In many natural systems, particles, agents, or organisms aggregate and display collective behavior. Aggregation systems include nanoparticle self-assembly, actin-filament networks in cells, and more. This project investigates aggregation systems with an eye towards insect swarms, bird flocks, fish schools, and other biological groups in which social interactions play a key role. The specific objectives are (1) to discover whether computationally challenging models can be accurately approximated with simpler, more tractable ones; (2) to use this understanding to model environmentally and economically destructive locust swarms; and (3) to classify complicated behavior in large data sets related to aggregations. The locust research impacts agriculture. In particular, it will yield insight on swarm suppression strategies. For instance, it may suggest crop-planting layouts that would avert the gregarious locust outbreaks that devastate farmers. Other key elements of this project, which is based at an undergraduate institution, include: extensive undergraduate student involvement and research training; a network of domestic and foreign colleges and universities; a pipeline from research to the classroom; enhancement of student research lab infrastructure; inclusion in research and advising activities of a female recent Ph.D. seeking a tenure-track position; a focus on the participation of underrepresented groups; and an educational public art exhibition on aggregations produced collaboratively with an undergraduate female artist and biology major.
The investigator and his colleagues study aggregation systems from continuum and discrete perspectives. A common aggregation modeling framework is conservation-type nonlocal PDE, which are analytically and computationally challenging. Degenerate Cahn-Hilliard approximations of a class of canonical models will be investigated with linear analysis, numerical simulation, phase plane analysis of equilibria, and a variational analysis of minimizers in order to evaluate the success of the local model in approximating the nonlocal one. Based on this understanding, the investigator will develop a model of phase polyphenic locusts interacting with the environment and use it to develop strategies that suppress destructive locust swarms. Stability analysis and numerical simulation will reveal environmental conditions likely to suppress a hysteretic bifurcation to a dangerous locust swarm. Finally, the investigator will characterize aggregation dynamics using topological data analysis. Data sets arising from numerical simulations and biological experiments will be analyzed with topological barcodes describing their persistent homology. This work will identify dynamical transitions in aggregation processes.
