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\centerline{\large \bf A PDE Model for Phase Transitions }
\centerline{\large \bf in  Liquid Crystals with Chirality}

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\centerline{P.~Bauman}
\centerline{\it Purdue University, USA}
\centerline{e-mail {\tt bauman@math.purdue.edu}}

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\centerline{M.C.~Calderer}
\centerline{\it University of Minnesota, USA}
\centerline{e-mail {\tt mcc@math.umn.edu}}

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\centerline{C.~Liu}
\centerline{\it Penn State University, USA}
\centerline{e-mail {\tt liu@math.psu.edu}}

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\centerline{D.~Phillips}
\centerline{\it Purdue University, USA}
\centerline{e-mail {\tt phillips@math.purdue.edu}}

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We study the Landau-de Gennes free energy used to describe the
transition between chiral nematic and smectic A liquid crystal phases.
We consider the phenomenology of the transition and discuss the
behavior of the material constants. Within the present mathematical
framework, the physically observed growth behavior of the {\it twist
  and bend} Frank constants, $K_2$ and $K_3$ respectively, plays a
major role in determining the transition regime. We show existence of
minimizers in a large class of admissible fields. Then under the
hypothesis that $K_2$ and $K_3$ are large, we establish estimates for
the transition regime separating the two phases. The work emphasizes
the interplay between two competing effects: the layer formation of
the smectic A phase and the twist tendency of the chiral nematic
phase.  Our discussion also illustrates the analogies as well as the
discrepancies in modeling and behavior between smectic A* liquid
crystals and superconducting materials described by the
Ginzburg-Landau theory.

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{\bf Presented by Patricia Bauman}

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