诸葛亮巧借东风—浅析伽利略航天轨道计划中的引力助推效应

本文扼要介绍了伽利略航天轨道计划，并以浅显的力学原理计算出伽利略探测器从地球飞向木星所需的初始速度。文中详细分析了伽利略探测器两次近飞地球的过程，揭示了引力助推效应在星际飞行中节省能量和控制航向的重大意义。     

Quasi Lp-Intersection Bodies

The purpose of this paper is to generalize the notion of intersection bodies to that of quasi Lp-intersection bodies. The Lp-analogs of the Busemann intersection inequality and the Brunn- Minkowski inequality for the quasi Lp-intersection bodies are obtained. The Aleksandrov Fenchel inequality for the mixed quasi Lp-intersection bodies is also established.     

Comparison Between the Full Quantum Dynamics and the Quantum—Semiclassical Models to Many—Particle Systems

We consider a simple collinear collision of a “classical“ particle with a harmonic oscillator within quantumsemiclassical model and full quantum dynamics model,in which the latter is solved analytically in squeezed state and exact diagonalization methods and acts as the exact solution of such a system.A comparison of these two models for different mass ratios between the “classical“ particle and the quantum particle is done,which gives a criterion when using the quantum-semiclassical model.     

Hartree-Fock解多重性的研究

本文利用推广的三能级可解模型对Hartree-Fock(HF)单粒位的自洽求解做了详细考察,指出求解过程中出现的多解性应当引起注意.此外,本文还讨论了HF解在力参数的某些区域发生突变的原因,它的稳定性以及它和两体相互作用强度的关系.     

Equilibrium Properties of Hard Sphere Fluid in Confined Geometries：a Density Functional Theory Study

One component hard-sphere fluid confined in two planar hard wllas is studied by means of density functional theroy with Rosenfeld functional and molecular dynamics simulation,the Validity of the Rosenfeld functional is examined,Chemical potential,grand potential and free energy as functions of the wall separation are obtained.     

Low—Lying States of the A^＋B^—A^＋B^— Coulomb systems in Two—Dimensional Quantum Dots

The features of the low-lying spectra of four-body A B-A B- systems have been dedudced based on symmetry,Using the method of few-body physics,we calculate the energy spectra of A B-A B- systems in a harmonic quantum dot.We find tha t the biexcition in a two-dimensional quantum dot may have other bound excited states and the quantum mechanical symmetry plays a crucial role in determining the energy levels and structures of the low-lying the quantum mechanical symmetry plays a crucial role in determining the energy levels and structures of the low-lying states.     

三维斯托克斯流动在扁球坐标系中的基本解及其应用

通过把Lamb基本解中的调和函数转换为扁球坐标系下的表达式,这项研究成功地得到了一个新的Stokes流动三维基本解.此基本解可用于解决任意多个扁椭球处于任意位置和方向时的流动问题.应用最小二乘法,三维流动问题中常遇到的收敛性差的困难在此得以完全克服.结果表明该方法具有准确度高,收敛性好和计算量小的特点.由于扁球可用于模拟从圆盘到圆球的多种物体形状,此基本解被用于系统地分析了各种几何因素对两个扁球所受力和力矩的影响.为了显示此方法的通用性,该基本解还用于研究了两例三个扁球的问题.     

多体机械手的一般动力学模型

本文建立了多体机械手的一般动力学方程.设多体系统是由任意数目的刚体组成的树形拓扑结构,并认为铰是柱铰链,允许具有相对转动和滑动.考虑到实际问题中摩擦力的影响,采用Newton-Euler方法,建立了运动方程.进一步通过构造分配矩阵,将动力学方程分离,得到了一组实用的力方程和运动方程.     

Analytical Structure Matching and Very Precise Approach to the Coulombic Quantum Three—Body Problem

A powerful approach to solve the Coulombic quantium three-body problem is proposed.The approach is expeonentially convergent and more efficient than the hyperspherical coordinate method and the correlaion-function hyperspherical harmonic method.This approach is numerically competitive with the variational methods.Such as that using the Hylleraas-type basis functions,Numerical comparisons are made to demonstrate the efficiency of this approach,by calculating the nonrelativistic and infinite-nuclear-mass limit of the ground state energy of the helium atom.The exponential convergency of this approach is due to the full matching between the analytical structure of the basis functions that are used in thuis paper and the true wavefunction.This full matching was not reached by most other methods.For example,the variational method using the Hylleraas-type basis does not reflects the logarithmic singularity of the true wavefunction at the origin as predicted by Bartlett and Fock.Two important approaches are proposed in this work to reach this full matching:the coordinate transfomation method and the asymptotic series method.Besides these,this work makes use of the least square method to substitute complicated numerical integrations in solving the Schroedinger equation without much loss of accuracy,which is routinely used by people to fit a theoretical curve with discrete experimental data,but here is used to simplify the computation.