5 research outputs found
Intersections of moving fractal sets
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
Efficient method of finding scaling exponents from finite-size Monte-Carlo simulations
Monte-Carlo simulations are routinely used for estimating the scaling
exponents of complex systems. However, due to finite-size effects, determining
the exponent values is often difficult and not reliable. Here we present a
novel technique of dealing with the problem of finite-size scaling. This new
method allows not only to decrease the uncertainties of the scaling exponents,
but makes it also possible to determine the exponents of the asymptotic
corrections to the scaling laws. The efficiency of the technique is
demonstrated by finding the scaling exponent of uncorrelated percolation
cluster hulls.Comment: The "previous version" of this is arXiv:0804.1911. This version is
published in EPJ
On Statistical Topography of Self-Affine Sets. Eneseafiinsete hulkade statistilisest topograafiast
On Statistical Topography of Self-Affine Sets. Eneseafiinsete hulkade statistilisest topograafiast
Doctoral thesis 1/2019
Doktorit\uf6\uf6 1/201