# Research data supporting "Toward automatic analysis of random monolayers: The effect of pair correlation". B-spline representations of total correlation function.

## Description

The files contain knots and coefficients of fourth order (cubic) B-spline representations approximating total correlation functions. We calculated the functions for the classical 2D RSA systems at five values of surface coverage. First, using the model, we produced hard-disk monolayers of surface coverage: 0.1, 0.2, 0.3, 0.4, and 0.5. For each coverage, we generated 20 replicas of a big system with the square simulation area As = 1E8 Ap, where Ap is the disk surface area. For each replica, we first calculated the pair-correlation function g(r) by counting disk pairs in narrow distance intervals of width dr = 0.01 a, where a is the disk radius. For each coverage, we calculated 20 replicas of the function g(r) in the range from r = 2a to r = 10a, i.e., in 800 narrow intervals. Next, we calculated replicas of the total correlation function h(r) = g(r) - 1. After ensemble averaging we got 800 discrete, arithmetic mean values of correlation function and standard deviations of the means, for each coverage. We identified and compared the maximum values of the standard deviation for each of the five coverages. The maximum standard deviations decreased with the increase in coverage from 6E-3 at coverage 0.1 to 7E-4 at coverage 0.5. Finally, we fit fourth order (cubic) B-spline representations to the mean total correlation functions. For that, we used the procedure DFC of SLATEC library. To calculate the total correlation function with the B-splines, you can use the procedure DBVALU of SLATEC library. Knot vectors in the attached files begin and end with three improper knots, in accordance with requirements of the procedure. For details, see the paper: P. Weroński & K. Pałka, "Toward automatic analysis of random monolayers: The effect of pair correlation", Measurement 179 (2021) 109536.

## Files

## Steps to reproduce

To use the files, download the version for linux or windows and unzip it. You will get ten files with self-explanatory names. To calculate the total correlation function with the B-splines, use the procedure DBVALU of SLATEC library v. 4.1 or compatible.