Exact Solution of the First-Order Perturbed Percus-Yevick Equation for
Language: English
Published by Forgotten Books, 2018
- Softcover
- New
Seller: Forgotten Books, London, United KingdomForgotten Books
AbeBooks seller since June 2, 2021
Condition: New
US$ 18.15
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Print on Demand. This book is a continuation of the author's previous work on the pair correlation function. It presents a solution to the first-order perturbed Percus -Yevick equation for arbitrary pair potentials of hard cores with repulsive tails, which bridges the gap between the statistical mechanics of hard sphere fluids, and fluids with continuous pair potentials. The study of the pair correlation function allows us not merely to compute thermodynamic quantities, but also to predict the structure of the fluid. The author's solution for the pair correlation function is found in the form of a series of successive density approximations. The central idea is to perturb the nonlinear P.Y. equation to obtain a linear integral equation for the first-order perturbed correlation functions, which can then be solved exactly for a general interparticle potential. The validity of the first-order perturbation theory is tested by evaluating the expression obtained for the first order direct correlation function in the particular case of a tail potential which is a replica of the core over a finite range. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book.…
Seller Inventory # 9781330587829_0
- Title
- Exact Solution of the First-Order Perturbed Percus-Yevick Equation for
- Author
- Jerome K. Percus
- Publisher
- Forgotten Books
- Publication year
- 2018
- Condition
- New
- Book Type
- print-on-demand item
- Binding
- Paperback
- Language
- English
- ISBN 10
- 1330587820
- ISBN 13
- 9781330587829
- Seller catalogs
- Calculus
Exact first‑order insight into how small tail forces reshape core correlations
This book develops a method to extend the Percus–Yevick equation, solved exactly for hard cores, to include a tail potential of arbitrary range. It shows how a first‑order perturbation leads to explicit formulas for the direct correlation function inside the core and the pair correlation function outside it. The approach blends distribution‑function theory with practical solutions, and it ties the results to known models like Debye–Hückel and Yukawa tails. The work also illustrates how linear responses emerge when tail effects are added and tests these ideas against exact statistical mechanics.
In this edition, you’ll see the step‑by‑step reduction of the perturbed equation to a solvable form, the construction of S‑neighbor representations, and the way boundary conditions at the hard core are used to determine constants of integration. The content connects abstract theory to explicit models, including a simple application to the glue model of Baxter and a discussion of when linear behavior appears in tails. Readers with a background in statistical mechanics or liquid‑state theory will gain a concrete toolkit for analyzing how long‑range interactions alter core structure.- Derivation of the first‑order direct correlation function inside the hard core and the first‑order pair correlation outside.
- Reduction of the perturbed equation to a fourth‑order differential form with clear boundary conditions.
- Examples that connect to Debye–Hückel, Yukawa, double Yukawa, and power‑law tail potentials.
- Discussion of linearity in tail models and conditions for first‑order phase behavior.
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Forgotten Books’ Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the quality of the aged text.
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