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
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...
Modeling the potential impact of rectal microbicides to reduce HIV transmission in bathhouses (with Romulus Breban, Ian McGowan, Elissa Schwartz, Peter Anton, and Sally Blower), Mathematical Biosciences and Engineering (2006)
We evaluate the potential impact of rectal microbicides for reducing HIV transmission in bathhouses. A...
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Unpublished Papers
Asymptotic dynamics of attractive-repulsive swarms (with Andrew Leverentz and Andrew J. Bernoff) (2008)
We classify and predict the asymptotic dynamics of a class of swarming models. The model...
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...