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Scale-invariant growth processes in expanding space.
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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 ISSN 1539-3755.
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Official URL: http://dx.doi.org/10.1103/PhysRevE.87.020102
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, Engineering and Medicine > 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: |
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| 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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