Boundary crossover in semi-infinite non-equilibrium growth processes
Résumé
The growth of stochastic interfaces in the vicinity boundry and the non-trivial crossover towards the behaviour deep in the bulk analysed. The causal interactions of the interface with the boundary lead to a roughness near to the boundary than deep in the bulk. This is exemplified in the semi- infinite Edwards-Wilkinson model in one dimension, from both its exact solution and numerical simulations, well from simulations on the semi-infinite one-dimensional Kardar-Parisi-Zhang model. The non-stationary scaling of interface heights and widths is analysed and a universal scaling form for the local height, profile is proposed.