Growing interfaces and the Kardar-Parisi-Zhang scaling exponents
The Kardar-Parisi-Zhang (KPZ) equation describes growing interfaces: dh/dt = nu*grad^2 h + (lambda/2)(grad h)^2 + noise. The nonlinear lambda term breaks detailed balance and places interfaces in the KPZ universality class with exponents alpha=1/2, beta=1/3, z=3/2 (1D). The interface width W(t) ~ t^beta is the hallmark signature.