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.
Articles
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...
Blogs and wikis as instructional tools: A social software implementation of Just-in-Time Teaching (with Jude A. Higdon), College Teaching (2009)
The Just-in-Time Teaching (JiTT) methodology of Novak and collaborators (1999) uses web-based tools to gather...
Review of “Continuum modeling in the physical sciences” by van Groesen and Molenaar, Biometrica (2009)
A model for rolling swarms of locusts (with Andrew J. Bernoff, Sheldon Logan, and Wyatt Toolson), European Physical Journal - Special Topics (2008)
We construct an individual-based kinematic model of rolling migratory locust swarms. The model incorporates social...
A nonlocal continuum model for biological aggregations (with Andrea L. Bertozzi and Mark E. Lewis), Bulletin of Mathematical Biology (2006)
We construct a continuum model for biological aggregations in which individuals experience long-range social attraction...
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Unpublished Papers
Forced patterns near a Turing-Hopf bifurcation (with Anne Catlla) (2009)
We study time-periodic forcing of spatially-extended patterns near a Turing-Hopf bifurcation point. A symmetry-based normal...
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...
Other
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...