  We present results of Monte Carlo simulations of the two dimensional
one-component plasma and of the Ginzberg-Landau model in the lowest Landau
level approximation, with both charges and vortices respectively confined
within a disc. In both models we see that as the temperature is reduced,
oscillations in the radial density develop which spread into the bulk from the
edge of the disc. The amplitude of these oscillations grows as the temperature
is lowered and the length scale over which the oscillations occurs is the same
as the correlation length for local crystalline order at that temperature. At
temperatures similar to those where earlier studies have reported a first-order
fluid-crystal phase transition, the correlation length is comparable to the
linear dimensions of the samples studied, which suggests that finite size
effects will be affecting the accuracy of their conclusions.
