  Numerical simulations of the time-dependent Swift-Hohenberg equation are used
to test predictions of Cross [Phys. Rev. A 25:1065-1076 (1982)] that
Rayleigh-Benard convection in the form of straight rolls or of an array of
dislocations may be observed in an annular domain depending on the values of
inner radius r_1, outer radius r_2, reduced Rayleigh number epsilon, and the
initial state. As r_1 is decreased for a fixed r_2 and for different choices of
epsilon and initial states, we find that there are indeed ranges of these
parameters for which the predictions of Cross are qualitatively correct.
However, when the radius difference r_2-r_1 becomes larger than a few roll
diameters, a new pattern is observed consisting of stripe domains separated by
radially-oriented grain boundaries. The relative stabilities of the various
patterns are compared by evaluating their Lypunov functional densities.
