Percolation of randomly distributed growing clusters: the low initial density regime
Department of Physics, University of Thessaloniki, 54124 Thessaloniki, Greece
Corresponding author: a firstname.lastname@example.org
Revised: 11 April 2011
Published online: 25 May 2011
We investigate the problem of growing clusters, which is modeled by two dimensional disks and three dimensional droplets. In this model we place a number of seeds on random locations on a lattice with an initial occupation probability, p. The seeds simultaneously grow with a constant velocity to form clusters. When two or more clusters eventually touch each other they immediately stop their growth. The probability that such a system will result in a percolating cluster depends on the density of the initially distributed seeds and the dimensionality of the system. For very low values of p we find a power law behavior for several properties that we investigate, namely for the size of the largest and second largest cluster, for the probability for a spanning cluster to occur, and for the mean radius of the finally formed droplets. We report the values of the corresponding scaling exponents. Finally, we show that for very low initial concentration of seeds the final coverage takes a constant value which depends on the system dimensionality.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2011