Recent items

Slides from our department Mathematics Colloquium (September 2012) summarizing results from some of the problems our interdisciplinary swarm group has been studying.

Quantifying and Tracing Information Cascades in Swarms.
Work with Rose Wang, Jen Miller, Joe Lizier and Mikhail Prokopenko in PLoS ONE measuring theoretical information transfer in swarms. We provide the first direct information-theoretic evidence for the long-held conjecture that the information cascades occur in waves rippling through the swarm. Our experiments also exemplify how features of swarm dynamics, such as cascades’ wavefronts, can be filtered and predicted.

Particle methods with deforming basis functions and field interpolation.
Slides from a minisymposium "Challenges and Synthesis in Meshfree Methods" organized with Prof. Toby Driscoll for the 2012 SIAM Annual Meeting. Followup discussions are hosted at The Center for Meshfree Dynamics site.

A Continuum Three-Zone Model for Swarms.
Work with Jennifer Miller, Allison Kolpas and Plinio Neto in Bulletin on Mathematical Biology where we establish and analyze a self-consistent, continuum model for swarming.

Using Wikis to Promote Active Inquiry in First Semester Calculus, in Teaching with Technology Volume 2: The Stories Continue. A fun project where I engaged students using images to create their own related rates and optimization problems that were a big more inspiring than the problems in text.

Measuring Information Storage and Transfer in Swarms in Proc. Eleventh European Conference on the Synthesis and Simulation of Living Systems (ECAL 2011), Paris, 2011. Published in Advances in Artificial Life, ECAL 2011. Work with Rosalind Wang, Jen Miller, Joseph Lizier and Mikhail Prokopenko on information transfer in swarms.

Slime mold inspired routing protocols for wireless sensor networks.
Work with Ke Li, Claudio Torres, Kyle Thomas and Chien-Chung Shen in Swarm Intelligence where we develop a routing protocol for sensor networks based on slime mold.

Global field interpolation for particle methods.
Work with Lorena Barba in Journal of Computational Physics on field interpolation (replacing one set of particles with another without inducing significant field errors).

Using Global Interpolation to Evaluate the Biot-Savart Integral for Deformable Elliptical Gaussian Vortex Elements.
A paper written with Rodrigo Platte and Travis Mitchell that appeared recently in SIAM Journal on Scientific Computing.

The evolution of Kirchhoff elliptic vortices.
A paper written with Travis Mitchell that appeared recently in Physics of Fluids.

Fall 2012

Math 611: Numerical analysis

All course materials will be delivered through the UD Sakai server.