Published: Oct. 31, 2013

Aggregation Dynamics: Numerical Approximations and Inverse Problems

Dustin Keck

Applied MathematicsUniversity of Colorado Boulder

Date and time: 

Thursday, October 31, 2013 - 2:00pm


ECOT 226 - APPM Conference Room


In this proposal, we investigate the accuracy and robustness of numerical simulations and inverse prob-
lems in bacterial aggregation. First, we study the impact of discretization strategy on the accuracy of solution
moment. We perform this investigation in anticipation of comparing with dierent distributions moments
reported by specic experimental devices. For multiplicative aggregation kernels, nite volume methods
are superior to nite element methods both in accuracy and computational eort. Conversely, for slowly
aggregating systems the nite element approach can produce as little error as the nite volume approach
and achieves more accuracy (at a substantially reduced cost) approximating the zeroth moment.
A better understanding of the Klebsiella pneumoniae aggregation dynamics could also lead to improve-
ments in the treatment of bacterially-mediated, life-threatening human illnesses. Therefore, to reach our
ultimate goal of comparing with experimental data, we examine the inverse problem of determining the
aggregation kernel from experimental data. While others have solved inverse problems involving the Smolu-
chowski coagulation equation, we will make the novel contribution of determining the conditions under which
the inverse problem is well-posed. Once we establish those conditions, we will solve the inverse problem with
a software implementation of parameter tting to actual experimental data. Finally, we will study the impact
of limited measurement domains on the parameter estimation inverse problem.