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。

三维双楔面定常激波相互作用

本文通过理论分析,将三维对称双楔面上定常激波相互作用简化到二维截面进行分析,利用二维非定常激波楔面反射理论求解该三维激波相互作用结构。同时,通过采用二阶精度的NND格式求解三维Euler方程,对该理论分析结果做出数值模拟验证。理论分析和数值模拟结果显示,对于三维双楔面超声速定常流动在取定的二维截面上激波结构兼有二维非定常及定常激波反射的性质,即形成了类似于二维非定常激波楔面反射的规则反射、单马赫反射、过渡马赫反射及双马赫反射等结构,同时其规则—马赫反射转变却遵循适用于二维定常激波反射的von Neumann准则。理论分析得出的各种反射结构的存在范围与数值模拟结果吻合良好。同时,探讨了两楔面间夹角以及楔面前缘后掠角对该激波结构的影响。

压缩真空场与原子非线性作用过程中的纠缠与消纠缠

用VonNeumann熵研究了附加克尔介质的压缩真空场与二能级原子依赖强度耦合相互作用量子体系的量子纠缠特性 .讨论了初始压缩真空场的压缩度以及克尔非线性作用的强度对该量子体系纠缠特性的影响 .结果表明 ,克尔介质的非线性作用的强弱可以改变体系量子纠缠的周期性 ;在初始压缩度较大 (r =5 )时 ,克尔介质的非线性作用可导致原子与场持续地处于最大纠缠态 ,无消纠缠态或持续地处于消纠缠态 .

A Lagrangian for von Karman Equations of Large Deflection Problem of Thin Circular Plate

By the semi-inverse method proposed by He, a Lagrangian is established for the large deflection problem of thin circular plate. Ritz method is used to obtain an approximate analytical solution of the problem. First order approximate solution is obtained, which is similar to those in open literature. By Mathematica a more accurate solution can be deduced.

A discussion about a class of stress intensity factors and its verification

In this paper, new formulae of a class of stress intensity factors for an infinite plane with two collinear semi-infinite cracks are presented. The formulae differ from those gathered in several handbooks used all over the world. Some experiments and finite element calculations have been developed to verify the new formulae and the results have shown its reliability. Finally, the new formulae and the old are listed to show the differences between them.

Asymptotic solutions to a class of nonlinear oscillation systems

In this paper, we present an asymptotic method for the analysis of a class of strongly nonlinear oscillators, derive second-order approximate solutions to them expressed in terms of their amplitudes and phases, and obtain the equations governing the amplitudes and phases, by which the amplitudes of the corresponding limit cycles and their behaviour can be determined. As an example, we investigate the modified van der Pol oscillator and give the second-order approximate analytical solution of its limit cycle. The comparison with the numerical solutions shows that the two results agree well with each other.

Enhancement of three-photon absorption cross-sections in a novel class of symmetrical charge transfer fluorene-based molecules

The three-photon absorption effect (3PA) of two novel symmetrical charge transfer fluorene-based molecules (abbreviated as BASF and BMOSF) has been determined by using a Q-switched Nd:YAG laser pumped with 38 ps pulses at 1064 nm in DMF. The measured 3PA cross-sections are 84 x 10(-78) and 114 x 10(-78) cm(6) s(2), respectively. The geometries and electronic excitations of these two molecules are systematically studied by PM3 and ZINDO/S methods. The relationships between 3PA cross-sections and intramolecular charge transfer are discussed micromechanically. The experimental and theoretical results have shown that the larger intramolecular charge transfer, which was characterized by the charge density difference between the ground state (SO) and the first excited state (S-I), the greater enhancement of the 3PA cross-sections. (c) 2005 Elsevier B.V. All rights reserved.

Large three-photon absorption cross-section in a novel class of bis-(N-carbazolyl) fluorene derivatives

Two novel symmetrical charge transfer fluorene derivatives (abbreviated as BCZF and BVCZF) with carbazole end-group as the donor moieties have been synthesized. Three-photon absorption cross-sections of these two compounds have been determined by using a Q-switched Nd:YAG laser pumped with 38 ps pulses at 1064 nm in DMF. The measured 3PA cross-sections are 140 x 10(-78) and 400 x 10(-78) cm(6) s(2) for BCZF and BVCZF, respectively. The geometries, electronic structures and electronic spectra of these two compounds are systematically studied by AM1 and ZINDO/S methods. On the basis of correct UV-vis spectra, the influence of different molecular structure on three-photon absorption cross-sections is discussed micromechanically. (C) 2005 Elsevier B.V. All rights reserved.