Dynamical behaviors of scroll rings in the presence of a dc electric field

Experimental observations of scroll rings in excitable media have shown that, a dc electric field perpendicular to the plane of the ring can change the rate at which the ring shrinks, and in some cases it may cause the scroll ring to expand even though its filament tension is positive. Here we propose a kinematical model to account for these effects by extending the theory of dynamics of the free scroll ring to include the influence of electric field. In addition, some other significant results, for example, the electric field can slow down the drift velocity of the scroll ring along its symmetry axis and in some situations may reverse its drift direction, are also predicted by the kinematical model. Direct numerical simulations of a reaction-diffusion model are performed, and the obtained results are in quantitative agreement with the numerical solutions of the kinematical model.