Browsing by Subject "Bubbles"

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    Essays on speculation.
    (2009-08) Slawski, Adam Wladyslaw
    I examine the question whether a disagreement based speculative trade can persist in an environment in which agents are learning. The speculative trade is understood as an equilibrium outcome, in which agents who buy the asset pay higher price for it, than they would be willing to had they not had the opportunity to re-trade it in the future. The corresponding notion of speculative bubble, which is analyzed in Essay 2, is understood as an excess of the equilibrium price over the current market fundamental. Harrison and Kreps (QJE 1978) provide an example of a persistent speculative trade. The agents start with different prior beliefs, which are concentrated on disjoint sets. This prevents them from learning. The resulting permanent disagreement leads to a speculative bubble, which is independent on any observed history of data. I extend this example by adding learning. In Essay 1, I set up a general equilibrium model of trading with differential beliefs and learning. The dividend process follows a general hidden Markov process. Using recursive techniques I develop tools to compute and analyze equilibria in this environment. I also provide conditions under which a speculative trade arises. In Essay 2, I apply those techniques to analyze the dynamics of a speculative bubble in a very special case of a Markov dividend process and the prior beliefs concentrated on two transition matrices. Those matrices represent two possible theories considered by agents. Agents put positive probabilities on both theories, hence they are learning. The resulting speculative bubble arises whenever the data does not convincingly favor any of the theories used by agents. I give conditions for the data generating process to lead to persistent speculative bubble. I also show that even though the speculative bubble reappears infinitely often it also happens very rarely on a typical sample path. In fact, the average time in between the periods of high bubble is infinity.
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    Euler-Lagrangian simulations of turbulent bubbly flow.
    (2011-03) Mattson, Michael David
    A novel one-way coupled Euler-Lagrangian approach, including bubble-bubble collisions, coalescence and variable bubble radius, was developed in the context of simulating large numbers of cavitating bubbles in complex geometries using direct numerical simulation (DNS) and large-eddy simulation (LES). This dissertation i) describes the development of the Euler-Lagrangian approach, ii) outlines the novel bubble coalescence model derived for this approach and iii) describes simulations performed of bubble migration in a turbulent boundary layer, bubble coalescence in a turbulent pipe ow and cavitation inception in turbulent flow over a cavity. The coalescence model uses a hard-sphere collision model is used and determines coalescence stochastically. The probability of coalescence is computed from a ratio of coalescence timescales, which are dynamically determined from the simulation. Coalescence in a bubbly, turbulent pipe ow (Re#28; = 1920) in microgravity was simulated with conditions similar to experiments by Colin et al. [1] and excellent agreement of bubble size distribution was obtained. With increasing downstream distance, the number density of bubbles decreases due to coalescence and the average probability of coalescence decreases due to an increase in overall bubble size. The Euler-Lagrangian approach was used to simulate bubble migration in a turbulent boundary layer (420 < Re#18; < 1800). Simulation parameters were chosen to match Sanders et al. [2], although the Reynolds number of the simulation is lower than the experiment. The simulations show that bubbles disperse away from the wall as observed experimentally. Mean bubble diffusion and profiles of bubble concentration are found to be similar to the passive scalar results, except very near the wall. The carrier-fluid acceleration was found to be the reason for moving the bubbles away from the wall. The one-way coupled Euler-Lagrangian approach was applied to simulate the experiment of cavitating turbulent ow over a cavity by Liu and Katz [3]. The classical Rayleigh-Plesset equation is integrated using adaptive time-stepping to accurately and efficiently solve for the change of the bubble radius over time. The one-way coupled Euler-Lagrangian model predicts cavitation inception at the trailing edge of the cavity and also in the vortices shed from the leading edge, in qualitative agreement with experiment.