  Exact results are obtained for random walks on finite lattice tubes with a
single source and absorbing lattice sites at the ends. Explicit formulae are
derived for the absorption probabilities at the ends and for the expectations
that a random walk will visit a particular lattice site before being absorbed.
Results are obtained for lattice tubes of arbitrary size and each of the
regular lattice types; square, triangular and honeycomb. The results include an
adjustable parameter to model the effects of strain, such as surface curvature,
on the surface diffusion. Results for the triangular lattice tubes and the
honeycomb lattice tubes model diffusion of adatoms on single walled zig-zag
carbon nano-tubes with open ends.
