BibTeX
@MISC{Sipos13phasetransitions,
author = {Maksim Sipos},
title = {PHASE TRANSITIONS IN FLUIDS AND BIOLOGICAL SYSTEMS },
year = {2013}
}
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Abstract
In this thesis, I consider systems from two seemingly different fields: fluid dynamics and microbial ecology. In these systems, the unifying features are the existences of global non-equilibrium steady states. I consider generic and statistical models for transitions between these global states, and I relate the model results with experimental data. A theme of this thesis is that these rather simple, minimal models are able to capture a lot of functional detail about complex dynamical systems. In Part I, I consider the transition between laminar and turbulent flow. I find that quantitative and qualitative features of pipe flow experiments, the superexponential lifetime and the splitting of turbulent puffs, and the growth rate of turbulent slugs, can all be explained by a coarse-grained, phenomenological model in the directed percolation universality class. To relate this critical phenomena approach closer to the fluid dynamics, I consider the transition to turbulence in the Burgers equation, a simplified model for Navier-Stokes equations. Via a transformation to a model of directed polymers in a random medium, I find that the transition to Burgers turbulence may also be in the directed percolation universality class. This evidence implies that the turbulent-to-laminar transition is statistical in nature and does not depend on details of the Navier-Stokes equations describing the fluid flow.
Keyphrases
phase transition fluid biological system directed percolation universality class fluid dynamic navier-stokes equation turbulent flow turbulent puff fluid flow burger turbulence turbulent slug different field minimal model pipe flow experiment complex dynamical system global state phenomenological model critical phenomenon approach closer superexponential lifetime random medium directed polymer microbial ecology turbulent-to-laminar transition qualitative feature simplified model statistical model model result unifying feature functional detail burger equation global non-equilibrium steady state growth rate experimental data
