  The motion of domain walls in ferromagnetic, cylindrical nanowires is
investigated numerically by solving the Landau-Lifshitz-Gilbert equation for a
classical spin model in which energy contributions from exchange, crystalline
anisotropy, dipole-dipole interaction, and a driving magnetic field are
considered. Depending on the diameter, either transverse domain walls or vortex
walls are found. The transverse domain wall is observed for diameters smaller
than the exchange length of the given material. Here, the system behaves
effectively one-dimensional and the domain wall mobility agrees with a result
derived for a one-dimensional wall by Slonczewski. For low damping the domain
wall mobility decreases with decreasing damping constant. With increasing
diameter, a crossover to a vortex wall sets in which enhances the domain wall
mobility drastically. For a vortex wall the domain wall mobility is described
by the Walker-formula, with a domain wall width depending on the diameter of
the wire. The main difference is the dependence on damping: for a vortex wall
the domain wall mobility can be drastically increased for small values of the
damping constant up to a factor of $1/\alpha^2$.
