Date of Award

Spring 1-1-2011

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Applied Mathematics

First Advisor

David M. Bortz

Second Advisor

John Crimaldi

Third Advisor

Keith Julien

Abstract

The post-fragmentation probability density of daughter flocs is one of the least well-understood aspects of modeling flocculation. This dissertation addresses the problem of determining an appropriate post-fragmentation probability density for common aggregate and biolm forming bacterial species, such as Klebsiella pneumoniae and Staphiloccocus epidermidis. We seek to characterize the post-fragmentation density using a three-pronged approach. First, we use 3D positional data of K. pneumoniae bacterial flocs in suspension and the knowledge of hydrodynamic properties of a laminar flow field and propose a model to construct a probability density of floc volumes after a fragmentation event, and we provide computational results which predict that the primary fragmentation mechanism for large flocs is erosion. Second, we consider an abstract evolution model for the flocculation dynamics and establish existence and well-posedness of solutions to the inverse problem. Third, a numerical approximation scheme based on the model is presented for inferring the post-fragmentation density from laboratory data for bacterial population size distribution, and the stability and robustness of identifying the post-fragmentation density is examined.

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