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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
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Official URL: http://dx.doi.org/10.1088/1742-5468/2015/11/P11031
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 | ||||||||
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| Subjects: | Q Science > QC Physics | ||||||||
| Divisions: | Faculty of Science > Centre for Complexity Science Faculty of Science > Mathematics |
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| 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: |
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| 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 | ||||||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC) | ||||||||
| Grant number: | EP/I014799/1 and EP/I01358X/1 |
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