Traveling-wave relaxation in elongated liquid crystal cells

We have made a theoretical study of Freedericksz relaxation in a long thin nematic liquid crystal cell subject to strong anchoring on the short ends and weak anchoring on the long sides. On removing an imposed magnetic field, three different types of relaxation behavior may be observed. Two of these are simple generalizations of one-dimensional relaxation channels, and are dominated by either the ends or the sides. The third is a traveling wave, nucleated by the strong anchoring ends of the cell but driven by the weak anchoring sides and is the result of a subtle balance between the two classical mechanisms. A phase diagram is derived, identifying the relaxation regimes as a function of the nondimensional initial field and the anchoring strength in the long cell limit. A comparison is made between numerical results and a simple one-dimensional theory derived from an asymptotic analysis. Surprisingly, the traveling wave behavior occurs for a large region of parameter space.