Equation For Pair Correlation Function Research Articles

Effect of an external action on a pair distribution function in a steady state

An external action that reduces a two-component equilibrium thermodynamic system to a nonequilibrium steady state with scalar fluxes has been studied. A system of integrodifferential equations for pair correlation functions has been obtained. These equations coincide with the second equations of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, but with different effective temperatures. Thus, ordinary integrodifferential equations for a pair correlation function with effective temperatures expressed in terms of the perturbed (nonequilibrium) Maxwellian momentum distribution function can be used to calculate the structural and thermodynamic properties of such a system.

Magnetic field generation in galactic molecular clouds

We discuss magnetic field generation in weakly ionized turbulent gas. We consider the case of nonzero mean magnetic field. We assume that fluctuations are isotropic, and derive evolution equation for pair correlation function of magnetic fluctuations. Stationary solution of this equation is presented.

Analytical solution to the equation for pair correlation function of particles formed in the course of phase separation in a glass

The problem of determining the pair correlation function of phase-separated particles from the experimental data obtained for the plane section of a sample has already been consul and in the literature. The integral equation relating the pair correlation function of monodisperse spherical particulers and the pair correlation function of their traces on the secant plane was obtained, and the method of numerical solution of this equation was elaborated with the aim of determining the pair correlation function of places. The present paper describes the analytical solution to this equation.

Model protein conformations via pair correlation functions, distance matrix, and embedding algorithm

A method of constructing three-dimensional structures of model protein conformations is presented. The method consists of self-consistent field integral equations for pair correlation functions of constituent units in a heteropolymer chain and the use of the distance matrix and the embedding algorithm for constructing conformations. The pair correlation functions obey integral equations that are derived from the Kirkwood hierarchy by applying closure approximations; they appear as a generalized form of the liquid-state Percus–Yevick integral equation. Model protein sequences that exhibit the formation of secondary-like patterns and tertiary-like structures are examined. These structural features are formed at low temperatures and they are stabilized by strong hydrogen bonding forces. To obtain the structure in three dimensions, the method of distance geometry is used to refine the distance matrix of a folded structure which is then embedded in the three-dimensional space by an embedding algorithm.

Solution of the Percus-Yevick equation for pair-correlation functions of molecular fluids.

The Percus-Yevick (PY) integral equation has been solved for two model fluids: (i) a fluid of hard ellipsoids of a revolution represented by a Gaussian overlap model, and (ii) a fluid the molecules of which interact via a Gay-Berne [J. Chem. Phys. 74, 3316 (1981)] model potential. The method used involves an expansion of angle dependent functions appearing in the integral equation in terms of spherical harmonics. The dependence of the accuracy of the results on the number of terms taken in the basis set is explored for both fluids at different densities, temperatures, and lengths to width ratios of the molecules. We have compared our results with those of computer simulations wherever they are available. We find that the PY theory gives reasonable values of the harmonic coefficients for both fluids at all fluid densities when all terms involving the index l up to six in the expansion are considered. For the Gay-Berne fluid we have developed a perturbation expansion for a calculation of the structure and thermodynamic properties of the isotropic phase.

Some results for hard spheres at a hard wall using the inhomogeneous Percus–Yevick equation and a modified Lovett–Mou–Buff–Wertheim equation

Some results are reported for the contact value of the density profile of hard spheres near a hard wall using the inhomogeneous Percus–Yevick equation for pair correlation functions and the Lovett–Mou–Buff–Wertheim (LMBW) equation to relate the pair functions to the singlet density profile. It is found that improved results are obtained if the LMBW is modified as suggested by Quintana et al.

Equation for Pair Correlation Function of n-Vector Model

On considere le modele n-vecteurs dans lequel chaque spin j a n composantes mais la longueur de spin n j 1/2 depend de j. On montre que l'on peut deduire un ensemble d'equations differentielles contenant seulement des fonctions de correlation de paire

Approximation schemes for strongly coupled two-component plasmas

A formalism appropriate for obtaining a self-consistent handling of the strongly coupled two-component plasma problem is discussed. The divergence of the classical electron-ion pair correlation function is removed with the aid of a phenomenological ''soft-core'' potential. The important formal development is the introduction of partial linear and nonlinear polarizabilities, their interrelations, and the linear and nonlinear fluctuation-dissipation theorems satisfied by them. The formalism is used to generalize existing strongly coupled one-component plasma theories for the two-component situations. Both the schemes based on the first Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) equation and the fluctuation-dissipation theorems, and the scheme based on the second BBGKY equation and the decomposition of the triplet correlation function are developed into self-consistent two-component equations. Algebraically, the equations appear as a set of three, coupled, nonlinear integral equations for pair correlation functions or polarizabilities. (AIP)

Erratum and addenda: Solution of a new integral equation for pair correlation function in molecular liquids

First Page

Solution of a new integral equation for pair correlation functions in molecular liquids

This paper discusses the first numerical solutions of the reference interaction site model (RISM) equation which was proposed by Chandler and Andersen [J. Chem. Phys. 57, 1930 (1972)] to provide a theory for the equilibrium pair correlations of molecular fluids in which the ``molecules'' are composed of fused hard spheres. The particular system studied herein is a one component fluid in which the molecules are symmetric ``diatomics'' (i.e., each is formed by two hard spheres of diameter σ with the centers of the spheres a distance L from each other). It is shown that the accuracy of the RISM equation for this molecular fluid is comparable to that of the Percus-Yevick equation for dense hard sphere fluids. Numerous calculations are presented which illustrate the usefulness of this theory in providing a detailed description of the intermolecular structure of complex fluids. One calculation provides a theory for the structure of liquid nitrogen.

Derivation of an integral equation for pair correlation functions in molecular fluids

A new integral equation for equilibrium pair correlation functions in molecular fluids is derived from a systematic functional Taylor expansion. The derivation employs a new Ornstein-Zernike-like equation and a generalization of the functional Taylor expansion techniques frequently employed to derive integral equations for radial distribution functions in simple atomic liquids.

Self-consistent correlation function approximation in Ising ferromagnets

Two modifications are proposed to improve the Weiss molecular field approximation of Ising ferromagnets: a pair of central spins was examined to yield self-consistent equations for pair correlation functions; the nearest neighbors of the central spins are also taken into account. Various correlation functions are related to each other, and a molecular field equation, which contains indeterminate parameters, is then derived. When applied to square lattice, the lowest order approximations may be obtained with very little computational work and are already in good agreement with Onsager's exact solutions. Results for the cubic lattice are also given. The indeterminate parameters may be adjusted to fit the correlation functions to the series expansion results, thus higher order approximations can be systematically calculated.