0_abstract.tex

\abstract{
Diffusive processes have been studied intensively since the 17th and 18th centuries. Significant progress was made in the 20th century, when Einstein modelled diffusion as a process where each particle in a diffusive system takes random steps in random directions through time, undergoing an overall random walk. This model, connected to statistical and differential equation descriptions of physical systems, has worked incredibly well to describe the average diffusing particle. However, this model fails to accurately capture the behavior of the extreme particles, such as those farthest from the origin or those which travel a certain distance first. Other methods have the potential to better describe the extremes, such as a random walk where each step is given a bias that changes in space and time. The work presented here seeks to measure extremes in diffusion numerically and experimentally. We make numerical measurements of the furthest particle, revealing that information about the environment itself can be extracted from measurements of the variance of the extreme particle location. We design an experimental system that will allow us to measure extreme first passage times in colloid diffusion. Finally, we make first passage time measurements of photons, which reveal the failure of the underlying Einstein random walk behind typically used photon transport models and show the need for a better model to describe the behavior and capture the extremes.

This dissertation includes previously published and unpublished coauthored material.
}