Exact Solution of the First-Order Perturbed Percus-Yevick Equation for Arbitrary Pair Potentials (Classic Reprint) - Softcover

Percus, Jerome K.

9781330587829: Exact Solution of the First-Order Perturbed Percus-Yevick Equation for Arbitrary Pair Potentials (Classic Reprint)

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ISBN 10: 1330587820 ISBN 13: 9781330587829

Verlag: Forgotten Books, 2018

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Excerpt from Exact Solution of the First-Order Perturbed Percus-Yevick Equation for Arbitrary Pair Potentials

The Ferous - Yevick approximate integral equation for the pair correlation function in classical statistical mechanics has been solved exactly for hard cores The direct correlation function is given in its non - vanishing domain by a low order polynomial, of degree one or three, for the case of one or three dimensional hard cores. Exact solutions of the p.y. Equation for potentials of arbitrary range have never been obtained, however. The object of this work is to examine the effect upon the correlation functions of adding a long-range interaction to the repulsive core. Although treated exhaustively in one - dimension, our technique is by no means limited to this, indeed being applicable to both three - dimensional non-polar and polar liquids.

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Excerpt from Exact Solution of the First-Order Perturbed Percus-Yevick Equation for Arbitrary Pair Potentials

The effect upon the correlation functions of a fluid of adding a pair potential of arbitrary range to a repulsive hard core is investigated in the case of the Percus-Yevick approximation of classical equilibrium statistical mechanics. The nonlinear P. Y. equation is perturbed, to first-order, and the resulting linear integral equation for the first-order correlation functions is then solved exactly for a general interparticle potential. The method of solution is presented for one-dimensional systems, but three-dimensional non-polar and polar liquids can be encompassed. Essential to the technique is the calculation of a certain zeroth-order quantity, which is proportional to the faltung of the hard core pair correlation function with itself, and which is composed of a sum of nth-neighbor contributions. Obtaining this quantity allows conversion of the first-order perturbed P. Y. integral equation to an ordinary differential equation of fourth order for the direct correlation function inside the core.

About the Publisher

Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com

This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

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