Advisor:  Dr. Wolfgang Bangerth

Committee:  Dr. Patrick Shipman,Dr. James Liu,Dr. Richard Finke

Title: Quantification and application of uncertainty in the formation of
nanoparticles

Abstract: Nanoparticles are essential across many scientific applications, but their properties are size-dependent. Despite the usefulness of producing monodisperse particle size distributions, it still remains a challenge to fully understand — and hence be able to control –nanoparticle formation reactions due to limitations in what can be observed experimentally. This thesis transfers mathematical, statistical, and computational techniques to this area of nanoparticle chemistry to substantially bolster the sophistication of the quantitative analysis used to better understand nanoparticle systems. First, more efficient software is developed to simulate the reactions. Then, parameter estimation is performed in a robust manner through

Bayesian inference, where I demonstrate the ability to parameterize nonlinear ordinary differential equations in such a way that I can fit the observed data and quantify the uncertainty in the parameter estimates. From Bayesian inference, I build three additional analysis frameworks. (1) Model selection through a Bayesian framework; (2)
optimizing the yield of the nanoparticle-forming reactions while accounting for uncertainty; and (3) optimizing future measurements to collect data providing the most new information. The culmination of this thesis provides a quantitative framework to analyze arbitrary nanoparticle systems to complement and fill in the gaps of the current experimental techniques.

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