Vortices in Motionless Media

Abstract

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.