜流动稳定性研究

本文研究了二维黏性流体薄膜沿非平整不均匀加热基底流动时非线性表面波的演化及其流动稳定性.利用长波摄动法推导出非平整线性加热基底上非线性表面波的零阶和一阶演化方程,基于所得演化方程,绘制出正弦波纹基底上液膜的表面波形图,并研究液膜流动的线性稳定性,分析了各无量纲参数对液膜线性稳定性的影响.分析结果表明:在正弦波纹基底上,液膜自由表面随同壁面作相同频率的正弦型波动,且液膜厚度沿流动方向逐渐变小;Marangoni数为稳定影响因素,随Marangoni数的增大,液膜稳定区域增大;Peclet数和倾角θ均为不稳定影响因素,随Peclet数和倾角θ的增大,液膜稳定区域减小;在非平整基底的波峰和波谷处,Peclet数、Marangoni数和倾角θ对稳定性的影响趋势一致,但基底波谷处的液膜稳定区域小于波峰处区域,流动更易失稳.     

A new approach with piecewise-constant arguments to approximate and numerical solutions of oscillatory problems

This paper is devoted to the development of a novel approximate and numerical method for the solutions of linear and non-linear oscillatory systems, which are common in engineering dynamics. The original physical information included in the governing equations of motion is mostly transferred into the approximate and numerical solutions. Therefore, the approximate and numerical solutions generated by the present method reflect more accurately the characteristics of the motion of the systems. Furthermore, the solutions derived are continuous everywhere with good accuracy and convergence in comparing with Runge-Kutta method. An approximate solution is developed for a linear oscillatory problem and compared with its corresponding exact solution. A non-linear oscillatory problem is also solved numerically and compared with the solutions of Runge-Kutta method. Both the graphical and numerical comparisons are provided in the paper. The accuracy of the approximate and numerical solutions can be controlled as desired by the number of terms in the Taylor series and the value of a single parameter used in the present work. Formulae for numerical computation in solving various linear and non-linear oscillatory problems by the new approach are provided in the paper.     

Dynamics of a polymer chain in an array of obstacles

On the basis of the model “polymer chain in an array of obstacles” the influence of the topology effects on the dynamics of concentrated polymer systems is investigated theoretically. The 1/z-expansion (where z is the coordinational number of the lattice of obstacles) is proposed for this problem. By means of this expansion the diffusion coefficient of a linear unclosed polymer chain is calculated. The equilibrium properties of linear closed chain (i.e. ring) unentangled with either of the edges of the lattice are investigated in detail. In particular, it is shown that the diffusion coefficient D of the center of mass of closed chain consisting of N links is proportional to N^−5/2.     

A Timoshenko beam reduced order model for shape tracking with a slender mechanism

We consider a flexible bio-inspired slender mechanism, modeled as a Timoshenko beam. It is coupled to the environment by a continuous distribution of compliant elements. We derive a reduced order model by projecting the governing partial differential equations along the linear modal basis of the Timoshenko beam. The coupling with the substrate allows us to formulate the problem in a control framework, and eventually to treat the system as a sensor to reconstruct the profile of the substrate through the deformation of the body. The coupling is modeled in the framework of two parameters elastic foundations. The convergence of the reduced order model with increasing number of basis functions is addressed in a suitable H¹ error norm. A closed loop force control is simulated for shape morphing when the system is coupled with a smooth substrate.     

三维对流扩散方程非等距网格上的四阶紧致格式及其多重网格方法

提出了数值求解三维变系数对流扩散方程非等距网格上的四阶精度19点紧致差分格式,为了提高求解效率,采用多重网格方法求解高精度格式所形成的大型代数方程组。数值实验结果表明本文方法对于不同的网格雷诺数问题,在精确性、稳定性和减少计算工作量方面均明显优于7点中心差分格式。     

Electromagnetic Modelling of Fine Features in Photonic Applications

Straightforward application of numerical modelling approaches to Photonic Band-Gap structures demands the use of fine meshes, notably finer that the size of a single scattering element, in order that high accuracy is achieved. However simulations employing sufficiently fine meshing to correctly represent the geometry of the scatterers lead to very long computational run-times and huge memory consumption. Such direct numerical approaches to PBG characterisation are only suited to the analysis of single unit cells or for benchmarking. In practice, the computational overheads significantly increase when one deals with an array of cells or when modelling the global behaviour of a large number of devices integrated on a single substrate. Therefore in order to model the macroscopic response of PBG structures the possibility of employing meshes of much larger size than the individual scattering elements has been explored. A suitable approach, initially developed for Electromagnetic Compatibility predictions, has been modified to permit modelling of Photonic Crystal Waveguides. The method provides second order accuracy and leaves a designer with the flexibility to discretise the entire problem space with an arbitrary number of scatterers per mesh cell. Results are first presented for small clusters of scatterers and subsequently for complete photonic structures.     

Non-iterative spot center location algorithm based on Gaussian for fish-eye imaging laser warning system

The directional accuracy of threaten laser is highly dependent on the laser spot center location accuracy for the laser warning system. On the basis of analyzing the spot features on wide field of view (FOV) fish-eye imaging laser warning system, a refinement of existing methodology based on fitting a 2D Gaussian distribution for estimating the center of the spot is developed. The proposed procedure is using a linear least squares based algorithm to determine the best-fitting parameters of the Gaussian. However, in contrast to the standard Gaussian Fitting procedure, this new scheme gives rise to equations that are rigorously linear in the transformed unknown parameters which can be solved easily by linear least squares estimators. To validate the accuracy of the proposed algorithms, experimental approaches with a type of laser warning detector and simulated threaten laser in laboratory are used to quantify its performance. The experimental results show that this method outperforms significantly the commonly used location technique. It is less susceptible to the non-100% fill ratio of CMOS and large unsymmetrical optical aberration of fish-eye lens. The positioning precision in paraxial region and 80° incident angle region are 1/60 pixels, 1/30 pixels respectively. The biggest error is less than 1/20 pixels. The proposed method is suitable for wide FOV laser warning system for high accuracy and low computational complexity.     

Heterogeneous nucleation on cleavage steps: I. Theory

A theory of the nucleation kinetics of clusters formed on the cleavage steps of a substrate surface during metal deposition is presented. The spatial distribution of clusters along steps is shown to evolve with time in a shape-preserving way. As a consequence it has been possible to derive an expression for the linear number density of clusters as a function of substrate temperature, deposition rate and the duration of the deposition.     

Hierarchical reconstruction for discontinuous Galerkin methods on unstructured grids with a WENO-type linear reconstruction and partial neighboring cells

The hierarchical reconstruction (HR) [Y.-J. Liu, C.-W. Shu, E. Tadmor, M.-P. Zhang, Central discontinuous Galerkin methods on overlapping cells with a non-oscillatory hierarchical reconstruction, SIAM J. Numer. Anal. 45 (2007) 2442-2467] is applied to the piecewise quadratic discontinuous Galerkin method on two-dimensional unstructured triangular grids. A variety of limiter functions have been explored in the construction of piecewise linear polynomials in every hierarchical reconstruction stage. We show that on triangular grids, the use of center biased limiter functions is essential in order to recover the desired order of accuracy. Several new techniques have been developed in the paper: (a) we develop a WENO-type linear reconstruction in each hierarchical level, which solves the accuracy degeneracy problem of previous limiter functions and is essentially independent of the local mesh structure; (b) we find that HR using partial neighboring cells significantly reduces over/under-shoots, and further improves the resolution of the numerical solutions. The method is compact and therefore easy to implement. Numerical computations for scalar and systems of nonlinear hyperbolic equations are performed. We demonstrate that the procedure can generate essentially non-oscillatory solutions while keeping the resolution and desired order of accuracy for smooth solutions.     

基于无导数优化方法的数值模式误差估计

初始场误差和模式误差是制约数值预报准确率的两个关键因素,本文主要考虑利用历史观测资料实现时空演变的模式误差的估计问题.通过把模式误差综合考虑成为准确模式中的未知项,把历史资料看作是带有未知项的准确模式的特解,构造了求解时空演变的模式误差项的反问题及其最优控制问题.给出了一个解决最优控制问题的无导数优化方法,该方法的优点是不需要建立原数值模式的切线性模式与伴随模式,它只需在增加一个外强迫项的基础上运行原数值模式即可实现模式误差项的最优估计.关于Burgers方程的算例表明,无论模式的初始状态是否准确已知,无导数优化方法都能有效解决时空演变的模式误差的最优估计问题,它为实际业务模式利用历史数据提取模式误差信息并显著地改进预报效果提供了一种方便可行的数值方法与理论依据.     

Numerical simulation of four-field extended magnetohydrodynamics in dynamically adaptive curvilinear coordinates via Newton–Krylov–Schwarz

Numerical simulations of the four-field extended magnetohydrodynamics (MHD) equations with hyper-resistivity terms present a difficult challenge because of demanding spatial resolution requirements. A time-dependent sequence of r-refinement adaptive grids obtained from solving a single Monge–Ampère (MA) equation addresses the high-resolution requirements near the x-point for numerical simulation of the magnetic reconnection problem. The MHD equations are transformed from Cartesian coordinates to solution-defined curvilinear coordinates. After the application of an implicit scheme to the time-dependent problem, the parallel Newton–Krylov–Schwarz (NKS) algorithm is used to solve the system at each time step. Convergence and accuracy studies show that the curvilinear solution requires less computational effort than a pure Cartesian treatment. This is due both to the more optimal placement of the grid points and to the improved convergence of the implicit solver, nonlinearly and linearly. The latter effect, which is significant (more than an order of magnitude in number of inner linear iterations for equivalent accuracy), does not yet seem to be widely appreciated.     

Microstructure and thermodynamics of inhomogeneous polymer blends and solutions

A free energy density functional theory (DFT) for nonuniform polymeric mixtures is proposed based on first order thermodynamic perturbation theory. The segment-density based free energy functional provides an accuracy comparable to the numerically intensive polymeric DFTs while preserving the computational simplicity of an atomic DFT. The presented applications for solutions and blends of branched and linear polymers demonstrate the capability of the theory to capture the entropic and enthalpic effects governing the microstructure.     

星载遥感影像几何精校正算法分析比较

在系统分析星载遥感影像的多种几何精校正算法,并从必须的控制点数目、算法复杂性、适用性能等几个方面予以综合比较后,选用RadarSat和QuickBirdII影像各一幅进行实验,讨论了不同算法不同控制点数目对星载遥感影像几何精校正准确度的影响.结果表明：当获取的控制点准确度高且分布均匀时,不同算法的校正准确度总体上随控制点数目增多而提高,但当控制点达到一定程度后,则增长缓慢;三次有理函数在星载光学影像几何精校正算法中准确度最高;严密投影仿射变换模型是针对少地面控制点的星载光学影像的一种有效的校正算法;直接线性变换模型、自校验直接线性变换模型、扩展的直接线性变换模型适用于商业光学遥感影像几何精校正处理;对于星载雷达影像,距离－多普勒模型准确度稳定,用少量的控制点即可达到较高的校正准确度.     

Accuracy in determining voice source parameters

The paper addresses the accuracy of an approximate solution to the inverse problem of retrieving the shape of a voice source from a speech signal for a known signal-to-noise ratio (SNR). It is shown that if the source is found as a function of time with the A.N. Tikhonov regularization method, the accuracy of the found approximation is worse than the accuracy of speech signal recording by an order of magnitude. In contrast, adequate parameterization of the source ensures approximate solution accuracy comparable with the accuracy of the problem data. A corresponding algorithm is considered. On the basis of linear (in terms of data errors) estimates of approximate parametric solution accuracy, parametric models with the best accuracy can be chosen. This comparison has been carried out for the known voice source models, i.e., model [17] and the LF model [18]. The advantages of the latter are shown. Thus, for SNR = 40 dB, the relative accuracy of an approximate solution found with this algorithm is about 1% for the LF model and about 2% for model [17] as compared to an accuracy of 7–8% in the regularization method. The role of accuracy estimates found in speaker identification problems is discussed.