
Physics 2013
Intersections of moving fractal setsDOI: 10.1209/02955075/103/10012 Abstract: Intersection of a random fractal or selfaffine 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 selfaffine 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 selfaffine curve with a line, and of two fractal sets. The analytical results are tested using MonteCarlo simulations.
