  Thermally activated escape of an over-damped particle from a metastable well
under the action of a time-ramped force is studied. We express the mean first
passage time (MFPT) as the solution to a partial differential equation, which
we solve numerically for a model case. We discuss two approximations of the
MFPT, one of which works remarkably well over a wide range of loading rates,
while the second is easy to calculate and can provide a valuable first
estimate.
