理想气体和范氏气体压强的讨论

1引言 理想气体是一个近似模型,它忽略了分子的体积(更确切地讲,也就是分子间的斥力)和分子间的引力,模型中的分子被看成了没有体积的质点.如果气体所占的体积为V,那么V也就是每个分子可以自由活动的空间.如果把分子看作有一定体积的刚球,则每个分子能自由活动的空间就不再等于V.范德瓦耳斯就是将气体分子看成有一定体积的刚球,将理想气体状态方程加以修正,得出了范德瓦耳斯(简称范氏)气体状态方程.     

重力场中理想气体密度分布的 Monte Carlo 模拟

利用Monte Carlo 方法模拟了重力场中理想气体的密度分布,直观展现了重力场中气体分子位置的改变和分布特点,讨论了分子质量和系统温度对气体密度分布曲线以及重力势能零点处密度n0的影响.模拟结果与玻耳兹曼分布律完全吻合.另外,模拟结果表明玻耳兹曼分布律不仅对纯的理想气体成立,而且对混合理想气体中各成分气体也成立.     

从气体吸附率看范德瓦耳斯气体模型的局限性

利用占据数方法和正则系综理论分别求出了费米气体、玻色气体和范德瓦耳斯气体的化学势,比较了这三种气体与理想气体吸附率的差异.指出:费米气体的吸附率高于理想气体,玻色气体则低于理想气体.存在一个临界温度,高于此温度,用范德瓦耳斯气体描述费米气体不如理想气体模型;低于此温度,用范德瓦耳斯气体描述玻色气体不如理想气体模型.     

p=2U／3V系统的态函数形式

给出了压强ｐ、内能Ｕ和体积Ｖ满足ｐ＝２Ｕ／３Ｖ的系统的态函数形式。并据此讨论了理想 玻色气体、理想费米气体和通常的理想气体的状太民方程不同的热力学原因。     

非理想气体状态方程与内能

内能公式给出：定量非理想气体经绝热自由膨胀过程后，气体的温度恒降低，但实际情况并非完全如此．本文给出新的气体状态方程与内能公式，并很好地解释了气体绝热自由膨胀和绝热节流膨胀温度变化的全部情况．     

非理想气体状态方程的推导

与一般方法不同，本文采取分子为ｆ＝　，的模型，应用麦克斯韦速度分布律导出了非理想气体状态方程．     

热质的运动与传递-热子气状态方程

基于相对论原理,提出能量的运动可以产生压强．在热质概念的基础上,针对理想气体,根据分子动理论建立了热子气状态方程,从而得到理想气体分子的热运动动能压强的表达式．基于硬球势能模型通过分子动力学模拟验证了热子气状态方程的正确性．     

从量纲分析观点看气体物态方程

从量纲分析的观点出发讨论气体物态方程的形式.指出理想气体的物态方程由量纲特征确定到只差一常数;玻意耳气体族的物态方程族由量纲特征完全确定;还给出了非理想气体物态方程的一般形式.     

麦克斯韦分布适用的范围

气体由大量的分子所组成,因为其数量很大,需要用统计方法来描写其无规则的热运动,麦克斯韦速度分布描写了这种寓于分子的无规则热运动中的统计规律性,应用麦氏分布可以导出气体的许多宏观的热性质。因此,对于麦克斯韦分布适用范围的理解就显得十分重要。 多数的著作仅笼统地说麦氏分布描写气体分子的速度分布,并未明确说明它适用于理想气体或非理想气体。也有一些教科书明确指明麦氏分布仅适用于理想气体。我们以为麦克斯韦分布也是适用于非理想气体的。现证明如下: 对于处在平衡态的气体,可以用吉布斯的正则分布来描写体系处在dD=dPl…dP…     

范德瓦耳斯（Van der Waals，Johannes Diederik 1837-1923）荷兰物理学家（Physicist，Netherlands）

1873年范德瓦尔斯的论文《论液态和气态的连续性》首次引起人们的注意，并为此而获得了博士学位。他认识到假定气体分子体积为零，且分子之间不存在引力，则理想气体定律就能从气体运动论导出。但考虑到上述假定均不真实，1881年给这个定律引入表示分子的大小和引力两个参量，得出一个更准确的公式。由于这些参量对每一种气体都不同，他继续研究而得出一个对所有物质都适用的方程。     

Composite Lane-Emden Equation as a Nonlinear Poisson Equation

After a quick review of the Lane-Emden equation and its properties, a composite of two different polytropes is introduced and some of the consequences are explored. The results are used to build a nonlinear electromagnetism with non-singular, solitonic solutions as charged particles.     

Solutions of CDG Equation and Modified CDG Equation

This article puts forward a new way to find solutions of CDG equation. The main results are:(i) According to the Lax pair of CDG equation, we introduce the modified CDG equation. (ii) An invariance depending on two parameters of M-CDG equation is found. (iii) Some solutions for CDG equation are obtained by using the invariance.     

Marchenko Equation for the Derivative Nonlinear SchrSdinger Equation

A simple derivation of the Marchenko equation is given for the derivative nonlinear Schrodinger equation. The kernel of the Marchenko equation is demanded to satisfy the conditions given by the compatibility equations. The soliton solutions to the Marchenko equation are verified. The derivation is not concerned with the revisions of Kaup and Newell.     

Propagation-Dispersion Equation

A propagation-dispersion equation is derived for the first passage distribution function of a particle moving on a substrate with time delays. The equation is obtained as the hydrodynamic limit of the first visit equation, an exact microscopic finite difference equation describing the motion of a particle on a lattice whose sites operate as time-delayers. The propagation-dispersion equation should be contrasted with the advection-diffusion equation (or the classical Fokker–Planck equation) as it describes a dispersion process in time (instead of diffusion in space) with a drift expressed by a propagation speed with non-zero bounded values. The temporal dispersion coefficient is shown to exhibit a form analogous to Taylor's dispersivity. Physical systems where the propagation-dispersion equation applies are discussed.     

Peakon Solutions to Supersymmetric Camassa-Holm Equation and Degasperis-Procesi Equation

In this paper,the supersymmetric Camassa-Holm equation and Degasperis-Procesi equation are derived from a general superfield equations by choosing different parameters.Their peakon-type solutions are shown in weak sense.At the same time,the dynamic behaviors are analyzed particularly when the two peakons collide elastically,and some results are compared with each other between the two equations.     

Derivation of Dirac's Equation from the Evans Wave Equation

The Evans wave equation [1] of general relativity is expressed in spinor form, thus producing the Dirac equation in general relativity. The Dirac equation in special relativity is recovered in the limit of Euclidean or flat spacetime. By deriving the Dirac equation from the Evans equation it is demonstrated that the former originates in a novel metric compatibility condition, a geometrical constraint on the metric vector qused to define the Einstein metric tensor. Contrary to some claims by Ryder, it is shown that the Dirac equation cannot be deduced unequivocally from a Lorentz boost in special relativity. It is shown that the usually accepted method in Clifford algebra and special relativity of equating the outer product of two Pauli spinors to a three-vector in the Pauli basis leads to the paradoxical result X = Y = Z = 0. The method devised in this paper for deriving the Dirac equation from the Evans equation does not use this paradoxical result.     

耗散子运动方程与福克-普朗克量子主方程

发展非线性耦合环境下精确、非微扰的量子耗散方法仍然是一个巨大的挑战.本文针对线性和二次耦合热浴模型,介绍了两种刻画系统与环境耦合动力学的有效方法.一个是耗散子运动方程（DEOM）理论,最近已被扩展到处理非线性耦合环境.另一个是推广的福克-普朗克量子主方程（FP-QME）方法,将在这项工作中基于DEOM推导给出.本文对这两种方法进行了详细的比较,并重点介绍了所涉及的准粒子图像、物理含义以及实现方案.     

The Breit Equation

Contrary to the conventional view, the Breit equation can be solved. This revised version was published online in August 2006 with corrections to the Cover Date.