混合物物态方程的体积相加模型和热力学自洽条件

 介绍了一个表列数据相加模型,用体积-压强迭代法编程计算混合物物态方程。在各组分材料物态方程满足热力学自洽条件的前提下,证明了混合物物态方程也满足热力学自洽条件。最后给出两个算例（空气和Xe-D₂体系）。     

基于Thomas-Fermi-Kirzhnits模型的物态方程研究

本文针对丝阵Z箍缩等高能量密度物理实验的数值模拟研究, 建立了一种适用温度、密度范围宽的三项式半经验物态方程. 三项式半经验物态方程包括零温自由能项, 电子热贡献项和离子热贡献项. 零温自由能项采用多项式拟合的方法确定. 多项式系数通过多项式计算的结果与高压缩比区域和压缩比为1时零温Thomas-Fermi-Kirzhnits模型计算的结果对应相等得到. 离子对物态方程的热贡献采用一种准谐振模型, 此谐振模型可以描述离子在固态相中的行为, 并且在高温度、低密度区域趋近于理想气体物态方程. 电子对物态方程的热贡献采用含温Thomas-Fermi-Kirzhnits模型计算. 利用所建立的三项式半经验物态方程计算了铝的等温压缩曲线, 并与实验数据做了对比. 给出了很宽温度、密度范围内铝的压强, 其数据与相应的SESAME数据库数据做了对比.     

新型爆轰产物物态方程

 从位力（Virial）理论和相似假设出发，建立了爆轰产物物态方程，命名为VLW物态方程。本物态方程既适用于高压下炸药爆轰性能的计算，也适用于较高压强与中等压强状态下火炮发射药与火箭推进剂燃烧性能的计算。     

基于比热的完全物态方程

在热力学中,一个封闭体系的完全物态方程指由两个状态量为自变量所确定的一种函数关系,由这个关系能够导出所有其他热力学量之间的关系.比如亥姆霍兹自由能F表示为体系的比体积v和温度T的函数F(v,T)时,就是这种完全物态方程.但是这种完全物态方程至今没有实际计算的表达式.我们以等温压强函数pT(v)和建立在德拜模型基础上的定容比热函数Cv(v,T)为基础,建立了一个有具体函数表达式的完全物态方程.用这种完全物态方程对几种固体金属材料进行了实际计算,所导出的热力学状态量和物性参数,与实验测量能够比较好地符合.这种完全物态方程在高温高压物理领域具有一定的应用价值.     

质子中子星物质的热力学性质

在相对论σ-ω-ρ模型的平均场近似下, 研究了质子中子星物质在均熵状态下的组成、温度和物态方程. 如给定每一个重子的熵, 一些热力学量的值将随重子密度的增加而增加, 当考虑超子时, 这些值会减小. 给定重子密度, 中子在S=2时的组分比S=1时的小, 而质子、电子、μ子在S=2时的组分比S=1时的大, 特别是在低密度区域. S是每个重子的熵. 保持重子密度不变, 在低密度区域, 超子在S=2时的组分比S=1时的大, 在高密度区域则相反. 同样, 在同一重子密度处, S=2时的温度、能量密度及压强分别比S=1时的大. 另外, 有限熵对粒子组分和温度的影响比对质子中子星物质的物态方程的影响大. 还研究了反粒子的贡献, 他们确实很小.     

混合物质高压状态方程的计算

 介绍了在温度相同的条件下,混合物中各组元通过密度-压强迭代法,达到温度和压强平衡,再结合叠加原理,编程计算出混合物质状态方程。为验证该程序,对氘氚与氩按不同比例混合时的状态参量进行了分析。当氘氚中含少量氩时,计算得到的状态方程与纯氘氚符合较好;同样地,氩中含少量氘氚时的状态方程也与纯氩的很接近。这说明该程序是可行的。     

高温高密度氢（氘）的物态方程——离解效应研究

 高温高压下流体氢将发生离解化学反应，形成具有相互作用的氢分子和氢原子混合体系，此时粒子间的相互作用复杂。利用单组分流体近似的范德瓦尔斯混合模型，将混合物粒子间的相互作用等效为单组分粒子间相互作用，从而简化了对体系的统计热力学处理；并由自由能函数极小化确定化学平衡时各组分含量、体系的内能、压强。研究了温度在10 000 K以下、密度在0.6 g/cm³以下（相应摩尔体积大于3.3 cm³/mol）区间的热致离解和压致离解现象对流体氢（氘）状态方程的影响。所得结果与双组分流体变分理论计算以及第一原理的分子动力学模拟、蒙特卡罗模拟结果以及二级轻气炮实验数据进行了比较，它们之间的一致性表明：用单组分流体近似的范德瓦尔斯混合模型处理氢（氘）分子的离解区域的物态方程是成功的。     

温稠密铝等离子体物态方程及其电离平衡研究

温稠密物质的物性参数在惯性约束聚变能源、Z箍缩等高能量密度物理领域的实验结果分析和物理过程数值模拟等方面有着重要的应用价值.本文应用部分电离等离子体模型,在理想自由能的基础上考虑了库仑相互作用、排斥体积作用和极化作用等非理想特性,开展了温稠密等离子体物态方程和电离平衡的研究.计算了温稠密铝等离子体的压强等物态方程数据和在密度为1.0×10^-4-3.0 g/cm^3,温度为1.0×10^4-3.0×10^4 K范围内的粒子组分.计算结果显示,铝等离子体的平均电离度在临界密度区域内随着密度的增加而突然增大.根据非理想Saha方程中有效电离能这一关键参数,分析了铝等离子体平均电离度在临界密度区域内随密度迅速增大的现象.     

统计自洽场INFERNO模型在金雨贡纽计算中的应用

以Liberman的统计自洽场INFERNO模型为基础,通过自洽求解每个温度密度点的统计自洽场Dirac方程,获得了金在宽广的温度与密度范围内的物态方程,其中包括以维里定理为基础的冷能、冷压计算,以及在宽广的温度与密度范围内的电子热能、热压计算。对离子热运动部分,采用简单的自由体积模型给出其热能及热压。在物态方程的基础上,又计算了金的理论雨贡纽,得到了与实验符合得比较好的结果。研究结果表明,INFERNO模型可用于物质在宽广的温度与密度范围内的物态方程计算。     

M-G模型的简化以及预热Mo实验结果分析

 在Mie-Grüneisen （M-G）物态方程的基础上进一步推导出预热材料的Hugoniot参数表达式,使得利用M-G物态方程确定材料在不同初始温度下的Hugoniot参数更简洁方便。Miller和Duffy测量了Mo在初始温度1 400 ℃下的状态方程,其结果并不符合M-G物态方程模型,导致一些问题需要进一步研究。     

Modified equation of state for pure and hard sphere mixtures in mean ionic activity coefficient calculations by mean spherical approximation model

A hard sphere equation of state (EOS) based on tetrakaidecahedron cell geometry (instead of spherical shape) and highly optimized molecular dynamic simulation data is proposed. The EOS is extended to hard sphere mixture and its performance for compressibility factor calculation at different diameter size of hard sphere mixtures by using various mixing rule is compared with Monte Carlo simulation data. The results indicated that for all mixing rules, the proposed EOS has minimum error comparing with computer simulation data. Also the residual prosperities are derived by using the proposed EOS. The residual properties are used in mean spherical approximation model (MSA) to evaluate the mean ionic activity coefficient of aqueous electrolyte solutions. The results are compared with those obtained by similar hard sphere equations of state and it is shown that the proposed EOS has a better performance in predicting the mean ionic activity coefficient.     

混合物状态方程的计算

多介质流体动力学过程的数值模拟往往涉及混合物状态方程的计算. 做图法和Newton 法是混合物状态方程计算常采用的方法, 前者虽直观精度却差, 后者计算效率高却只具有局部收敛性, 当解与其初始猜测值相差较远时Newton法不一定能够获得收敛解. 为此, 本文给出一种具有大范围收敛性的嵌入算法(imbedding method)求解混合物状态方程, 其基本思想是通过引入嵌入参数, 将待解的混合物状态方程和易解的混合物状态方程线性组合, 构成嵌入方程组, 当嵌入参数从0连续地变化到1 时, 嵌入方程组的解由易解的混合物状态方程的解连续地变化为待解的混合物状态方程的解. 嵌入方程组可由Newton法迭代求解, 也可转化为以嵌入参数为自变量的常微分方程组, 从而易于由成熟的计算方法如梯形法等进行求解. 进一步利用热力学基本关系, Maxwell形式的微分方程描述了压力和温度随嵌入参数的演化速率与应变速率和组分质量分数演化速率的关系. 对铅锡混合物热力学量的计算表明了本文算法的有效性.     

氘、氦及其混合物状态方程第一原理研究

利用量子分子动力学方法对氘、氦及其混合物的状态方程进行了研究. 计算了氦在密度0.32-5 g/cm³, 温度1000-50000 K范围内的状态方程, 并与化学模型的结果进行了比较; 同时计算了冲击Hugoniot曲线, 与气炮实验的结果符合得很好. 通过计算对分布函数及态密度, 探讨了氦在高温高压下发生金属-绝缘体转变的机理. 计算了氘在密度0.19-0.84 g/cm³, 温度20-50000 K范围内的状态方程; 并计算了理论Hugoniot状态, 由于没有考虑原子的零点运动, 在低温区, 理论结果比实验值小. 对氘氦混合物的状态方程进行了研究, 计算了温度和密度区间为100-50000 K, 0.19-0.84 g/cm³, 不同混合度下的293个状态点的状态方程. 对线性混合近似进行了考查, 结果表明线性混合近似是一个粗略的近似.     

The equation of state of QCD under hard-dense-loop approximation

Based on the method proposed by Zong et al.,we calculate the equation of state(EOS) of QCD at zero temperature and finite quark chemical potential under the hard-dense-loop(HDL) approximation.A comparison between the EOS under HDL approximation and the cold,perturbative EOS of QCD proposed by Fraga,Pisarski and Schaffner-Bielich is made.It is found that when μ is less than 4.7 GeV,the pressure density calculated using HDL approximation is much larger than that calculated using pertur-bation theory.This enha...     

Thermodynamic properties of the Lennard-Jones FCC solid: perturbation theory parameterisation and Monte Carlo simulation

This work is concerned with a valid representation of the solid-phase equation of state (EOS), the validity of which is evaluated by comparing to Monte Carlo (MC) simulation results. The proposed EOS has been developed by employing an optimal division of the Lannard-Jones (LJ) potential and an effective temperature- and density-dependent diameter into the framework of the simplified perturbation theory. Then, with the aim of extending to the chain systems, the conventional chain contribution (i.e. TPT1) is added to the proposed model (i.e. the atomic LJ system). Finally, the solid-state EOS based on Helmholtz free energy will be introduced for low temperature and high density conditions. To verify the accuracy of the proposed model, its performance is compared with the results of MC simulation. The comparison between the obtained results from the proposed model and the MC simulations shows that the EOS can satisfactorily predict the properties of the solid LJ system, both for the atomic system and for the chains.     

A modified equation of state for Xe at high pressures by molecular dynamics simulation

The exact equation of state （EOS） for the fission gas Xe is necessary for the accurate prediction of the fission gas behavior in uranium dioxide nuclear fuel, However, the comparison with the experimental data indicates that the applicable pressure ranges of existing EOS for Xe published in the literature cannot cover the overpressure of the rim fission gas bubble at the typical UO2 fuel pellet rim structure. Based on the interatomic potential of Xe, the pressure-volume-temperature data are calculated by the molecular dynamics （MD） simulation. The results indicate that the data of MD simulation with Ross and McMahan＇s potential [M. Ross and A. K. McMahan 1980 Phys. Rev. B 21 1658] are in good agreement with the experimental data. A preferable EOS for Xe is proposed based on the MD simulation. The comparison with the MD simulation data shows that the proposed EOS can be applied at pressures up to 550 MPa and 3 GPa and temperatures 900 K and 1373 K respectively. The applicable pressure range of this EOS is wider than those of the other existing EOS for Xe published in the literature.     

Numerical investigation on acoustic cavitation characteristics of an air-vapor bubble: Effect of equation of state for interior gases

The cavitation dynamics of an air-vapor mixture bubble with ultrasonic excitation can be greatly affected by the equation of state (EOS) for the interior gases. To simulate the cavitation dynamics, the Gilmore-Akulichev equation was coupled with the Peng–Robinson (PR) EOS or the Van der Waals (vdW) EOS. In this study, the thermodynamic properties of air and water vapor predicted by the PR and vdW EOS were first compared, and the results showed that the PR EOS gives a more accurate estimation of the gases within the bubble due to the less deviation from the experimental values. Moreover, the acoustic cavitation characteristics predicted by the Gilmore-PR model were compared to the Gilmore-vdW model, including the bubble collapse strength, the temperature, pressure and number of water molecules within the bubble. The results indicated that a stronger bubble collapse was predicted by the Gilmore-PR model rather than the Gilmore-vdW model, with higher temperature and pressure, as well as more water molecules within the collapsing bubble. More importantly, it was found that the differences between both models increase at higher ultrasound amplitudes or lower ultrasound frequencies while decreasing as the initial bubble radius and the liquid parameters (e.g., surface tension, viscosity and temperature of the surrounding liquid) increase. This study might offer important insights into the effects of the EOS for interior gases on the cavitation bubble dynamics and the resultant acoustic cavitation-associated effects, contributing to further optimization of its applications in sonochemistry and biomedicine.     

A Model Study of Equation of State of QCD at Finite Chemical Potential and Zero Temperature

In this paper, we give a direct method for calculating the partition function, and hence the equation of state （EOS） of QCD at finite chemical potential and zero temperature. In the EOS derived in this paper the pressure density is the sum of two terms： the first term P（μ）｜μ=0 （the pressure density at μ = 0） is a μ-independent constant; the second term, which is totally determined by G[μ] （p） （the dressed quark propagator at finite μ）, contains all the nontrivial μ-dependence. By applying a general result in the rainbow-ladder approximation of the Dyson-Schwinger approach obtained in our previous study [Phys. Rev. C 71 （2005） 015205], G[μ]（p） is calculated from the meromorphic quark propagator proposed in [Phys. Rev. D 67 （2003） 054019]. From this the full analytic expression of the EOS of QCD at finite μ and zero T is obtained （apart from the constant term P（μ）｜μ=0, which can in principle be caJculated from the CJT effective action）. A comparison between our EOS and the cold, perturbative EOS of QCD of Fraga, Pisarski and Schaffner-Bielich is made. It is expected that our EOS can provide a possible new approach for the study of neutron stars.