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Title:History Induced Critical Scaling in Disordered Media and Super Diffusive Growth in Highly Advective Random Environments
Author(s):Carpenter, John Halsey
Director of Research:Dahmen, Karin A.
Department / Program:Physics
Subject(s):Random Field Ising Model (RFIM)
population biology
Abstract:The behavior of non-equilibrium systems in the presence of quenched random disorder is studied. In noisy, hysteretic systems, the role of driving force history is studied in the context of the non-equilibrium, zero-temperature Random Field Ising Model (RFIM). The RFIM was originally developed as a simple model for disordered magnets, but has applications far beyond magnetic systems. Previous work examining history effects in models and experiments are briefly reviewed, followed by a summary of the saturation loop behavior of the RFIM. A numerical scaling analysis of the AC demagnetization curve of the RFIM is performed, examining the effect of the underlying disorder on avalanche size distributions, correlation functions, and spanning avalanches. Furthermore, a similar scaling analysis for nested, concentric, symmetric subloops is performed via an analysis of history-induced disorder. Next the effects of long range demagnetizing fields on the demagnetization curve and subloops are studied. Finally, an analysis of corrections to scaling for subloops is presented, along with a derivation of the exponent relations. Disorder in population biology is studied for the case of a spreading cluster of bacteria in a highly advective environment with inhomogeneous nutrient concentration. A model reaction-diffusion equation with Fisher growth terms is introduced with a brief discussion of previous work on similar equations and experiments. The linear two-dimensional problem is mapped onto a simplified one-dimensional equation. Numerical simulations of concentration profiles reveal anomalous growth and super-diffusive spreading in the direction perpendicular to the convection velocity. A time characterizing the crossover from pure diffusion to this super-diffusive behavior is perturbatively calculated. The crossover time’s dependence on the velocity and disorder strength is then tested numerically. Two-dimensional simulations of the full linear reaction-diffusion equation also show the onset of super-diffusive growth in concentration contour maps. On the other hand, with nonlinear growth in two dimensions, a symmetric wave front develops with a propagation velocity greater than the minimum Fisher velocity. An expression is derived and tested for this velocity.
Issue Date:2004-10
Genre:Dissertation / Thesis
Rights Information:© 2004 John Halsey Carpenter
Date Available in IDEALS:2012-07-02
Identifier in Online Catalog:5090544

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