Projects per year
Abstract
We consider an extension of the zero-range process to the case where the hop rate depends on the state of both departure and arrival sites. We recover the misanthrope and the target process as special cases for which the probability of the steady state factorizes over sites. We discuss conditions which lead to the condensation of particles and show that although two different hop rates can lead to the same steady state, they do so with sharply contrasting dynamics. The first case resembles the dynamics of the zero-range process, whereas the second case, in which the hop rate increases with the occupation number of both sites, is similar to instantaneous gelation models. This new 'explosive' condensation reveals surprisingly rich behaviour, in which the process of the condensate's formation goes through a series of collisions between clusters of particles moving through the system at increasing speed. We perform a detailed numerical and analytical study of the dynamics of condensation: we find the speed of the moving clusters, their scattering amplitude, and their growth time. We finally show that the time to reach steady state decreases with the size of the system.
Original language | English |
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Article number | 095001 |
Number of pages | 27 |
Journal | Journal of physics a-Mathematical and theoretical |
Volume | 47 |
Issue number | 9 |
DOIs | |
Publication status | Published - 17 Feb 2014 |
Keywords / Materials (for Non-textual outputs)
- zero-range process
- condensation
- migration process
- misanthrope process
- driven diffusive systems
- BACKGAMMON MODEL
- DYNAMICS
- UNIVERSE
- SYSTEMS
Fingerprint
Dive into the research topics of 'Condensation in stochastic mass transport models: beyond the zero-range process'. Together they form a unique fingerprint.Projects
- 2 Finished
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Theoretical Models for evolution with migration
Waclaw, B. (Principal Investigator)
1/04/12 → 31/03/14
Project: Research
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Design Principles for New Soft Materials
Cates, M. (Principal Investigator), Allen, R. (Co-investigator), Clegg, P. (Co-investigator), Evans, M. (Co-investigator), MacPhee, C. (Co-investigator), Marenduzzo, D. (Co-investigator) & Poon, W. (Co-investigator)
7/12/11 → 6/06/17
Project: Research
Profiles
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Martin Evans
- School of Physics and Astronomy - Personal Chair in Statistical Physics
Person: Academic: Research Active