1. Biological Swarming:
How do natural agents self-organize into the beautiful, coherent patterns that surround us? We are studying discrete models of self-propelling, interacting agents and the arising morphologies they create as the relevant parameters and environmental conditions are changed. Practical applications for the control of unmanned vehicle systems are being studied as well. These natural and artifical ensembles, their stability and passage to the continuum can be analyzed through the tools of statistical mechanics. We also use Lyapunov functions and numerical methods to understand the fascinating emergence and properties of collective behavior.
2. Biological Systems:
We try to understand the basic phenomenology driving complex biological processes through simple mathematical and physical modeling. We use random sequential adsorption processes to study protein depostion and ratcheting in polymer translocation, surface reaction kinetics for the trigerring of viral fusion in HIV or influenza virus, and first passage time events for the study of ordered or random ligand-receptor binding such as oxygen to hemoglobin. I have also worked on bacterial mobility, on charge transfer phenomena in macromolecules and in surface science.
How do criminals and law enforcement agents interact against a dynamic background to favor or prevent the formation of hot spots of criminal activity? Criminals and cops models offer very interesting platforms for the study of equilibrium and non equilibrium statistical mechanics in disorded media. We use elements from random walks, first passage times, nucleation events in random systems, and pattern formation for our agent based models of foraging criminals.