Analysis of optical elements with the local plane-interface approximation

The local plane-interface approximation (LPIA) is a method for propagating electromagnetic fields through the inhomogeneous regions (e.g., elements) of an optical system. The LPIA is the superclass of all approximations that replace the usually curved optical interfaces with local tangential planes. Therefore the LPIA is restricted to smooth optical surfaces. A maximum radius of curvature of the optical interface of the order of a few wavelengths is a rough estimate for the validity of the LPIA. Two important approximation levels of the LPIA are the thin-element approximation (TEA) and a geometric-optical version of the LPIA (LPIA(ray)). The latter combines the wave-optical propagation of an electromagnetic field in the homogeneous region of an optical system with a ray-tracing step in the inhomogeneous region. We discuss the regions of validity of the LPIA in general and the approximation levels LPIA(ray) and TEA in detail.     

A local approximation based multi-objective optimization algorithm with applications

Optimization techniques are useful tools to the design of complex systems. Especially in case of multiple conflicting performance indexes, the knowledge of the tradeoffs by means of Pareto optimality can help the designer to achieve the best solution. Due to the increasing power of the computing tools, more and more accurate and time consuming models are used. In this case, the Pareto set computation can be a hard task (the Pareto set can be nonconvex, nonlinearities and discontinuities can occur) and the efficiency and the accuracy become crucial features for an optimization algorithm. In this paper an optimization algorithm based on local approximation of the objective and constraints functions is presented and tested with some well known test functions. The optimal design of the suspension system of a ground vehicle is performed by the new algorithm in order to reach the best tradeoff by means of road holding, comfort, working space and cornering behavior. The numerical results show that the proposed algorithm has good accuracy and high efficiency if compared to some widely used methods. The results are explained providing some general observations on the efficiency of local approximation based algorithm an other well known algorithms.     

磁头局部结构的优化设计和数值分析

在磁头磁盘系统中,磁头尾端与磁盘的气膜最小,局部结构承受很大的气膜压力,其气膜压力的大小和分布对磁头飞行稳定性有重要的影响.采用优化设计理论对磁头尾端局部结构进行设计,可明显改善气膜承载性能.最后,采用提出的优化设计方法对负压型磁头结构进行设计.数值分析和实验测试表明,优化后的磁头结构飞高性能参数明显得到改善.     

Failures of local approximation in finite-element methods

It is shown that standard finite-element discretizations of second-order differential equations (i.e. Galerkin and subdomain methods) using conforming linear elements may fail to approximate the original equation locally if the finite-element grid is irregular or if subdomains are chosen improperly. This failure of local approximation can lead to spurious computational results when subdomain methods are used, but these difficulties can be averted by a judicious choice of subdomains. The conditions which the subdomains must satisfy in order for local approximation to hold are derived and used to construct an algorithm for choosing them properly. The relation of these local results to the global convergence properties of the Galerkin method is discussed.     

A Trefftz function approximation in local boundary integral equations

 In the present paper the Trefftz function as a test function is used to derive the local boundary integral equations (LBIE) for linear elasticity. Since Trefftz functions are regular, much less requirements are put on numerical integration than in the conventional boundary integral method. The moving least square (MLS) approximation is applied to the displacement field. Then, the traction vectors on the local boundaries are obtained from the gradients of the approximated displacements by using Hooke's law. Nodal points are randomly spread on the domain of the analysed body. The present method is a truly meshless method, as it does not need a finite element mesh, either for purposes of interpolation of the solution variables, or for the integration of the energy. Two ways are presented to formulate the solution of boundary value problems. In the first one the local boundary integral equations are written in all nodes (interior and boundary nodes). In the second way the LBIE are written only at the interior nodes and at the nodes on the global boundary the prescribed values of displacements and/or tractions are identified with their MLS approximations. Numerical examples for a square patch test and a cantilever beam are presented to illustrate the implementation and performance of the present method. Received 6 November 2000     

Simulation of light propagation by local spherical interface approximation

A new local elementary interface approximation is introduced for the modeling of wave propagation through interfaces between homogeneous media. The incident wave and the surface profile are approximated locally by a spherical wave and a spherical surface, respectively. The wave field travels through the modulated structure according to the laws of geometrical optics, being refracted by the surface and propagating to the output plane locally as a geometric spherical wave. Diffraction theory is applied to propagate the field from the output plane onwards. We provide comparisons of the method with the thin-element approximation, the local plane-wave and interface approach, and rigorous diffraction theory using a sinusoidal surface-relief grating as an example. We illustrate the power of the new method by applying it to the analysis of a diffractive beam splitter.     

Discrete dipole approximation simulations of scattering by particles with hierarchical structure

We use the discrete dipole approximation (DDA) method to calculate the intensity and the linear polarization degree of light scattered by agglomerated debris particles with hierarchical structure as functions of size parameter (varying from x = 2 to x = 14) and phase angle. Such structures are important, e.g., for cometary and interplanetary dust particles. Calculations for three combinations of refractive index were made, which correspond to regions of water ice, organic matter, and silicates. We examine the photometric and polarization properties of agglomerated particles with prefractal (Whitten-Sander model) and nonfractal porous structures of particle fragments formed by dipoles. We find that the aggregated particles can produce significant negative polarization at small phase angles. Increasing the packing density of dipoles and/or refractive index makes the negative polarization more prominent. The depth of the negative polarization branch depends on the type of internal structure: the negative polarization branch of particles having nonfractal structure is noticeably shallower in comparison with that of those having a prefractal structure. The negative polarization branch depth strongly depends on the imaginary part of the refractive index and increases with decreasing absorption. Polarization phase curves for agglomerated debris particles become smoother as the number of hierarchical levels increases.     

Higher approximation in the Chapman-Enskog expansion for shock structure

Summary The Chapman-Enskog expansion for the solution of the Boltzmann equation has been reexamined and certain inconsistencies in the procedure have been pointed out. For a steady state one-dimensional Boltzmann equation, the expansion is modified with the help of the PLK method. Macroscopic equations up to Burnett level of approximation are then obtained. Finally, these equations are used to examine the structure of a shock wave in a gas consisting of Maxwellian molecules. It is shown that new Burnett equations give solutions for all values of the Mach number.This research was conducted under the sponsorship of the Office of Naval Research under Contract No. Nonr 839(34), Project No. NR 061–135. The author would like to thank Dr. Martin H. Bloom for his interest in the problem. Thanks are also due to Mrs. W. Thorsen for carrying out the calculations and plotting the curves. The author is also grateful to the reviewer for many helpful comments.     

用多面体逼近球体及其在工业设计中的应用

球体是工业设计中常用的造型语言,但由于某些需要或限制,往往采用多面体来近似表示球体。文章提出了用多面体逼近球体效果的评判标准和改进方法,以及多面体对球体的逼近在工业设计中的应用,最后以实例加以说明。     

Optimal design of the two-level distributed network with dual homing local connections

To keep abreast of the ever-tightening robustness standards of communication services, we consider the topological design of the two-level network where a sufficient level of structural redundancy is imposed: the embedded backbone subnet is fully meshed and each user node is connected to two different backbone nodes. This complicated design problem for the dual homing full-mesh network is formulated as a 0-1 integer problem so that the key structural characteristics of the single homing network design model are carried over. By applying the usual dual-based solution procedure, we develop ours, which consists of three dual and one primal subprocedures. The computational experiments conducted with a variety of test problems illustrate the effectiveness of the proposed solution approach.     

A higher order method based on local maximum entropy approximation

We present here a generalization of local maximum entropy (max‐ent) approximation for high orders of consistency (i.e. quadratic, cubic, …). The method is based upon the application of the de Boor's algorithm to the standard, linear local max‐ent approximation. The resulting approximation possesses some interesting properties, such as non‐negativity, ??^∞ smoothness, exact interpolation on the boundary and variation diminishing (no Gibbs effect). The resulting structure has many similarities with B‐spline surfaces, but without the tensor‐product structure typical of that approximation. Examples are provided of its use in the framework of a Galerkin method showing the potential of the proposed method in solving boundary value problems. Copyright © 2010 John Wiley & Sons, Ltd.     

局部约束结构振动的模态研究

制动盘/摩擦块系统的制动过程属于局部接触振动问题。摩擦块局部接触(约束)会对系统模态及固有频率造成影响,进而影响制动噪声的产生。将刹车盘简化为一维循环梁结构,并建立了在摩擦块作用下的运动方程。首先计算无接触时梁自由振动的模态(参考模态)。然后用线性弹簧代替局部接触,列写出连续条件并计算模态,得到所谓局部非连续基函数。将局部非连续基函数与参考模态进行正交化处理后,作为参考模态的补充,用于计算系统响应。与差分法结果比较表明,与传统模态方法相比,局部非连续基函数法更为准确。研究发现局部接触会抑制循环结构振动的对称性,导致正弦或余弦模态消失,以及刚度非线性和摩擦作用,会使振动是波动型的。该工作为基于局部非连续基函数法研究摩擦结构不稳定振动机理打下了基础。     

Finite-circle method for component approximation and packing design optimization

In this article, the finite-circle method is introduced for 2D packing optimization. Each component is approximated with a group of circles and the non-overlapping constraints between components are converted into simple constraints between circles. Three new algorithms—the bisection algorithm, the three-step algorithm, and the improved three-step algorithm with gap—are developed to automatically generate fewer circles approximating the components. The approximation accuracy, the circle number, and the computing time are analyzed in detail. Considering the fact that packing optimization is an NP-hard problem, both genetic and gradient-based algorithms are integrated in the finite-circle method to solve the problem. A mixed approach is proposed when the number of components is relatively large. Various tests are carried out to validate the proposed algorithms and design approach. Satisfactory results are obtained.     

Supporting product architecture design using computational design synthesis with network structure constraints

A product’s architecture can affect many aspects of product and process quality, from technical performance to the design effort required, production costs and satisfaction of later lifecycle requirements. This paper explores how computational tools can augment creative methods in product architecture design. Based on an empirical study aiming to understand the context of product architecture design, a new computational method is proposed to support this activity. In the method, product architectures—networks of components linked by connections—can be synthesised using constraints on the structure of the network to define the set of ‘realisable’ architectures for a product. An example illustrates how the method might be used on a real design problem, including the construction of an appropriate set of network structure constraints and the identification of promising architectures from the synthesis results. Preliminary evaluation of the method’s usability, assessed through a laboratory experiment, and its utility, assessed through application to a real historical design problem, supported by initial validation by an engineer from the case study company, suggests that the method has value for engineering design practice.     

Optimization of radar antennas during design by uniform approximation

A method is proposed for designing radar antennas in the uniform approximation. We consider the possibilities and criteria for optimization during the design process. We present results of computations and antenna optimizations that confirm the correctness of the proposed approach. Translated from Izmeritel'naya Tekhnika, No. 6, pp. 20–23, June, 2000.     

基于使用的界面结构设计探讨

用户界面不仅指窗口和对话框 ,而且指用户使用软件系统的整个过程。基于使用的用户界面设计过程 ,也就是界面结构的设计过程。本文通过一个例子探讨利用UML的用例模型和抽象原型技术进行界面结构的设计过程     

Broadband microwave-absorbing honeycomb structure with novel design concept

In this study, a novel broadband microwave-absorbing honeycomb structure is designed using a new concept and is fabricated. To efficiently improve the absorbing performance, the proposed novel design concept uses the transverse direction of a honeycomb structure made out of a lossy material. In that the honeycomb structure can be used in the transverse to the ribbon direction, the effective thickness in terms of the incident EM waves becomes very large, resulting in the enhancement of absorption bandwidth. The designed absorbing honeycomb structure was fabricated using glass/epoxy-MWCNT prepregs and the autoclave process. The measured absorbing performance of the fabricated absorbing honeycomb structure using a free-space measurement system satisfied −10 dB absorption from 3 GHz to 16 GHz. When the performance of the absorbing honeycomb structure is considered in terms of the absorbing bandwidth, because most tracking radars use the C band and/or the X band due to their resolutions, the verified return loss of the absorbing honeycomb structure was found to be superior. It was shown that a lightweight and broadband absorber could be implemented without the use of a magnetic material and without limitations on the thickness.     

Optimum design sensitivity based on approximation concepts and dual methods

An optimum design sensitivity analysis capability is reported which exploits the approximation concepts-dual method formulation of the minimum weight structural sizing problem. An efficient iterative solution technique is used to facilitate determination of sensitivity derivatives for both primal and dual variables. Estimates on the useful range of parameter perturbations, over which the optimum design sensitivity projections can be expected to yield satisfactory revised optimum designs, are also obtained. Numerical results for several example problems will be presented to illustrate the effectiveness of the capability reported.     

Correlated lattice models in the local approximation — Aspects of a numerical renormalization group treatment

The numerical renormalization group method is applied to an Anderson impurity with an energy dependent coupling to the conduction band. We describe how the discrete spectra resulting from the numerical calculation can be reliably smoothed using a continued fraction expansion. The investigations are connected with the study of models in infinite spatial dimensions.     

Electronic shell structure of cluster quantum mechanical effects in the semiclassical approximation

The electronic shell structure of spherical and circular potential wells of finite depth is examined as an extension of the semiclassical analysis of Balian and Bloch. The resulting analytical expressions for the electronic density of states are in good agreement with results of numerical calculations. For circular discs the oscillating structure in the density of states shows a different supershell pattern than for spheres. This is a consequence of the difference in the effective multiplicity of the closed paths, which is determined by the quantization momentum. The positions of the maxima and minima in the density of states depend strongly on the phase shifts in the particle waves arising for each reflection at the cluster surface. These phase shifts have to be determined from a quantum mechanical calculation. Thus the electronic shell structure of spherical clusters has a close similarity with electromagnetic resonances of dielectric spheres (whispering gallery modes).