Universal self-similarity of propagating populations

作者：Eliazar Iddo^*; Klafter Joseph

来源：Physical Review E, 2010, 82(1): 011112.

DOI：10.1103/PhysRevE.82.011112

This paper explores the universal self-similarity of propagating populations. The following general propagation model is considered: particles are randomly emitted from the origin of a d-dimensional Euclidean space and propagate randomly and independently of each other in space; all particles share a statistically common-yet arbitrary-motion pattern; each particle has its own random propagation parameters-emission epoch, motion frequency, and motion amplitude. The universally self-similar statistics of the particles' displacements and first passage times (FPTs) are analyzed: statistics which are invariant with respect to the details of the displacement and FPT measurements and with respect to the particles' underlying motion pattern. Analysis concludes that the universally self-similar statistics are governed by Poisson processes with power-law intensities and by the Frechet and Weibull extreme-value laws.

• 出版日期2010-7-12