Pinning force in active media

Pinning of vortices by defects plays an important role in various physical
(superconductivity, superfluidity, ...) or biological (propagation in
cardiac muscle) situations. Which defects act as pinning centers? We propose
a way to study this general problem by using an advection field to quantify
the attraction between an obstacle and a vortex. A full solution is obtained
for the real Ginzburg-Landau equation (RGLE). Two pinning mechanisms are
found in excitable media. Our results suggest strong analogies with the RGLE
when the heterogeneity is excitable. Unpinning from an unexcitable obstacle
is qualitatively harder, resulting in a stronger pinning force. We discuss
the implications of our results to control vortices and propose experiments
in a chemical active medium and in cardiac tissue.