AAAR 33rd Annual Conference
October 20 - October 24, 2014
Rosen Shingle Creek
Orlando, Florida, USA
Abstract View
Divine Proportion Shape Invariance of DLCA Fractal Aggregates: An Analytical Theory
William Heinson, Amit Chakrabarti, CHRIS SORENSEN, Kansas State University
Abstract Number: 266 Working Group: Aerosol Physics
Abstract This paper reconsiders an analytic theory, the restricted hierarchical model (RHM, Sorensen and Oh, Phys. Rev. E58, 7545 (1998)), for Diffusion Limited Cluster Aggregates (DLCA) that accurately predicts the fractal dimension of the aggregates. However, a three parameter description involving the fractal dimension, prefactor and aggregate shape is both necessary and sufficient for a complete description of fractal aggregate morphology. We show that aggregate shape is poorly described by the principal radii of gyration and best described by side length ratios of circumscribing rectangular solids with side directions determined by the principal radii of gyration. We find for simulated clusters in three spatial dimensions the side lengths are related in a geometric manner. The RHM yields accurate values for these ratios and the fractal dimensions of the aggregates via a simple analytic calculation. Simulations of the RHM yield accurate predictions for the prefactor of the aggregates. Hence the RHM provides a complete three parameter description of DLCA aggregates. Finally, and remarkably, we find that aggregate shape is described by the Divine Proportion in d = 2 and its generalization in d = 3.