Topaz has an active research program focusing on the modeling, computation, and
analysis of nonlinear systems, and is particularly interested in natural systems that
spontaneously self-organize or form patterns. 



Topological data analysis of biological aggregation models (with Lori Ziegelmeier and Tom Halverson), PLoS One (2015)

We apply tools from topological data analysis to two mathematical models inspired by biological aggregations...



Social Aggregation in Pea Aphids: Experiment and Random Walk Modeling (with Christa Nilsen, John Paige, Olivia Warner, Benjamin Mayhew, Ryan Sutley, Mathew Lam, and Andrew J. Bernoff), PLOS One (2013)


Nonlocal aggregation equations: A primer of swarm equilibria (with Andrew J. Bernoff), SIAM Review (2013)


Locust dynamics: Behavioral phase change and swarming (with Maria R. D'Orsogna, Leah Edelstein-Keshet, and Andrew J. Bernoff), PLoS Computational Biology (2012)

Locusts exhibit two interconvertible behavioral phases, solitarious and gregarious. While solitarious individuals are repelled from...



Instabilities and patterns in coupled reaction-diffusion layers (with Anne J. Catlla and Amelia McNamara), Physical Review E (2012)

We study instabilities and pattern formation in reaction-diffusion layers that are diffusively coupled. For two-layer...


Contributions to Books


Fractional bandwidth reacquisition algorithms for VSW-MCM (with Ben Cook, Daniel Marthaler, Andrea L. Bertozzi, and Mathieu Kemp), Multi-robot systems: From swarms to intelligent automata (2003)

Autonomous underwater vehicles are gradually being recognized as key assets in future combat systems. Central...




Pattern formation in two-frequency forced Faraday waves (2002)

This dissertation investigates pattern selection in two-frequency forced Faraday waves. In this system, a fluid...