Compton散射对等离子体中亚皮秒超高斯脉冲传输特性的影响

应用多光子非线性Compton散射模型、非线性薛定谔方程及龙格-库塔算法和变分法,研究了Compton散射对亚皮秒超高斯脉冲在等离子体传输的影响,给出了该脉冲传输演化的修正方程,并进行了数值计算,结果表明:与Compton散射前相比,Compton散射使脉宽压缩程度和非线性效应增大,脉冲展宽降低,非线性增强效应有效地削弱了色散效应;使脉宽趋于最大和最小时频率抖动,啁啾不为0;使超高斯脉冲振幅、啁啾和脉宽随传输距离增大振荡演化加快,频率和相位呈线性关系的抖动,脉冲中心位置呈准线性关系;Compton散射对超高斯脉冲保形传输有重要影响。     

一类二阶微分方程的异宿解

利用变分法获得了一类二阶微分方程异宿解存在的一个充分条件.将连续情况下的二阶微分方程异宿解研究推广到离散情况下来研究.     

用变分法设计与计算最速拐弯线路

本文在已知拐弯速度变化规律的条件下,对拐弯线路为直线与圆弧时研究了最速拐弯线路,例如机器人避障等涉及拐弯轨道的运行线路的设计与计算;并对拐弯线路为直线与任意平滑曲线时,用变分法求出了经过拐弯线路时间的泛函最小值,证得了直线与圆弧就是最速的拐弯线路。     

三维轧制变形场的配置法解

本文用变分法-配置法研究了轧制时的变形问题。计算结果与实验结果吻合较好,说明配置法是一种较好的方法,应继续研究并推广使用。     

界面裂纹问题中的弹性T项和应力强度因子

研究两相材料有限板含单边界面裂纹的断裂力学特性，对不同的材料组合用广义变分法分析了不同尺寸试件和裂纹长度下的应力强度因子和弹性T项，讨论了材料特性对应力强度因子和弹性T项的作用．分析了试件尺寸和裂纹长度对应力强度因子和弹性T项的影响．     

STUDY OF THE EQUIVALENT THEOREM OF GENERALIZED VARIATIONAL PRINCIPLES IN ELASTICITY

The relations of all generalized variational principles in elasticity are studied by employing the invariance theorem of field theory. The infinitesimal scale transformation in field theory was employed to investigate the equivalent theorem. Among the results found particularly interesting are those related to that all generalized variational principles in elasticity are equal to each other. Also studied result is that only two variables are independent in the functional and the stress-strain relation is the variational constraint condition for all generalized variational principles in elasticity. This work has proven again the conclusion of Prof. Chien Wei-zang.     

Research on the discrete variational method for a Birkhoffian system

In this paper, we present a new integration algorithm based on the discrete Pfaff-Birkhoff principle for Birkhoffian systems. It is proved that the new algorithm can preserve the general symplectic geometric structures of Birkhoffian systems. A numerical experiment for a damping oscillator system is conducted. The result shows that the new algorithm can better simulate the energy dissipation than the R-K method, which illustrates that we can numerically solve the dynamical equations by the discrete variational method in a Birkhoffian framework for the systems with a general symplectic structure. Furthermore, it is demonstrated that the results of the numerical experiments are determined not by the constructing methods of Birkhoffian functions but by whether the numerical method can preserve the inherent nature of the dynamical system.     

量子棒中弱耦合极化子有效质量的温度依赖性

基于Tokuda-Lee-Low-Pines变分法研究了温度对非均匀抛物限制势下量子棒中弱耦合极化子有效质量的影响,推导出量子棒中弱耦合极化子的有效质量m*随量子棒纵横比e'、电子-声子耦合强度α和温度参数γ的变化规律.数值计算结果表明,量子棒中弱耦合极化子的横向有效质量m?*和纵向有效质量mx*均随电子-声子耦合强度...     

具有变号位势的Klein-Gordon-Maxwell系统解的多重性

研究一类有变号位势的Klein-Gordon-Maxwell系统解的多重性.当非线性项是凹凸混合项且凸项在无穷远处满足广义超线性增长时,利用变分方法获得了系统解的多重性结果.     

《量子力学》自学辅导之九—定态微扰论和变分法（续）

《量子力学》自学辅导之九──定态微扰论和变分法（续）曾心愉，宋宇辰，裴文杰（复旦大学物理系；复旦大学理论物理骨干教师班，上海２００４３３）１．２简并态微扰沦简并态下，微扰的作用可能使能级发生分裂，即微扰可使简并消除或部分消除。（１）零级近似。设的某个...