Triangle Distribution and Equation of State for Classical Rigid Disks

The triangle distribution function f⁽³⁾ for three mutual near neighbors in the plane describes basic aspects of short-range order and statistical thermodynamics in two-dimensional many-particle systems. This paper examines prospects for constructing a self-consistent calculation for the rigid-disk-system f⁽³⁾. We present several identities obeyed by f⁽³⁾. A rudimentary closure suggested by scaled-particle theory is introduced. In conjunction with three of the basic identities, this closure leads to an unique f⁽³⁾ over the entire density range. The pressure equation of state exhibits qualitatively correct behaviors in both the low-density and the close-packed limits, but no intervening phase transition appears. We discuss extensions to improved disk closures, and to the three-dimensional rigid-sphere system.     

并联型光电设备稳定平台稳定解算研究

并联型光电设备稳定平台是针对光电跟踪系统需要而设计的一种新型并联机构,具有两个相互独立的转动自由度。以并联稳定平台为研究对象,介绍了动载体下并联稳定平台的工作原理,进行了并联稳定平台的运动学分析。采用齐次坐标变换方法,推导了从大地坐标系到平台定坐标系的转移矩阵,建立了并联稳定平台的稳定解算模型,进行了并联稳定平台的数值仿真研究。结果表明：随着旋转角增大,并联稳定平台的姿态角偏差和方位角偏差越来越大;在实际控制系统中若不考虑旋转角作用,这将严重影响并联型光电设备稳定平台的稳定精度。该研究为并联型稳定平台控制系统设计提供了一定的理论依据。     

Perturbative Treatment for Stationary State of Local Master Equation

The local approach to construct master equation for a composite open system with a weak internal coupling is simple and seems reasonable. However, it is thermodynamic consistent only when the subsystems are resonantly coupled. Efforts are being made to understand the inconsistency and test the validity of the local master equation. We present a perturbative method to solve the steady-state solutions of linear local master equations, which are demonstrated by two simple models. The solving process shows the stationary state as the result of competition between incoherent operations and the unitary creating quantum coherence, and consequently relate quantum coherence with thermodynamic consistency.     

Accurate First-Principle Equation of State for the One-Component Plasma

Accurate “first-principle” expressions for the excess free energy F_ex and internal energy of U_ex of the classical one-component plasma (OCP) are obtained. We use the Hubbard-Schofield transformation that maps the OCP Hamiltonian onto the Ising-like Hamiltonian, with coefficients expressed in terms of equilibrium correlation functions of a reference system. We use the ideal gas as a reference system for which all the correlation functions are known. Explicit calculations are performed with the high-order terms in the Ising-like Hamiltonian omitted. For small values of the plasma parameter Γ the Debye-Huckel result for F_ex and U_ex is recovered. For Γ ? 1, these depend linearly on Γ in accordance with the Monte Carlo findings for the OCP. The MC data for the internal energy are reproduced fairly well by the expression for U_ex obtained.     

Equation of State of Protoneutron Star Matter

We have calculated the equation of state of protoneutron star matter by using the lowest order constrained variational method. In our calculations, the modern Argonne potential (AV₁₈) together with its older model potential (AV₁₄) are used. It is found that the equation of state for high lepton fraction is stiffer than for low lepton fraction. It is seen that the increasing effect of pressure due to high lepton fraction and due to entropy are comparable. It is shown that the temperature and adiabatic index depend on the values of both entropy and lepton fraction.     

The Brueckner-Hartree-Fock Equation of State for Nuclear Matter and Neutron Skin

The equation of state for nuclear matter is presented within the Brueckner-Hartree-Fock(BHF) scheme,by using the realistic Argonne V18 or Bonn B two-nucleon potentials plus their corresponding microscopic three-nucleon forces.It is then applied to calculate the properties of finite nuclei within a simple liquid-drop model,and we compare the calculated volume,surface,and Coulomb parameters with the empirical ones from the liquid drop model.Nuclear density distributions and charge radii in good agreement with the experimental data are obtained,and we predict the neutron skin thickness of various nuclei.     

Bound State Solutions of the Klein-Gordon Equation for the Mathews-Lakshmanan Oscillator

We study a boundary-value problem for the Klein-Gordon equation that is inspired by the well-known Mathews-Lakshmanan oscillator model. By establishing a link to the spheroidal equation, we show that our problem admits an infinite number of discrete energies, together with associated solutions that form an orthogonal set in a weighted L ²-Hilbert space.     

基于Boltzmann模型方程的气体运动论HPF并行算法

从修正的BGK-Blotzmann模型方程出发,引入离散速度坐标技术对气体分子速度分量进行离散降维,基于非定常时间分裂数值计算方法和无波动、无自由参数的NND耗散差分格式,发展直接求解气体分子速度分布函数的气体运动论有限差分数值格式,提出了一套能有效模拟各流域三维绕流问题的气体运动论统一算法,在分析研究气体运动论数值算法内在并行度的基础上,开展各流域三维绕流问题统一算法的HPF（高性能FORTRAN）并行化程度设计,建立一套能有效模拟各流域复杂外形体绕流的HPF并行算法软件,并进行了不同Knudsen(克努森）数下三维球体绕流及类“神舟号”返回舱外形体绕流的初步数值实验,将计算结果与过渡区有关实验数据及各流域气体绕流现象进行比较分析,证实了发展的气体运动论HPF并行算法在求解稀薄流到连续流不同流域复杂绕流问题方面的可行性。     

On the Equation of State of Coulomb Systems

A quantum statistical expression is given for the pressure of multi-component plasmas which is correct up to the second cluster coefficient. The Montroll-Ward formula for the pressure is evaluated for any degree of degeneration. As an example the thermodynamic stability of an electronhole plasma is discussed.     

First-Principles Calculation of Static Equation of State and Elastic Constants for GaSe

The all-electron full potential augmented plane-wave plus local orbital （APW_Io） method with the local-density approximation （LDA） is used to calculate the static equation of state （EOS） and elastic constants of crystalline GaSe. After the full relaxation of atomic positions, the calculated band structure at ambient pressure is consistent with the experimental data to the extent expected to give the known limits of LDA one-electron energies. The equilibrium lattice parameters found here exhibit the usual LDA-induced contraction. However, constrained with the experimental cell volume, the interlayer separation exhibits an expansion due to the LDA underestimate of the weak interlayer bonding. The calculated values of elastic constants are in good agreement with acoustic measurements. The pressure derivatives of the lattice constants derived from the theoretical elastic constants are in very good agreement with x-ray spectra measurements. Two analytical EOSs have been determined at pressures up to 4.5 GPa. The pressure evolution of the structure indicates that the layer thickness decreases slightly under pressure.     

A Comparative Study for the Equation of State of Dense Fluid Hydrogen

Recent developments in shock-wave experimental techniques have allowed the 100 GPa range to be probed. Driven by a two-stage gas gun (Livermore, USA) or chemical explosives (Chernogolovka, Russia), the multiple shock-wave technique has been applied to determine the equation of state and the electrical conductivity of dense hydrogen and deuterium fluids. In single shock wave experiments driven by the NOVA laser, the principle Hugoniot curve of deuterium was determined. Interesting effects such as dissociation and the transition to metallic-like conductivities occur under these conditions. The equations of state applied so far to analyze the experimental data are compared and a new semi-empirical equation of state is given.     

Equation of State Grid with the Quark-Meson-Coupling Model

In this work, we present the preliminary results of an equation of state (EoS) grid for possible use in core-collapse supernova simulations. We treat uniform matter made of nucleons using the quark-meson coupling (QMC) model. We show a table with a variety of thermodynamic quantities, which covers the proton fraction range Y _p = 0?0.65 with the linear grid spacing ΔY _p = 0.01 (66 points) and the density range ρ _B = 10¹⁴ ? 10¹⁶g cm^?3 with the logarithmic grid spacing Δlog₁₀(ρ _B /[g cm^?3]) = 0.1 (21 points). This preliminary study is performed at zero temperature, and our results are compared with the widely used EoS already available in the literature.     

Equation of State in the Fugacity Format for the Two-Dimensional Coulomb Gas

We derive the general form of the equation of state, in the fugacity format, for the two-dimensional Coulomb gas. Our results are valid in the conducting phase of the Coulomb gas, for temperatures above the Kosterlitz–Thouless transition. The derivation of the equation of state is based on the knowledge of the general form of the short-distance expansion of the correlation functions of the Coulomb gas. We explicitly compute the expansion up to order in the activity ζ. Our results are in very good agreement with Monte Carlo simulations at very low density.     

范氏方程、玻意耳温度与理想气体状态方程的偏差

1 引言 众所周知,理想气体状态方程只适用于稀薄的气体,从分子动理论看,理想气体的分子间没有相互作用力,理想气体是"永久气体",不可能液化.     

Equation of State of Tantalum up to 133GPa

The static equation of state （EOS） of tantalum （Ta） is determined by in situ energy-dispersive synchrotron powder x-ray diffraction in a diamond anvil cell （DAC） up to 133GPa. The body-centered-cubic （bcc） phase of Ta is found to be stable over the entire pressure range investigated. The bulk moduli and its first pressure derivative of Ta are constrained by fitting the determined pressure-volume data to Vinet form EOS： B0 =192.65±（3.08）GPa and B＇0 =3.58±（0.11）. For the sake of avoiding the affect of non-hydrostatic stress, argon is used as a pressure media. A careful checking of the stress state of the sample is presented simultaneously.     

Exact solutions of relativistic perfect fluid hydrodynamics for a QCD Equation of State

The half-life of the mirror $\beta$ decay of ³¹S has been measured at the IGISOL facility at the University of Jyv?skyl?. The value obtained is $T_{1/2}(^{31}S)=(2553.4\pm 1.8)$ ms, in agreement with previous measurements, but with a precision that is better by a factor of ten than the literature value previously adopted. When the new result is combined with the Q_EC value measured recently at JYFLTRAP, a precision of better than $10^{-3}$ is obtained for the ft value.     

The Equation of State for the Hydrogen Plasma on Account of Atom-Atom Interaction

The equation of state for the hydrogen plasma is investigated quantumstatistically in the case of chemical equilibrium between electrons protons, H-atoms and H₂-molecules. In order to take into account the formation of H₂-molecules it is necessary to know the fourth cluster coefficient. For the numerical calculation a pair approximation of the fourth cluster coefficient is given on the basis of the many-channel scattering theory.