This thesis is composed of two problems. The first is a systems level analysis of the carbon concentrating mechanism in cyanobacteria. The second presents a theoretical analysis of femtosecond laser melting for the purpose of hyperdoping silicon with sulfur. While these systems are very distant, they are both relevant to the development of alternative energy (production of biofuels and methods for fabricating photovoltaics respectively). Both problems are approached through analysis of the underlying diffusion equations.
