基于Lissajous图技术的波长移相标定方法

波长移相干涉仪可应用于大口径光学元件的检测。研究了基于Lissajous图技术的波长移相标定方法,实现了干涉图间移相量的计算,解决了在不同干涉腔长下进行测试时移相量需控制成为一个特定值的问题。首先通过模拟仿真,验证了方法的正确性;然后编写程序对已知移相量的实际干涉图进行计算。结果表明,在干涉图对比度较好以及对计算的两点选择恰当的情况下,计算出的相对误差在4%范围内。     

液固反应微观-宏观关联模型及实验验证

当液一固反应为流体扩散控制时,以缩核模型为基础,得到了单颗粒消溶时粒径的变化规律,满足平方反比定律;在单颗粒消溶的基础上,建立了颗粒群消溶模型,得到了单颗粒微观反应模型和颗粒群宏观反应特征的关联关系.以不同种类的石灰石在不同温度和pH值下的消溶过程为例,对液固反应的微观-宏观关联模型进行了实验验证,实验和数学模型吻合较好.该关联模型对完善液固反应理论体系,实现宏观实验数据反推微观化学反应参数的测量技术具有重要意义.     

Singular Wave Solutions of Two Integrable Generalized KdV Equations

We present some singular wave solutions such as multi-peaked periodic waves, multi-peaked kink waves, multi-peaked peakons as well as kink-compactons, associated with singular curves of generalized KdV equation and modified KdV equation. When a trajectory intersects with the singular curve, it may be divided into segments. Different combinations of these segments may lead to different singular wave solutions, while at the intersection points, peaks on the waves can be observed.     

Wronskian Form Solutions for a Variable Coefficient Kadomtsev–Petviashvili Equation

Starting from a simple transformation, and with the aid of symbolic computation, we establish the relation- ship between the solution of a generalized variable coefficient Kadomtsev-Petviashvili （vKP） equation and the solution of a system of linear partial differential equations. According to this relation, we obtain Wronskian form solutions of the vKP equation, and further present N-soliton-like solutions for some degenerated forms of the vKP equation. Moreover, we also discuss the influences of arbitrary constants on the soliton and N-soliton solutions of the KPII equation.     

基于解析法的超导发电机磁场分析与结构优化

混合型高温超导发电机采用高温超导带材作励磁材料,结构上与传统电机有较大的不同,设计方法也不尽相同.本文基于傅里叶变换将超导发电机的励磁集中绕组等效为沿转子圆周正弦分布的激励源,建立了超导发电机磁场分析模型.对电机气隙磁场分布进行了求解,并分析了不同绕组张角时气隙磁密波形中的谐波含量.通过参数化分析,研究了不同环境屏、转子的尺寸对电机功率密度的影响.采用有限元法对磁场求解结果进行了验证,结果一致性较好.研究结果表明,励磁绕组张角会对电机气隙磁密波形产生影响,合理设置超导发电机环境屏及转子结构,可以提高超导发动机的功率密度.     

含相变微粒流体热对流启动的Galerkin解

采用Bubnov-Galerkin方法对有恒壁温条件下,两平板间夹有含相变颗粒流体的自然对流热启动瑞利数进行了近似解析求解,求出了临界瑞利数Racr和波频数kcr随相变物质浓度,以及在相变温度范围内随加热表面温度的解析关系表达式.从而,为实现该类功能性潜热流体的自然对流传热强化,及其优化控制蓄热过程有理论指导意义.     

Similarity Solutions for Generalized Variable Coefficients Zakharov-Kuznetsov Equation under Some Integrability Conditions

In this paper, the symmetry method has been carried over to the generalized variable coefficients Zakharov- Kuznetsov equation. The infinitesimal symmetries and the optimal system are deduced and from this optimal system seven basic fields are determined, and for every vector field in the optimal system the admissible forms of the coefficients are found and this also leads us to transform the given equation into partial differential equations in two variables. After using some referenced transformations the mentioned partial differential equations eventually reduce to ordinary differential equations. The search for solutions to those equations has yielded many exact solutions in most cases.     

均质球体在半圆形凹槽中的运动分析——一维方向可自由移动的半圆形凹槽的情形

用动力学的方法,建立均质球体与一维方向可自由移动的半圆形凹槽组成的系统的运动微分方程,进一步分析均质球体在半圆形凹槽内做无滑滚动的临界角,并求出均质球体大角度振动周期的精确公式和近似公式.     

晶体X射线衍射实验的数据分析模式

针对粉末X射线衍射谱分析软件CSM的特点,利用CSM软件附带的用户程序库功能,实现了固溶体的物相分析和固溶度的定量计算,扩展了CSM软件的使用范围,提高了物相分析的准确程度.     

The geometric phase of the quantum systems with slow but finite rate of the external time-dependent field

With the help of the time-dependent gauge transformation technique, we have studied the geometric phase of a spin-half particle in a rotating magnetic field. We have found that the slow but finite frequency of the rotating magnetic field will make the difference between the adiabatic geometric phase and the exact geometric phase. When the frequency is much smaller than the energy space and the adiabatic condition is perfectly guaranteed, the adiabatic approximation geometric phase is exactly consistent with the adiabatic geometric phase. A simple relation for the accuracy of the adiabatic approximation is given in terms of the changing rate of the frequency of the rotating magnetic field and the energy level space.