Efficient numerical studies of scaling properties and pattern formation during surface growth/erosion by surface mapping on a binary lattice gas model

We show how surfaces can be mapped onto two-dimensional lattice gases with binary site values, where surface growth/erosion is described by one-dimensional forward/backward migration of dimers, respectively. Using this mapping and a bit-coded numerical algorithm, very efficient simulations on large spatiotemporal scales have been performed. In addition, the bit-coding allows parallel simulations of 32 systems on a single 64-bit CPU core by the use of particular bit-pair (dimer) locations of the 64 bit words for each system. Using this novel mapping and the internal massive parallelization, we provide high-precision scaling results for the Kardar- Parisi-Zhang (KPZ) and Edwards-Wilkinson type of surface growth. The (smoothing/roughening) surface diffusion can be described by the correlated (attracting/repelling) motion of dimers and Mullins diffusion scaling can be simulated. The combination of competing KPZ and Mullins processes enables to generate various surface patterns (dots/ripples) analogously to the nonequilibrium states seen in driven Ising models. The relation of surface roughness and wavelength coarsening and the role of initial conditions (flat/tilted) will be analyzed.