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• W2159193889 abstract "Many physical systems are found in non-equilibrium states, and the usual methods of statistical mechanics cannot be used to describe them. In general, this means that many more kinds of behaviour are possible, and that the universality seen in equilibrium statistical mechanics does not necessarily occur. However, in some models a critical point appears, and the properties of systems near this critical point may exhibit universal behaviour. In this thesis, we will discuss two kinds of models in which this occurs. A simple model used to study physics far from equilibrium is a system of reacting and diffusing particles, which may be maintained far from equilibrium by the breaking of detailed balance. For many of these simple systems it is possible to construct a field theory, which can then be studied using renormalization group techniques to determine universal properties. Models with pair annihilation of particles and branching to produce several new particles are studied here, with the addition of anomalous diffusion, in which transport occurs via Lkvy flights. Anomalous diffusion is interesting as a model for some physical situations, and also makes it possible to vary cont,inuously the expansion parameter in the renormalization group calculation. The results of analytic calculations and simulations are compared and show the same critical behaviour, with quantities such as the density behaving as power laws close to a critical point. Another system with interesting dynamics is a complex fluid, or a sol close to its gel transition. The structure of the fluid is modelled by the clusters studied in percolation theory: particles are bonded instantaneously with their nearby neighbours, with a probability p. The geometric properties of this model are well understood, behaving as power laws close to a critical point p,, at which a cluster which spans the entire sample first appears. Adding dynamics then produces a model in which material properties rnay be calculated, which may have interesting behaviour near the critical point. In particular, the viscosity, which characterizes the non-equilibrium behaviour, is shown by molecular dynamics simulation t,o diverge as a power law close to p,." @default.
• W2159193889 created "2016-06-24" @default.
• W2159193889 creator A5087293322 @default.
• W2159193889 date "2004-01-01" @default.
• W2159193889 modified "2023-09-27" @default.
• W2159193889 title "Non-equlibrium dynamics : reaction-diffusion systems and viscous flow near the gelation transition" @default.
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