Complex structures adapted to magnetic flows

Let $M$ be a compact real-analytic manifold, equipped with a real-analytic Riemannian metric $g$, and let $\beta$ be a closed real-analytic 2-form on $M$, interpreted as a magnetic field. Consider the Hamiltonian flow on $T^{1}M$ that describes a charged particle moving in the magnetic field $\beta$. Following an idea of T. Thiemann, we construct a complex structure on a tube inside $T^{1}M$ by pushing forward the vertical polarization by the Hamiltonian flow “evaluated at time $i$”. This complex structure fits together with $\omega -{\pi }^1\beta$ to give a Kähler structure on a tube inside $T^{1}M$. When $\beta =0$, our magnetic complex structure is the adapted complex structure of Lempert–Szőke and Guillemin–Stenzel.We describe the magnetic complex structure in terms of its $(1,0)$-tangent bundle, at the level of holomorphic functions, and via a construction using the embeddings of Whitney–Bruhat and Grauert. We describe an antiholomorphic intertwiner between this complex structure and the complex structure induced by $-\beta$, and we give two formulas for local Kähler potentials, which depend on a local choice of vector potential $1$-form for $\beta$. Finally, we compute the magnetic complex structure explicitly for constant magnetic fields on ${\mathbb{R}}^2$ and $S^2$.     

Stability analysis of nonlinear microwave circuits in time domain

Frequency-domain based methods are not valid to analyze a nonlinear microwave circuit with general, arbitrary nonlinearities. Therefore, analysis of nonlinear microwave circuits in time-domain is presented. Subharmonics and instabilities can be predicted. As examples, Josephson junction and the Schottkybarrier mixer diode are discussed.     

Numerical methods for solving one-dimensional cochlear models in the time domain

In this article, a robust numerical solution method for one-dimensional (1-D) cochlear models in the time domain is presented. The method has been designed particularly for models with a cochlear partition having nonlinear and active mechanical properties. The model equations are discretized with respect to the spatial variable by means of the principle of Galerkin to yield a system of ordinary differential equations in the time variable. To solve this system, several numerical integration methods concerning stability and computational performance are compared. The selected algorithm is based on a variable step size fourth-order Runge-Kutta scheme; it is shown to be both more stable and much more efficient than previously published numerical solution techniques.     

Massive nonlinear sigma models and BPS domain walls in harmonic superspace

Four-dimensional massive nonlinear sigma models and BPS wall solutions are studied in the off-shell harmonic superspace approach in which supersymmetry is manifest. The general nonlinear sigma model can be described by an analytic harmonic potential which is the hyper-Kähler analog of the Kähler potential in theory. We examine the massive nonlinear sigma model with multi-center four-dimensional target hyper-Kähler metrics and derive the corresponding BPS equation. We study in some detail two particular cases with the Taub-NUT and double Taub-NUT metrics. The latter embodies, as its two separate limits, both Taub-NUT and Eguchi–Hanson metrics. We find that domain wall solutions exist only in the double Taub-NUT case including its Eguchi–Hanson limit.     

缩比模型的宽频时域太赫兹雷达散射截面(RCS)研究

本文首次以钛宝石飞秒激光振荡级为抽运源,搭建了国内首套宽频时域太赫兹雷达(带宽0.1—1.3 THz)并进行了基于标准球的系统校正验证.利用该雷达测量了太赫兹波段三种缩比模型的散射时域信号.通过改进后的后向投影算法对模型的轮廓外形进行了成像研究,验证了新型时域散射信号成像机理.太赫兹雷达更高的频率,宽谱的特征和高分辨率成像的能力有望用于隐形外形设计过程,成为新兴的太赫兹散射特征研究平台.     

Compatibility of symplectic structures adapted to noncommutatively integrable systems

It is known that any integrable, possibly degenerate, Hamiltonian system is Hamiltonian relative to many different symplectic structures; under certain hypotheses, the ‘semi-local’ structure of these symplectic forms, written in local coordinates of action-angle type, is also known. The purpose of this paper is to characterize from the point of view of symplectic geometry the family of all these structures. The approach is based on the geometry of noncommutatively integrable systems and extends a recent treatment of the nondegenerate case by Bogoyavlenskij. Degenerate systems are comparatively richer in symplectic structures than nondegenerate ones and this has the counterpart that the bi-Hamiltonian property alone does not imply integrability. However, integrability is still guaranteed if a system is Hamiltonian with respect to three suitable symplectic structures. Moreover, some of the properties of recursion operators are retained.     

Antireflection subwavelength structures analyzed by using the finite difference time domain method

Antireflection subwavelength structures (ASSs) are analyzed by using the finite difference time domain (FDTD) method in the visible light spectrum. Low reflectance can be obtained by both the conical and pyramidal shapes over a broadband range. Comparing the reflectance of different structure shapes and aspect ratios by the FDTD method, it shows that the antireflection efficiencies of the pyramidal structures are better than that of the conical structures when the aspect ratio is up to 0.8. It is found that, for the conical structure surface, the average transmittance increases gradually with the aspect ratio and the average transmittance is about 99.6% with the aspect ratio of 2.0. However, for the pyramidal structure with the aspect ratio ranging from 1.0 to 2.0, the average transmittance is up to 99.7%.     

Wave-front engineering by Huygens-Fresnel principle for nonlinear optical interactions in domain engineered structures

Wave-front engineering for nonlinear optical interactions was discussed. Using Huygens-Fresnel principle we developed a general theory and technique for domain engineering with conventional quasi-phase-matching (QPM) structures being the special cases. We put forward the concept of local QPM, which suggests that the QPM is fulfilled only locally not globally. Experiments agreed well with the theoretical prediction. The proposed scheme integrates three optical functions: generating, focusing, and beam splitting of second-harmonic wave, thus making the device more compact.     

Time domain simulation in photonics: A comparison of nonlinear dispersive polarisation models

The paper investigates and compares a range of different models currently used for modelling nonlinear optical phenomena. The models are implemented in the numerical time domain Transmission Line Modelling (TLM) method and include a Kerr model and different formulations of the Duffing model. The models are used to simulate an all-optical limiter for a CW input and results compared with ones available in the literature. This enables a comparison to be made between the different models, from which it is concluded that the Duffing model has some advantages, when modelling materials and phenomena involving more than one frequency, arising from its ability to describe dispersive effects. These conclusions are further supported by the simulation results obtained for a pulse input.     

最小二乘支持向量域的混沌时间序列预测

从支持向量域SVD(Support Vector Domain)出发，根据Takens延时相空间重构思想，利用支持向量机非线性映射，建立了混沌时间序列和混沌非线性相轨迹运动的SVD预测模型.采用数据集作为支持对象元素，机器自学习缩小模型泛化误差的上界，利用最小二乘支持向量域(SVD)，预测了Henon/Lorenz/Rossler三种混沌时间序列.预测结果表明，三种预测模型将集合映射到一个更高维特征空间，通过嵌入维数，实现了序列预测，误差随嵌入维数变化趋于恒定，与支持向量机(SVM)相比，SVD所需支持向量少，收敛速度快，鲁棒性强，核函数选择容易灵活，且存在自适应方法.网格点数提高了10—20倍，序列预测在小样本、非线性、未知概率密度条件下，预测和实际值取得了一致. 关键词： 支持向量域 混沌 最小二乘 时间序列预测     

Information-theory-based snake adapted to multiregion objects with different noise models

We propose a segmentation technique adapted to objects composed of several regions with gray-level fluctuations described by different probability laws. This approach is based on information theory techniques and leads to a multiregion polygonal snake driven by the minimization of a criterion without any parameters to be tuned by the user. We demonstrate the improvements obtained with this approach as well as its low computational cost. This approach is compatible with applications such as object recognition and object tracking with nonrigid deformation in images perturbed by different types of optical noise.     

On the theory of second-harmonic generation in 2D nonlinear photonic crystals with arbitrary domain structures

Theoretical analysis is given to second-harmonic generation in 2D nonlinear photonic crystals of rectangular symmetry with rectangular domains. Formulas for the nonlinear response of the crystal with an arbitrary domain structure are derived within the approximation of a given field. A possibility of calculating time profiles of second-harmonic pulses down to the femtosecond range is demonstrated.     

An efficient multi-domain spectral algorithm for the simulation of dispersive metallic structures in the time domain

In this article, we present a multi-domain formulation of the spectral time domain algorithm for the simulation of dispersive materials. We propose a leap-frog time-stepping scheme similar to the finite-difference time domain method in order to minimize memory usage. Dispersive material behavior is modelled in the frequency domain and used in our time-domain algorithm by introducing auxiliary differential equations for the macroscopic polarization. Absorbing boundary conditions are presented that can be used with dispersive materials. The numerical investigation of structures with material parameters fitted to experimental data shows excellent agreement with theoretical calculations.     

Reconstructing bifurcation diagrams from noisy time series using nonlinear autoregressive models

We introduce a formalism for the reconstruction of bifurcation diagrams from noisy time series. The method consists in finding a parametrized predictor function whose bifurcation structure is similar to that of the given system. The reconstruction algorithm is composed of two stages: model selection and bifurcation parameter identification. In the first stage, an appropriate model that best represents all the given time series is selected. A nonlinear autoregressive model with polynomial terms is employed in this study. The identification of the bifurcation parameters from among the many model parameters is done in the second stage. The algorithm works well even for a limited number of time series.     

Experimental evaluation of time domain models for ultrasound attenuation losses in photoacoustic imaging

Understanding and compensating ultrasound attenuation losses is an important issue in photoacoustic imaging. To contribute to this effort, simulated attenuated time domain waveforms are compared to experimental waveforms. The experimental waveforms are acquired by transmitting broadband ultrasound pulses through distilled water and porcine fat tissue. Three well-known modeling approaches are examined in detail with regard to accuracy and computation time. Furthermore, the influence of attenuation on imaging resolution is addressed. In the present paper, the focus lies on the calculation of attenuated detector signals. The results, however, also provide clues about the quality of image reconstruction.     

Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview

Here, we review the basic concepts and applications of the phase-field-crystal (PFC) method, which is one of the latest simulation methodologies in materials science for problems, where atomic- and microscales are tightly coupled. The PFC method operates on atomic length and diffusive time scales, and thus constitutes a computationally efficient alternative to molecular simulation methods. Its intense development in materials science started fairly recently following the work by Elder et al. [Phys. Rev. Lett. 88 (2002), p. 245701]. Since these initial studies, dynamical density functional theory and thermodynamic concepts have been linked to the PFC approach to serve as further theoretical fundamentals for the latter. In this review, we summarize these methodological development steps as well as the most important applications of the PFC method with a special focus on the interaction of development steps taken in hard and soft matter physics, respectively. Doing so, we hope to present today's state of the art in PFC modelling as well as the potential, which might still arise from this method in physics and materials science in the nearby future.     

On using moving windows in finite element time domain simulation for long accelerator structures

A finite element moving window technique is developed to simulate the propagation of electromagnetic waves induced by the transit of a charged particle beam inside large and long structures. The window moving along with the beam in the computational domain adopts high-order finite element basis functions through p refinement and/or a high-resolution mesh through h refinement so that a sufficient accuracy is attained with substantially reduced computational costs. Algorithms to transfer discretized fields from one mesh to another, which are the keys to implementing a moving window in a finite element unstructured mesh, are presented. Numerical experiments are carried out using the moving window technique to compute short-range wakefields in long accelerator structures. The results are compared with those obtained from the normal finite element time domain (FETD) method and the advantages of using the moving window technique are discussed.