Thermoundulations versus convection instability in cholesteric liquid crystals: A novel type of pattern competition

We show that in cholesteric liquid crystals subject to a vertical external temperature gradient a new type of pattern competition exists: Either a dynamic instability (convection) as in nonequilibrium systems or a static instability (thermoundulations) as in constrained pattern-forming equilibrium systems can arise first---depending on the pitch---as the temperature gradient is increased. Numerical estimates are given for both instabilities: Convection occurs first for large pitches and thermoundulations dominate for small pitches.