We study the dynamics of an exactly solvable lattice model for inhomogeneous
interface growth. The interface grows deterministically with constant velocity
except along a defect line where the growth process is random. We obtain exact
expressions for the average height and height fluctuations as functions of
space and time for an initially flat interface. For a given defect strength
there is a critical angle between the defect line and the growth direction
above which a cusp in the interface develops. In the mapping to polymers in
random media this is an example for the transverse Meissner effect.
Fluctuations around the mean shape of the interface are Gaussian.Comment: 10 pages, late
