THE STUDY OF GAY–BERNE FLUID: INTEGRAL EQUATIONS METHOD

2009 ◽  
Vol 23 (05) ◽  
pp. 753-769 ◽  
Author(s):  
REZA KHORDAD ◽  
MEHRAN MOHEBBI ◽  
ABOLLA KESHAVARZI ◽  
AHMAD POOSTFORUSH ◽  
FARNAZ GHAJARI HAGHIGHI

We study a classical fluid of nonspherical molecules. The components of the fluid are the ellipsoidal molecules interacting through the Gay–Berne potential model. A method is described, which allows the Percus–Yevick (PY) and hypernetted-chain (HNC) integral equation theories to be solved numerically for this fluid. Explicit results are given and comparisons are made with recent Monte Carlo (MC) simulations. It is found that, at lower cutoff l max , the HNC and the PY closures give significantly different results. The HNC and PY (approximately) theories, at higher cutoff l max , are superior in predicting the existence of the phase transition in a qualitative agreement with computer simulation.

2010 ◽  
Vol 15 (3) ◽  
pp. 371-381
Author(s):  
Behrouz Fathi Vajargah ◽  
Mojtaba Moradi

In this paper, we consider the Monte Carlo method for finding the solution of nonlinear integral equations at a fixed point xo‐ In this method, simulated Galton‐Watson branching process is employed for solving the proposed integral equation. The main goal of this paper is to compare the behavior of three classifications of branching process based on the mean progeny, i.e. the subcritical, critical and supercritical process.


2018 ◽  
Vol 22 (4) ◽  
pp. 1673-1678
Author(s):  
Yi Tian

A thermal problem can be always modeled using an integral equation. This paper uses the Monte Carlo method based on the simulation of a continuous Markov chain to solve Fredholm integral equations of the second kind. Some examples are given to show the efficiency of the present work.


Author(s):  
E. S. Page ◽  
D. R. Cox

ABSTRACTEstimators are given for the solution by Monte Carlo methods of the Fredholm integral equation of the second kind and the variances of the estimators are compared. Two integral equations arising in sequential analysis are considered in detail; some numerical examples are given.


Sign in / Sign up

Export Citation Format

Share Document