Emergence of skew distributions in controlled growth processes

Details Emergence of skew distributions in controlled growth processes Emergence of skew distributions in controlled growth processes

2011-04-03

arxiv.org/abs/1104.0366v1

Physical Review E 82, 061115 (2010)

Physics

Condensed Matter

Statistical Mechanics

9 pages, 3 figures

Scientific paper

10.1103/PhysRevE.82.061115

Starting from a master equation, we derive the evolution equation for the size distribution of elements in an evolving system, where each element can grow, divide into two, and produce new elements. We then probe general solutions of the evolution quation, to obtain such skew distributions as power-law, log-normal, and Weibull distributions, depending on the growth or division and production. Specifically, repeated production of elements of uniform size leads to power-law distributions, whereas production of elements with the size distributed according to the current distribution as well as no production of new elements results in log-normal distributions. Finally, division into two, or binary fission, bears Weibull distributions. Numerical simulations are also carried out, confirming the validity of the obtained solutions.

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