  We simulated a growth model in 1+1 dimensions in which particles are
aggregated according to the rules of ballistic deposition with probability p or
according to the rules of random deposition with surface relaxation (Family
model) with probability 1-p. For any p>0, this system is in the
Kardar-Parisi-Zhang (KPZ) universality class, but it presents a slow crossover
from the Edwards-Wilkinson class (EW) for small p. From the scaling of the
growth velocity, the parameter p is connected to the coefficient of the
nonlinear term of the KPZ equation, lambda, giving lambda ~ p^gamma, with gamma
= 2.1 +- 0.2. Our numerical results confirm the interface width scaling in the
growth regime as W ~ lambda^beta t^beta, and the scaling of the saturation time
as tau ~ lambda^(-1) L^z, with the expected exponents beta =1/3 and z=3/2 and
strong corrections to scaling for small lambda. This picture is consistent with
a crossover time from EW to KPZ growth in the form t_c ~ lambda^(-4) ~ p^(-8),
in agreement with scaling theories and renormalization group analysis. Some
consequences of the slow crossover in this problem are discussed and may help
investigations of more complex models.
