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

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.

本数据集文件包含用于近似径向分布函数（radial distribution function, RDF）的三阶（二次）B样条（B-spline）表示的节点与系数。
我们通过事件驱动分子动力学（event-driven molecular dynamics）生成了表面覆盖率为0.85的硬圆盘单层体系，并计算了该体系的径向分布函数。具体而言，我们使用Aleksandar Donev开发的程序PackLSD.64.x来制备该单层体系，该程序可从https://cims.nyu.edu/~donev/Packing/PackLSD/Instructions.html获取。我们启动了包含8.5×10^7个圆盘的模拟，初始表面覆盖率为0.1，随后逐步增大圆盘尺寸。在nml参数文件中，我们将圆盘膨胀速率参数expansions_设为0.001。当表面覆盖率达到0.85时，停止模拟。
我们生成了26个复本的大体系，模拟盒为恒定面积的正方形盒子。对于每个复本，我们首先通过在宽度dr=1×10^-3 a的窄距离区间内统计圆盘对数目，计算离散形式的径向分布函数g(r)，其中a为圆盘半径。在RDF斜率变化极快的区间3.9900 ≤ r ≤4.0020内，我们将环厚度设为1×10^-4。对于每个体系复本，我们在88108个窄区间内计算平均距离与径向分布函数，并对中心粒子进行平均。我们在r=2a至r=90a的范围内生成了26组g(r)函数数据，对其求平均后，得到88108个离散的径向分布函数算术平均值及其均值的标准差。经计算，径向分布函数标准差的最大值为0.009。
最终，我们针对平均径向分布函数拟合了三阶（二次）B样条表示。为此，我们使用了SLATEC库中的DFC过程，共使用3786个有效节点。
若要通过B样条计算径向分布函数，可使用SLATEC库中的DBVALU过程。附件文件中的节点向量首尾均带有两个非有效节点，以符合该过程的要求。详细信息请参阅论文：P. Weroński & K. Pałka, "Roughness spectroscopy of particle monolayer: Implications for spectral analysis of the monolayer image", Measurement 196 (2022) 111263.