Bulk dynamics for interfacial growth models
Cristobal Lopez, Pedro L. Garrido, Francisco de los Santos
Abstract
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 arbitrary addition of particles (though it can be easily generalized to consider substraction) 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 it is assumed a well-defined interface 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 (KPZ) equation. A Monte Carlo simulation illustrates the theoretical results.
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