Bulk dynamics for interfacial growth models
We study the influence of the bulk dynamics of a growing cluster of particles on the properties of its interface. First, we define a general bulk growth model by means of a continuum Master equation for the evolution of the bulk density field. This general model just considers an arbitrary addition of particles (though it can be easily generalized to consider subtraction) with no other physical restriction. The corresponding Langevin equation for this bulk density field is derived where the influence of the bulk dynamics is explicitly shown. Finally, when a well-defined interface is assumed for the growing cluster, the Langevin equation for the height field of this interface for some particular bulk dynamics is written. In particular, we obtain the celebrated Kardar-Parisi-Zhang equation. A Monte Carlo simulation illustrates the theoretical results.
Lopez
C
Instituto Mediterraneo de Estudios Avanzados, CSIC-Universitat de les Illes Balears, E-07071 Palma de Mallorca, Spain.
Garrido
PL
de Los Santos F