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Abstract:
We present recent experimental results for three pattern-forming systems in which non-variational effects play an important role. The first is thermal convection in a shallow horizontal layer of fluid with temperature-dependent properties. In this system, a hexagonal lattice of convection cells forms at onset. This lattice becomes unstable to rolls when the temperature difference is increased sufficiently. In the ''roll'' state, the rolls are curved and the system forms stable rotating spirals. The rotating spiral states are associated with non-variational effects. Secondly, we discuss the formation of localized pulses in binary-mixture convection near onset. These pulses would not exist in a potential system. In narrow channels, they have been observed as stable states. In systems which are spatially extended in two dimensions they can form spontaneously, and can be long-lived. The third topic which we discuss is the Kuppers-Lortz instability in a thin horizontal layer of a Boussinesq fluid heated from below and rotated about a vertical axis. In this case, the pattern which forms immediately above the onset of convection is non-periodically time dependent even though the amplitude grows continuously from zero as the temperature difference is increased. The dominant mechanism of the instability is found to involve the motion of boundaries between coherent regions of convection rolls of a given orientation. The time dependence could not occur in a variational system. Since it occurs for arbitrarily small amplitudes, one might hope that it is amenable to theoretical analysis.
