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\centerline{\large \bf The evolution equation for a disclination in a nematic liquid crystal}

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\centerline{Paolo Cermelli}
\centerline{\it Universit\`a di Torino, Italy}
\centerline{e-mail {\tt cermelli@dm.unito.it}}

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\centerline{Eliot Fried}

\centerline{\it University of
Illinois at Urbana-Champaign, USA}
\centerline{e-mail {\tt e-fried@uiuc.edu}}

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We extend the Ericksen--Leslie theory for nematic fluids to account for
the presence of disclinations. We obtain an evolution equation in which the
resultant of the Eshelby stress at a disclination is proportional to the
velocity of the disclination with respect to the material. Included among
our results is a resolution of Eshelby's paradox concerning the nature of
the force acting on a disclination. As an application, we show how surface
disclinations can be described using within our framework, and how these defects act
to curve the free surface of the fluid, in competition with surface
tension, and, thus, to create cusps at the surface.

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{\bf Presented by Paolo Cermelli}

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