Analytic solution of the RISM equation forn s-atomic symmetric molecules

A general method of an analytic solution of the RISM equation based on the Baxter factorization is explicitly extended to three- and four-atomic symmetric homonuclear molecules. Results of higher order approximations (beyond the zero pole approximation) are compared with numerical results and it is shown that the analytic solution converges to the numerical one for allL}<1. The role of poles of the intramolecular structural function 1/W(k) depending on the number of sites, site-site span, and density is discussed.     

On the analytical solution of the Ornstein-Zernike equation with Yukawa closure

We discuss the solution of the Ornstein-Zernike equation for most general closure consisting of a sum ofM Yukawa-type exponentials. A formal solution for the factored case is bound for an arbitrary mixture of hard spheres introducing a general scaling matrix of dimensions M×M. A sufficient number of equations for this matrix is obtained from symmetry considerations and the boundary condition. We discuss also restricted and semirestricted case, for which explicit solutions in terms of the scaling parameters and input parameters are found.     

Correlation functions for diatomic symmetric molecules from the RISM equation

Using the solution of the RISM equation for diatomic symmetric molecules outlined in a previous paper, the site-site radial distribution function (RDF) is calculated and compared with the Monte Carlo results and the numerical RDF of Lowden and Chandler. The RDF calculated here and the numerical RDF of Lowden and Chandler agree well at intermediate and high densities. At low density, however, both have systematic errors. The agreement between the RDF calculated here and the Monte Carlo results suggests that a simplified formulation of the RISM solution may serve well as a reference system in a perturbation theory for diatomic fluids.     

Solution of the Ornstein-Zernike equation with Yukawa closure for a mixture

The Ornstein-Zernike equation with Yukawa closure forr > _ij] for a mixture is solved. We utilize the Fourier transform or factorization technique introduced by Baxter. The general solution is obtained in the form of algebraic equations.     

Solution of the Yukawa closure of the Ornstein-Zernike equation

The solution of the Ornstein-Zernike equation with Yukawa closure [c(r)= forr>1] is generalized for an arbitrary number of Yukawas, using the Fourier transform technique introduced by Baxter. Full equivalence to the results of Waisman, Høye, and Stell is proved for the case of a single Yukawa. Finally, a convenient form of the Laplace transform ofg(s) is found, which can be easily inverted to give a stepwise, rapidly converging series forg(r).This research was partially supported by National Science Foundation, the Norwegian Research Council for Science and Humanities, and the donors of the Petroleum Research Fund, administered by the American Chemical Society.     

Solution of the Ornstein-Zernike equation for a mixture of hard ions and Yukawa closure

The solution of the Ornstein-Zernike equation with Yukawa closure discussed in an earlier paper is simplified and extended to the more general case of several exponentials with real or complex exponents. The interesting case of an ionic mixture with Yukawa closure is solved explicitly. This case corresponds to ionic melts (molten salts).Supported by the Center of Environment and Energy Research of the University of Puerto Rico, OCEGI, and in part by NSF grant CHE-77-14611.     

Analytic solution of the multiloop Baxter equation

The asymptotic spectrum of anomalous dimensions of gauge-invariant operators in maximally supersymmetric Yang–Mills theory is believed to be described by a long-range integrable spin chain model. We focus in this study on its sl(2)$sl(2)$ subsector spanned by the twist-two single-trace Wilson operators, which are shared by all gauge theories, supersymmetric or not. We develop a formalism for the solution of the perturbative multiloop Baxter equation encoding their asymptotic anomalous dimensions, using Wilson polynomials as basis functions and Mellin transform technique. These considerations yield compact results which allow analytical calculations of multiloop anomalous dimensions bypassing the use of the principle of maximal transcendentality. As an application of our method we analytically confirm the known four-loop result. We also determine the dressing part of the five-loop anomalous dimensions.     

Analytic solution of the Percus-Yevick equation for sticky hard sphere potential

It is shown that within the Percus-Yevick approximation the radial distribution function for sticky (i.e. with a surface adhesion) hard spheres satisfies a linear differential equation with retarded right-hand side. Using the theory of distributions and the Green's function technique the analytic solution of this equation is found and explicit formulas are given enabling one to evaluate the radial distribution function both for sticky and non-attractive hard spheres for any distance and any density.     

Analytic solution to the Eliashberg equation for the superconducting critical temperatures

The analytic solutions to the Eliashberg equation for the superconducting T_c obtained by the Chinese physicists, mainly Wu and his co-workers, during the years 1977–1985 are systematically reviewed. Two independent and mutually complementary formulae which hold in the regions λ > Λ and λ < Λ, respectively are obtained. Here, Λ is a material dependent parameter and its definition will be given in the paper. The analytic derivations and the properties of these two formulae are discussed and analysed in detail. The values of T_c calculated from them are compared with the experimental values and the numerical solutions of the Eliashberg equation. They are compared further with those given by other T_c formulae proposed by previous authors and some comments are given.     

Analytic solution for Telegraph equation by differential transform method

In this article differential transform method (DTM) is considered to solve Telegraph equation. This method is a powerful tool for solving large amount of problems (Zhou (1986) [1], Chen and Ho (1999) [2], Jang et al. (2001) [3], Kangalgil and Ayaz (2009) [4], Ravi Kanth and Aruna (2009) [5], Arikoglu and Ozkol (2007) [6]). Using differential transform method, it is possible to find the exact solution or a closed approximate solution of an equation. To illustrate the ability and reliability of the method some examples are provided. The results reveal that the method is very effective and simple.     

Analytic solution of Percus-Yevick equation for fluid of hard spheres

A new method of analytic solution of the Percus-Yevick equation for the radial distribution functiong(r) of hard-sphere fluid is proposed. The original non-linear integral equation is reduced to non-homogeneous linear integral equation of Volterra's type of the second order. The kernel of this new equation has a polynomial form which allows to find analytic expression forg(r) itself without using the Laplace transformation. In addition, the first three moments of the total correlation function can be found.     

离散修正KdV方程的解析近似解

将同伦分析法进行了推广,使之适用于求解离散修正KdV方程.获得了由指数函数表达的亮孤子解,该解析近似解与精确解符合很好.数值模拟结果说明了同伦分析法对求解复杂非线性问题的有效性和潜力.     

一类广义Sine-Gordon扰动方程的解析解

利用同伦映射方法研究了一类广义Sine-Gordon方程. 首先引入一个同伦变换. 然后构造了原方程解的迭代关系式. 最后得到了问题的解析解. 关键词： 孤子 扰动 同伦映射     

Analytic properties of the T matrix for two Yukawa potentials

A study is made of the behavior of the residues at the Regge poles of the partial-wave T matrix on the mass shell as a function of the energy E for nonrelativistic scattering on an exponential potential and two Yukawa potentials. It is shown that the residues do not have left-hand cuts in the E plane.     

Critical behaviour in MSA for a symmetric Yukawa mixture

We study a symmetric binary mixture of equidiameter hard-spheres with repulsive Yukawa interaction for unlike atoms and attractive Yukawa interaction for like atoms. Due to a fully analytical approach we find that, for all values of the Yukawa exponentz0, the critical exponents are of the mean-spherical type. The critical region gets narrower with the increase of the range of the potential, causing a failure of the ordinary numerical analysis. Therefore, the previous analysis, based on numerically accessible region near the critical point, that predicted the mean-field structure of the critical exponents for small values ofz, was not adequate.     

Solution of the Ornstein-Zernike equation for a soft-core Yukawa fluid

A model for simple fluids is proposed in which the radial distribution function has a parametric form appropriate to a soft-core fluid for interparticle separationr R, whereR is some range parameter. Forr > R, the direct correlation function is assumed to be of Yukawa form. The Ornstein-Zernike equation is solved for this system, yielding the radial distribution and the total correlation function for the entire range of interparticle separation. Methods of relating the model fluid to a real fluid by assigning values to the parameters are discussed.Supported by ARGC grant No. B7715646R.