单摆运动的非线性求解

本文给出了单摆运动非线性微分方程的精确解,并得到了单摆运动周期与初始条件的关系。当初始条件满足一定关系时,单摆的运动状态并不由初始条件唯一确定,而有两种可能,因此状态空间出现分支点,这是非线性方程解的特征.     

基于MATLAB下对单摆实验中大摆角问题的讨论

借助MATLAB计算软件,研究无阻尼状态下单摆的大摆角运动,给出了任意摆角下单摆运动周期的精确解。同时利用MATLAB函数库中的ode45函数,求解出大摆角下的单摆的运动方程及其运动规律,为单摆实验中大摆角问题的讲解提供了较好的教学辅助手段。     

红外微位移传感器在测重力加速度实验中的应用

用单摆测量重力加速度是大学普通物理实验中的一个基础实验,测量的核心问题是如何精确的测量单摆周期,常有秒表法、光电探测器、霍耳位置传感器等方法.这些方法各有优缺点,但无法测出单摆在摆动过程中的运动情况.本文设计的基于红外微位移传感器的精密测量装置,不仅可以对单摆周期进行精确测     

有阻尼单摆的冲击波解

研究和分析有阻尼单摆的运动方程,应用近似法方程时发现存在冲击波解并精确求解.同时结合有阻尼单摆的相图分析冲击波解存在的物理意义.     

用线性插值法求单摆运动周期的近似解

利用线性插值的方法,提出了一个任意摆角条件下的单摆运动周期的近似公式.并利用Mathematica软件将该公式与精确解进行了比较,还与其他近似公式进行了对比.结果表明,该公式的近似程度相当好.     

无阻尼单摆运动微分方程的反正切分式变换精确解

无阻尼单摆运动微分方程是一种具有物理背景的非线性常微分方程,研究其精确解和解法是非线性科学中的一个重要内容.在F展开法的基础上,应用反正切分式变换正弦函数方法,并引入Riccati辅助方程,得到了4种无阻尼单摆方程精确解的结果.达到了丰富此类方程求解技巧和精确解的目的.总结得出此类方程应用反正切分式变换方法具有一定普适性的结论.     

单摆系统的振动研究

通过求解变张力弦振动微分方程的边值问题,给出摆线与摆球的质量比为任意值时单摆系统运动的一般解和本征频率满足的方程.利用该方程求得高精度的单摆系统周期数值解,特别是拟合出单摆系统作基频振动时一个范围大、精度高的周期近似公式.同时将理论与实验进行比较,结果二者相符.     

关于变摆长的单摆运动与相关的铅直运动的耦合

研究了一个变摆长单摆运动的例子,在平面极坐标系下给出了描述该运动的二阶微分方程组.采用微分方程高精度数值解法得到了随时间变化的摆角、摆长、摆长变化率以及运动轨迹的数值精确解.在小摆角近似下,采用迭代方法推导出摆角、摆角变化率的一级近似解析表达式和摆长、摆长变化率的二级近似解析表达式.由解析表达式得到的数值结果与数值精确解相比较,二者在前几个摆动周期内相吻合.     

非线性系统受迫振动的周期解

理论上采用近似法求解,并用数学软件作图,分析和讨论了单摆自由振动的非等时性以及非线性受迫振动周期解与线性受迫振动稳态解的重要差别．     

用单摆测重力加速度实验中单摆周期的测定

对用单摆测重力加速度实验中单摆周期的测定进行了研究,给出了一种基于电子秒表的自动测量单摆周期的可靠装置,改进了传统单摆周期测量的不足,提高了测量单摆周期的精度.     

Finite element analysis of AC loss in non-twisted Bi-2223 tape carrying AC transport current and/or exposed to DC or AC external magnetic field

AC losses in Bi-2223 superconducting tapes carrying AC transport current and/or exposed to DC or AC magnetic field are calculated with a numerical model based on the finite element method. Superconducting property is given by the E–J characteristic represented by a power law using equivalent conductivity. First, transport loss and magnetization loss are calculated numerically and compared with measured values. The calculated losses almost agree with the measured losses. Frequency dependencies of calculated and measured transport losses are compared with each other. Next, the influence of DC external magnetic field on the transport loss is studied. DC external magnetic field reduces n that is an exponent in the power law connecting resistivity and current density. The numerically calculated transport loss increases with increasing DC magnetic field. Finally, the total loss of superconducting tape carrying AC transport current in AC magnetic field is calculated. In the perpendicular magnetic field, the calculated total loss is lager than the sum of the transport loss and the magnetization loss, while they almost agree with each other in the parallel magnetic field.     

Thermophysical properties of stable and metastable liquid copper and nickel by molecular dynamics simulation

Molecular dynamics simulation combined with an embedded atom method (EAM) potential was applied to the calculation of the specific heat and the diffusion coefficient for superheated and undercooled liquid copper and nickel as functions of temperature. The system contains 108,000 atoms. The calculated results show that the enthalpy increases linearly with the rise of temperature. There are no breaks at their melting temperatures of 1356 and 1726 K. It is found that the calculated specific heats of Cu and Ni are 32.75 and 36.11 J/mol/K respectively. The calculated mean square displacements increase linearly with calculated time. The diffusion coefficients are exponentially dependent on temperature. Moreover, the calculated results are in good agreement with the reported experimental results for the specific heat and diffusion coefficient.     

在超重核区应用Viola-Seaborg公式研究α衰变寿命

在超重核区(Z≥104)使用文献[7—9]给出的3组参数应用Viola-Seaborg公式计算了α衰变寿命,所得结果与实验值进行比较,发现其结果与实验值相差较大。为此,利用最小二乘法分别在重核区和超重核区重新对参数进行了拟合,得到的计算结果与实验值相比符合得较理想,尤其是由超重核得到的参数的结果非常理想。     

Inelastic mean free path, surface excitation parameter, and differential surface excitation parameter in Au for 300-3000 eV electrons

An analytical approach for simultaneously determining an inelastic mean free path (IMFP), a surface excitation parameter (SEP) and a differential SEP (DSEP) with absolute units was applied for the analysis of absolutely measured reflection electron energy loss spectra for Au. The IMFP, SEP and DSEP in Au for 300-3000 eV electrons are successfully obtained. The obtained DSEPs show a reasonable agreement with those theoretically calculated. The present SEPs were compared with those calculated by several empirical equations, revealing that the present SEPs are close to those calculated using the Oswald's equation. The IMFPs for Au determined by the present analysis were compared with those calculated by the TPP-2M predictive equation, revealing that the present IMFPs are in fairly good agreement with those calculated by the TPP-2M equation. The results confirmed that the present approach is effective for experimentally determining the SEP, DSEP, and IMFP for electrons in solids.     

描述混合物固液相变的两个近似模型

 提出了描述混合物固液相变的两个近似模型：混合相模型和等效物质模型。通过对304钢的计算和比较表明，由两个模型计算得到的结果与直接利用304钢的材料参数计算得到的结果相符合。     

Ionization potential of atoms and multiply charged ions versus the nuclear charge

The terms of ions and atoms are calculated with a method based on the Bohr model. The ionization potentials of helium-like, lithium-like, and beryllium-like ions are calculated as functions of the nuclear charge and electron quantum numbers. The results calculated are in satisfactory agreement with experimental data. The accuracy of the method is found to rise with the nuclear charge of ions.     

质子与裂变核238U反应的理论计算

利用球型光学模型、耦合道理论、核内级联、激子模型、蒸发模型、带宽度涨落修正的Hauser-Feshbach模型,Bohr-Wheeler裂变理论,对入射能量从阈能到200 MeV的p+²³⁸U各种反应进行了计算,计算结果和实验符合较好.     

铁Hugoniot曲线的Ab initio计算

以ＧＧＡ－ＬＡＰＷ冷能计算为基础，应用经典统计理论计算了铁的Ｈｕｇｏｎｉｏｔ性质，包括：Ｐ－Ｖ曲线、Ｐ－Ｔ曲线、热容、Ｇｒｕｅｎｅｉｓｅｎ参数，计算结果基本上与实验符合。     

固氖高压物态方程的量子理论计算

 运用Hartree-Fock计算方法和原子团簇理论,研究了高压下面心立方晶体氖中的二体相互作用、三体相互作用对中心原子势能及冷能的贡献。结合零点振动能,计算得到了固氖在4~208 GPa压强范围内的等温物态方程。结果表明,在较高压强区域内,等温压缩线与高压实验数据符合得非常好;在压强超过100 GPa的区域内,计算得到的等温压缩线较目前已有的理论研究结果系统地改善并提高了3%~5%,精确地解释了固氖的高压实验数据。     

Analyzing Semicircular Groove Guide with the Conformal Mapping Technique

Semicircular groove guide is a kind of waveguide for millimeter waves. In this paper, a conformal mapping technique is used to analyze it. Several semicircular groove guides are calculated with the method. It is shown that their cutoff wavelength calculated by the method are very close to those calculated by the transverse resonance method.