Research data supporting "Toward automatic analysis of random monolayers: The effect of pair correlation". B-spline representations of integral Ic(q).
Description
The files contain knots and coefficients of third order (quadratic) B-spline representations approximating the integral Ic(q) appearing in the equation for power spectral density of particle or cavity monolayer. The integral depends on the total correlation function of objects forming the monolayer. We used B-spline representations of the correlation functions computed for the classical RSA systems at five values of surface coverage: 0.1, 0.2, 0.3, 0.4, and 0.5. For each coverage, we generated 20 replicas of the correlation function, as described at http://dx.doi.org/10.17632/s4k84ccxww.2. Next, for each replica, we numerically computed the integral using the procedure DBFQAD of SLATEC library. This way we got 1E5 values of the integral at equidistant wavenumbers in the interval from 1E-3 to 1E2. After ensemble averaging we got 1E5 arithmetic mean values of the integral 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 1E-3 at coverage 0.1 to 8E-5 at coverage 0.5. Finally, we fit B-spline representations to the averaged integrals. For that, we used the B-spline fitting procedure splrep of the package SciPy.interpolate included in the Python-based open-source library SciPy. Considering the very small values of maximum standard deviations of the means, we used third order (quadratic) B-splines with the default knot vector generated by the procedure splrep, i.e., with the knot separation distance equal about 1E-3. To calculate the integral with the B-splines you can use the procedures splev or BSpline of the module SciPy.interpolate of SciPy library v. 1.1.0. Knot vectors in the attached files begin and end with two improper knots, in accordance with the requirements of the procedures. 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 integral with the B-splines, use the procedures splev or BSpline of the module SciPy.interpolate of SciPy library v. 1.1.0 or compatible.