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Explosive condensation in symmetric mass transport models

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Chau, Yu-Xi, Connaughton, Colm and Grosskinsky, Stefan (2015) Explosive condensation in symmetric mass transport models. Journal of Statistical Mechanics : Theory and Experiment, 2015 (11). P11031. doi:10.1088/1742-5468/2015/11/P11031 ISSN 1742-5468.

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Official URL: http://dx.doi.org/10.1088/1742-5468/2015/11/P11031

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Abstract

We study the dynamics of condensation in a misanthrope process with nonlinear jump rates and factorized stationary states. For large enough density, it is known that such models have a phase separated state, with a non-zero fraction of the total mass concentrating in a single lattice site. It has been established in (Waclaw and Evans 2012 Phys. Rev. Lett. 108 070601) for asymmetric dynamics that such processes exhibit explosive condensation, where the time to reach the stationary state vanishes with increasing system size. This constitutes a spatially extended version of instantaneous gelation which has previously been studied only in mean-field coagulation models. We show that this phenomenon also occurs for symmetric dynamics in one dimension if the non-linearity is strong enough, and we find a coarsening regime where the time to stationarity diverges with the system size for weak non-linearity. In higher space dimensions explosive condensation is expected to be generic for all parameter values. Our results are based on heuristic mean field arguments which are confirmed by simulation data.

Item Type: Journal Article
Subjects: Q Science > QC Physics
Divisions: Faculty of Science, Engineering and Medicine > Research Centres > Centre for Complexity Science
Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Condensation, Monomers , Coagulation, Gelation
Journal or Publication Title: Journal of Statistical Mechanics : Theory and Experiment
Publisher: Institute of Physics Publishing Ltd.
ISSN: 1742-5468
Official Date: 27 November 2015
Dates:
DateEvent
27 November 2015Published
22 October 2015Accepted
1 September 2015Submitted
Volume: 2015
Number: 11
Article Number: P11031
DOI: 10.1088/1742-5468/2015/11/P11031
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access (Creative Commons)
Date of first compliant deposit: 2 June 2016
Date of first compliant Open Access: 3 June 2016
Funder: Engineering and Physical Sciences Research Council (EPSRC)
Grant number: EP/I014799/1 and EP/I01358X/1

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