Boundary-imposed spiral drift.

Abstract

Spiral waves constitute an example of self-sustained activity that has been observed in various excitable media such as cardiac muscle @1#, cultures of the slime mold Dictiostelium-Discoideum @2#, or oscillating chemical reactions, such as the Belousov-Zhabotinsky ~BZ! reaction @3#. The study of spiral properties, which rarely depend on the medium that sustains them, has constituted an important challenge to the scientists for decades, so considerable effort has been devoted experimentally @4,5#, numerically @6,7#, and theoretically @8–10# to the understanding of such structures. Despite that these previous studies provide an important background on spiral properties, little is known about the interaction between the waves and the medium where they spread. Only recently, some authors have turned their attention to this phenomenon, although from different points of view. Davidenko et al. @11# observed drifting spiral waves in isolated cardiac tissue and Biktashev and Holden @12# described a defibrillation method in which they considered the boundary effects, in addition to an external forcing. On the other hand, Davydov and Zykov @13# considered this effect in small media where the length of the front was comparable to the extent of the medium. They concluded that a rigid rotation can become unstable when the spiral tip is initially displaced from the center of the medium. This prediction was corroborated by the experiments carried out by Muller and Zykov @14# in a small Petri dish using the BelousovZhabotinsky reaction @3#. Besides, Sepulchre and Babloyantz @15,16# studied spiral motion in a small medium—a few wavelengths—for a system near the Hopf bifurcation and with relaxation oscillation in square and circular geometries. Finally, other authors proved theoretically @17,18# that rigid rotation is not generic. They showed that the interaction with a boundary ~qualitatively similar to the interaction with other spirals @19# or with defects @20#! gives rise to localized deformations, small in comparison with the spiral wavelength and, consequently, to the drifting of a spiral as a whole. The purpose of this paper is to investigate experimentally how the boundaries induce the drift of a rotating vortex in a round medium when a vortex is initially displaced from the geometrical center of the medium. II. MATERIALS AND METHODS