The fractal behavior of the shortest path aggregation: simulations and RG calculations

Xiang Rong Wang

Physica A: Statistical Mechanics and its Applications, 1994, vol. 205, issue 1, 380-390

Abstract: The shortest-path aggregation (SPA) is an irreversible process in which particles are attached to the cluster on the closer perimeter sites to the release site. Randomness is introduced via the choice of sites from which the particles are sequentially released. This model generates random fractals which have dendritic structures. Simulations and kinetic real-space renormalization group calculations on a two-dimensional square lattice are presented. Numerically, we find Df=1.20±0.01 for the fractal dimension of the clusters. The universal behavior of the model against the way of releasing particles is observed. We find a transition from a weak correlation region to a strong correlation region. In particular, we find the fractal dimension D=1.20±0.01 when the released particles are weakly correlated, while a one-dimensional object is obtained when the correlation is strong. Analytically, 2 × 2 and 3 × 3 cell real-space renormalization group calculations yield Df = 1.19 and 1.21, respectively, in good agreement with the simulations. A set of heirarchical dimensions D(q) are also computed for the SPA cluster on the square lattice.

Date: 1994
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0378437194905169
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:205:y:1994:i:1:p:380-390

DOI: 10.1016/0378-4371(94)90516-9

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().