In 2017 we received a grant from the NSF Division of Mathematical Sciences to support a new REU Site in Mathematical Modeling at UCLA. This site forms one part of the Computational and Applied Math REU at UCLA. In the augural year of the REU site, student teams worked on three different projects:
Modeling interactions between germinating fungal spores.
Students used a combination of experiments in microfluidic wells and on plates, and image analysis of large microscopy fields to measure the effect that interactions have on the growth rate of fungi. In particular they focused on quantifying whether spores gain (cooperate) or lose (compete) fitness by sharing resources and territory, and whether in these interactions spores are capable of telling genetically similar neighbors apart from neighbors that are genetically different from them.
Studying recidivism and patterns of crime in the homeless population of Western Los Angeles.
Working with data shared with us by the Pacific Division of the LA Police Department students studied the connections in space and time between homelessness and crime. In particular they evaluated whether homelessness is intrinsically criminal (i.e. whether all homeless people are prone to being arrested), and mapped out the distance between where homeless live, and where they are arrested, to predict how shifts in the future locations of the homeless population may affect future arrest patterns.
The Fluid Mechanics of how suspensions containing heavy particles flow down surfaces.
Students used experiments and mathematical modeling to study the flow of viscous fluids containing one or more types of heavy particles. In particular they focused on the early stages of flow, in which particles first start to separate out in the fluid due to a combination of settling and shear induced dispersion. Additionally, they studied how multiple different particles suspended in the same fluid may spontaneously separate (or not) in flow.