Free radial oscillation of a sphere in relativistic elasticity theory

The spherically symmetric free radial oscillation in the first post-Newtonian approximation for a homogeneous and isotropic elastic sphere with a constant density is studied. Based on the Xu, Wu, and Soffel formalism, the relation of the oscillation frequency of the sphere with the radius, mass density, and elastic constants of the sphere is derived by using the successive approximation method.

液体多脉冲及2D NMR实验的计算机模拟

现代多脉冲及2D NMR技术是过去十年中发展起来的崭新的NMR实验方法。计算机模拟做为NMR实验的强有力分析手段已日益受到重视。国内这方面工作开展得尚很少；国外发表的工作主要采用的是数字模拟，存在分析结果不够直观、物理意义不够清晰等缺陷。本论文工作采用乘积算符方法研制出对分析多脉冲及2D NMR实验普适的模拟程序PROPER；在乘积算符基础上，针对磁等性自旋体系，提出了实用的对称化乘积算符及多量子积算符方法。一、多脉冲及2D NMR实验的计算机模拟 1. 采用乘积算符方法在本所PDP－11／23微机上研制了多脉冲及2D NMR实验的模拟程序PROPER。该程序对不超过4核（I ＝ 1／2）的同核及异核弱耦合自旋体系非选择性脉冲序列的分析是普遍适用的。受计算机内存的限制，PROPER程序所能处理的脉冲序列脉冲间隔数目一般不超过10。2. 应用PROPER模拟程序对INEP和DEPT脉冲序列进行了分析比较；特别对BIRD脉冲序列的各种相位变型进行了模拟分析，给出了分析结果，分析过程中考虑了影响BIRD作用效果的同核耦合因素。应用结果表明，PROPER程序计算正确、迅速、给出的模拟结果较通常的数字模拟方法简单、直观、物理意义清楚，便于分析。由于采用算符模拟，结果的输出打印比较费时。目前，PROPER程序正在改进和完善之中。二、多脉冲及2D NMR实验的密度算符描述 1. 针对磁等性自旋（I ＝ 1／2）体系，首次提出了对称化乘积算符描述方法。在通常的乘积算符基础上，引入了对称化乘积算符，并对其数理基础进行了详细论证。推导了算符循环对易关系决定的Liourill-Von Neumann方程的解，给出了算符间普遍存在的循环对易关系及其相应的演化公式。据此，以InS(I = 1/2, S = 1/2; n = 2,3)自旋体系为例，对DEPT脉冲序列进行了分析；结果表明，该方法较通常的乘积算符方法对磁等性自旋体系的分析要简单、实用，且物理意义更加明确。由于该方法涉及较多的算符对易关系，因此不易计算机编程。2. 在对称化乘积算符基础上引入了多量子积算符的概念。以In(I = 1/2; n = 2,3)体系为例，给出了两者的互换关系。推导出了具有标量耦合作用的两组合粒子体系普适的多量子积算符环对易关系及相应的演化解析式。多量子积算符方法可望将1／2－自旋磁等性组合粒子表象与自旋大于1／2的单粒子表象统一起来，并为计算机模拟提供新的数学方法。该方法尚有待于进一步研究。

DISORDER POINT FOR 2D ELECTRONS IN A HALF-FILLED LANDAU-LEVEL

Short-range correlations of two-dimensional electrons in a strong magnetic field are shown to be triangular in nature well below half-filling, but honeycomb well above half-filling. The half-filling point is thus proposed, and qualitatively confirmed by three-body correlation calculations, to be a new type of disorder point where short-range correlations change character. A wavefunction study also suggests that nodes become unbound at half-filling. Evidence for incompressibility but deformability of the half-filling state earlier suggested by Fano, Ortolani and Tosatti, is also presented and found to be in agreement with recent experiments.

An All-E-Beam Lithography Process for the Patterning of 2D Photonic Crystal Waveguide Devices

We present an all-e-beam lithography (EBL) process for the patterning of photonic crystal waveguides.The whole device structures are exposed in two steps. Holes constituting the photonic crystal lattice and defects are first exposed with a small exposure step size (less than 10nm). With the introduction of the additional proximity effect to compensate the original proximity effect, the shape, size, and position of the holes can be well controlled.The second step is the exposure of the access waveguides at a larger step size (about 30nm) to improve the scan speed of the EBL. The influence of write-field stitching error can be alleviated by replacing the original waveguides with tapered waveguides at the joint of adjacent write-fields. It is found experimentally that a higher exposure efficiency is achieved with a larger step size;however,a larger step size requires a higher dose.