Morphological transition between diffusion-limited and ballistic aggregation growth patterns

Abstract

In this work, the transition between diffusion-limited and ballistic aggregation models was revisited using a model in which biased random walks simulate the particle trajectories. The bias is controlled by a parameter λ, which assumes the value λ = 0 (1) for ballistic (diffusion-limited) aggregation model. Patterns growing from a single seed were considered. In order to simulate large clusters, a new efficient algorithm was developed. For λ = 0, the patterns are fractal on the small length scales, but homogeneous on the large ones. We evaluated the mean density of particles ρ in the region defined by a circle of radius r centered at the initial seed. As a function of r, ρ reaches the asymptotic value ρ0(λ) following a power law ρ = ρ0 + Ar −γ with a universal exponent γ = 0.46(2), independent of λ. The asymptotic value has the behavior ρ0 ∼ |1 − λ| β , where β = 0.26(1). The characteristic crossover length that determines the transition from DLA-to BA-like scaling regimes is given by ξ ∼ |1 − λ| −ν , where ν = 0.61(1), while the cluster mass at the crossover follows a power law M ξ ∼ |1 − λ| −α , where α = 0.97(2). We deduce the scaling relations β = νγ and β = 2ν − α between these exponents.

Aggregation in a mixture of Brownian and ballistic wandering particles

“…In this work, we used careful simulations to analyze the transition between DLA-and BA-like regimes in a model where both random and ballistic trajectories are included. Differently from the previously described models [10,13], the trajectories are not characterized by distinct behaviors at short (random) and large (ballistic) scales. Indeed, we are interested in the scaling of clusters grown from a mixture of particles, which can follow either ballistic or random trajectories.…”

“…This transition between DLA and BA regimes was introduced by Meakin [13] in a early generalization of the DLA model. This model is very similar to that analyzed by Ferreira et al [10]. The main difference is that the drift of all trajectories is fixed at a lattice direction in the Meakin's model, in which, along the trajectory, the particle is moved one step in the drift direction with probability P , or moves at random to one of its four nearest-neighbor sites with probability 1 − P .…”

“…In a recent work, Ferreira et al [10] built a model in which the particles follow random trajectories with drifts at random directions. The bias is controlled by a parameter λ that, when varied, leads the model from BA (λ = 0) to DLA (λ=1).…”

Growth of electrodeposited gold on glassy carbon from a thiosulphate–sulphite electrolyte

“…[2] In fact, the direction of dendrite growth is indicative of slow-surface diffusion of individual gold nuclei or particle on the glassy carbon. An analogy to our findings is the behaviour of crystalline water on Au surfaces, [20] where surface diffusion of individual water crystals (or nuclei) were shown to lead to instabilities that could develop into dendrites. We believe that these results show, for the first time, dendrite growth of electrodeposited gold perpendicular to the current vector, i.e.…”

Phase transition in diffusion limited aggregation with patchy particles in two dimensions

“…This includes the effect of long range attraction [14], effect of electric * Corresponding author. field on DLA structures [15], Slippery diffusion-limited aggregation to mimic aggregation of non-shear bonds in colloidal systems [16], random walkers with drift [17], DLA aggregation of persistent random walkers [18].…”