David J. Arnold
I use differential equations to model real world problems, and I am particularly interested in fluid mechanics. Some of my research projects are described below.
Spiral particle separators
In collaboration with Claudia Falcon and Mike Lindstrom, I work in the UCLA Applied Math Lab studying particle-laden flows. Such flows feature a variety of interesting phenomena, and we couple mathematical modelling and analysis with experiments to help improve the modelling and understanding of such complex flows.
Models for environmental crime
Poaching and illegal deforestation are two examples of environmental crime that are of significant concern to many governments around the world. Protected regions such as National Parks are targets for such crime, and, with limited budget for patrols, finding effective patrol strategies is an important goal. Our method utilises the level set method to allow use to model arbitrarily-shaped regions, and include terrain features. We are able to assess the effectiveness of given patrol strategies to help identify those which would best protect a National Park.