# Research data supporting "Roughness spectroscopy of particle monolayer: Implications for spectral analysis of the monolayer image". B-spline representation of radial distribution function.

## Description

The files contain knots and coefficients of third order (quadratic) B-spline representation approximating a radial distribution function (RDF). We calculated the function for a hard-disk monolayer generated with event-driven molecular dynamics, of surface coverage 0.85. Specifically, to produce the monolayer, we used the program PackLSD.64.x by Aleksandar Donev, available at https://cims.nyu.edu/~donev/Packing/PackLSD/Instructions.html. We started the simulation of 8.5E7 disks at the initial surface coverage of 0.1 to gradually increase their size. In the nml parameter file, we set the disk expansion rate parameter expansions_=0.001. Once the surface coverage achieved 0.85, we stopped the simulation. We generated 26 replicas of the big system with a constant area of square simulation box. For each replica, we first calculated the discrete RDF g(r) by counting disk pairs in narrow distance intervals of width dr = 1E-3 a, where a is the disk radius. In the narrow interval 3.9900 ≤ r ≤ 4.0020, where the slope of the RDF changes extremely rapidly, we used the ring thickness 1E-4. For each replica of the system, we calculated the mean distance and RDF over the 88108 narrow intervals, averaging over the central particles. We calculated 26 replicas of the function g(r) in the range from r = 2a to r = 90a. Averaging over them, we got 88108 discrete, arithmetic mean values of RDF and standard deviations of the means. We identified the maximum value of the RDF standard deviation to be 0.009. Finally, we fit a third order (quadratic) B-spline representation to the mean RDF. For that, we used the procedure DFC of SLATEC library, with 3786 proper knots. To calculate the RDF with the B-spline, you can use the procedure DBVALU of SLATEC library. The knot vector in the attached file begins and ends with two improper knots, in accordance with requirements of the procedure. For details, see the paper: P. Weroński & K. Pałka, "Roughness spectroscopy of particle monolayer: Implications for spectral analysis of the monolayer image", Measurement 196 (2022) 111263.

## Files

## Steps to reproduce

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