Solution of the Percus-Yevick equation for hard disks

In two papers in the Journal of Chemical Physics we proposed a new (numerical) method to find solutions of the Percus-Yevick equation. Our first paper showed how this could be done for hard disks (i.e. in two dimensions) and the follow up paper extended this (in principle) to hyperspheres in any even dimension. The references for these two papers are as follows:

Several groups have contacted us to ask for the data that we generated so that they can use it to determine the pair correlation function, g(r), and the Fourier transform of structure function, S(k), for hard disks. This page is intended to make this data publicly available, though we would appreciate appropriate citations in any work that uses our data (!)

In our approach, we express all quantities as power series in the packing density, &rho . This approach has the advantage that one relatively long calculation (to determine the coefficients) yields enough information to determine other properties, such as g(r) and S(k), for different values of &rho with relatively little additional calculation.

The data we have made available can be used to generate g(r) and S(k) for HARD DISKS ONLY. You will need to download three files:

  • The matlab code that produces graphs of g(r) and S(k) at three different values of &rho is here

  • The 10MB file containing the coefficients you need to calculate g(r) is here.

  • The 0.5MB file containing the coefficients you need to calculate S(k) is here.

The only thing you should need to change is the values of &rho that you want g(r) and S(k) to be plotted for. You do this on lines 24, 28 and 32. Beware that using large values of &rho may cause the power series to diverge. In our experience things should be fine provided &rho<0.8 but you may still need to take a larger number of iterations (maxits) to ensure reasonable convergence. Also, you should remember that &rho is not the same as the packing density &eta . In fact, &rho= 4&eta/&pi .

If you really want data for other dimensionalities, please contact me!

This page was most recently updated on the 20th of January, 2010.