Breathing mode in a pattern-forming system with two competing lengths

We study interfacial pattern formation during directional growth from the isotropic phase of a cholesteric liquid crystal that, at equilibrium, has a length 2π/${\mathit{q}}_0$. We find an oscillatory first instability to the cellular pattern and a second bifurcation to an oscillatory mode (breathing mode) when the pattern’s wave number, q is 0.5${\mathit{q}}_0$<q<${\mathit{q}}_0$. The breathing-mode frequency is linear in q. This is the first observation in pattern-forming systems of an oscillatory mode due to competition between two incommensurate but comparable lengths.