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Session Q02 - Mechanisms for Pattern Formation.
Invited session, Friday morning, March 24, 8:00
Ballroom A2, San Jose Convention Center
Because they spatially "self-organize" on large scales in response to weak external forces, liquid crystal states of matter are well-known for their technological relevance in colorful, high resolution, low power consuming Flat Panel Displays. However, over the past 20 years, qualitatively new results in nonlinear physics have also emerged from fundamental research on liquid crystal states of matter. Most recently we found that long range elastic forces at traveling chiral liquid crystal interfaces result in patterns with features more familiarly associated with living systems: they are nonequilibrium, nonlinear, dissipative states showing both spatial and temporal order. ^1 \hfil \par In particular, there is an oscillatory first instability to a cellular pattern and a second bifurcation to an oscillatory mode (breathing mode). We explain the emergence of temporal order as resulting from competition between two incommensurate but comparable lengths: the cholesteric pitch as the equilibrium length scale and the pattern wavelength as the nonequilibrium scale. \hfil \par As the pulling speed is increased novel patterns arise at the flat interface for cholesteric-isotropic interfaces. First one obtains a nonequilibrium phase winding regime due to a coupling between the helix structure and gradients in impurity concentration and at even higher pulling speeds, an orientationally disordered state. \medskip \par\noindent ^* This work, in collaboration with H. R. Brand, University of Bayreuth, F.R.G. was partially supported by NATO Collaborative Research Grant 890777 and a 1993 John Simon Guggenheim Fellowship (PEC). \par\noindent 1. See for example: P. E. Cladis and H. R. Brand in Spatio-Temporal Patterns in Nonequilibrium Complex Systems, Proceedings Volume XXI, SFI Studies in the Sciences of Complexity, P. E. Cladis and P. Palffy-Muhoray (eds), Addison-Wesley (1994) p.123, and references therein.