HIGH-ORDER CLUSTER INTEGRALS FOR THE LATTICE-GAS MODEL
Journal Title: Дослідження в математиці і механіці - Year 2018, Vol 23, Issue 2
Abstract
In the paper, for the known statistical lattice-gas model, a new method is proposed to define the high-order reducible cluster integrals on the basis of the Cauchy--Hadamard theorem and recently established strict information about the convergence radius of the virial expansions for pressure and density in powers of activity. Compared with previous studies (where the whole set of reducible cluster integrals were evaluated on the basis of the extremely limited number of low-order irreducible integrals), the proposed complex method to approximate the reducible cluster integrals yields the theoretical values of pressure at the saturation and boiling points considerably close to each other as well as to the Lee--Yang solution for the two-dimensional lattice gas.
Authors and Affiliations
S. Y. Ushcats, M. V. Ushcats, A. N. Alekseev
Keywords
Related Articles
- EP ID EP558806
- DOI 10.18524/2519-206x.2018.2(32).149707
- Views 77
- Downloads 0
A Bernstein type inequality for fractional logarithmic derivatives of polynomials in 𝐿0
The study of integral equations with power-laws-logarithmically kernels, as well as problems related to the Fourier series of integrable functions led to fractional-logarithmic derivatives and integrals. In this paper fr...
On a two-step algorithm in structural and parametric optimization problems of linear control systems.
This paper deals with applying of a two-step optimization algorithm for structural and parametric optimization problems of linear control systems with fixed and floating switching points.
QA-DEFORMATION OF SURFACE OF NEGATIVE GAUSSIAN CURVATURE
An infinitesimal deformation with the given law of changing the element of area of a surface in Euclidean three-space was considered in this article. Such deformation in the article was called the quasiareal infinitesima...
The rheology simulation for a inhomogeneous structure of the shear fluid flow into slender clearances
The theory of shear flow structure into slender clearances on the basis of variable viscosity was constructed. The power dependence on local velocity deformation and on distance bounding hard surfaces into priwall layers...
Variational method of homogeneous solutions for axisymmetric elasticity problems
A variational method of homogeneous solutions for solving of axisymmetric elasticity problems for semiinfinite and finite cylinders with free lateral surface has been developed. As an example of application of the method...