In contrast to the equilibrium case, there is no general theoretical framework for the treatment of many-body nonequilibrium systems. Therefore, simple model systems, amenable to detailed analytical or numerical treatment, are important in the understanding of such systems. Phase transitions and ordering are fundamental phenomena which have been extensively studied in equilibrium statistical physics. In this work, we investigate these phenomena in several model driven diffusive systems. We introduce the 'bus route model', a simple microscopic model in which jamming of a conserved driven species is mediated by the presence of a non-conserved quantity. Jamming proceeds via a strict phase transition only in a prescribed limit; outside this limit, we find sharp crossovers and transient coarsening. Next, we study flocking, the collective motion of many self-driven entities, in a one-dimensional lattice model. We find the existence of an ordered phase characterized by the presence of a single large 'flock' which exhibits stochastic reversals in direction. Using numerical finite-size scaling, we analyse the continuous phase transition from this ordered phase to a homogeneous phase and we calculate critical exponents. Finally, we study a model of shear-induced clustering; we find evidence for a discontinuous jamming transition with hysteresis. We also study the kinetics of jamming.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:660144 |
| Date | January 1999 |
| Creators | O'Loan, Owen James |
| Publisher | University of Edinburgh |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/1842/12718 |
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