  Numerical integration of a stochastic Landau-Lifshitz-Gilbert equation is
used to study dynamic processes in single-domain nanoscale magnets at nonzero
temperatures. Special attention is given to including thermal fluctuations as a
Langevin term, and the Fast Multipole Method is used to calculate dipole-dipole
interactions. It is feasible to simulate these dynamics on the nanosecond time
scale for spatial discretizations that involve on the order of 10000 nodes
using a desktop workstation. The nanoscale magnets considered here are single
pillars with large aspect ratio. Hysteresis-loop simulations are employed to
study the stable and metastable configurations of the magnetization. Each
pillar has magnetic end caps. In a time-dependent field the magnetization of
the pillars is observed to reverse via nucleation, propagation, and coalescence
of the end caps. In particular, the end caps propagate into the magnet and meet
near the middle. A relatively long-lived defect is formed when end caps with
opposite vorticity meet. Fluctuations are more important in the reversal of the
magnetization for fields weaker than the zero-temperature coercive field, where
the reversal is thermally activated. In this case, the process must be
described by its statistical properties, such as the distribution of switching
times, averaged over a large number of independent thermal histories.
