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. 



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...



A primer of swarm equilibria (with Andrew J. Bernoff), SIAM Journal on Applied Dynamical Systems (2011)

We study equilibrium configurations of swarming biological organisms subject to exogenous and pairwise endogenous forces....



Forced patterns near a Turing-Hopf bifurcation (with Anne Catlla), Physical Review E (2010)

We study time-periodic forcing of spatially-extended patterns near a Turing-Hopf bifurcation point. A symmetry-based normal...



Asymptotic dynamics of attractive-repulsive swarms (with Andrew Leverentz and Andrew J. Bernoff), SIAM Journal on Applied Dynamical Systems (2009)

We classify and predict the asymptotic dynamics of a class of swarming models. The model...


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...


Unpublished Papers


Social aggregation in pea aphids: Experimental measurement and stochastic modeling (with John Paige, Olivia Warner, Benjamin Mayhew, Ryan Sutley, Matthew Lam, and Andrew J. Bernoff) (2013)

From bird flocks to fish schools and ungulate herds to insect swarms, social biological aggregations...



Tuberculosis screening for international students at a Midwestern liberal arts college (with Grace Goetzke and Victor Addona) (2008)

Participants: 318 international students at Macalester College screened for latent tuberculosis infection via tuberculin skin...




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...