Perturbation theory based direct correlation function for fluids with hard core potentials

Using second-order Barker–Henderson perturbation theory we are able to derive an explicit expression for the direct correlation function of fluids with hard core potentials. Using the obtained direct correlation function, one can explicitly calculate all thermodynamic properties of simple fluids with hard core potentials. Comparisons with computer simulation data show good agreement for both thermodynamic properties and the static structure factor of the hard core double Yukawa potential.     

A parametrisation of the direct correlation function for the square-shoulder fluid

We introduce a parametrisation of the direct correlation function for the square-shoulder fluid and demonstrate that this parametrisation is in quantitative agreement with the numerical solution of the Ornstein–Zernike equation within the Percus–Yevick approximation. Moreover, the radial distribution function obtained from the parametrisation reproduces quantitatively Monte Carlo simulation data. Our results show that the parametrisation is accurate over a large regime of densities for different interaction ranges and potential strengths.     

Zero-frequency elastic moduli of uniform fluids

A statistical mechanical treatment of equilibrium elasticity of a uniform fluid phase based on density functional theory is presented. Bulk expressions for the stress tensor and the zero-frequency elastic moduli tensor involving the direct correlation function are found.     

直接相关函数对双模晶体相场模型相图的影响

研究了直接相关函数峰宽及 k=0处峰对双模晶体相场模型相图的影响. 结果表明, 随着峰宽的增加, 有序相的相区范围不断增大. 而增大峰宽比可使体心立方(bcc)相区范围缩小, 面心立方(fcc)相区范围大幅增加.直接相关函数 k=0峰的引入则使相图被压缩, 两相共存区变窄, 液相稳定区域增加. 关键词： 晶体相场模型 双模近似 相图 直接相关函数     

The direct correlation function of a one-dimensional Ising model

The strictly finite range of the direct correlation function for a homogeneous nearest neughbor Ising chain is shown to persist in the presence of arbitrary site-dependent coupling constants and an arbitrary external field. A method is developed to examine the range of the direct correlation function for many-neighbor interactions. It is found from numerical examples that, in general, third-neighbor and higher interactions induce long-range direct correlations, as does the presence of a field in the second-neighbor case.     

Solution of Ornstein-Zernike equation for one-dimensional fluids

The application of Wiener-Hopf factorisation procedure as adopted by Baxter has been used to solve the one-dimensional Ornstein and Zernike (oz) equation for a fluid of interacting hard rods. Exact solution is obtained for the Kac potential in the van der Waals limit. We also obtain perturbative results which agree exactly with the lowest order calculations of Kac, Uhlenbeck and Hemmer.     

Structure study of simple fluids

The structure function of simple monatomic liquids like neon and argon is studied in an approximation scheme where intermediate functionQ(r) is extended beyond hardcore diameter rather than the direct correlation functionC(r). The calculated values show good agreement with experimental values.     

The incoherent scattering function and related correlation functions in hard sphere fluids at short times

For a classical fluid of hard spheres and hard disks exact expressions for all densities and wave vectors are derived for the coefficients oft ⁿ in the short-time expansion of the incoherent intermediate scattering function (n = 0, 1,..., 4) and the velocity correlation function (n=0,1,2). Similarly, we obtain the coefficient of the leading term in the short-time behavior of the cumulants of the displacements. Furthermore,S(k, ) has a high-frequency tail ^–4, characteristic for the hard-sphere fluid, which leads to a modification of the standard sum rules. We present estimates for the frequency range, in which this tail may be observed in neutron scattering off noble gases. The results are also compared with Enskog's theory and molecular dynamics calculations.     

Theoretical and analytical radial distribution function for dense fluids

The ‘identical particles in quasi-mean potential energy field’ assumption was used to derive the approximate theoretical and analytical radial distribution function (RDF) for dense fluids through solving the two-body Schrödinger equation and using the first-order perturbation method. The theoretical and analytical expressions of RDF can save much computation time in calculating the thermodynamics properties of fluids and may make the statistical mechanics theories comparable with the equation of state method that is currently widely used in physics, chemistry and technology. The calculated properties for argon by this RDF fit well with the experimental data of reference over a very wide range of conditions, including dense fluids (liquid phase and dense gas), critical point, and dilute gas, in which the pair potential and the Axilrod-Teller three body interaction were considered. The extensive practical application of this model for science and technology needs further investigation.     

Relation between the free energy and the direct correlation function in the mean spherical approximation

It is shown that the direct correlation function of a mixture of hard ions in the mean spherical approximation (MSA) can be expressed in terms of overlap functions of charged spherical shells. In particular, if the system is a mixture of pairs of ions of equal size and opposite charge, then the MSA direct correlation function is given by the electrostatic energy of a pair of charged shells, of radius equal to the radius of the hard ion plus 1/(2). This direct correlation function can be derived from a free energy functional, and a simple extension to nonuniform systems is given.     

Fortran codes for the correlation functions of hard sphere fluids

Our Fortran codes for hard sphere fluids and their mixtures for the correlation functions that arise from the Percus–Yevick theory and the Verlet–Weis semi-empirical correction have proven useful during a period of nearly four decades and continue to be useful. In order to make these codes even more widely available, a brief summary is presented here and listings of these codes are given in the electronically accessible Supplementary Material to this paper.     

On the calculation of equilibrium time correlation functions in hard-sphere fluids

We discuss in detail techniques that have been used to determine single-particle equilibrium time correlation functions in a hard-sphere fluid on the basis of kinetic theory. The accuracy of various procedures is assessed.On leave from Interuniversitair Reactor Instituut, Delft, The Netherlands.     

One-dimensional rigorous hole theory of fluids: Internally constrained ensembles

A hole in a fluid is specified in a well-defined manner. The concentration of holes is a thermodynamic property of the fluid and we derive this concentration in three different ensembles for a one-dimensional fluid of hard rods. The thermodynamics of these rigorously defined holes is developed, and the properties of holes are explored. The ensemble in which the concentration of holes is maintained fixed exhibits dramatic properties. Finally, pair correlation functions for hard rods in the various ensembles are computed. Contrary to a frequently made assumption, the equilibrium number of holes is found to never be proportional to the probability of finding a single hole in the fluid. Constraining the concentration of holes as well as the density leads to dramatic structural effects prominently displayed by the pair correlation function. The ensemble in which the concentration of holes is fixed is an example of an internally constrained metastable system.     

相关测速声呐底混响时空相关函数与载体俯仰角的关系

由于载体在运动过程中存在姿态的变化,不考虑载体姿态的理论相关函数会影响相关声呐的测速精确度。考虑载体俯仰角对发射信号海底照射区域的影响,引入不同权重的多阶贝塞尔函数,得到改进后的理论相关函数。同时,根据相关测速声呐发射参数,给出了基于FOM模型的海底回波仿真。仿真结果表明,改进的理论相关函数将相关声呐的测速误差降至1%以下。载体的俯仰角对时空相关函数产生影响。考虑载体俯仰角的理论相关函数更贴近实际情况,与仿真结果的相关系数吻合的较好,能够更加准确的估计载体速度。     

A modified soft-core fluid model for the direct correlation function of the square-shoulder and square-well fluids

We propose a simple analytical expression of the direct correlation function for the square-shoulder and square-well fluids. Our approximation is based on an ansatz for the direct correlation function of a modified soft-core fluid, whose parameters are adjusted by fitting the data obtained from Monte Carlo computer simulations. Moreover, it is complemented with a Wertheim-like parametrization to reproduce correctly the direct correlation inside the hard-core. We demonstrate that this approach is in quantitative agreement with the numerical solution of the Ornstein–Zernike equation within the Percus–Yevick approximation. We also show that our results are accurate in a large regime of densities for different interaction ranges and potential strengths. Therefore, this opens up the possibility of introducing the square-shoulder or the square-well potentials as new reference systems in advanced theoretical approximations.     

Equilibrium state of a classical fluid of hard rods in an external field

The external field required to produce a given density pattern is obtained explicitly for a classical fluid of hard rods. All direct correlation functions are shown to be of finite range in all pairs of variables. The one-sided factors of the pair direct correlation are also found to be of finite range.Supported in part by U.S. ERDA, Contract No. E(11-1)-3077.     

Pair correlation function for Ising spins with competing dynamics

An interacting Ising spin system on a lattice with the competing influence of spin-flip (Glauber) and spin-exchange (Kawasaki) dynamics is studied. The exact nonequilibrium steady-state solution of the pair correlation function in one dimension is derived and compared with the simulation data. The two-dimensional solution, under some Ansatz, is also discussed.