Department of Microsystems Engineering, University of Freiburg, Georges-Köhler-Allee 103, 79110 Freiburg, Germany
Cluster of Excellence livMatS, Freiburg Center for Interactive Materials and Bioinspired Technologies, University of Freiburg, Georges-Köhler-Allee 105, 79110 Freiburg, Germany
Example illustrating the contact of a rough sphere that behaves as a nominally flat rough surface at small normal forces while it follows the Hertzian theory of smooth spheres at large normal forces. This dataset is similar to the simulations in https://doi.org/10.1063/1.4950802 The topographies were generated with the following Python code: ``` from SurfaceTopography.Generation import fourier_synthesis from SurfaceTopography.Special import make_sphere import numpy as np a0 = 1 # Pixel size radius = 10000 n = 1024 hprms = 0.01 np.random.seed(0) roughness = fourier_synthesis( (n, n), physical_sizes=(n, n), rms_slope=hprms, hurst=0.8, short_cutoff=4, long_cutoff=256 ) sphere = make_sphere(radius, (n, n), (n, n), centre=(n // 2 + 1, n // 2 + 1 ), kind="paraboloid") roughness.to_matrix(f"rough_flat.txt") sphere.to_matrix(f"smooth_sphere.txt") roughness._heights += sphere.heights() roughness.to_matrix(f"rough_sphere.txt") ```