21 research outputs found
On the origins of scaling corrections in ballistic growth models
We study the ballistic deposition and the grain deposition models on
two-dimensional substrates. Using the Kardar-Parisi-Zhang (KPZ) ansatz for
height fluctuations, we show that the main contribution to the intrinsic width,
which causes strong corrections to the scaling, comes from the fluctuations in
the height increments along deposition events. Accounting for this correction
in the scaling analysis, we obtained scaling exponents in excellent agreement
with the KPZ class. We also propose a method to suppress these corrections,
which consists in divide the surface in bins of size and use only
the maximal height inside each bin to do the statistics. Again, scaling
exponents in remarkable agreement with the KPZ class were found. The binning
method allowed the accurate determination of the height distributions of the
ballistic models in both growth and steady state regimes, providing the
universal underlying fluctuations foreseen for KPZ class in 2+1 dimensions. Our
results provide complete and conclusive evidences that the ballistic model
belongs to the KPZ universality class in dimensions. Potential
applications of the methods developed here, in both numerics and experiments,
are discussed.Comment: 8 pages, 7 figure
Local vs. long-range infection in unidimensional epidemics
We study the effects of local and distance interactions in the unidimensional
contact process (CP). In the model, each site of a lattice is occupied by an
individual, which can be healthy or infected. As in the standard CP, each
infected individual spreads the disease to one of its first-neighbors with rate
, and with unitary rate, it becomes healthy. However, in our model, an
infected individual can transmit the disease to an individual at a distance
apart. This step mimics a vector-mediated transmission. We observe the
host-host interactions do not alter the critical exponents significantly in
comparison to a process with only L\'evy-type interactions. Our results
confirm, numerically, early field-theoretic predictions.Comment: 8 pages, 6 figures, to appear on Frontiers in Physic
Continuous and discontinuous absorbing-state phase transitions on Voronoi-Delaunay random lattices
We study absorbing-state phase transitions in two-dimensional
Voronoi-Delaunay (VD) random lattices with quenched coordination disorder.
Quenched randomness usually changes the criticality and destroys discontinuous
transitions in low-dimensional nonequilibrium systems. We performed extensive
simulations of the Ziff-Gulari-Barshad (ZGB) model, and verified that the VD
disorder does not change the nature of its discontinuous transition. Our
results corroborate recent findings of Barghatti and Vojta [Phys. Rev. Lett.
{\bf 113}, 120602 (2014)] stating the irrelevance of topological disorder in a
class of random lattices that includes VD and raise the interesting possibility
that disorder in nonequilibrium APT may, under certain conditions, be
irrelevant for the phase coexistence. We also verify that the VD disorder is
irrelevant for the critical behavior of models belonging to the directed
percolation and Manna universality classes.Comment: 7 pages, 6 figure