Applications of Circle Packing Moduli Brock Williams Texas

Applications of Circle Packing Moduli Brock Williams Texas Tech University

Including Joint Work With � Roger � John W. Barnard Calhoun � Levi Johnson � Kent Pearce � Hamed � Arun Sari-Sarraf Shammanna

Work Supported By Grants 727944 742402 745472 1035096 0930257 Grant T 365 Z 110259

Circle Packings A circle packing is a configuration of circles with a specified pattern of tangencies.

Circle Packings

Realization of the Triangulation

Discrete Conformal Maps About 900 Circles in Each Packing

Discrete Conformal Maps About 12000 Circles in Each Packing

Modulus of Ring Domain r D 1 R

Circle Packing Modulus

Cotton Maturity Image from Google Maps.

Cotton Fibers Immature cotton fibers are round, thick, and hollow. As they mature, the lumen collapses and the cellulose thins. Cross section of fiber

“Rounding the Fiber Out”

Disease Modeling In work with John Calhoun, we’ve used random walk ideas to model disease outbreaks.

Zombie Virus

Previous Zombie Work Munz, Hudea, Imad, and Smith published a PDE model of a zombie outbreak in 2009. They found logistic growth of the zombie population (and corresponding logistic decay of the human population).

Our Model � Incorporates additional parameters such as ◦ Geography of the City ◦ Hospitals ◦ Human Offensive Capability � Predicts human population survival under some circumstances

Conformal Landscape

Effect on the Disease Human Population Zombie Population

A Different Conformal Landscape

Effect on the Disease Human Population Zombie Population

Thanks! Questions?