Patterns and scaling properties in a ballistic deposition model

Aggregation in a mixture of Brownian and ballistic wandering particles

In this paper, we analyze the scaling properties of a model that has as limiting cases the diffusion-limited aggregation (DLA) and the ballistic aggregation (BA) models. This model allows us to control the radial and angular scaling of the patterns, as well as their gap distributions. The particles added to the cluster can follow either ballistic trajectories, with probability Pba, or random ones, with probability Prw=1-Pba. The patterns were characterized through several quantities, including those related to the radial and angular scaling. The fractal dimension as a function of Pba continuously increases from df approximately 1.72 (DLA dimensionality) for Pba=0 to df approximately 2 (BA dimensionality) for Pba. However, the lacunarity and the active zone width exhibit a distinct behavior: they are convex functions of Pba with a maximum at Pba approximately 1/2. Through the analysis of the angular correlation function, we found that the difference between the radial and angular exponents decreases continuously with increasing Pba and rapidly vanishes for Pba>1/2, in agreement with recent results concerning the asymptotic scaling of DLA clusters.

Dynamic rearrangements and packing regimes in randomly deposited two-dimensional granular beds

We study the structural properties of two-dimensional granular packings prepared by random deposition from a source line. We consider a class of random ballistic deposition models based on single-particle relaxation rules controlled by a critical angle, and we show that these local rules can be formulated as rolling friction in the framework of dynamic methods for the simulation of granular materials. We find that a packing prepared by random deposition models is generically unstable, and undergoes dynamic rearrangements. As a result, the dynamic method leads systematically to a higher solid fraction than the geometrical model for the same critical angle. We characterize the structure of the packings generated by both methods in terms of solid fraction, contact connectivity, and anisotropy. Our analysis provides evidence for four packing regimes as a function of solid fraction, the mechanisms of packing growth being different in each regime.

Dynamical scaling behavior in two-dimensional ballistic deposition with shadowing

The dynamical scaling behavior in two-dimensional ballistic deposition with shadowing is studied as a function of the angular distribution of incoming particles and of the underlying lattice structure. Using a dynamical scaling form for the surface box number, results for the scaling of the surface fractal dimension are also presented. Our results indicate that, in addition to the usual self-affine universality class corresponding to vertical deposition, there exist at least two additional universality classes characterized by distinct values of the coarsening and roughening exponents p and beta describing the evolution of the lateral feature size and surface roughness with film thickness, as well as the surface fractal dimension D(f). For the case of a uniform angular distribution corresponding to an anisotropic flux, we find p=beta=1 and D(f) approximately 1.7. However, for ballistic deposition with an isotropic flux (corresponding to a "cosine" angular distribution), we find p approximately 2/3 and D(f) approximately 1.5 while the effective roughening exponent beta approximately 0.52-0.64 was found to be slightly lattice dependent. In both cases, anomalous scaling of the height-height correlation function is also observed. In contrast, vertical deposition leads to a self-affine surface with p=2/3, beta=1/3, and D(f)=1. The asymptotic scaling behavior appears to depend on the behavior of the angular distribution at large angles but does not depend on other details. An analysis that clarifies the relationship between the launch angle distribution used in the simulations and the flux distribution is also presented.