Transition to phase chaos in directional solidification: A two-mode interaction picture

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Abstract
Interface dynamics are analyzed in directional growth of liquid crystals in a two-mode interaction picture. We find that this simple model retains many interesting features observed experimentally including order and chaotic motion. We discover that the parity-broken mode undergoes an instability characterized by a permanent hopping between q and 2q states (where q is the wave number). On increase of the two-mode coupling the interface motion enters a chaotic regime via a quasiperiodicity route. Chaos manifests itself by an erratic change of the drift direction of the pattern between left and right. We tentatively call it phase chaos.