梯度表面能材料表面上液滴形状的数值模拟

本文建立了固体表面上静止液滴的势能方程,根据能量最小化原理,当系统总势能取得最小值时,液滴将处于平衡状态.采用有限元方法,将初始自由液面离散化,通过曲面上节点的虚拟位移,改变自由液面的拓扑结构,使系统总势能取得最小值,从而得到静止液滴的形状.并应用该方法对均质表面和梯度表面能材料表面上的液滴界面进行了数值模拟,得到了均质材料表面和梯度表面能材料表面上静止液滴的界面形状及分布.     

固体潮相关的地球表面形变和涨落

在月球和太阳的引力作用下,地球的固体表面也发生与海水表面类似的周期性涨落,这种现象称为固体潮.固体潮的形成原因与海潮相同,但其计算问题远比后者复杂.本文用开尔文地球模型和比较简单的方法计算固体潮相关的地球表面方程和涨落幅度,并进行相关问题的讨论.     

漂浮气泡形状的研究

用最小势能原理证明液面上漂浮的足够大气泡呈半球状.     

惯性的本质

本文系统地阐述了“惯性”概念的产生、发展，和当代物理学对此问题的认识。     

星球自转角速度的上限

许多星球都有自转运动,在随星球转动的参考系中,星球的各质点受到惯性离心力的作用,使其呈现扁旋转椭球形状.转动越快,惯性离心力越大,当转速大于某临界值时星球会破裂.本文从最小势能原理出发,严格计算星球自转角速度的上限.     

液滴发生器系统中流速及振荡频率的确定

 根据Rayleigh流体不稳定原理,确定了射流振荡波频率范围,分析了充电偏转过程,推导出了每滴液滴的充电量和受偏转电场偏转的电场力的大小。在压强为0.02,0.03,0.04,0.05,0.06 MPa下测量了喷射孔孔径分别为0.10,0.11,0.15 mm的射流初始速率,确定了最佳偏转振荡频率与射流初始速率和充电环长度的关系表达式。     

液滴发生器系统中流速及振荡频率的确定

根据Rayleigh流体不稳定原理,确定了射流振荡波频率范围,分析了充电偏转过程,推导出了每滴液滴的充电量和受偏转电场偏转的电场力的大小。在压强为0.02,0.03,0.04,0.05,0.06 MPa下测量了喷射孔孔径分别为0.10,0.11,0.15 mm的射流初始速率,确定了最佳偏转振荡频率与射流初始速率和充电环长度的关系表达式。     

在惯性系中求解落体偏东问题

在惯性系中从机械能守恒出发求解了落体偏东问题并计算了下落过程中质点的引力势能与动能的转化.     

引潮力对月球及人造卫星轨道平面的影响

讨论了引潮力对月球及人造卫星轨道平面的影响,计算结果与观测值的相对误差为3.8%.     

阿基米德原理在非惯性系中同样成立

阿基米德原理是在惯性系中由实验总结出来的.本文经过理论推导,得出在非惯性系中同样成立.     

探索惯性系

针对牛顿力学框架的两大疑难,结合朗格惯性系的定义,从理论上分析了星球参考系与质心参考系,并指出了在什么条件下它们可以充当惯性系.     

"惯性系"考(续)

3 星球参考系不是惯性系 3.1 星球参考系 以星球的中心(也是它的质心)为原点,建一相对于局域惯性系的坐标架O′-x′y′z′平动的坐标架,本文称此坐标架为星球参考系.星球相对于此坐标架可以转动.     

球状物体作微形变时弹性势能的研究

研究一个弹性球在保持体积不变的前提下,形变为长旋转椭球时的弹性势能.首先通过最小势能原理和物理条件确定位移函数,然后根据弹性势能密度-应变-位移三者之间的关系,通过积分计算得到弹性势能,并且进行了有益的讨论.     

Gravitational Perturbations on Local Experiments in a Satellite: The Dragging of Inertial Frame in the HYPER Project

We consider a nearly free falling Earth satellite where atomic wave interferometers are tied to a telescope pointing towards a faraway star. They measure the acceleration and the rotation relatively to the local inertial frame. We calculate the rotation of the telescope due to the aberrations and the deflection of the light in the gravitational field of the Earth. We show that the deflection due to the quadrupolar momentum of the gravity is not negligible if one wants to observe the Lense-Thirring effect of the Earth. We consider some perturbation to the ideal device and we discuss the orders of magnitude of the phase shifts due to the residual tidal gravitational field in the satellite and we exhibit the terms which must be taken into account to calculate and interpret the full signal. Within the framework of a geometric model, we calculate the various periodic components of the signal which must be analyzed to detect the Lense-Thirring effect. We discuss the results which support a reasonable optimism. As a conclusion we put forward the necessity of a more complete, realistic and powerful model in order to obtain a final conclusion on the theoretical feasibility of the experiment as far as the observation of the Lense-Thirring effect is involved.     

双层耦合Lengel-Epstein模型中的超点阵斑图

用双层耦合的Lengel-Epstein模型, 研究了两个子系统的图灵模对斑图的影响,发现其波数比在斑图的形成和选择过程中起着重要作用.当波数比为1时,双层系统未能发生耦合,只能出现条纹和六边形斑图;当波数比处于1-√17 的范围时,两子系统发生耦合,图灵模之间发生共振相互作用,得到种类丰富的超点阵斑图,包括暗点、点-棒和复杂超六边、Ⅰ-型和Ⅱ-型白眼、类蜂窝和环状超六边等斑图;当波数比大于√17 , 系统选择的斑图类型不再变化,均为环状超六边斑图.数值模拟得到的条纹、六边形、超六边点阵、Ⅱ-型白眼斑图和类蜂窝斑图均已在介质阻挡放电系统实验中观察到. 另外,还得到了超点阵斑图的波数随两个扩散系数乘积D_uD_v的变化曲线,发现其随的D_uD_v增大而减小. 关键词： 耦合系统 超点阵 波数比 数值模拟     

弹簧的质心在哪里

讨论质量不可忽略的静止弹簧的质量分布和质心位置问题.     

从容器内液体中取出任意形状物体的最小功

由功能原理,导出了从容器内液体中取出任意形状物体所做的最小功公式.     

Orientational dependence of the potential of mean force for a discotic liquid crystal near a substrate

In this work we calculate the potential of mean force for a discotic liquid crystal (DLC) confined in a slab geometry. We have set the reaction coordinate as the distance between a DLC test particle with a fixed orientation and a wall with face-on anchoring. Five different orientations of the DLC test particle are explored, which correspond to parallel and perpendicular orientations with regard to the anchoring promoted by the walls, and three intermediate orientations between the parallel and perpendicular configurations. The potential of mean force reflects the strong effect of the system's anisotropy: particles with the wrong orientation are energetically penalised whilst the particles with the correct orientation are favoured.