A molecular-dynamics technique is utilized to calculate the melting curve o
f submonolayer and complete layers of krypton atoms physisorbed onto a sphe
rical substrate. Two models of the substrate are used. In the first model t
he substrate is treated as a spherical continuum whose differential element
s interact with krypton atoms via Lennard-Jones (LJ) potential. Hysteresis
is present in the melting transition for low coverages, which disappears as
the melting becomes more gradual near complete coverage. The melting tempe
rature at completion is very sensitive to second-layer promotion, which in
turn depends strongly on the radial boundary conditions. In the second mode
l the melting transition is also examined for 100 Kr atoms adsorbed onto sp
heres that exhibit corrugation in their potential interactions with the asd
orbate. Addition of corrugation in the form of a C-60 lattice effectively s
erves to merely raise the average LJ substrate sphere density slightly and
leave the melting transition unaffected, but replacing the LJ sphere with a
cubic carbon lattice raises the melting temperature by about 3 K (4.6%) wh
ile dramatically affecting the desorption behavior of the adlayer and lower
ing its spatial order. Various bond-orientational distributions and snapsho
t configurations are employed in understanding the completion process.