地球中光滑隧道内自由质点的运动

本文考虑到地球自转的影响，应用引力场强的概念，导出了质点在地球中任意一条光滑隧道内运动的微分方程．同时指出：在某些特殊隧道内的自由质点，其运动是简谐振动，但对于其它隧道来说，质点从一端进入后，或者作简谐振动而以隧道中某点为返转点，或者从另一端抛出而不再返回．     

在极坐标下质点的轨道微分方程

本文根据直线来与曲线（ｃ）间的交角公式导出ｃｔｇ＝ｒ＇（θ）／ｒ（θ）的形式，由此微分方程可得到 ｒ（θ） 的积分式，便可直接求得极坐标形式的质点运动的轨 道方程．此法给解决质点运动轨迹的问题带来方便．     

均匀重力场中质点在光滑圆柱面上的挠曲线运动

本文研究了均匀重力场中的质点在光滑圆柱面上的挠曲线运动,用牛顿定律或拉格朗日方程推导质点的运动微分方程,然后解得质点脱离圆柱面的位置满足的方程以及脱离前的运动时间,最后导出用椭圆积分表示的挠曲线运动轨迹的参数解析表达式。     

可自由平动光滑凹槽中质点运动的数值分析

运用保守力系的拉格朗日方程,对可自由移动光滑凹槽中质点以及凹槽系统的运动过程建立了微分方程.通过数值积分的方法求解该方程,研究了在凹槽初速度为零和不为零两种条件下质点的运动规律.结果表明,在两种不同初始条件下,质点的运动规律存在区别.     

用等效质点法求解刚体的平面运动

本文利用等效质点的方法，将刚体的平面运动化为质点的运动，在很大程度上简化了有关问题的求解。     

幂律引力作用下从拱点抛出质点的运动轨道

用把方程的解设为余弦函数多项式的一种直接方法,求解了受幂律引力作用的质点一类非线性轨道微分方程,从而得出在幂律引力作用下从拱点抛出质点的运动轨道是正弦螺线。     

转动参考系中质点运动的动力学分析及数值模拟

转动参考系中质点在惯性力作用下的运动是力学教学的难点，本文分别在匀角速转动参考系、变角速转动参考系和惯性系下对该问题的动力学进行分析，得出质点的动力学微分方程；并基于欧拉法，利用Matlab软件对该问题的动力学微分方程进行了数值计算求解和模拟，直观地画出了质点的运动轨迹，基于程序数据对该问题的运动规律进行了较为深入的分析。将研究内容融入教学中，提高了教学效果，培养了学生解决实际问题的能力，对海洋科学、大气科学等相关的专业的后续专业课学习产生了积极的影响。     

从陈子定理看经典力学

从陈子定理可以演绎出描写质点运动的各种表示方式，从陈子定理可以推导出质点动力学的基本定理，包括牛顿运动三定律，动能定理，质心运动定理。     

论恒力作用下质点的相对论运动

在相对论情况下，讨论了受恒力作用的质点的运动规律。     

竖直面内光滑任意曲线单侧约束解除点的一般公式及其应用

利用直角坐标系中的质点运动微分方程和机械能守恒定律,推导出质点沿竖直面内任意的光滑曲线运动过程中单侧约束解除点的一般公式,并用它研究了约束曲线是二次曲线、立方抛物线、正弦曲线、双曲正弦线和普通摆线的情况.     

Maximal neutrino mixing from an attractive infrared fixed point

In the Standard Model (and MSSM), renormalization effects on neutrino mixing are generally very small and the attractive fixed points are at vanishing neutrino mixing. However for multi-Higgs extensions of the Standard Model, renormalization effects on neutrino mixing can be large and nontrivial fixed points are possible. Here we examine a simple two-Higgs model. For two flavors, maximal mixing is an attractive infrared fixed point. For three flavors, the neutrino mass matrix evolves towards large off-diagonal elements at low energies. The experimentally suggested bimaximal neutrino mixing pattern is one possible attractive infrared fixed point.     

辐射压对非同步转动双星系统洛希势函数的影响

辐射压是影响大质量恒星结构和演化不可忽视的重要物理因素. 根据辐射压对非同步转动的洛希势函数的影响, 数值计算了洛希瓣的大小和3个拉格朗日点的位置和相应的势函数, 并与同步转动的洛希模型计算的结果做了对比. 结果发现: 辐射压可以整体地减小大质量恒星表面的重力加速度, 而转动离心力能最大减少赤道附近的重力加速度. 辐射压和非同步转动均可以明显地改变洛希瓣的大小和3个拉格朗日点的位置和势函数, 影响双星系统物质交换的时间. 因此, 研究辐射压, 非同步转动等物理因素对大质量双星系统洛希势函数的影响, 对密近双星的演化具有重要意义. 关键词： 恒星结构与演化 转动 辐射压     

New methods in potential theory

A theory of equigravitating bodies by which external force fields of volumetric axially symmetric figures can be represented by unitary integrals is developed. This theory is being developed in three directions. The first is connected with the proof of the existence of equigravitating line segments. Such line segments can have both real and imaginary distributions of density; however, the mass and external potential remain real values. The ends of line segments coincide with special points (these are cusp points on the surfaces or special points of the analytical continuation of the external potential inside the body). At two special points, the body has only one line equigravitating segment, otherwise the line segments are compound or form equigravitating “skeletons.” At the isolated special points, external gravitational fields can be presented by a set of line segments and mass points. The second direction is based on a representation of the external gravitational field of volumetric axially symmetric figures with an equator plane by means of potentials of flat round disks. Such disks are obtained on the line segments with symmetric density distributions. The return is always true: for homogeneous or any nonuniform round disk, it is possible to find an equigravitating line segment. It manages to construct chains of “spheroid-disk-line segment” equigravitating bodies. The third direction of this theory is connected with the development and expansion on the scope of the method of confocal transformations. This method is modified and applied not only to continuous homogeneous ellipsoids, but also to non-uniform stratified ellipsoids with a stratification of the general type, as well as to homogeneous and nonuniform shells. Any elementary or thick ellipsoidal shells (and continuous nonuniform stratified ellipsoids) connected by special confocal transformations equigravitate each other.     

基于光纤光栅传感的管道滑坡监测方法研究

针对铺设在滑坡体内的管道,提出了基于光纤光栅传感的管道滑坡监测方法。阐述了已知管道上三点应力求最大应力的方法。采用温度自补偿式光纤光栅应变传感器监测管体应力,对传感器测量的5.12汶川地震后管体应力数据进行分析。结果表明:地震对滑坡有显著影响,发生了浅层滑动面的较大位移;管体的应力都有显著增长,但总应力水平还低于预警阈值,尚处于安全状态。     

Three particles on a ring

We study the ergodic properties of three classical particles of unequal mass moving on a ring and colliding like hard points.Although it is generally believed that this system is ergodic, we show that extensive numerical calculations do not support this belief.This may be connected with our discovery that for vanishing total momentum, any initial state with one particle at rest is periodic, independent of the mass values.The analogous periodicity for two unequal mass particles bouncing in a one-dimensional box can be understood on the basis of a remarkable property of a billiard in the form of a rectangular triangle.     

Escape dynamics in collinear atomic-like three mass point systems

The present paper studies the escape mechanism in collinear three point mass systems with small-range-repulsive/large-range-attractive pairwise interaction. Specifically, we focus on the asymptotic behaviour for systems with non-negative total energy.On the zero energy level set there are two distinct asymptotic states, called 1+1+1escape configurations, where all the three separations infinitely increase as t→∞. We show that 1+1+1 escapes are improbable by proving that the set of initial conditions leading to such asymptotic configurations has zero Lebesgue measure. When the outer mass points are of the same kind we deduce the existence of a heteroclinic orbit connecting the 1+1+1 escape configurations. We further prove that this orbit is stable under parameter perturbation.In the positive energies’ case, we show that the set of initial conditions leading to 1+1+1 escape configurations has positive Lebesgue measure.     

Distribution coefficient algorithm for small mass nodes in material point method

When using the time explicit material point method to simulate interaction of materials accompanied by large deformations and fragmentation, one often encounters a numerical instability caused by small node mass, because acceleration on a mesh node is obtained by dividing the total force on the node by the mass of the node. When the material points are in the far sides of the cells containing the node, typically happening near material interfaces, the node mass can be very small leading to artificially large acceleration and then numerical instability. For the case of small material deformations, this instability is typically avoided by placing the material points away from cell boundaries. For cases with large deformations, with the exception of initial conditions, there is no control on locations of the material points. The instability caused by small mass nodes is often encountered. To avoid this instability tiny time steps are usually required in a numerical calculation.     

Chaos in the one-dimensional gravitational three-body problem

We have investigated the appearance of chaos in the one-dimensional Newtonian gravitational three-body system (three masses on a line with -1/r pairwise potential). In the center of mass coordinates this system has two degrees of freedom and can be conveniently studied using Poincare sections. We have concentrated in particular on how the behavior changes when the relative masses of the three bodies change. We consider only the physically more interesting case of negative total energy. For two mass choices we have calculated 18 000 full orbits (with initial states on a 100x180 lattice on the Poincare section) and obtained dwell time distributions. For 105 mass choices we have calculated Poincare maps for 10x18 starting points. Our results show that the Poincare section (and hence the phase space) divides into three well defined regions with orbits of different characteristics: (1) There is a region of fast scattering, with a minimum of pairwise collisions. This region consists of 'scallops' bordering the E=0 line, within a scallop the orbits vary smoothly. The number of the scallops increases as the mass of the central particle decreases. (2) In the chaotic scattering region the interaction times are longer, and both the interaction time and the final state depend sensitively on the starting point on the Poincare section. For both (1) and (2) the initial and final states consist of a binary + single particle. (3) The third region consists of quasiperiodic orbits where the three masses are bound together forever. At the center of the quasiperiodic region there is a periodic orbit discovered (numerically) by Schubart in 1956. The stability of the Schubart orbit turns out to correlate strongly with the global behavior.     

Mass measurement on the rp-process waiting point 72Kr

The mass of one of the three major waiting points in the astrophysical rp process 72Kr was measured for the first time with the Penning trap mass spectrometer ISOLTRAP. The measurement yielded a relative mass uncertainty of deltam/m=1.2x10(-7) (deltam=8 keV). (73,74)Kr, also needed for astrophysical calculations, were measured with more than 1 order of magnitude improved accuracy. We use the ISOLTRAP masses of 72-74Kr to reanalyze the role of 72Kr (T(1/2)=17.2 s) in the rp process during x-ray bursts and conclude that 72Kr is a strong waiting point delaying the burst duration with at least 80% of its beta-decay half-life.