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Nonuniversal effects in mixing correlated-growth processes with randomness: Interplay between bulk morphology and surface roughening

To construct continuum stochastic growth equations for competitive nonequilibrium surface-growth processes of the type RD+X that mixes random deposition (RD) with a correlated-growth process X, we use a simplex decomposition of the height field. A distinction between growth processes X that do and do not create voids in the bulk leads to the definition of the {\it effective probability} $p_{\mathrm{eff}}$ of the process X that is a measurable property of the bulk morphology and depends on the {\it activation probability} $p$ of X in the competitive process RD+X. The bulk morphology is reflected in the surface roughening via {\it nonuniversal} prefactors in the universal scaling of the surface width that scales in $p_{\mathrm{eff}}$. The equation and the resulting scaling are derived for X in either a Kardar-Parisi-Zhang or Edwards-Wilkinson universality class in $(1+1)$ dimensions, and illustrated by an example of X being a ballistic deposition. We obtain full data collapse on its corresponding universal scaling function for all $p \in (0;1]$. We outline the generalizations to $(1+n)$ dimensions and to many-component competitive growth processes.