In this paper, unit moving trihedron is first constructed for a point on the surface of a revolution ellipsoid. Via translation, the origin of the trihedron coincides with that of Cartesian coordinates established at ...In this paper, unit moving trihedron is first constructed for a point on the surface of a revolution ellipsoid. Via translation, the origin of the trihedron coincides with that of Cartesian coordinates established at the center of the ellipsoid, and then through two coordinate rotations, the trihedron completely coincides with the Cartesian coordinates. Transformation formulae between the moving trihedron and unit Cartesian coordinate frameworks as well as transformation of point displacement between two unit coordinate frameworks are presented. Based on the above transformation formulae between two different coordinate frameworks, due to the fact that the displacement and moving trihedron of the point are both functions of the geodetic coordinates, components in the corresponding axis for differential of displacement vector and geodetic curves arc differential at the point in geodetic system can be obtained through complicated derivation. Displacement gradient matrix at the point in geodetic system is also given. Finally, expressions of strain and rotation tensor in geodetic coordinates are presented. Geometric meanings of the rotation tensor are explained in detail. The intrinsic relationship between strain tensors of sphere and ellipsoid are also discussed.展开更多
In atomic,molecular,and nuclear physics,the method of complex coordinate rotation is a widely used theoretical tool for studying resonant states.Here,we propose a novel implementation of this method based on the gradi...In atomic,molecular,and nuclear physics,the method of complex coordinate rotation is a widely used theoretical tool for studying resonant states.Here,we propose a novel implementation of this method based on the gradient optimization(CCR-GO).The main strength of the CCR-GO method is that it does not require manual adjustment of optimization parameters in the wave function;instead,a mathematically well-defined optimization path can be followed.Our method is proven to be very efficient in searching resonant positions and widths over a variety of few-body atomic systems,and can significantly improve the accuracy of the results.As a special case,the CCR-GO method is equally capable of dealing with bound-state problems with high accuracy,which is traditionally achieved through the usual extreme conditions of energy itself.展开更多
Eddy-covariance observations from the Beijing 325-m meteorological tower are used to evaluate the effects of coordinate rotation on the turbulent exchange of momentum and scalars during wintertime haze pollution(Janua...Eddy-covariance observations from the Beijing 325-m meteorological tower are used to evaluate the effects of coordinate rotation on the turbulent exchange of momentum and scalars during wintertime haze pollution(January-February 2013). Two techniques are used in the present evaluation; namely, the natural wind coordinate(NWC) and the planar fit coordinate(PFC), with the latter being applied by means of two methods for linear regression(i.e., overall and sector-wise). The different techniques show a general agreement in both turbulent fluxes and transport efficiencies, especially evident at the lower, 140-m level above the ground(compared to the higher, 280-m level), perhaps implying that the selection of a technique for coordinate rotation(NWC or PFC) is less of a concern for a sufficiently low level, despite the complexities of urban terrain. Additionally, sector-wise regression is a recommended approach for practical application of the PFC in a complex urban environment subjected to particulate pollution, because this method is found to produce a better correlation between the mean vertical velocity at the 140- and 280-m heights.展开更多
Analysis of slender beam structures in a three-dimensional space is widely applicable in mechanical and civil engineering. This paper presents a new procedure to determine the reference coordinate system of a beam ele...Analysis of slender beam structures in a three-dimensional space is widely applicable in mechanical and civil engineering. This paper presents a new procedure to determine the reference coordinate system of a beam element under large rotation and elastic deformation based on a newly introduced physical concept: the zero twist sectional condition, which means that a non-twisted section between two nodes always exists and this section can reasonably be regarded as a reference coordinate system to calculate the internal element forces. This method can avoid the disagreement of the reference coordinates which might occur under large spatial rotations and deformations. Numerical examples given in the paper prove that this procedure guarantees the numerical exactness of the inherent formulation and improves the numerical efficiency, especially under large spatial rotations.展开更多
A method for fabricating a micro-optical structure based on sample rotation and two-laser-beam interference is proposed. The rotation process is analyzed using the coordinate transformation in matrix presentation and ...A method for fabricating a micro-optical structure based on sample rotation and two-laser-beam interference is proposed. The rotation process is analyzed using the coordinate transformation in matrix presentation and the theoretical expressions of the optical field distributions corresponding to different sample rotations. By rotating the samples and changing the laser wavelength, various special micro-optical structures can be obtained, such as equally spaced concentric rings and irregular trapezoidal lattices; these structures are demonstrated by simulating the corresponding optical field distributions. The proposed approach may be developed into a low-cost laser interference lithography technology for the fabrication of various micro-optical structures.展开更多
六极铁作为高能同步辐射光源(High Energy Photon Source,HEPS)储存环八铁单元的重要部件之一,其技术工艺较为复杂,对加工精度和中心引出精度要求都很高。本文对HEPS六极铁的机械中心引出标定方案进行了研究,利用极缝偏差角对常规标定...六极铁作为高能同步辐射光源(High Energy Photon Source,HEPS)储存环八铁单元的重要部件之一,其技术工艺较为复杂,对加工精度和中心引出精度要求都很高。本文对HEPS六极铁的机械中心引出标定方案进行了研究,利用极缝偏差角对常规标定坐标系进行旋转,使三个极缝面更接近理论位置,从而减小磁铁主场斜分量;对每块磁铁进行两次机械中心标定,极缝间距的实测值与设计值的标准偏差在0.015 mm,坐标系旋转前后的基准点偏差标准值为0.09 mm,旋转角最大可达0.6 mrad。这种考虑极缝偏差角的建系方法可以提高标定的精度,能为实际工作中同类型、准直精度有相同要求的设备标定提供参考,有利于加速器装置的顺利安装,对加速器准直测量具有十分重要的意义。展开更多
传统流水线CORDIC(Coordinate Rotation Digital Computer,CORDIC)算法精度不高,输出延时较大,并且需要依靠剩余角度计算进行旋转方向的判断,占用较大的资源。针对以上问题,本文采用角度二极化重编码方法消除剩余角度计算,通过折叠角度...传统流水线CORDIC(Coordinate Rotation Digital Computer,CORDIC)算法精度不高,输出延时较大,并且需要依靠剩余角度计算进行旋转方向的判断,占用较大的资源。针对以上问题,本文采用角度二极化重编码方法消除剩余角度计算,通过折叠角度区间将角度映射于区间[0,π/4]。结合查找表以及合并迭代技术,减少角度计算的迭代次数和硬件单元,降低输出时延,只需要3个周期就能完成CORDIC计算。使用结果重映射方法完成正弦和余弦的全象限实现。寄存器资源消耗为传统算法的35.37%,输出时延减少85%。基于180nm CMOS工艺,完成CORDIC算法的ASIC实现。正弦和余弦的平均绝对误差分别为2.5472×10^(-6)、1.9396×10^(-6),相比较于传统CORDIC算法,精度提升一个数量级。展开更多
文摘In this paper, unit moving trihedron is first constructed for a point on the surface of a revolution ellipsoid. Via translation, the origin of the trihedron coincides with that of Cartesian coordinates established at the center of the ellipsoid, and then through two coordinate rotations, the trihedron completely coincides with the Cartesian coordinates. Transformation formulae between the moving trihedron and unit Cartesian coordinate frameworks as well as transformation of point displacement between two unit coordinate frameworks are presented. Based on the above transformation formulae between two different coordinate frameworks, due to the fact that the displacement and moving trihedron of the point are both functions of the geodetic coordinates, components in the corresponding axis for differential of displacement vector and geodetic curves arc differential at the point in geodetic system can be obtained through complicated derivation. Displacement gradient matrix at the point in geodetic system is also given. Finally, expressions of strain and rotation tensor in geodetic coordinates are presented. Geometric meanings of the rotation tensor are explained in detail. The intrinsic relationship between strain tensors of sphere and ellipsoid are also discussed.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.91636216,11974382,and 11474316)the Chinese Academy of Sciences Strategic Priority Research Program(Grant No.XDB21020200)+1 种基金by the YIPA Programthe support of NSERC,SHARCnet,ACEnet of Canada。
文摘In atomic,molecular,and nuclear physics,the method of complex coordinate rotation is a widely used theoretical tool for studying resonant states.Here,we propose a novel implementation of this method based on the gradient optimization(CCR-GO).The main strength of the CCR-GO method is that it does not require manual adjustment of optimization parameters in the wave function;instead,a mathematically well-defined optimization path can be followed.Our method is proven to be very efficient in searching resonant positions and widths over a variety of few-body atomic systems,and can significantly improve the accuracy of the results.As a special case,the CCR-GO method is equally capable of dealing with bound-state problems with high accuracy,which is traditionally achieved through the usual extreme conditions of energy itself.
基金funded by the National Basic Research Program of China(Grant No.2014CB447900)National High Technology Research and Development Program(Grant No.2014AA06A512)Ministry of Environmental Protection of China through its Special Funds for Scientific Research on Public Welfare(Grant No.201409001)
文摘Eddy-covariance observations from the Beijing 325-m meteorological tower are used to evaluate the effects of coordinate rotation on the turbulent exchange of momentum and scalars during wintertime haze pollution(January-February 2013). Two techniques are used in the present evaluation; namely, the natural wind coordinate(NWC) and the planar fit coordinate(PFC), with the latter being applied by means of two methods for linear regression(i.e., overall and sector-wise). The different techniques show a general agreement in both turbulent fluxes and transport efficiencies, especially evident at the lower, 140-m level above the ground(compared to the higher, 280-m level), perhaps implying that the selection of a technique for coordinate rotation(NWC or PFC) is less of a concern for a sufficiently low level, despite the complexities of urban terrain. Additionally, sector-wise regression is a recommended approach for practical application of the PFC in a complex urban environment subjected to particulate pollution, because this method is found to produce a better correlation between the mean vertical velocity at the 140- and 280-m heights.
文摘Analysis of slender beam structures in a three-dimensional space is widely applicable in mechanical and civil engineering. This paper presents a new procedure to determine the reference coordinate system of a beam element under large rotation and elastic deformation based on a newly introduced physical concept: the zero twist sectional condition, which means that a non-twisted section between two nodes always exists and this section can reasonably be regarded as a reference coordinate system to calculate the internal element forces. This method can avoid the disagreement of the reference coordinates which might occur under large spatial rotations and deformations. Numerical examples given in the paper prove that this procedure guarantees the numerical exactness of the inherent formulation and improves the numerical efficiency, especially under large spatial rotations.
基金Project supported by the National Natural Science Foundation of China(Grant No.61505074)the National Basic Research Program of China(Grant No.2013CBA01703)+1 种基金the Hong Liu Young Teachers Training Program Funded Projects of Lanzhou University of Technology,China(Grant No.Q201509)the National Undergraduate Innovation Training Program of China(Grant No.201610731030)
文摘A method for fabricating a micro-optical structure based on sample rotation and two-laser-beam interference is proposed. The rotation process is analyzed using the coordinate transformation in matrix presentation and the theoretical expressions of the optical field distributions corresponding to different sample rotations. By rotating the samples and changing the laser wavelength, various special micro-optical structures can be obtained, such as equally spaced concentric rings and irregular trapezoidal lattices; these structures are demonstrated by simulating the corresponding optical field distributions. The proposed approach may be developed into a low-cost laser interference lithography technology for the fabrication of various micro-optical structures.
文摘传统流水线CORDIC(Coordinate Rotation Digital Computer,CORDIC)算法精度不高,输出延时较大,并且需要依靠剩余角度计算进行旋转方向的判断,占用较大的资源。针对以上问题,本文采用角度二极化重编码方法消除剩余角度计算,通过折叠角度区间将角度映射于区间[0,π/4]。结合查找表以及合并迭代技术,减少角度计算的迭代次数和硬件单元,降低输出时延,只需要3个周期就能完成CORDIC计算。使用结果重映射方法完成正弦和余弦的全象限实现。寄存器资源消耗为传统算法的35.37%,输出时延减少85%。基于180nm CMOS工艺,完成CORDIC算法的ASIC实现。正弦和余弦的平均绝对误差分别为2.5472×10^(-6)、1.9396×10^(-6),相比较于传统CORDIC算法,精度提升一个数量级。
