范德瓦耳斯和他的状态方程

在物理学发展史上，范德瓦耳斯对气—液流体系统做了开创性的研究工作，建立了人类历史上第一个既能反映气、液各相性质，又能描述相交和临界现象的状态方程。范德瓦耳斯的理论成就和研究方法对热力学、统计力学和低温物理学的发展产生了重要而深远的影响。文章系统探讨了范德瓦耳斯方程产生的历史背景、科学意义和局限性，讨论了范德瓦耳斯的理论和方法对当代物理学的启发意义。     

Phase transitions and fluctuations in ultrarelativistic matter with the Van der Waals equation of state

The paper deals with the thermodynamical properties of ultrarelativistic matter described by the Van der Waals equation of state under condition of free creation and annihilation of particles. In such a system phase transitions take place. Near the phase transitions the behaviour of the system radically depends on which of thermodynamical variable—the temperature or the density of energy—is independent. Some astrophysical consequences of the results obtained are discussed.     

On the generalization of the Van der Waals equation of state for mixtures

For pure fluids, the dependence of the Van der Waals parameter a on the temperature and density have been examined. The Van der Waals equation of state with an accurate hard-core part and temperature- and density-dependent parameters a_ij has been applied to fluid mixtures. The calculated p^E and V^I are compared with experimental data for AN₂ at 1–120 atm.     

具有时滞状态反馈的随机Van der Pol系统的动力学研究

研究了时滞及时滞反馈控制参数对Van der Pol系统极限环幅值的影响. 运用自适应的平均场近似方法给出了系统的线性化近似及系统参数Lyapunov稳定性的边界条件, 同时给出了Van der Pol系统的关联时间和功率谱密度的数值模拟结果. 通过与平均场近似下的解析结果比较后发现, 数值模拟结果和理论结果符合.进一步讨论了时滞反馈控制参数、噪声强度以及时滞对关联时间和功率谱密度的影响. 关键词： 平均场近似 关联时间 Lyapunov稳定性     

Exact solutions for nonstatic perfect fluid spheres with shear and an equation of state

It is shown that fairly general assumptions about the relevant physical and mathematical quantities in the study of nonstatic and spherically symmetric perfect fluid configurations usually single out the Friedmann-Lemaître solutions as the only physically plausible ones. In addition three new classes of exact solutions having shear and acceleration are presented, as well as a generalization of Wesson's stiff fluid solution.     

范德瓦尔斯方程的分子平均场理论推导

利用气体分子动理论和分子平均场理论,导出了真实气体物态方程--范德瓦尔斯方程,并与统计力学严格的理论推导结果作比较,得到了反映真实气体分子作用域大小的一个较为具体的参考值.     

Anisotropic spheres with variable energy density in general relativity

Interior solutions of Einstein field equations for anisotropic spheres with variable energy density are obtained. The solutions for uniform energy density [10] and for radial pressure equal to zero [11] are particular cases of the present solution. With this solution we are also able to discuss an anisotropic gas sphere. Physically it explains larger red-shifts of different quasi-stellar objects. The results of the model have been used to explain the behaviour of a neutron stars and conclude that the maximum mass of a neutron star does not exceed two solar masses, which confirms the Chandrasekhar limit.     

Anisotropic spheres with uniform energy density in general relativity

An ansatz is developed to obtain interior solutions of the Einstein field equations for anisotropic spheres. This procedure necessitates a choice for the energy-density and the radial pressure. A class of solutions for a uniform energy-density source is presented. These anisotropic spheres match smoothly to the Schwarzschild exterior and are well-behaved in the interior of the sphere.     

Anisotropic fluid spheres in general relativity

A procedure is developed to find static solutions for anisotropic fluid spheres from known static solutions for perfect fluid spheres. The method is used to obtain four exact analytical solutions of Einstein’s equations for spherically symmetric self-gravitating distribution of anisotropic matter. The solutions are matched to the Schwarzschild exterior metric. The physical features of one of the solutions are briefly discussed. Many previously known perfect fluid solutions are derived as particular cases.     

Modified Van der Pauw Method of Measuring the Electrical Conductivity Tensor of Anisotropic Semiconductor Films

Russian Physics Journal - For a solution of the boundary electrodynamic problems, the paper proposes the original method of measuring the specific conductivity tensor components of anisotropic...     

A comprehensive approach to an equation of state for hard spheres and Lennard-Jones fluids

We present a simple method of obtaining various equations of state for hard sphere fluid in a simple unifying way.We will guess equations of state by using suitable axiomatic functional forms (n=1,2,3,4,5) for surface tension S n m (r),r ≥ d/2 with intermolecular separation r as a variable,where m is an arbitrary real number (pole).Among the equations of state obtained in this way are Percus-Yevick,scaled particle theory and Carnahan-Starling equations of state.In addition,we have found a simple equation of state for the hard sphere fluid in the region that represents the simulation data accurately.It is found that for both hard sphere fluids as well as Lennard-Jones fluids,with m=3/4 the derived equation of state (EOS) gives results which are in good agreement with computer simulation results.Furthermore,this equation of state gives the Percus-Yevick (pressure) EOS for the m=0,the Carnahan-Starling EOS for m=4/5,while for the value of m=1 it corresponds to a scaled particle theory EOS.     

Some qualitative properties of the Van der Pol equation inferred from its singular set

It is shown that the singular set of an extended “inverse” integral curve x(y) of the Van der Pol equation is covered with local extrema of x(y) that are stable with respect to small perturbations in the equation. As a consequence, the qualitative behavior of x(y) can be determined and some of its important properties can be understood.     

范德瓦耳斯气液状态方程纵横谈

首先强调了范氏方程是气液系统的状态方程,范氏方程可以很好地说明物质气态和液态的相互转变．分析了焦-汤效应,简述了气体的液化与低温的获得．     

The effect of van der Waals-type interactions in metals: A pseudopotential model

A model has been developed for the long-range part of the ion-ion interaction of simple metallic many-particle systems. The investigation is based on the local pseudopotential theory. The essential point in the examination is the consideration of interactions of van der Waals-type in the determination of the direct ion-ion potential and the ion-electron pseudopotential. Numerical calculations performed for liquid rubidium near the melting point show that these interactions are distinctly reflected in the long-range part of the ion-ion potential. The reference potential used in the study had been calculated without parameters by means of the experimentally determined pair correlation function.     

Equation of state for anisotropic spheres

We present a new class of exact interior solutions for anisotropic spheres to the Einstein field equations with a prescribed energy density. This category of solutions has similar energy density profiles to the models of Chaisi and Maharaj (Gen. Rel. Grav. 37, 1177–1189, 2005) whose approach we follow in the integration process. A distinguishing feature of the solutions presented is that they satisfy a barotropic equation of state linearly relating the radial pressure to the energy density.     

Integral equation approximations for fluids of hard spheres with linear quadrupoles

In this paper we solve numerically several integral equation theories for the dense quadrupolar hard-sphere fluid. Closure approximations obtained by expanding the hypernetted-chain equation are shown to give pair-correlation functions and internal energies in good agreement with Monte Carlo calculations. The mean spherical approximation, however, is found to be extremely poor.