Mapping a depinning transition to polynuclear growth

We develop a phenomenological mapping between submonolayer polynuclear growth (PNG) and the interface dynamics at and below the depinning transition in the Kardar–Parisi–Zhang equation for a negative non-linearity λ. This is possible since the phase transition is of first order, with no diverging correlation length as the transition is approached from below. The morphology of the still-active and pinned configurations and the interface velocity are compared to the PNG picture. The interface mean height scales as erf(t).