2013/01/31 by Hans Dierckx, Evelien Brisard, Henri Verschelde +1 · 1 citation
Physics and Astronomy · Mathematics · #math-ph #math.MP #nlin.AO #nlin.PS
paper · pdf · doi:10.1103/physreve.88.012908
published as Physical Review E 88 012908 (2013) · preprint before submission to Physical Review E
arxiv created 2013/05/07 · arxiv updated 2014/08/20
Rotating spiral waves organize spatial patterns in chemical, physical and biological excitable systems. Factors affecting their dynamics such as spatiotemporal drift are of great interest for par- ticular applications. Here, we propose a quantitative description for spiral wave dynamics on curved surfaces which shows that for a wide class of systems, including the BZ reaction and anisotropic cardiac tissue, the Ricci curvature scalar of the surface is the main determinant of spiral wave drift. The theory provides explicit equations for spiral wave drift direction, drift velocity and the period of rotation. Depending on the parameters, the drift can be directed to the regions of either maximal or minimal Ricci scalar curvature, which was verified by direct numerical simulations.