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Bulk dynamics for interfacial growth models

Lopez, Cristobal; Garrido, Pedro L. ; de los Santos, Francisco
Phys. Rev. E 62, 4747 , (2000)

We study the influence of the bulk dynamics of a growing cluster of
particles on the properties of its interface.
First, we define
a {it 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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