Nonequilibrium dynamics in fiber networks, aggregation, and sand ripples
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Doctoral thesis (article-based)
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Dissertations / Laboratory of Physics, Helsinki University of Technology, 116
AbstractIn nonequilibrium dynamical systems the rich macroscopic behavior arises from simple microscopic processes. While the dominant transport mechanism is often diffusion, there are important dynamics also beyond the diffusive scale. This thesis concentrates on these issues and the effects of spatial fluctuations in various nonequilibrium systems using computer simulations and theoretical arguments. First, the combination of one-dimensional diffusion theory and random walk simulations is demonstrated to be a powerful tool for analyzing gas diffusion through paper-like structures. An efficient simulation method including the effects of fiber sorption is presented. When sorption is present, the characterization of dynamic diffusion processes is not possible using only the usually measured diffusion constant. The deviations between the theory and simulations suggest that the former is invalid for low porosities or thicknesses. Next, the dynamical behavior in aggregation is considered within a one-dimensional model. This model, as in aggregation systems generally, obeys dynamic scaling described by a time-dependent, characteristic length. However, the first-passage quantities involve other scales. A novel mean-field theory is developed to extract the asymptotic time-dependence of unaggregated clusters, which is shown to relate to the small size tail of the cluster size distribution, a quantity of primary importance in aggregation. Then the effect of the presence of two scales on the dynamic scaling properties is discussed by considering the sites staying unvisited by clusters. When an external field like gravitation is applied, the aggregation dynamics is shown to be dominated by the process leading to the fastest growing characteristic length and the dynamic phase diagram is predicted. Finally, coarsening of sand ripples is considered in one-dimensional mass transfer models motivated by sand ripple evolution. When mass is transferred preferably from large ripples to small ones, the ripple size distribution is calculated exactly and is given by a product measure. The approach towards the final state is discussed, leading to a universal decay which depends on the symmetry of the mass transfer. In the case of small clusters vanishing rapidly from the system, the noise in the dynamics is demonstrated to be irrelevant, but the mean-field theory developed fails to account for the numerically observed universality with respect to the initial ripple size distribution.
diffusion, persistence, spatial fluctuations, paper
- E.K.O. Hellén, J.A. Ketoja, K.J. Niskanen, and M.J. Alava, Diffusion through Fiber Networks, J. Pulp Pap. Sci. 28, 55-62 (2002). [article1.pdf] © 2002 PAPTAC. By permission.
- E.K.O. Hellén and M.J. Alava, Persistence in Cluster-Cluster Aggregation, Phys. Rev. E 66, 026120-1-9 (2002). [article2.pdf] © 2002 American Physical Society. By permission.
- E.K.O. Hellén, P.E. Salmi, and M.J. Alava, Cluster Survival and Polydispersity in Aggregation, Europhys. Lett. 59, 186-192 (2002). [article3.pdf] © 2002 EDP Sciences. By permission
- E.K.O. Hellén, P.E. Salmi, and M.J. Alava, Cluster Persistence in One-Dimensional Diffusion-Limited Cluster-Cluster Aggregation, accepted for publication in Phys. Rev. E (11 pages). [article4.pdf] © 2002 American Physical Society. By permission.
- E.K.O. Hellén, T.P. Simula, and M.J. Alava, Dynamic Scaling in One-Dimensional Cluster-Cluster Aggregation, Phys. Rev. E 62, 4752-4756 (2000). [article5.pdf] © 2000 American Physical Society. By permission.
- E.K.O. Hellén and J. Krug, Coarsening of Sand Ripples in Mass Transfer Models, Phys. Rev. E 66, 011304-1-9 (2002). [article6.pdf] © 2002 American Physical Society. By permission.