Equation of State of the Hard-Disk Fluid from Approximate Integral Equations

Abstract

The Percus-Yevick, hypernetted-chain, and "pressure-consistent' integral equations have been solved, using numerical Hankel transforms, for a fluid of two-dimensional hard cores. The thermodynamic quantities obtained from these solutions are presented and compared among themselves and with the results of other theories; a comparison of computed pair distribution functions g with a Monte Carlo g is also presented. The Percus-Yevick equation is found to give the best over-all results.

Solution of the Percus-Yevick equation for hard disks

“…This means that the present analysis necessarily yields both correlation functions and therefore provides the equation of state. Note that Lado [9] solved the problem using approximate integral equations, in contrast to our exact integral equations. The advantage of the current method is that one can improve the precision at will, and that it may be generalized to higher even dimensions.…”

Solution of the Percus–Yevick equation for hard hyperspheres in even dimensions

“…d = 2) 35 . Rather than computing the equation of state for various densities ρ (as in earlier work 29 ), we compute the virial coefficients, B i , which are defined by…”

“…In two dimensions an approximate numerical solution of the PY equation was found by Lado 29 . Leutheusser 23 was able to fit many of Lado's results using an ansatz for the direct correlation function.…”

Reference hypernetted chain theory for ferrofluid bilayer: Distribution functions compared with Monte Carlo

“…The parameter ξ is chosen to achieve consistency of the virial p v and compressibility pressures p c , [30][31][32] where for our case…”

“…Then we determine the indirect correlation function γ ref μν of the reference system by solving the homogeneous variant of OZ equation (9) and the pressure-consistent (PC) closure [30][31][32] (also called the Rowlinson-Lado closure 33 ),…”