Advertisement

Numerical Organizing Centers

  • Arthur T. Winfree
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 12)

Abstract

This first of two new chapters (16 and 17) for the Y2K edition tries to succinctly relate twenty years’ “experimental mathematics” about two- and three-dimensional rotors, following up the new parts of Chapter 9’s Section C. It stresses unsolved problems that await the reader’s attention. As noted in 1978’s Chapter 10 (Section C: Transition to Bestiary), Chapters 11 through 23 are less about concepts than about the specific experimental systems by which our many-forked tree of guesswork is pruned toward reality. This chapter combines mathematical concepts with numerical experiments that test conjectures about the solutions of equations, largely by providing counterexamples to steer thinking away from minefields. Equations in this area do not exactly represent physical mechanisms; to that extent they are only metaphors for the laboratory phenomena. These metaphors are awkward analytically, so to find their implications we do a fair amount of intuitive guessing and numerical simulating. The numerical experiments are in some respects as effective as laboratory experiments for disillusioning ourselves from mental mirages. In this mode we learn principally from failures: failures to produce a quantitatively workable incarnation of some hypothesis, or failures of the quantitative incarnation to do what a simpler analytical model does. And we learn from unexpected encounters with alternative solutions.

Keywords

Hopf Bifurcation Vortex Ring Rotor Period Excitable Medium Vortex Filament 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    The most sophisticated model deployed to date indicates the latter: Chudin et al. (1999).Google Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Arthur T. Winfree
    • 1
  1. 1.Department of Ecology and Evolutionary BiologyUniversity of ArizonaTucsonUSA

Personalised recommendations