Bloch方程的解析解及其在水峰抑制和特形脉冲设计中的应用

用Laplace变换方法求出了Bloch方程在各种不同物理条件下的解析解,这些解析解物理图象清楚,便于分析,克服了数值解中的困难.解析解和相应的结论已用于水峰抑制和特形脉冲的设计.对于水峰抑制,本文指出抑制效果是有极限的,并给出了抑制效果的极限以及最佳抑制时间的近似计算公式.在特形脉冲的模拟过程中,我们发现只有同时考虑全部四类解析解,才能得到正确的模拟结果,另外,模拟还表明,要在保持激励频谱形状不变的条件下,得到不同倾倒角的脉冲必须改变激励脉冲的形状,相应实验的结果与我们给出的上述结论完全吻合。     

特形脉冲的欧拉角

本文提出了用量子力学的空间转动变换算符描述特形脉冲的方法。它把任意的特形脉冲用三个欧拉角来表示,并且使得在特形脉冲下的相干演化可以很容易地利用多极NMR理论,张量算符理论或者积算符理论来分析,作为例子,用数值方法计算了高斯脉冲的三个参数。     

光纤陀螺及其船用航姿系统的姿态解算

介绍了光纤陀螺的工作原理，分析了光纤陀螺用于船用航姿系统的姿态算法，对四元数算法和等效转动矢量算法进行了介绍。并在船舶摇摆运动条件下作了仿真，仿真表明四元数的四阶Runge-Kutta算法是一种较适合船用光纤陀螺捷联航姿系统的算法。     

特形脉冲调制中射频泄漏的影响及其补偿

模拟器件的非理想因素和电路分布参数等影响造成了特形脉冲调制时的射频泄漏;这些射频泄漏将对特形脉冲的激发轮廓产生缺陷.本文从特形脉冲的射频调制原理着手,分析了射频泄漏对选择激发轮廓的影响,并采用一种新的相位循环方法对它进行补偿.实验的结果表明这种补偿方法有一定的实用性.     

脉冲形状对定域谱中水峰抑制作用的影响

报道了用MRI中STEAM方法获得定域谱(MRS)的实验结果,用相位正交、时间一长一短的二个特形脉冲对水峰进行预饱和照射,得到抑制水峰的MRS.这种方法抑制水峰的效果比用梯度散相压水峰的效果好。对于三种常见的特形脉冲,用GAUSS脉冲得到效果最好的实验结果。     

特形脉冲的设计与计算机模拟

根据LiouvillevonNeumann方程从理论上对特形脉冲做了全面的描述,提出了一种具体的调幅特形脉冲设计方案:首先将待设计的脉冲展成一个有限Fourier级数,然后根据Bloch方程的解析解准确计算出各阶正弦、余弦波的频谱,再将这些频谱组合后与该脉冲的理想频谱进行比较构成误差函数,最后运用鲍威尔-模拟退火组合优化算法计算出全局最优Fourier系数,即可得到所需脉冲的表达式.应用此设计方案,得到了体系处于热平衡态时的特形激励脉冲和反转脉冲的具体表达式.计算机模拟表明,所得脉冲的频谱具有较好的选择性 关键词： 核磁共振 特形脉冲 Bloch方程 鲍威尔模拟退火组合优化算法     

四旋翼飞行器姿态解算与滤波

四旋翼飞行器的运动控制关键在于对飞行过程中的实时姿态角控制。目前实时姿态角信息还不能直接测量出来。为了能利用已有的传感器数据解算出更准确的姿态角,通过物理实验详细分析了四旋翼飞行器姿态角的解算和滤波算法。首先,通过联立欧拉方向余弦矩阵与四元数矩阵,得到用四元数表达的姿态角表达式。然后,结合加速度计和磁强计实时测量的数据,分别采用互补滤波和卡尔曼滤波两种方法来补偿四元数结果,分别分析如何选取最佳参数,并对比分析了两种滤波方式的优缺点。在一定精度要求范围内,这两种滤波方式都能获得更加准确的姿态角,但是互补滤波相对卡尔曼滤波有一定的解算时延。因此在精度要求一般的系统中,这两种滤波方式都可以用来求解姿态角,卡尔曼滤波方法则更适于对实时性要求更高的系统。     

微机在物理实验中的应用：第六讲 应用举例

例1.应用游戏接口逻辑电平输出端AN0～AN2控制步进电机的转动步进电机是一种将电脉冲信号变换为角位移的控制电动机。一般使用配套驱动电源,其中具有脉冲分配器,使得步进电机的角位移量与输入脉冲数成比例。当输入一个脉冲时,步进电机旋转一个θ角。如输入N个脉冲时,则旋转N×θ角度,且在时间上     

弹性细杆弯曲的Kirchhoff方程的违约校正求解

采用Euler四元数表示的Kirchhoff方程来研究受力挤压作用下的弹性细杆的拓扑构形，进一 步研究弹性细杆的力学性质；将得到的微分方程与约束条件组成微分代数方程后再转化为微 分方程规范形式以便求解；为满足边界条件，应用数值打靶法求解边值条件，并将弹性细杆 在力作用下的拉压过程用Matlab仿真出来.同时对由于误差导致的违约现象进行处理，并针 对欧拉参数的特征，选取合适的修正系数以保持方程的稳定性. 关键词： DNA Euler四元数 Kirchhoff方程 弹性细杆 违约修正     

四元数在量子力学中的应用

把双四元数推广到了二级双四元数，并设计了一种态函数的四元数表示法，从而用四元数表述了相对论量子力学，使四元数物理学形成了系统，用四元数表示的算符和状态，对于导出算符间的对易关系和状态的洛伦兹变换性质是方便的。     

Elimination of Rotational Degrees of Freedom in Expansion Methods for Three Nucleons

 Euler angles determining rotations of a system as a whole are conveniently separated in three-particle basis functions. Analytic integration of matrix elements over Euler angles is done in a general form. Results for the Euler angle integrated matrix elements of a realistic NN interaction are listed. The partial wave decomposition of correlated three-body states is considered. E-mail address: efros@mbslab.kiae.ru Received May 4, 2002; accepted July 26, 2002     

Scattering of Gaussian beam by arbitrarily shaped inhomogeneous particles

A hybrid finite element-boundary integral method is applied to characterize the scattering of an arbitrarily incident-focused Gaussian beam by arbitrarily shaped inhomogeneous particles. Specifically, the Davis–Barton fifth-order approximation in combination with rotation Euler angles is used to represent the arbitrarily incident Gaussian beams. The finite element method is employed to formulate the fields in the interior region of the inhomogeneous particle, while the boundary integral equation is applied to represent the fields in the exterior region. The interior and exterior fields are coupled by means of the field continuity conditions. To reduce the computational burden, the frontal method and the multilevel fast multipole algorithm are adopted to solve the resultant matrix equation. Numerical results for differential scattering cross sections of several selected inhomogeneous particles are presented and can be served as further study on this subject.     

Determination of the rotational diffusion tensor of macromolecules in solution from nmr relaxation data with a combination of exact and approximate methods--application to the determination of interdomain orientation in multidomain proteins

In this paper we present a method for determining the rotational diffusion tensor from NMR relaxation data using a combination of approximate and exact methods. The approximate method, which is computationally less intensive, computes values of the principal components of the diffusion tensor and estimates the Euler angles, which relate the principal axis frame of the diffusion tensor to the molecular frame. The approximate values of the principal components are then used as starting points for an exact calculation by a downhill simplex search for the principal components of the tensor over a grid of the space of Euler angles relating the diffusion tensor frame to the molecular frame. The search space of Euler angles is restricted using the tensor orientations calculated using the approximate method. The utility of this approach is demonstrated using both simulated and experimental relaxation data. A quality factor that determines the extent of the agreement between the measured and predicted relaxation data is provided. This approach is then used to estimate the relative orientation of SH3 and SH2 domains in the SH(32) dual-domain construct of Abelson kinase complexed with a consolidated ligand.     

Numerical simulation of Gaussian beam scattering by complex particles of arbitrary shape and structure

An efficient numerical method based on the surface integral equations is introduced to simulate the scattering of Gaussian beam by complex particles that consist of an arbitrarily shaped host particle and multiple internal inclusions of arbitrary shape. In particular, the incident focused Gaussian beam is described by the Davis fifth-order approximate expressions in combination with rotation defined by Euler angles. The established surface integral equations are discretized with the method of moments, where the unknown equivalent electric and magnetic currents induced on the surfaces of the host particle and the internal inclusions are expanded using the Rao–Wilton–Glisson (RWG) basis functions. The resultant matrix equations are solved by using the parallel conjugate gradient method. The proposed numerical method is validated and its capability illustrated in several characteristic examples.     

Transformations of spherical beam shape coefficients in generalized Lorenz-Mie theories through rotations of coordinate systems. IV. Plane waves

This paper is the fourth of a series devoted to the transformation of beam shape coefficients through rotations of coordinate systems. These coefficients are required to express electromagnetic fields of laser beams in expanded forms, for instance for use in some generalized Lorenz-Mie theories. The main result of Part I has been the theorem of transformation of beam shape coefficients under rotations. Part II dealt with the special case of on-axis axisymmetric beams. Part III dealt with other special cases, namely when the Euler angles specifying the rotation are given some special values. The present Part IV studies another special case, namely the one of plane waves viewed as special on-axis axisymmetric beams, and can therefore be viewed as a special case of Part II. Unexpectedly, it is found that, in general, although plane waves are fairly trivial, their expansions require using non trivial beam shape coefficients, exactly as required when dealing with arbitrary shaped beams.     

Techniques of non-orthogonal magnetic resonance imaging and its clinical application

A technique to obtain non-orthogonal magnetic resonance (MR) images in the body has been developed using a simple three-dimensional model (3-DM). Images were obtained with multiple non-orthogonal planes, without subjecting patients to uncomfortable oblique positions. Eighty-two patients were studied using non-orthogonal planes. Euler angle determinations (EAD) were developed for different anatomical locations as well as for multiple clinical situations. One or all three Euler angles were changed using the EAD to define any plane of orientation relative to reference orthogonal frame. In a series of 12 patients for postoperative evaluation of Mustard and Senning procedure, the demonstration of anastomotic site was superior with angled coronal planes when compared to the routine coronal views in 83% of the studies. With the use of EAD, acquisition time for non-orthogonal planes can be reduced. 3-DM aids in the understanding of the Euler angles and leads to multiple non-orthogonal planes.     

Study of nonlinear system stability using eigenvalue analysis: Gyroscopic motion

General computational multibody system (MBS) algorithms allow for the linearization of the highly nonlinear equations of motion at different points in time in order to obtain the eigenvalue solution. This eigenvalue solution of the linearized equations is often used to shed light on the system stability at different configurations that correspond to different time points. Different MBS algorithms, however, employ different sets of orientation coordinates, such as Euler angles and Euler parameters, which lead to different forms of the dynamic equations of motion. As a consequence, the forms of the linearized equations and the eigenvalue solution obtained strongly depend on the set of orientation coordinates used. This paper addresses this fundamental issue by examining the effect of the use of different orientation parameters on the linearized equations of a gyroscope. The nonlinear equations of motion of the gyroscope are formulated using two different sets of orientation parameters: Euler angles and Euler parameters. In order to obtain a set of linearized equations that can be used to define the eigenvalue solution, the algebraic equations that describe the MBS constraints are systematically eliminated leading to a nonlinear form of the equations of motion expressed in terms of the system degrees of freedom. Because in MBS applications the generalized forces can be highly nonlinear and can depend on the velocities, a state space formulation is used to solve the eigenvalue problem. It is shown in this paper that the independent state equations formulated using Euler angles and Euler parameters lead to different eigenvalue solutions. This solution is also different from the solution obtained using a form of the Newton-Euler matrix equation expressed in terms of the angular accelerations and angular velocities. A time-domain solution of the linearized equations is also presented in order to compare between the solutions obtained using two different sets of orientation parameters and also to shed light on the important issue of using the eigenvalue analysis in the study of MBS stability. The validity of using the eigenvalue analysis based on the linearization of the nonlinear equations of motion in the study of the stability of railroad vehicle systems, which have known critical speeds, is examined. It is shown that such an eigenvalue analysis can lead to wrong conclusions regarding the stability of nonlinear systems.     

Quantum description of five-particle systems in principal-axis hyperspherical coordinates

To describe a 5-particle system, ‘principal-axis hyperspherical’ coordinates (made up of one hyperradius and eight angles as internal coordinates) and three Euler angles as external (rotational) coordinates are used. A mathematical procedure to derive, in a systematic manner, the exact quantum mechanical Hamiltonian of the system in terms of these coordinates is presented. A generalized angular momentum vector operator, which allows the generation of a profitable standard representation for the angular part of the problem, is introduced.     

The Mathai-Quillen formalism and topological field theory

These lecture notes give an introductory account of an approach to cohomological field theory due to Atiyah and Jeffrey which is based on the construction of Gaussian shaped Thom forms by Mathai and Quillen. Topics covered are: an explanation of the Mathai-Quillen formalism for finite dimensional vector bundles; the definition of regularized Euler numbers of infinite dimensional vector bundles; interpretation of supersymmetric quantum mechanics as the regularized Euler number of loop space; the Atiyah-Jeffrey interpretation of Donaldson theory; the construction of topological gauge theories from infinite dimensional vector bundles over spaces of connections.