中性粒子在Ioffe阱中的经典运动方程的Floquet解

研究中性粒子在Ioffe阱中近原点区域的囚禁时,阱中的磁场可以呈现出一种简明的形式.磁矩μ反平行于磁场的中性粒子在阱中与磁场发生相互作用,借助相互作用势,可以获得粒子在阱中的经典运动方程.在一定的条件下,采用迭代近似的目的,将方程演化为马丢方程的形式,利用传统的WKBJ目的可实现方程的近似求解.研究阱中中性粒子的囚禁问题时,感兴趣的是马丢方程的Floquet解,即周期为π,2π的全周期和半周期解,欲获得这种周期解,马丢方程中的参数λ和q必须满足一定的关系,为此必须选择阱的特定参数和粒子的特定初始条件,对这一问题进行了探索性的研究.     

强流环形电子束在同轴永磁Halbach结构磁路中传输的初步分析

利用有限元程序SUPERFISH计算求解了同轴永磁Halbach结构磁路的磁场,并推导出该磁场位形磁感应强度各分量的近似表达式.利用流体模型分析了作用在电子束上的力并导出了改进马丢方程形式的径向力平衡方程,给出了平衡条件;利用2.5维全电磁粒子模拟程序研究了强流环形电子柬在该周期系统中传输的物理过程.计算得出强流相对论电子束的稳定传输与电子束电流,电子束厚度,磁场强度,电子束入射角度等因素有关.分析认为利用同轴永磁Halbach结构磁路导引数KA的环形电子束,并使之稳定传输是可能的.同时该磁场聚焦形式也为Ubitron中的束一波相互作用提供了一个作用机制.     

强流环形电子束在同轴永磁Halbach结构磁路中传输的初步分析

利用有限元程序SUPERFISH计算求解了同轴永磁Halbach结构磁路的磁场, 并推导出该磁场位形磁感应强度各分量的近似表达式. 利用流体模型分析了作用在电子束上的力并导出了改进马丢方程形式的径向力平衡方程, 给出了平衡条件; 利用2.5维全电磁粒子模拟程序研究了强流环形电子束在该周期系统中传输的物理过程. 计算得出强流相对论电子束的稳定传输与电子束电流, 电子束厚度, 磁场强度, 电子束入射角度等因素有关. 分析认为利用同轴永磁Halbach结构磁路导引数KA的环形电子束, 并使之稳定传输是可能的. 同时该磁场聚焦形式也为Ubitron中的束--波相互作用提供了一个作用机制.     

紧凑型反应堆中的单粒子动力学

针对紧凑型聚变反应堆独特的磁势阱结构, 使用蒙特卡罗方法研究单个高能带电粒子的约束动力学行为。考虑到磁场位型的局域平坦性, 在足够小的计算区域或足够短的时间内, 带电粒子基本上在一个常数磁场中的运动。基于此, 给出精确保证能量守恒的粒子运动方程逐点解析解, 该计算方案具有长时间追踪的能力。模拟结果表明: 对于初始位置和速度方向随机分布的具有1千电子伏能量的高能氘粒子, 大约有7%的概率能够约束至10 ms量级。由于粒子运动方程的求解过程不依赖于具体的磁场位型, 所以它可以方便地应用到具有任意位型的磁约束装置中。     

相对运动、集体振动、单粒子激发相互耦合系统输运过程的理论描述

考虑一个具有相对运动、内禀激发(包括集体振动、单粒子激发)相互耦合系统,在对相对运动做经典近似的条件下,并对内禀自由度采用与时间有关的投影算符方法,可以得到相对运动、集体振动及单粒子激发的耦合方程的一般理论形式。在一级玻恩近似和声子单粒子相互作用矩阵元的无规位相近似下,并忽略相对运动与声子单粒子之间相互作用高次项(只考虑到一次项),我们得到比较简单便于进行数值计算的耦合方程。这个理论适用于描述重离子深度非弹性散射,核裂变等核反应输运过程。     

介绍几种粒子阱的量子及经典理论

介绍了几种粒子阱的量子理论，并提出一种经典处理方法来解释粒子被磁场及激光束的囚禁     

一维均匀势场中含时薛定谔方程的求解

本文详细讨论了一维均匀势场中含时薛定谔方程的求解.求解的思想是以均匀势场中经典粒子的运动作为参考，从经典粒子的运动轨迹出发，构建出量子情形下描述粒子运动的高斯波包形式的演化波函数，进而借助含时薛定谔方程确定波函数的具体形式.在上述思想指导下，推导得出了坐标表象和动量表象下均匀势场内一维粒子的传播子函数.同时，作为比较，狄拉克态矢量符号提供了另一种得到上述传播子函数的途径.     

光阱中布朗粒子动力学分析

通过对光阱中的布朗粒子进行动力学方程求解,由解的结果分析得到观测系统的性能要求．结果表明：光阱中布朗颗粒服从Boltzmann分布;对其运动的观测需要纳米量级的空间分辨率和毫秒量级的时间分辨率．     

解析几何法在磁场边界类问题中的应用

带电粒子在磁场中的运动常常以压卷题的形式出现在各地模拟卷和高考卷中．这类命题综合性强,难度较大,要求学生能灵活地把数学思想方法与物理模型相互渗透．而“应用数学处理物理问题的能力”正是《考试说明》提出的“五种能力”之一．分析近三年的磁场类命题,可以发现“求磁场分布区域”或“求粒子运动区域”出现的频率较高,它们的核心就是“求磁场中的瞌线方程”,而求曲线方程正是解析几何的基本问题之一,因此我们完全可以用数学方法来探求．     

非薛定谔方程法估算重力场中的粒子能级

求解重力(线性势)场中的粒子能级时，若用薛定谔方程求解，过程十分繁琐，且仍得不到精确的初等函数式结果．本文避开繁琐的求解，运用几种简单易行的近似方法估算各能级的大小，结果较为成功。     

A study on the evaluation of usefulness depending on the image reconstruction method in bone SPECT scan

The recent advances in image-processing techniques have led to the development of many methods to reduce the scan time without degrading the image quality. In particular, tomography has improved image reconstruction methods with the concomitant improvement of high-quality images. In this study, PRECEDENCE 16 was used to reconstruct images using the filtered back projection method, which is generally used, and the Astonish method and three-dimensional ordered-subsets expectation maximization method, which are based on repetition techniques. In qualitative and quantitative analysis of the reconstructed images, a comparison was made between images with different acquisition times and between images with the same acquisition time, which aimed at determining the optimal method for reconstructing high-quality images. A blind test for qualitative analysis confirmed almost no difference in image quality depending on the image acquisition time. Furthermore, in quantitative analysis, there was no significant difference in image quality depending on the image acquisition time. On the other hand, the results of the analysis in the image reconstruction method with the same acquisition time demonstrated a significant difference. The images reconstructed by the Astonish method, which uses a repetition technique, are believed to be excellent because they have high resolution and provide clinical diagnostic information. This study confirmed that the reconstruction method with a repetition technique could be used to improve image quality and reduce the scan time, despite not being in general use until recently due to the lengthy time needed for image reconstruction and lack of storage space.     

固体材料低温比热测量技术综述

材料低温比热测量对新材料研究和应用具有重要意义,低温比热测量是低温物理研究领域最活跃的研究方向之一。对低温比热测量研究历史作了简单的介绍,对各种低温比热测量方法的原理、应用、发展进行了较全面的综述分析,对超低温、强磁场、放射性样品等特殊情况下比热测量作了讨论。     

光纤化学传感同步吸收-荧光法的建立

建立一种光纤化学传感同步测定吸收光谱和荧光光谱的新方法。自制同步吸收-荧光比色皿,结合光纤化学传感技术,建立同步吸收-荧光光谱法检测仪器,分别测定罗丹明B,维生素B₂,维生素B₆等溶液的同步吸收-荧光光谱,且与传统的紫外-可见吸光光度法和荧光法进行对比。同步吸收-荧光光谱法测得罗丹明B,维生素B₂,维生素B₆与传统吸光光度法和荧光光谱法检测的吸收光谱图和荧光光谱的图谱大体一致。最大荧光强度波长与传统的荧光方法比较准确度高,但最大吸收波长略有偏差。同步吸收-荧光光谱法等同于同步测定荧光物质的吸收光谱和荧光光谱,实现二光谱合二为一,测定最大发射波长时准确度高,但最大吸收波长略有偏差,值得深一步研究。     

Explicit multi-symplectic method for the Zakharov—Kuznetsov equation

We propose an explicit multi-symplectic method to solve the two-dimensional Zakharov-Kuznetsov equation. The method combines the multi-symplectic Fourier pseudospectral method for spatial discretization and the Euler method for temporal discretization. It is verified that the proposed method has corresponding discrete multi-symplectic conservation laws. Numerical simulations indicate that the proposed scheme is characterized by excellent conservation.     

Optimization of the algorithms for estimating the ultrasonic attenuation along the propagation path

In this study, we perform statistical analysis on two methods used to estimate the total ultrasound attenuation along the propagation path from the surface of the transducer to a region of interest at a particular depth; namely, the spectral-fit method and the multiple-filter method. We derive mathematical equations for the bias and variance in the attenuation estimates as a function of region of interest (ROI) size, imaging system bandwidth, and number of independent Gaussian filters (for the multiple filter method). We use numerical simulations to validate the mathematical equations and compare the two algorithms. The results show that the variance in the total attenuation coefficient estimates obtained with the two methods are comparable, and that the estimates are unbiased. For the multiple filter method, the optimal number of Gaussian filters is two.     

Some of the factors involved in the Sarvazyan method for recording ultrasound field distributions with special reference to the application of ultrasound in physiotherapy

The mapping of ultrasound fields using the dye paper method is described. The mode of action by which the dye concentration is increased has been investigated. Microbubbles on the paper surface and microstreaming of dye solution seem to be essential features of the mapping method. The streaming is thought to inhibit the formation of a dye depletion layer near the paper to an extent dependent on local sound intensity A linear relation between streaming velocity and intensity is derived.     

RC串联电路相移测量方法的研究

利用电压法、李萨茹图形法和双轨迹法分别测量了RC串联电路的相移,并将实验值与理论值进行了比较。研究表明,在所选择的频率波段内,这三种方法测量的实验值与理论值符合的很好,具有高精度、测量装置简单、操作方便等优点。通过对以上三种测量方法的研究,能够让学生从直观上更深入地理解对RC串联电路的特性。     

Explicit Multi-Symplectic Splitting Methods for the Nonlinear Dirac Equation

In this paper, we propose two new explicit multi-symplectic splitting methods for the nonlinear Dirac (NLD) equation. Based on its multi-symplectic formulation, the NLD equation is split into one linear multi-symplectic system and one nonlinear infinite Hamiltonian system. Then multi-symplectic Fourier pseudospectral method and multi-symplectic Preissmann scheme are employed to discretize the linear subproblem, respectively. And the nonlinear subsystem is solved by a symplectic scheme. Finally, a composition method is applied to obtain the final schemes for the NLD equation. We find that the two proposed schemes preserve the total symplecticity and can be solved explicitly. Numerical experiments are presented to show the effectiveness of the proposed methods.     

约束系统量子化中Dirac方法与Faddeev-Jackiw方法的等价性

对约束系统量子化中Dirac方法和 Faddeev-Jackiw方法进行了讨论，并对它们的运动方程、正则量子化的等价性进行证明.找出了两种方法中约束的对应关系. 关键词： Faddeev-Jackiw方法 Dirac方法 约束系统 正则量子化