Vortices in Motionless Media

[+] Author and Article Information
A. T. Winfree

326 Biological Sciences West, Department of Ecology and Evolutionary Biology, University of Arizona, Tucson AZ 85718

Appl. Mech. Rev 43(12), 297-309 (Dec 01, 1990) (13 pages) doi:10.1115/1.3119156 History: Online April 30, 2009


Three-dimensional continua capable of recurrent local activation are observed—both in the laboratory and in mathematical models—to support persistent self-organizing patterns of activity most conveniently described in terms of vortex lines. These lines generally close in rings, which may be linked and knotted. In some cases they adopt stable configurations resembling tiny dynamos of millimeter dimensions. The dynamics of these “organizing centers” has been investigated in certain chemical reactions, in heart muscle, and numerically in digital computers. The pertinent mathematical principles appear to entail consequences of local reaction and neighborhood diffusion, in the form of a dependency of the vortex filament’s lateral motion upon its local geometry and, when too closely approached by another segment of vortex filament, upon the distance and orientation involved.

Copyright © 1990 by American Society of Mechanical Engineers
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