强流直线感应加速器中束流质心横向运动初步计算

 “神龙一号”强流脉冲加速器由72个直线感应加速腔和18个用于测试和真空泵接口的多功能腔组成。直线感应加速器的研制建造中磁轴对中偏差和聚焦磁场的自然偏差所引起的束流质心偏移轨道中心是不可避免的，由于束脉冲期间存在能散，使束流产生Corkscrew运动,导致束流品质变坏。而束脉冲期间的能散只能减小到一定水平，因此必需采取一定的措施抑制Corkscrew幅度的增长。在加速器的安装阶段，脉冲悬丝技术被应用于准直加速段聚焦磁场，并在磁轴准直测试的同时对磁场固有倾斜偏差进行初步校正。根据脉冲悬丝测试所得实验数据，采用传输矩阵法对加速段束质心轨迹进行了初步估计，计算中考虑了各加速腔聚焦磁场的倾斜和偏移误差。给出了计算结果和分析。     

转动定律实验拓展问题研究

准确地画出了转动系统各物理量间关系与矢量方向;论述了转动惯量实验方程组的建立与求解的完备性;证明了只有传动滑轮质量m0必须非常小时,才会对实验结果影响忽略不计;论证了转动系统平衡条件为满足质心坐标和惯量系数同时为零。     

用龙格-库塔法求解非线性方程组

本文介绍了一种求解非线性方程组的新方法龙格-库塔法。     

Modeling Dual-Drive Gantry Stages with Heavy-Load and Optimal Synchronous Controls with Force-Feed-Forward Decoupling

The application of precision dual-drive gantry stages in intelligent manufacturing is increasing. However, the loads of dual drive motors can be severely inconsistent due to the movement of heavy loads on the horizontal crossbeam, resulting in synchronization errors in the same direction movement of dual-drive motors. This phenomenon affects the machining accuracy of the gantry stage and is an critical problem that should be immediately solved. A novel optimal synchronization control algorithm based on model decoupling is proposed to solve the problem. First, an accurate physical model is established to obtain the essential characteristics of the heavy-load dual-drive gantry stage in which the rigid-flexible coupling dynamic is considered. It includes the crossbeam’s linear motion and rotational motion of the non-constant moment of inertia. The established model is verified by using the actual system. By defining the virtual centroid of the crossbeam, the cross-coupling force between dual-drive motors is quantified. Then, the virtual-centroid-based Gantry Synchronization Linear Quadratic Regulator (GSLQR) optimal control and force-Feed-Forward (FF) decoupling control algorithm is proposed. The result of the comparative experiment shows the effectiveness and superiority of the proposed algorithm.     

Orlicz Brunn-Minkowski理论

本文主要介绍Orlicz Brunn-Minkowski理论,并从下面3个方面介绍该理论:Orlicz投影体和Orlicz质心体、Orlicz加法与其相关体积不等式、Orlicz Minkowski问题.     

细直杆无滑动脱离水平面的必要条件

该文研究的是起初竖直静置于水平面上的非均质细直杆的倾倒过程,利用质心运动定理、机械能守恒定律和定轴转动定理导出了直杆在下端不滑动情况下所受支持力的表达式,据此指出了直杆能够脱离水平面的必要条件同时包括两部分：对直杆质量分布的要求;对直杆与水平面之间的静摩擦因数的要求。     

离轴径向偏振光束及其传输特性

基于Wolf近轴传输理论, 导出离轴径向偏振光束光强的解析表达式, 并研究离轴量对离轴径向偏振光束传输中光强分布的影响, 同时根据一阶矩质心位置的定义推导出离轴径向偏振光束的质心坐标, 研究其质心位置的变化规律. 结果表明, 与径向偏振光束不同, 离轴径向偏振光束在近场处传输时光强分布不均匀, 随着传输距离的增加, 光强分布均匀性逐渐得到改善, 而径向偏振光束在传输中始终保持空心对称光斑. 离轴量较小时, 近场处光强分布呈非对称空心面包圈形, 随着传输距离增达到一定程度, 光强分布演化为对称空心面包圈形, 离轴量越小, 演变距离越短; 离轴量较大时, 随着光束的传输离轴径向偏振光束的空心部分消失, 逐渐由空心面包圈形向高斯型演变, 径向偏振光束特性消失. 另一方面, 离轴径向偏振光束的质心不随传输距离的改变而改变. 质心纵坐标恒为零, 质心横坐标与光斑尺寸及离轴量相关. 随着光斑尺寸增大, 质心横坐标成线性增长. 当离轴量较小时, 质心横坐标随离轴量的增大呈非线性增长, 增长量不明显; 离轴量较大时, 质心横坐标随离轴量的增大呈线性增长, 且变化明显.     

Extended Koopmans' theorem at the second-order perturbation theory

The extended Koopmans' theorem (EKT), when combined with the second-order Møller−Plesset (MP2) perturbation theory through the relaxed density matrix approach [J. Cioslowski, P. Piskorz, and G. Liu, J. Chem. Phys. 1997, 107, 6,804], provides a straightforward way to calculate the ionization potentials (IPs) as an one electron quantity. However, such an EKT-MP2 method often suffers from the negative occupation problem, failing to provide the complete IP spectra for a system of interest. Here a small positive number scheme is proposed to cure this problem so as to remove the associated unphysical results. In order to obtain an in-depth physical interpretation of the EKT-MP2 method, we introduce a Koopmans-type quantity, named KT-MP2, based on which the respective contribution from the relaxation and the correlation parts in the EKT-MP2 results are recognized. Furthermore, the close relationship between the EKT-MP2 method and the derivative approach of the MP2 energy with respect to the orbital occupation numbers [N. Q. Su and X. Xu, J. Chem. Theory Comput. 2015, 11, 4,677] is revealed. When these MP2-based methods are applied to a set of atoms and molecules, new insights are gained on the role played by the relaxation and the correlation effects in the electron ionization processes.     

Irregularly shaped space-filling truncated octahedra

For any parent tetrahedron ABCD, centroids of selected sub-tetrahedra form the vertices of an irregularly shaped space-filling truncated octahedron. To reflect these properties, such a figure will be called an ISTO. Each edge of the ISTO is parallel to and one-eighth the length of one of the edges of tetrahedron ABCD and the volume of the ISTO is 3/16-th the volume of the tetrahedron. The ISTO is symmetric about the centroid of tetrahedron ABCD and each face is symmetric about a centre and has an opposite face that is parallel and congruent. The area of the faces of the ISTO is not proportional to that of the generating tetrahedron.