Preservation of stability properties near fixed points of linear Hamiltonian systems by symplectic integrators

Based on reasonable testing model problems, we study the preservation by symplectic Runge-Kutta method (SRK) and symplectic partitioned Runge-Kutta method (SPRK) of structures for fixed points of linear Hamiltonian systems. The structure-preservation region provides a practical criterion for choosing step-size in symplectic computation. Examples are given to justify the investigation.     

A smoothing Newton method for NCPs with the P0-property

In this paper, we first investigate a two-parametric class of smoothing functions which contains the penalized smoothing Fischer-Burmeister function and the penalized smoothing CHKS function as special cases. Then we present a smoothing Newton method for the nonlinear complementarity problem based on the class of smoothing functions. Issues such as line search rule, boundedness of the level set, global and quadratic convergence are studied. In particular, we give a line search rule containing the common used Armijo-type line search rule as a special case. Also without requiring strict complementarity assumption at the P₀-NCP solution or the nonemptyness and boundedness of the solution set, the proposed algorithm is proved to be globally convergent. Preliminary numerical results show the efficiency of the algorithm and provide efficient domains of the two parameters for the complementarity problems.     

Absorption coefficient measurement of high-resistivity germanium at 2.52 THz by Brewster’s angle method

Brewster’s angle method was adopted to measure the absorption coefficient of a set of high-resistivity germanium samples at 2.52 THz in this paper. Numerical simulations were firstly carried out to evaluate the errors during measurement. The experimental setup was improved, and measurement was carried out based on a CW THz laser at 2.52 THz.     

Numerical investigations of a multi-walled carbon nanotube-based multi-segmented optical antenna

Motivated by the fabrication potential of multi-walled carbon nanotube structures, we numerically investigated a paired structure consisting of two metallic spheres each grown on one end of a multi-walled nanotube. The paired two-segmented structure is capable to convert free-space radiation into an intense near-field, and, hence, acting as an optical antenna. Vice versa the presence of the two nanotubes enable a current source at the antenna feed to more efficiently energy into the radiation modes, resulting e.g. in correspondingly altered luminescence lifetimes when an excited single molecule is placed in the feed point. Furthermore, the structure represents a mean to localize light on a sub-wavelength scale within different materials, which is interesting in the context of a fabrication technology for integrated nanophotonic components with different material combinations. The optical properties of the nano-antenna are analyzed by means of numerical simulations using the finite element method. Our investigations have revealed that the field enhancement, the resonances, and the radiation patterns can be easily tuned since all these quantities strongly depend on the size of the nanotubes and the metallic spheres, as well as on their material properties The structure we propose here carries a great potential for bio-sensing, for tip-enhanced spectroscopy applications, and for interfacing integrated photonic nano circuits.     

Large negative and positive lateral shift on reflection from a left-handed prism coated with a weakly absorbing dielectric film

A large negative or positive lateral shift of the beam reflected from a left-handed prism coated with a weakly absorbing dielectric film is investigated theoretically. It is shown that the large lateral shift can be negative as well as positive due to the formation of the unusual guided modes in the weakly absorbing film near the resonant condition, which acts the same effect as the surface wave. This unusual guided wave can travel a longer distance than the surface wave. These giant negative and positive lateral shifts are almost fifty times larger than that from the lossless structure [Wang in Appl. Phys. Lett. 87:221102, 2005]. The sign of this large lateral shift could be controlled easily by adjusting the parameters of the present structure.     

Self-organized periodic surface structures on ZnO induced by femtosecond laser

Self-organized periodic surface structures on ZnO have been observed after multiple linearly polarized femtosecond laser pulse irradiation. The observed self-organized structures are attributed to the second harmonics in the sample surface excited by the incident laser. The grating orientation could be adjusted by the laser polarization direction. We also find that fluences play an important role in the formation of self-organized nanostructures.     

非球形烟尘粒子后向散射场的光谱分析

在利用后向散射法测量烟尘浓度和粒径的过程中,对炯尘粒子模型的后向散射光谱特性进了计算,确定影响后向散射光谱强度的主要因素并进行分析.对实际排放的烟尘进行显微观察表明,利用椭球、圆柱和广义切比雪夫3种非球模型可以较好地模拟烟尘粒子,其等效直径约1 μm.通过"T矩阵法"对这3种非球形粒子模型后向散射场的光谱特性进行了分析,结果表明:非球形粒子的可见/红外波段后向散射现象较球形粒子明显,特别是广义切比雪夫粒子的后向散射光强最高可达到前向的3.5倍;对于吸收性非球形粒子(复折射率m=1.57-0.56i),后向散射光强远大于非吸收性非球形粒子(复折射率m=1.57-0.001i);随着粒子等效半径的增大,光源波长也应随之增加.这为在实际测量时光源及方位的选择提供了理论依据.     

Piecewise homotopy perturbation method for solving linear and nonlinear weakly singular VIE of second kind

The purpose of this paper is to obtain the approximation solution of linear and strong nonlinear weakly singular Volterra integral equation of the second kind, especially for such a situation that the equation is of nonsmooth solution and the situation that the problem is a strong nonlinear problem. For this purpose, we firstly make a transform to the equation such that the solution of the new equation is as smooth as we like. Through modifying homotopy perturbation method, an algorithm is successfully established to solve the linear and nonlinear weakly singular Volterra integral equation of the second kind. And the convergence of the algorithm is proved strictly. Comparisons are made between our method and other methods, and the results reveal that the modified homotopy perturbation is effective.     

气粒混合物非灰辐射特性合并宽窄谱带K分布模型

气粒混合物辐射问题具有全场性、非灰性、耦合性等特点,准确预估高温燃气/粒子非灰辐射特性是非常重要的。本文将合并宽窄谱带K分布模础(CWNBCK)与离散坐标法(DOM)结合,开展了非灰气粒混合物辐射换热问题的模拟工作,分别验证了一维和三维情况下应用该模型的准确性,给出不同工况下的热流源项、壁面热流或辐射热流等。结果表明:该模型能够给出与SNB模型精度基本相同的结果,考虑其计算效率的提高,可以在工程实际中应用该模型计算非灰气粒混合物辐射换热。     

椭圆柱形光学黑洞红外辐射特性分析

本文主要采用时域有限差分(FDTD)方法计算了二维椭圆柱形光学黑洞的红外辐射特性。并且采用几何光学近似(GOA)对椭圆柱形的光学黑洞的光线入射轨迹进行分析和比较。研究结果表明,FDTD计算的光学黑洞内的能流分布结果与GOA计算的光学黑洞内的光线入射轨迹结果相吻合,椭圆柱形光学黑洞的红外辐射特性主要受折射率梯度和入射波长的影响。