Analysis and characterisation of statistical properties on rough surfaces - Abril, Leidy Milena Leal (2021)
Statistical properties of random surfaces are widely studied since these are found in a lot of natural phenomena. Long-range spatial correlations quantified by the Hurst exponent are imposed within the surfaces through the Fourier filtering method. In addition, one can extract isoheight lines from rough surfaces and mapped them to percolation lines. Therefore, based on the percolation theory, we have studied the curves coupled to random surfaces with positive Hurst exponents. We obtain graphics for the roughness exponent, the fractal dimension for the case H=0, the mass of the isoheight lines and the kurtosis of the height distribution as functions of the Hurst exponent. Our results show that the height distribution of percolation lines does not have Gaussian behaviour.