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\centerline{\large \bf The dynamics of nematic liquids in linear flows:}
\centerline{\large \bf molecular theory and averaged descriptions}

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\centerline{M. Gregory Forest}
\centerline{\it University of North Carolina at Chapel Hill, USA}
\centerline{e-mail {\tt forest@amath.unc.edu}}

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\centerline{Qi Wang}
\centerline{\it Florida State University, USA}
\centerline{e-mail {\tt wang@math.fsu.edu}}

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\centerline{Ruhai Zhou}
\centerline{\it University of North Carolina at Chapel Hill, USA}
\centerline{e-mail {\tt ruhai@amath.unc.edu}}

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Nematic polymers are pervasive in biological and synthetic soft
matter.  The Tobacco Mosaic Virus and spider silk are two natural
examples of macromolecules which exhibit nematic ordering, yet whose
behavior is dynamically more complex than small-molecule liquid
crystals.  We present a hierarchy of models for nematic polymers:
Leslie-Ericksen theory, second-moment tensor models of Landau-deGennes
type, and kinetic theory of Doi and Hess.  For bulk dynamics of
homogeneous nematic liquids in linear flows (e.g., simple shear), the
orientational dynamics decouples.  The models listed above then reduce
to two, five, and infinite-dimensional dynamical systems for the
orientational response to linear flow.  We report theory, analysis,
and simulation of the shear flow problem for nematic polymers from
each of these scales of description.  Contact with related
discoveries, especially the seminal contributions of Italian
colleagues (Greco, Maffettone, Marrucci, Virga and others), will be
emphasized.

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{\bf  Presented by M. Gregory Forest}

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