Date of Award

Summer 8-2017

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Physics and Astronomy

Committee Chair

Dr. James V. Lambers

Committee Chair Department

Mathematics

Committee Member 2

Dr. Christopher Winstead

Committee Member 2 Department

Physics and Astronomy

Committee Member 3

Dr. C. S. Chen

Committee Member 3 Department

Mathematics

Committee Member 4

Dr. David T. Brown

Abstract

We solve the first order reaction-diffusion equations which describe binding-diffusion kinetics using a photobleaching scanning profile of a confocal laser scanning microscope approximated by a Gaussian laser profile. We show how to solve these equations with prebleach steady-state initial conditions using a time-domain method known as a Krylov Subspace Spectral (KSS) method. KSS methods are explicit methods for solving time- dependent variable-coefficient partial differential equations (PDEs). KSS methods are advantageous compared to other methods because of their stability and their superior scalability. These advantages are obtained by applying Gaussian quadrature rules in the spectral domain developed by Golub and Meurant. We present a simple approximate analytical solution to the reaction-diffusion equations, as well as a computational solution that is first-order accurate in time. We then use this solution to examine short- and long-time behaviors.

ORCID ID

orcid.org/0000-0002-4246-7827

Available for download on Thursday, August 01, 2019

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