  The emergence of new techniques for the fabrication of nematic droplets with
nontrivial topology provides new routes for the assembly of responsive devices.
Here we perform a numerical study of spherical nematic droplets on fibres. We
analyse the equilibrium textures and find that, under certain conditions,the
nematic can avoid the nucleation of topological defects. We consider in detail
a homeotropic nematic droplet wrapped around a fibre with planar anchoring. We
investigate the effect of an electric field on the texture of this droplet such
type of system. In the presence of a DC field, the system undergoes a
Freederickzs-like transition above a given threshold $E_c$. We also consider AC
fields, at high and low frequencies, and find that the textures are similar to
those observed for static fields, in contrast with recently reported
experiments.
