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Applications of Circle Packing Moduli

Applications of Circle Packing Moduli. Brock Williams Texas Tech University. Including Joint Work With. Roger W. Barnard John Calhoun Levi Johnson Kent Pearce Hamed Sari- Sarraf Arun Shammanna. Work Supported By. Grants 727944 742402 745472 1035096 0930257. Grant T365Z110259.

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Applications of Circle Packing Moduli

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  1. Applications of Circle Packing Moduli Brock Williams Texas Tech University

  2. Including Joint Work With • Roger W. Barnard • John Calhoun • Levi Johnson • Kent Pearce • Hamed Sari-Sarraf • ArunShammanna

  3. Work Supported By Grants 727944 742402 745472 1035096 0930257 Grant T365Z110259

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

  5. Circle Packings

  6. Circle Packings

  7. Realization of the Triangulation

  8. Discrete Conformal Maps About 900 Circles in Each Packing

  9. Discrete Conformal Maps About 12000 Circles in Each Packing

  10. Modulus of Ring Domain r 1 R D

  11. Circle Packing Modulus

  12. Circle Packing Modulus

  13. Circle Packing Modulus

  14. Cotton Maturity Image from Google Maps.

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

  16. “Rounding the Fiber Out”

  17. “Rounding the Fiber Out”

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

  19. Zombie Virus

  20. 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).

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

  22. Conformal Landscape

  23. Conformal Landscape

  24. Effect on the Disease Human Population Zombie Population

  25. A Different Conformal Landscape

  26. A Different Conformal Landscape

  27. Effect on the Disease Human Population Zombie Population

  28. Thanks! Questions?

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