  Suppose a solid has a crack filled with a gas. If the crack reaches the
surrounding medium, how long does it take the gas to diffuse out of the crack?
Iterated Brownian motion serves as a model for diffusion in a crack.
  If \tau is the first exit time of iterated Brownian motion from the solid,
then P(\tau>t) can be viewed as a measurement of the amount of contaminant left
in the crack at time t. We determine the large time asymptotics of P(\tau>t)
for both bounded and unbounded sets. We also discuss a strange connection
between iterated Brownian motion and the parabolic operator
{1/8}\Delta^2-\frac{\partial}{\partial t}.
