On the expansions of intermediate orbit for general planetary theory

Intermediate orbit for general planetary theory is constructed in the form of multivariate Fourier series with numerical coefficients. The structure and efficiency of the derived series are illustrated by giving various statistical properties of the coefficients.The ability of the recently proposed elliptic function approach to compress the Fourier series representing the intermediate orbit is investigated. Our results confirm that when mutual perturbations of a pair of planets are considered the elliptic function approach is quite efficient and allows one to compress the series substantially. However, when perturbations of three or more planets are under study the elliptic function approach does not give any advantages.     

Preliminary Study on the Translunar Halo Orbits of the Real Earth–Moon System

The computation of translunar Halo orbits of the real Earth–Moon system (REMS) has been an open problem for a long time, but now, it is possible to compute Halo orbits of the REMS in a systematic way. In this paper, we describe the method used for the numerical computation of Halo orbits for a time span longer than 41 years. Halo orbits of the REMS are computed from quasi-periodic Halo orbits of the quasi-bicircular problem (QBCP). The QBCP is a model for the dynamics of a spacecraft in the Earth–Moon–Sun system. It is a Hamiltonian system with three degrees of freedom and depending periodically on time. In this model, Earth, Moon and Sun are moving in a self-consistent motion close to bicircular. The computed Halo orbits of the REMS are compared with the family of Halo orbits of the QBCP. The results show that the QBCP is a good model to understand the main features of the Halo family of the REMS.     

A note on estimation of the Jacobian elliptic parameter in cnoidal wave theory

A new and simple calculating technique for the Jacobian elliptic parameter is presented in this study. The technique is very useful in generating a train of cnoidal waves in both laboratory and numerical wave tanks. Upon specification of water depth, the wave height and either the wave period or the wavelength, the proposed technique uses the Newton–Raphson method to estimate the Jacobian elliptic parameter directly, without trial and error procedures or look-up in tables. It is shown that the technique provides equally accurate results as the ad hoc methods previously used.     

Inversely-Mapped Analytical Solutions for Flow Patterns around and within Inclined Elliptic Inclusions in Fluid-Saturated Rocks

In this paper, an inverse mapping is used to transform the previously-derived analytical solutions from a local elliptical coordinate system into a conventional Cartesian coordinate system. This enables a complete set of exact analytical solutions to be derived rigorously for the pore-fluid velocity, stream function, and excess pore-fluid pressure around and within buried inclined elliptic inclusions in pore-fluid-saturated porous rocks. To maximize the application range of the derived analytical solutions, the focal distance of an ellipse is used to represent the size of the ellipse, while the length ratio of the long axis to the short one is used to represent the geometrical shape of the ellipse. Since the present analytical solutions are expressed in a conventional Cartesian coordinate system, it is convenient to investigate, both qualitatively and quantitatively, the distribution patterns of the pore-fluid flow and excess pressure around and within many different families of buried inclined elliptic inclusions. The major advantage in using the present analytical solution is that they can be conveniently computed in a global Cartesian coordinate system, which is widely used in many scientific and engineering computations. As an application example, the present analytical solutions have been used to investigate how the dip angle of an inclined elliptic inclusion affects the distribution patterns of the pore-fluid flow and excess pore-fluid pressure when the permeability ratio of the elliptic inclusion is of finite but nonzero values.     

中国近海棱梭群体形态学和耳石形态学研究

为研究棱梭不同地理群体间的形态差异,使用多元统计分析方法对采集自金门、厦门、虎门、湛江、北海和防城港6个地点邻近海域的棱梭群体样本的形态和矢耳石形态两方面进行比较研究。对棱梭样本的形态研究结合传统形态学和地标形态学开展,对矢耳石的形态研究则将传统耳石形态分析法和椭圆傅里叶分析法相结合,形态和耳石形态数据的分析结果相似。主成分分析结果表明从28个棱梭形态量度指标提取的前8个主成分累积贡献率为65. 868%,从85个耳石形态指标提取的前23个主成分的累积贡献率为79. 290%,根据临界值85. 000%可以推断这6个棱梭群体间形态和耳石形态上的差异不能够单独依靠少数指标来判断;聚类分析的结果总体显示出群体间差异与地理距离等因素相关联的分布规律;在判别分析中形态学量度指标的综合判别正确率为75. 9%,而耳石形态学指标的综合判别正确率略低,为69. 3%;对棱梭形态量度指标的单因子方差分析显示湛江棱梭群体与其他群体在形态上存在显著差异的量度指标较少。栖息地环境、饵料组成和海流等可能是导致形态学差异和耳石形态差异形成的主要因素。另一方面,理化因子的相似性和群体间的交流会减弱群体间形态和耳石形态的差异。     

Comparative study of otolith and sulcus morphology for stock discrimination of yellow drum along the Chinese coast

Otolith morphology is widely used for fish stock identification. The sulcus, a structure on the medial side of the otolith, is an important feature in morphological analysis. This study was conducted to evaluate the feasibility of using sulcus morphology for stock identification and to compare its performance with commonly used otolith morphology analysis. Otoliths were collected and analyzed from three geographical groups (the Huanghe (Yellow) River estuary, HHE;the Jiaozhou Bay, JZB;and the Changjiang (Yangtze) River estuary, CJE) of yellow drum Nibea albiflora. The results show that the analysis of sulcus morphology based on shape indices (SIs), elliptic Fourier coefficients (EFc), and a combination of the two parameters identified stocks at overall classification rates of 51.0%, 72.5%, and 73.2%, respectively. These classification rates are similar to those obtained using otolith morphology analysis (57.0%, 73.8%, and 76.5% by SIs, EFc, and their combination, respectively). The findings suggest that sulcus morphology is comparable to the commonly used otolith morphology for identifying stocks of sciaenids, such as the yellow drum. For both otolith and sulcus morphology, EFc could identify the stocks more efficiently than SIs, while the combination of SIs and EFc was even better.     

东海三定点周日海流观测的准调和分析

应用短期资料的潮流准调和分析方法,对东海三定点测站获得的表、中、底3层的25h连续海流资料进行了分析,计算了3测站O1,K1,M2,S2,M4,MS4 6个主要分潮的北、东分量潮流调和常数,并给出了各测站在各层的潮流椭圆要素。计算结果表明：该海区潮流属于正规半日潮流性质,半日分潮流的北分量大于东分量,呈现旋转流的性质,按顺时针向旋转。分析结果也反映出表层、中层的浅水分潮在观测海流中所占的份额高于底层的浅水分潮。结果有助于了解该海区的潮流性质并为潮流数值模拟提供校验实测数据。通过与同期获得的悬浮物浓度剖面数据的比对,将有助于研究潮流与该地区悬浮泥沙浓度分布之间的关系。     

Thermal bending of thin, anisotropic, clamped elliptic plates

The present note deals with the exact analytical solution of thermal bending of clamped, anisotropic, elliptic plates in the case where the thermal field is given by an expression of the type T(x,y,z)=z(Ax²+Cxy+By²).The problem is of basic interest in some ocean and mechanical structural systems since anisotropic materials are commonly used in those fields. Obviously the case of an orthotropic material constitutes a particular situation of the problem under study.     

mKdV-sine-Gordon方程丰富的相互作用解

基于mKdV-sine-Gordon方程的Wronsk解的形式和结构,提出了Wronsk形式展开法,通过这一方法求得了该方程的丰富的相互作用解,该方法的主要特征是不要求Wronsk行列式元素满足线性偏微分方程组。     

Dynamic stress concentration and scattering of SH-wave by interface elliptic cylindrical cavity

In this paper, the dynamic stress concentration and scattering of SH-waves by bi-naterial structures that possess an interface elliptic cavity are investigated. First, by using the complex function method, the Green‘s function is constructed. This yields the solution of the displacement field for an elastic half space with a semi-elliptic canyon impacted by an anti-plane harmonic line source loading on the horizontal surface. Then, the problem is divided into an upper and lower half space along the horizontal interface, regarded as a harmony model. In order to satisfythe integral continuity condition,the unknown anti-plane forces are applied to the interface. The integral equations with unknown forces can be established through the continuity condition, and after transformation, the algebraic equations are solved numerically. Finally, the distribution of the dynamic stress concentration factor (DSCF) around the elliptic cavity is given and the effect of different parameters on DSCF is discussed.