Test of multiscaling in a diffusionlimitedaggregation model using an offlattice killingfree algorithm
Abstract
We test the multiscaling issue of diffusionlimitedaggregation (DLA) clusters using a modified algorithm. This algorithm eliminates killing the particles at the death circle. Instead, we return them to the birth circle at a random relative angle taken from the evaluated distribution. In addition, we use a twolevel hierarchical memory model that allows using large steps in conjunction with an offlattice realization of the model. Our algorithm still seems to stay in the framework of the original DLA model. We present an accurate estimate of the fractal dimensions based on the data for a hundred clusters with 50 million particles each. We find that multiscaling cannot be ruled out. We also find that the fractal dimension is a weak selfaveraging quantity. In addition, the fractal dimension, if calculated using the harmonic measure, is a nonmonotonic function of the cluster radius. We argue that the controversies in the data interpretation can be due to the weak selfaveraging and the influence of intrinsic noise.
 Publication:

Physical Review E
 Pub Date:
 January 2006
 DOI:
 10.1103/PhysRevE.73.011407
 arXiv:
 arXiv:condmat/0504338
 Bibcode:
 2006PhRvE..73a1407M
 Keywords:

 61.43.Hv;
 81.10.Aj;
 68.35.Fx;
 Fractals;
 macroscopic aggregates;
 Theory and models of crystal growth;
 physics of crystal growth crystal morphology and orientation;
 Diffusion;
 interface formation;
 Condensed Matter  Statistical Mechanics
 EPrint:
 8 pages, 9 figures