  Adsorbed gases within, or outside of, carbon nanotubes may be analyzed with
an approximate model of adsorption on lattice sites situated on a cylindrical
surface. Using this model, the ground state energies of alternative lattice
structures are calculated, assuming Lennard-Jones pair interactions between the
particles. The resulting energy and equilibrium structure are nonanalytic
functions of radius (R) because of commensuration effects associated with the
cylindrical geometry.
  Specifically, as R varies, structural transitions occur between
configurations differing in the "ring number", defined as the number of atoms
located at a common value of the longitudinal coordinate (z). The thermodynamic
behavior of this system is evaluated at finite temperatures, using a
Hamiltonian with nearest-neighbor interactions. The resulting specific heat
bears a qualitative resemblance to that of the one-dimensional Ising model.
