Cluster growth poised on the edge of break-up: Size distributions with small exponent power-laws

Koponen, Ismo T.; Riekki, K.A.

doi:10.1016/j.physa.2008.01.013

Cited by 2 publications

(1 citation statement)

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“…However, every population of species (or system components) is finite because it is constrained by landscape heterogeneities, anthropic constraints, and/or biological factors. We believe that these factors control together the minimum and the maximum aggregate-size; thus, the distribution of the aggregates [114]. On the theoretical viewpoint the distribution is scale-free.…”

Section: Resultsmentioning

confidence: 92%

Power-law of Aggregate-size Spectra in Natural Systems

Convertino¹,

Simini²,

Catani³

et al. 2013

ICST Trans Co Sys

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Patterns of animate and inanimate systems show remarkable similarities in their aggregation. One similarity is the double-Pareto distribution of the aggregate-size of system components. Different models have been developed to predict aggregates of system components. However, not many models have been developed to describe probabilistically the aggregate-size distribution of any system regardless of the intrinsic and extrinsic drivers of the aggregation process. Here we consider natural animate systems, from one of the greatest mammals -the African elephant (Loxodonta africana) -to the Escherichia coli bacteria, and natural inanimate systems in river basins. Considering aggregates as islands and their perimeter as a curve mirroring the sculpting network of the system, the probability of exceedence of the drainage area, and the Hack's law are shown to be the the Korčak's law and the perimeter-area relationship for river basins. The perimeter-area relationship, and the probability of exceedence of the aggregate-size provide a meaningful estimate of the same fractal dimension. Systems aggregate because of the influence exerted by a physical or processes network within the system domain. The aggregate-size distribution is accurately derived using the null-method of box-counting on the occurrences of system components. The importance of the aggregate-size spectrum relies on its ability to reveal system form, function, and dynamics also as a function of other coupled systems. Variations of the fractal dimension and of the aggregate-size distribution are related to changes of systems that are meaningful to monitor because potentially critical for these systems.

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Section: Resultsmentioning

confidence: 92%