  We use full nematohydrodynamic simulations to study the statics and dynamics
of monolayers of cholesteric liquid crystals. Using chirality and temperature
as control parameters we show that we can recover the two-dimensional blue
phases recently observed in chiral nematics, where hexagonal lattices of
half-skyrmion topological excitations are interleaved by lattices of trefoil
topological defects. Furthermore, we characterise the transient dynamics during
the quench from isotropic to blue phase. We then proceed by confining
cholesteric stripes and blue phases within finite-sized tactoids and show that
it is possible to access a wealth of reconfigurable droplet shapes including
disk-like, elongated, and star-shaped morphologies. Our results demonstrate a
potential for constructing controllable, stable structures of liquid crystals
by constraining 2D blue phases and varying the chirality, surface tension and
elastic constants.
