Universal scaling properties of ballistic deposition and Eden growth on surfaces

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Abstract
The structures generated by ballistic deposition and Eden growth from a surface can be divided in a natural way (defined by the growth process) into 'trees' or clusters of connected sites or particles. The structure of these trees can be characterised by the exponents nu perpendicular to (=p) and nu /sub ///(=q) which describe how their heights (h) and widths (w) grow with increasing size s (w approximately sp, h approximately sq). In addition, the distribution of sizes can be described by the power law Ns approximately s- tau where Ns is the number of trees of size s. Both the individual trees and the complete deposit are compact so that the exponents p, q and tau satisfy the simple scaling relationships (d-1)p+q=1 and tau =2-q. The exponents p, q and tau seem to be universal for off-lattice ballistic deposition, on-lattice ballistic deposition and Eden growth models. However, the corresponding exponents for the river network model are different from those for Eden growth and ballistic deposition. From the two-dimensional Eden model and ballistic deposition models values of about 0.40, 0.60 and 1.40 were obtained for p, q and tau , respectively. In three dimensions p approximately=0.28, q approximately=0.46 and tau approximately=1.54.

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