Topic status: We're looking for students to study this topic.
In 1827, while observing the erratic motion of pollen grains suspended in water, Scottish botanist Robert Brown was led to the discovery that became known as Brownian motion. In 1855, German physiologist Adolf Fick developed his law of diffusion, relating the net motion of particles to the gradient in their concentration. These two concepts are related: Brownian motion at the microscopic scale gives rise to Fickian diffusion at the macroscopic scale. But what happens when motion at the microscopic scale is not Brownian? In this case, the correct macroscopic model is one of non-Fickian, or anomalous diffusion. This type of diffusion has applications in areas such as cellular biology and contaminant transport, among many others. This project would be an investigation into the phenomenon of anomalous diffusion, incorporating numerical simulation at both microscopic and macroscopic scales, with applications to the aforementioned areas.