HL-2M 磁体系统安装中的定位与测量

为提高磁体系统安装精度,在 HL-2M 集成大厅建立 63 个基准点构成测量基准网,并利用激光跟 踪仪等高精度测量设备建立每个磁体的局部坐标系,测量特征点的局部坐标;基于测量基准网和公共测量点,采 用最佳拟合得到坐标转换矩阵,以此得到特征点在测量基准网的位置,指导磁体安装。完成安装后的中心柱同支 撑基础的同轴度为∅2.03mm;PF1~PF4 线圈安装标高偏差为±0.5mm,与中心柱的同轴度为∅2.60mm;PF5/6/7/8 线圈与中心柱的同轴度偏差小于∅3.00mm,标高偏差在[−1mm, 1mm]区间内。基于以上方法所得到的线圈安装精 度都满足设计需求。     

Trigonometrically fitted Runge–Kutta methods for the numerical solution of the Schrödinger equation

In this paper we construct two trigonometrically fitted methods based on a classical Runge–Kutta method of England with fifth algebraic order. The methods will be used for the integration of the radial Schrödinger equation and have high efficiency as the results show. The efficiency is higher when using higher energy and this can be explained by the error analysis of the methods. More specifically the new methods have lower powers of the energy in the local truncation error and that keeps the error at lower values.PACS: 0.260, 95.10.EActive Member of the European Academy of Sciences and Arts     

A family of two-stage two-step methods for the numerical integration of the Schr?dinger equation and related IVPs with oscillating solution

We develop a family of six methods for the numerical integration of the Schr?dinger equation and related initial value problems with oscillating solution. Three of the methods are constructed so that they are P-stable, using the methodology of Wang (Comp Phys Comm 171(3):162–174, 2005). Also two of these three methods are trigonometrically fitted with trigonometric orders one and two. The other three methods are constructed so that they are trigonometrically fitted with orders one, two and three. We show that there is an equivalence between the three pairs of methods, as if the property of P-stability can be substituted by an extra trigonometric order, that is the P-stable method is equivalent to the method with trigonometric order one, the P-stable method with trigonometric order one is equivalent to the method with order two, and the P-stable method with order two is equivalent to the method with order three. There is a condition that we choose the same frequency for the P-stability test problem y′′ = −θ ² y and the functions that the method has to integrate exactly, in order to be trigonometrically fitted: {cos(ω x), sin(ω x), x cos(ω x), x sin(ω x), x ² cos(ω x), x ² sin(ω x)}. A stability analysis and a local truncation error analysis are performed on the methods and also the v–s diagrams are produced, where v = ω h and s = θ h. Finally the methods are applied to IVPs with oscillating solutions, such as the one-dimensional time independent Schr?dinger equation and the nonlinear problem.     

Two optimized symmetric eight-step implicit methods for initial-value problems with oscillating solutions

In this paper, we present two optimized eight-step symmetric implicit methods with phase-lag order ten and infinite (phase-fitted). The methods are constructed to solve numerically the radial time-independent Schr?dinger equation with the use of the Woods–Saxon potential. They can also be used to integrate related IVPs with oscillating solutions such as orbital problems. We compare the two new methods to some recently constructed optimized methods from the literature. We measure the efficiency of the methods and conclude that the new method with infinite order of phase-lag is the most efficient of all the compared methods and for all the problems solved. T. E. Simos—Highly Cited Researcher, Active Member of the European Academy of Sciences and Arts.     

High order multistep methods with improved phase-lag characteristics for the integration of the Schr?dinger equation

In this work we introduce a new family of 12-step linear multistep methods for the integration of the Schr?dinger equation. The new methods are constructed by adopting a new methodology which improves the phase lag characteristics by vanishing both the phase lag function and its first derivatives at a specific frequency. This results in decreasing the sensitivity of the integration method on the estimated frequency of the problem. The efficiency of the new family of methods is proved via error analysis and numerical applications. T. E. Simos is a highly cited researcher, active member of the European Academy of Sciences and Arts. Corresponding member of the European Academy of Sciences, corresponding member of European Academy of Arts, Sciences and Humanities.     

Phase diagrams of lyotropic cholesteric fluids

Experimental investigations of lyotropic cholesterics fluids are presented which show that changes in the shape anisotropy and chirality of the micellar population determine the topology of the temperature-concentration phase diagrams. For given amounts of the substances which induce the chirality and modify the shape anisotropy of the micelles, two distinct biaxial cholesteric phases are disclosed in the phase diagrams. This is interpreted in the framework of the catastrophe theory of phase transitions.     

A new symmetric linear eight-step method with fifth trigonometric order for the efficient integration of the Schrödinger equation

On the basis of a classical symmetric eight-step method, an optimized method with fifth trigonometric order for the numerical solution of the Schrödinger equation is developed in this work. The local truncation error analysis of the method proves the decrease of the maximum power of the energy in relation to the corresponding classical method, which renders the method highly efficient. This is confirmed by comparing the method to other methods from the literature while integrating the equation. The superiority of the method is strengthened by the existence of a larger interval of periodicity of the new method in comparison to the corresponding classical method.     

A new family of symmetric linear four-step methods for the efficient integration of the Schrödinger equation and related oscillatory problems

In this article we develop a family of three explicit symmetric linear four-step methods. The new methods, with nullified phase-lag, are optimized for the efficient solution of the Schrödinger equation and related oscillatory problems. We perform an analysis of the local truncation error of the methods for the general case and for the special case of the Schrödinger equation, where we show the decrease of the maximum power of the energy in relation to the corresponding classical methods. We also perform a periodicity analysis, where we find that there is a direct relationship between the periodicity intervals of the methods and their local truncation errors. In addition we determine their periodicity regions. We finally compare the new methods to the corresponding classical ones and other known methods from the literature, where we show the high efficiency of the new methods.     

High order phase fitted multistep integrators for the Schrödinger equation with improved frequency tolerance

In this work we introduce a new family of 14-steps linear multistep methods for the integration of the Schrödinger equation. The new methods are phase fitted but they are designed in order to improve the frequency tolerance. This is achieved by eliminating the first derivatives of the phase lag function at the fitted frequency forcing the phase lag function to be ‘flat’ enough in the neighbor of the fitted frequency. The efficiency of the new family of methods is proved via error analysis and numerical applications.