BREATHING MODE IN A PATTERN-FORMING SYSTEM WITH 2 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 2-pi/q0. 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 0.5q0 < q < q0. 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.