[Propagation of autowaves in capillaries thick with moving viscous excitable medium].

We consider the propagation of autowaves in the moving liquid excitable medium. The shapes of the autowave fronts in cases of the Poiseuille and Couette flows are determined in flat capillaries within a kinematic approach. We show the existence of a critical velocity for the flows above which the autowave fronts should break off. The possibility of a diode effect--the one-way capillary conductivity--is studied. The results of computer simulations are in good agreement with the theoretical predictions.

Propagation of curved activation fronts in anisotropic excitable media.

We study theoretical and numerical propagation of autowave fronts in excitable two-variable (activator-inhibitor) systems with anisotropic diffusion. A general curvature-velocity relation is derived for the case that the inhibitor diffusion is neglected. This relation predicts the break of an activation front when the front curvature exceeds a critical value, which is corroborated by computer simulations of a particular reaction-diffusion model. Some qualitative effects associated with the inhibitor diffusion are studied numerically. It is found that the critical value of curvature decreases with an increase in the inhibitor diffusion coefficient. The core of a spiral wave increases in size and turns through an angle which depends on the inhibitor diffusion coefficient. PACS Numbers: 05.50. +q, 05.70. Ln., 82.40. -g, 87.10. +e.