Ali, Adnan, Ball, Robin, Grosskinsky, Stefan and Somfai, Ellák (2013) Scale-invariant growth processes in expanding space. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Volume 87 (Number 2). Article number 020102. doi:10.1103/PhysRevE.87.020102

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Abstract

Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting particles, and their large scale behavior depends on the overall growth geometry. We establish an exact relation between statistical properties of structures in uniformly expanding and fixed geometries, which preserves the local scale invariance and is independent of other properties such as the dimensionality. This relation generalizes standard conformal transformations as the natural symmetry of self-affine growth processes. We illustrate our main result numerically for various structures of coalescing Lévy flights and fractional Brownian motions, including also branching and finite particle sizes. One of the main benefits of this approach is a full, explicit description of the asymptotic statistics in expanding domains, which are often nontrivial and random due to amplification of initial fluctuations.

Item Type:	Journal Article
Divisions:	Faculty of Science > Physics
Journal or Publication Title:	Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)
Publisher:	American Physical Society
ISSN:	1539-3755
Official Date:	February 2013
Dates:	Date Event February 2013 Published
Volume:	Volume 87
Number:	Number 2
Page Range:	Article number 020102
DOI:	10.1103/PhysRevE.87.020102
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

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