Pattern Formation in Liquid Crystals

Abstract

What does viscous fingering have in common with crystal growth? It is not only the visual similarity of the patterns the two seemingly unrelated phenomena can generate under certain circumstances, but also the same underlying physics which controls both growth processes. The common behaviour - diffusion limited growth - leads to morphological instability in which a growing surface is unstable with respect to spacially periodic perturbations. Several theoretical and simulation studies have shown that the simple model is biased in its large scale morphology by the local anisotropy of the growth rules.