一题多解在力学教学中的应用研究

结合实例 ,讨论了一题多解在力学教学中的两种应用 .同一问题用不同的观点去分析 ,得出相同的结果 ;一个基本问题衍生出一系列不同的问题 ,用类似的方法求解 .教学实践证明 ,一题多解既可以加深学生对力学理论体系的理解 ,又可以开阔思路 ,增强解决实际问题的能力 .     

势能函数与刚体的平衡和稳定

物体处在保守力场中的某个位置而具有的能量称为势能．势能存在的条件是物体间存在相互作用的保守力，其性质由保守力而定，数值随状态而变．势能属于整个系统．主要探讨了如何应用势能函数和势能曲线以及势能函数的微分来判断刚体是否处于平衡和平衡的稳定性．     

UO分子结构与势能函数及基态分子热力学性质

在U的相对论有效原子实势近似和O原子6 311G 全电子基函数下,用密度泛函B3LYP方法计算得到UO分子的结构与势能函数、力常数与光谱数据.同时计算得到UO基态X7∑分子在298K时的标准生成热力学函数ΔfH0、ΔS0和ΔfG0,分别为490.432kJ/mol,106.204J/mol·K和458.768kJ/mol.     

H与CF3O2自由基反应的理论研究

用从头算(ab initio)方法和密度泛函理论(DFT)对H与CF3O2自由基的反应进行了研究，在HF／6-31G。和B3LYP／6-31G基组水平上，对该反应过程中可能出现的中间体和过渡态的构型及能量进行了优化，并分析了反应过程中生成的产物，对各过渡态，利用内禀反应坐标IRC来进行验证，在B3LYP／6-31G构型优化的基础上，用B3LYP／6-311G和B3LYP／6-311 G计算了反应过程中各物种的总能量和相对能量，根据相对能量绘制的势能剖面图直观地反映了H CF3O2的反应机理，由势能面得出，反应生成CF3O和OH的历程最容易发生，这与实验事实是一致的.     

直链淀粉结构的分子动力学模拟

为了研究直链淀粉的结构，构建并优化了200个单体组成的直链淀粉模型．在DreidingⅡ力场、热力学温度为300K条件下对直链淀粉进行lns分子动力学模拟计算．分析了直链淀粉分子力学优化的结构、1 ns时的结构以及势能最低时的结构，其结果将有助于对直链淀粉结构功能的进一步研究．     

势能为什么是一个物体系所共有的?

一些教材虽然强调势能是物体系的，但一般说来未能深入阐明这一认识的依据。为此，文章以重力势能为例引发讨论。鉴于某一个力做功与参照系选择有关，指出保守力的做功应强调是一对作用力和反作用力做功之和保持不变，与参照系选择无关。并以这个作功之和的负值来定义势能的增量，以此来说明势能是属于物体系所共有的。     

一个非等谱非线性Schr(o)dinger方程的解及其无穷守恒律

该文用Hirota方法求出一个非等谱非线性Schr(o)dinger方程的类孤子解,并给出其无穷守恒律;通过变换得到相应非等谱散焦非线性Schr(o)dingger方程的解.     

Wave Damping and Refraction-Diffraction Due to Variable Depth Porous Bottom

The refraction-diffraction of surface waves due to porous variable depth has been the subject of many investigations. In the present study, we extend the boundary-value problem of impermeable varying topography to that of a variable depth porous seabed, which is the situation most likely to be encountered in practical problems of coastal engineering. A wave-induced fluid motion is applied to the porous bottom, while the well-known linear potential theory is applied to the free-water above the bottom. Eigenfunction expansions are employed to derive the matching condition and the so-caUed modified dispersion relation. As a result of the porous bottom, the wavenumber becomes a complex value, of which the real part represents the spatial periodicity while the imaginary part refers to the energy dissipation. The characteristics of water waves over a porous bottom are studied in detail. By neglecting the non-propagating modes which only have a local effect and damp exponentially with distance, we derive a mathematical model to represent the characteristics of both the wave refraction-diffraction and wave-damping. The developed model is applied to the damping problem of waves over submerged porous breakwaters.     

Velocity Distribution of Slurry in Horizontal Pipe When Solid Particles Sliding

Based on the laws of momentum conservation and impulse in accelerating process, the distribution on speed of ununiform slurry flow in a horizontal pipe was studied. According to the momentum change of solid particles and conveying liquid of slurry flow during accelerating, and some effect factors, the relationship between the speed of solid particles and the speed of conveying liquid was obtained.When dealing with the friction between sliding solid particles and pipe, it is pivotal to reasonably distribute component of friction to each solid particle. The friction coefficient between solid particles was obtained by forces analysis and theoretic calculation, and can be used to calculate the friction force on every solid particle. The effect of friction on speed of ever), solid particle was investigated through the impulse law. The result is more accurate than that by using uniform friction on solid particles. It is completely new method to use above theory to get solid particles speed distribution, conveying liquid speed distribution and slurry speed distribution.     

物流园区辐射范围的界定——基于GIS通达性分析的改进势能模型

剖析物流园区辐射范围准确界定对其可持续发展的重要性及现有传统空间划分模型在其界定中所存在的缺陷.立足于传统势能模型，针对其在“规模”参数确定和“距离”参数测度上存在脱离实际的情况，通过建立物流园区综合实力指标体系来修正原模型中“规模”参数和引入作为物流园区存在前提条件的通达性来测度“距离”参数，构建了基于通达性分析的改进势能模型.以四川省成都市新津物流园区的规划为例，通过利用GIS软件实现了对该模型的实例操作，最后界定其辐射范围.实践证明此方法科学合理，可操作性强，对物流园区规划体现出较强的指导作用.