Condensation is an emergent phenomenon in complex systems that is observed in both physical and social sciences, from granular polydisperse spheres to macroeconomic studies. The critical behaviour of condensation in such systems is of continual interest in research. In this thesis we study this in the context of interacting particle systems, in particular the recently introduced explosive condensation process. We firstly provide a review of the mathematical foundations of interacting particle systems from the aspects of Markov processes. This includes the formulation of factorised hop rates, stationary product measures, the equivalence of ensembles and how these properties are related to condensation. Subsequently, we give a review of key interacting particle systems of interest, namely the zero-range process, inclusion process and the explosive condensation process. We then introduce two models that have similar stationary weights scaling as the explosive condensation process and include them in our study in the thermodynamic limit. The density and the maximum site occupation are derived under the stationary distribution, and from this we are able to identify the choice of parameters that could lead to a phase transition. Exact results for these models using the generator are di�cult to obtain. For the main results of this study, we therefore analyse the formation of condensate using a heuristic approach. The microscopic interactions leading to the formation of an explosive condensate are structurally studied, and this leads to a comprehensive model with a timescale analysis. The time to condensation is shown to vanish as the thermodynamic limit is reached, depending on the choice of parameter values. Throughout the thesis, theoretical results are supported by Monte Carlo simulation and numerical calculations where appropriate. A modification of the conventional Gillespie algorithm is proposed. The new algorithm improves e�ciencies but is also able to preserve key stochastic properties, and is used throughout the simulation of the main findings.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:682940 |
| Date | January 2015 |
| Creators | Chau, Yu-Xi |
| Publisher | University of Warwick |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://wrap.warwick.ac.uk/77689/ |
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