Intersections of moving fractal sets
Statistical Mechanics
2013-07-30 v1
Abstract
Intersection of a random fractal or self-affine set with a linear manifold or another fractal set is studied, assuming that one of the sets is in a translational motion with respect to the other. It is shown that the mass of such an intersection is a self-affine function of the relative position of the two sets. The corresponding Hurst exponent h is a function of the scaling exponents of the intersecting sets. A generic expression for h is provided, and its proof is offered for two cases --- intersection of a self-affine curve with a line, and of two fractal sets. The analytical results are tested using Monte-Carlo simulations.
Keywords
Cite
@article{arxiv.1307.4242,
title = {Intersections of moving fractal sets},
author = {Indrek Mandre and Jaan Kalda},
journal= {arXiv preprint arXiv:1307.4242},
year = {2013}
}