Multifractal structures of mass and growth probability distributions in diffusion-limited aggregation on hierarchical lattices

Takashi Nagatani
Phys. Rev. A 38, 2632 – Published 1 September 1988
PDFExport Citation

Abstract

The scaling structures of the mass and growth probability distributions in the generalized diffusion-limited aggregation (η model) on the hierarchical lattices are derived by making use of the real-space renormalization-group method. In the dielectric breakdown language, the process is formulated as a random multiplicative process of current on the surface of the aggregate. The mass and growth probability distributions are related to the bulk and surface structures of the aggregate. The mass scaling of the clusters generated by the processes is found and compared with the scaling structure of the growth probability distribution. The dependences of the α-f spectra of the mass and growth probability distributions are shown on the parameter η describing the different dielectric breakdown models.

  • Received 22 February 1988

DOI:https://doi.org/10.1103/PhysRevA.38.2632

©1988 American Physical Society

Authors & Affiliations

Takashi Nagatani

  • College of Engineering, Shizuoka University, Hamamatsu 432, Japan

References (Subscription Required)

Click to Expand
Issue

Vol. 38, Iss. 5 — September 1988

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review A

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×