Shlesinger-Hughes stochastic renormalization, iterated logarithmic tails and multiple hierarchical fractal aggregation

Marcel Ovidiu Vlad

Physica A: Statistical Mechanics and its Applications, 1994, vol. 207, issue 4, 483-491

Abstract: The multiple hierarchical fractal aggregation is used as an illustration for a new type of asymptotic behavior of fractal random processes defined in terms of a multiple Shlesinger- Hughes renormalization procedure. The joint probability distributions of aggregate sizes for a multiple association process are analyzed based on the following set of assumptions: (a) the system contains basic units of different types; however, each aggregate is made up of a single type of units; (b) the size of a single aggregate obeys a geometrical distribution of the Flory type; (c) the aggregation process occurs in a hierarchical way, i.e. each aggregate of a given type triggers the generation of a complex of another type. A chain of joint size probability distributions is introduced. We show that these probability distributions depend on the probabilities that a unit from a given aggregate is active, that is, that it may trigger the aggregation process of basic units of another type. These probabilities generate a chain of fractal exponents which characterize the asymptotic behavior of the size probability distributions. The probability distribution attached to a succession of q + 2 aggregation processes has a very long tail with a logarithmic shape: it is an inverse power of the qth iterate logarithm of size n, ln ln…ln n. This decay law is much slower than the inverse power laws characteristic for the usual statistical fractals.

Date: 1994
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0378437194902054
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:207:y:1994:i:4:p:483-491

DOI: 10.1016/0378-4371(94)90205-4

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 ().