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Coarsening dynamics in condensing zero-range processes and size-biased birth death chains
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Jatuviriyapornchai, W. and Grosskinsky, Stefan (2016) Coarsening dynamics in condensing zero-range processes and size-biased birth death chains. Journal of Physics A: Mathematical and Theoretical, 49 (18). pp. 1-26. 185005. ISSN 1751-8113.
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Official URL: http://dx.doi.org/10.1088/1751-8113/49/18/185005
Abstract
Zero-range processes with decreasing jump rates are well known to exhibit a condensation transition under certain conditions on the jump rates, and the dynamics of this transition continues to be a subject of current research interest. Starting from homogeneous initial conditions, the time evolution of the condensed phase exhibits an interesting coarsening phenomenon of mass transport between cluster sites characterized by a power law. We revisit the approach in Godrèche (2003 J. Phys. A: Math. Gen. 36 6313) to derive effective single site dynamics which form a nonlinear birth death chain describing the coarsening behavior. We extend these results to a larger class of parameter values, and introduce a size-biased version of the single site process, which provides an effective tool to analyze the dynamics of the condensed phase without finite size effects and is the main novelty of this paper. Our results are based on a few heuristic assumptions and exact computations, and are corroborated by detailed simulation data.
| Item Type: | Journal Article | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Stochastic systems, Dynamics | ||||||||
| Journal or Publication Title: | Journal of Physics A: Mathematical and Theoretical | ||||||||
| Publisher: | IOP Publishing Ltd | ||||||||
| ISSN: | 1751-8113 | ||||||||
| Official Date: | 1 April 2016 | ||||||||
| Dates: |
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| Volume: | 49 | ||||||||
| Number: | 18 | ||||||||
| Number of Pages: | 26 | ||||||||
| Page Range: | pp. 1-26 | ||||||||
| Article Number: | 185005 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 15 September 2016 | ||||||||
| Date of first compliant Open Access: | 1 April 2017 | ||||||||
| Funder: | Thailand |
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