用类比法推导分子平均自由程公式的关键问题

为了指出部分学生在用类比法推导分子平均自由程公式时出现的错误并给出正确的推导,采用弹性刚球模型讨论分子之间的相互碰撞过程。用类比法推导分子的平均自由程公式,要解决的关键问题是推导分子的平均相对速率服从麦克斯韦速率分布律。平均相对速率是平均相对速度的大小,因此先由麦克斯韦速度分布律导出处在平衡态的混合理想气体分子相对速度的分布函数,并得出相对速度瓫r也服从麦克斯韦速度分布律,再取特殊情况即得出同种分子碰撞的相对速度分布函数。然后根据麦克斯韦速度分布函数和速率分布函数的关系,导出平均相对速率服从麦克斯韦速率分布律。     

分子射线中分子的频率分布

由麦克斯韦速率分布率导出分子射线中分子按频率分布 ,并给出了分子射线中分子按频率分布中的三个特征频率、分界动能和分界温度。     

Matlab在麦克斯韦速率分布律中的应用

用Matlab软件对麦克斯韦速度及速率分布函数进行了编程,绘制了相应的分布曲线,讨论了不同温度和不同分子质量时麦克斯韦速率分布曲线的变化,并用Matlab的符号计算功能计算了分布在三个典型速率区间的分子数占总分子数的百分比,所有变化规律均符合热学理论中的分子运动规律,为教学提供了参考。     

理想气体分子相对速度分布的推导

采用与推导麦克斯韦速度分布完全对应的推导方法讨论了理想气体分子间相对速度分布的推导。为使推导更紧凑,本文从分布函数梯度的几何意义出发建立分布函数满足的微分方程。发现推导相对速度分布与推导速度分布最大的不同之处和难点在于指数函数中待定常数的确定,而通常在近似讨论平均相对速率时常用的一个公式恰好可以帮助确定这一常数。两种分布函数的教学可以采用一一对应的方式进行。     

关于气体中有无速率为无穷大分子的再讨论

本文以较简捷的方法讨论了气体分子速率问题，给出了计算分子最大速率的理论公式，通过这些讨论可更加深入地理解气体中分子的运动情况，准确地理解麦克斯韦速率分布函数。     

速度分布、速率分布中的几率最大问题

速度分量vx的分布函数为可见,在vx=0处有一极大值,如图1所示.考虑其他两个分量vy、vz的情况,且因速度分布函数f(v)等于三个速度分量分布函数的乘积,则在vx=0、vy=0、v2=0附近单位速度间隔内分子出现的几率最大. 为了讨论方便,我们在速度空间中引入点密度p来描述分布.点密度定义为可以看出,点密度p随v的增加而减少,在原点(v=0)处有一极大值,速率v愈大则点密度愈小,为高斯分布,如图2所示.在速度空间中,在原点(vx=0、vy=0、vz=0)处点密度有一极大值.即是说,按照麦克斯韦速度分布律,在vx=0、 vy=0、 vz=0附近单位速度间隔内分子出现的几率最大. …     

由实验曲线求气体分子速率分布函数

气体分子速率分布函数ｆ（ｖ）＝４／√π（ｍ／２ｋＴ）＾３／２ｖ＾２ｅ－ｍｖ＾２／２ｋＴ，最初是由麦克斯韦用统计理论推导出来的。本文阐述了一种从实验曲线出发寻求这一分布函数的方法，虽不严廑，但过程简单，便于掌握。     

分子束频率分布函数的研究

从分子束的速率分布函数出发,推导了分子束的频率分布函数,求出平均频率、方均根频率和最概然频率,并与分子束的速率分布函数相应的特征物理量逐一比较,说明它们的物理意义,得出了用分子束的频率分布函数解决分子束问题更为简便的结论．     

混合气体分子速率分布函数的演化过程研究

利用蒙特卡罗方法,对混合气体分子速率分布函数的演化过程以及不同成分间的能量转移过程进行了研究。数值模拟结果表明,随着碰撞次数的增多,速率分布函数逐渐趋向于相应的麦克斯韦分布函数,而弛豫过程的快慢与各成分的分子质量有关。     

分子射线的速率分布的实验

分子射线实验是直接验证麦克斯韦气体分子速率分布律的实验．本文较系统地介绍了关于分子射线实验的历史、并作了较详细的理论推导．同时指出了目前国内外教材中的某些错误．     

A CONCENTRATED MASS ON THE SPINNING UNCONSTRAINED BEAM SUBJECTED TO A THRUST

The dynamic stability of a spinning unconstrained beam subjected to a pulsating follower forceP₀ +P₁cos Ωt is analyzed. A concentrated mass is located at an arbitrary location on the beam, and the stability of the beam is studied with the mass at various locations. The beam is analyzed using the Timoshenko-type shear deformation theory with the rotary inertia. Hamilton's principle is used to derive the equations of motion, and the spinning speed of the beam with various non-dimensional parameters subjected to a pulsating follower force is investigated. The finite element method is applied to analyze the spinning beam model, and the method of multiple scales is used to investigate the dynamic stability characteristics. A pulsating follower force is applied, and then the stability regions are changed with the transitions of the stability area in many regions. The results show that the concentrated mass increases the dynamic stability of the spinning unconstrained beam subjected to a thrust. As the spinning speed of the beam is increased, the instability regions are reduced, but various slight instability regions are additionally developed.     

DYNAMIC ANALYSIS OF A ROTATING CANTILEVER BEAM BY USING THE FINITE ELEMENT METHOD

A finite element analysis for a rotating cantilever beam is presented in this study. Based on a dynamic modelling method using the stretch deformation instead of the conventional axial deformation, three linear partial differential equations are derived from Hamilton's principle. Two of the linear differential equations are coupled through the stretch and chordwise deformations. The other equation is an uncoupled one for the flapwise deformation. From these partial differential equations and the associated boundary conditions, are derived two weak forms: one is for the chordwise motion and the other is for the flapwise motion. The weak forms are spatially discretized with newly defined two-node beam elements. With the discretized equations, the behaviours of the natural frequencies are investigated for the variation of the rotating speed. In addition, the time responses and distributions of the deformations and stresses are computed when the rotating speed is prescribed. The effects of the rotating speed profile on the vibrations of the beam are also investigated.     

关于分子分布律的教学

从教学角度来探讨既能使学生掌握统计概念又不至于使用太多的数学推导,由玻耳兹曼分布率导出麦克斯韦速率分布律。     

超声分子束注入密度和宽度对托克马克装置加料深度的影响

基于HL-2A托卡马克装置的真实磁场位形,应用大型边缘等离子体湍流模拟程序BOUT++中的子程序模块trans-neut对不同的超声分子束注入(SMBI)密度和宽度进行模拟.在SMBI过程中,保持单位时间内分子注入个数和注入速度恒定,在恒定通量情况下,通过调整注入分子束密度和宽度来研究SMBI注入深度的变化.研究结果表明:在注入密度较小、注入宽度较大时,SMBI的注入深度更深,分子和原子的分解率和电离率的时空区域较宽.分子分解局域化会抑制全局分解率的增长,而分解局域化又会引发局域分解率的加速增长,进而促进全局分解率的增长,促进效果占优导致在注入速度一定的情况下,恒定通量的分子注入发散角越小,分子注入深度越浅.     

THE DYNAMIC ANALYSIS OF A BEAM-MASS SYSTEM DUE TO THE OCCURRENCE OF TWO-COMPONENT PARAMETRIC RESONANCE

The objective of this paper is an analytical and numerical study of the dynamics of a beam--mass system. Special attention is given to the phenomena arising due to the motion of the attached mass and modal interactions produced by the existence of multi-component, specifically two-component, parametric resonance under primary resonance. The two-component parametric resonance occurs when the sums or the differences among internal frequencies are the same, or close, as the dimensionless speed parameter of the moving mass. The effects of two-component parametric resonance post on dynamic condition are investigated. Resonance generated by more than two-component modes are neglected due to its remote probability of occurrence in nature.The mechanics of the problem is Newtonian. Based on the assumption that when the moving mass is set in motion the mass is assumed to be rolling on the beam, the mechanics, including the effects due to friction and convective accelerations, of the interface between the moving mass and the beam are determined.Based on the Bernoulli-Euler beam theory, the coupled non-linear equations of motion of an inextensible beam with an attached moving mass are derived. By employing Galerkin procedure, the partial differential equations which describe the motion of a beam-mass system are reduced to an initial-value problem with finite dimensions. The method of multiple time scales is applied to consider the solutions and the occurrence of internal resonance of the resulting multi-degree-of-freedom beam--mass system with time dependent coefficients.     

Electron beam modeling and analyses of the electric field distribution and space charge effect

In electron beam technology, one of the critical focuses of research and development efforts is on improving the measurement of electron beam parameters. The parameters are closely related to the generation, emission, operation environment, and role of the electron beam and the corresponding medium. In this study, a field calculation method is proposed, and the electric field intensity distribution on the electron beam's cross-section is analyzed. The characteristics of beam diffusion caused by the space charge effect are investigated in simulation, and the obtained data are compared with the experiment. The simulation demonstrated that the cross-sectional electric field distribution is primarily affected by the electron beam current, current density distribution, and electron beam propagation speed.     

HL—1M托卡马克脉冲超声分子束注入等离子体及杂质特性研究

文内叙述了在ＨＬ－１Ｍ托卡马克脉冲分子束注入实验中观测到的等离子体和杂质行为。分子束注入减小了杂质辐射,有效地提高了电子密度,改善了等离子体的约束性能。     

自由电子激光振荡器中电子束能量跳跃对增益的影响

 微脉冲中电子束能量、电流的跳跃会影响电子束的质量, 从而也影响激光的增益。在CAEP FIR FEL 理论设计模型参数的基础上,利用一维定态程序对电子束能量跳跃对增益的影响进行了数值研究,并与非定态程序计算结果进行比较,给出可容许的能量跳跃范围。