I am an associate professor working at ASU. I am mainly interested in the mathematical modeling of biological systems and especially those which develop self-organized dynamics.
My research focuses on three areas.
- Data-model comparisons. The goal of modeling complex systems is to understand how individuals interact in order to form large complex structures. Many models of self-organized dynamics are able to reproduce several types of behaviors observed in nature (e.g. vortex formation, flocking). Experimental data allows to distinguish between those models which are biologically relevant.
- The derivation of macroscopic models. Many biological systems can be described at two different levels. At a microscopic level, we simply observe the motion of many agents (bird, fish, pedestrian…). At a macroscopic level, we observe a mass of individual moving in a coherent manner. The derivation of macroscopic model aims at connecting these two descriptions. It enables to rely the collective behavior of large groups of agents to simple individual mechanisms.
- Analytics and numerical study of the macroscopic models derived. Once we have derived a macroscopic model (PDE), we can extract new informations about the system. For example, we can look for its long time behavior. In general, there is no explicit solutions to the macroscopic system. For this reason a main concern is to find well-adapted schemes to solve numerical the macroscopic system.