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Title: Dynamics of condensation in stochastic particle systems
Author: Cao, Jiarui
ISNI:       0000 0004 5916 0180
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2016
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Condensation is a special class of phase transition which has been observed throughout the natural and social sciences. The understanding of the critical behaviour of such systems is a very active area of current research, in particular a mathematical description of the formation and time evolution of the condensate. In this thesis we study these phenomena in several models. In particular we focus on the recently introduced inclusion process, and we compare it with related classical mass transport models such as zero range processes. We first give a brief review of relevant definitions and properties of interacting particle systems, in particular recent literatures on the condensation and stationary behaviour of a large class of interacting particle systems with stationary product measures, which forms the theoretical basis of this thesis. The second part of this thesis is on the dynamics of condensation in the inclusion process on a one-dimensional periodic lattice in the thermodynamic limit. This generalises recent results which were limited to finite lattices and symmetric dynamics. Our main focus is firstly on totally asymmetric dynamics which have not been studied before, which we compare to exact solutions for symmetric systems. We identify all the relevant dynamical regimes and corresponding time scales as a function of the system size, including a coarsening regime where clusters move on the lattice and exchange particles, leading to a growing average cluster size. After establishing the general approach to study dynamics of condensation in totally asymmetric processes, we extend the results to more general partially asymmetric cases as well as higher dimensional cases. In the third part of this thesis we derive some preliminary exact results on symmetric systems through duality, which recovers heuristic results in previous chapter and allows us to treat coarsening in the infinite lattice directly.
Supervisor: Not available Sponsor: University of Warwick
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics