  We report the results of Monte Carlo simulations of the Lebwohl--Lasher model
of nematic liquid crystals confined to cylindrical cavities with homeotropic
anchoring. We show that the ratio of the bulk to surface couplings is not in
general equal to the corresponding parameter K/W used in elastic theory (where
K is the Frank elastic constant in the one constant approximation and W is the
surface anchoring strength). By measuring the temperature dependence of K/W
(which is equivalent to the surface extrapolation length) we are able to
reconcile the results of our simulations as well as others with the predictions
of elastic theory. We find that the rate at which we cool the system from the
isotropic to nematic phase plays a crucial role in the development of the final
director structure, because of a large free energy barrier separating different
director structures as well as the temperature dependence of $K/W$. With a
suitably fast cooling rate we are able to keep the system out of a metastable
planar state and form an escaped radial structure for large enough systems.
