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 $P_{ba}$, or random ones, with probability $P_{rw}=1-P_{ba}$. The patterns were characterized through several quantities, including those related to the radial and angular scaling. The fractal dimension as a function of $P_{ba}$ continuously increases from $d_f\approx 1.72$ (DLA dimensionality) for $P_{ba}=0$ to $d_f\approx 2$ (BA dimensionality) for $P_{ba}=1$. However, the lacunarity and the active zone width exhibt a distinct behavior: they are convex functions of $P_{ba}$ with a maximum at $P_{ba}\approx1/2$. Through the analysis of the angular correlation function, we found that the difference between the radial and angular exponents decreases continuously with increasing $P_{ba}$ and rapidly vanishes for $P_{ba}>1/2$, in agreement with recent results concerning the asymptotic scaling of DLA clusters.Comment: 7 pages, 6 figures. accepted for publication on PR

The harmonic measure of diffusion-limited aggregates including rare events

We obtain the harmonic measure of diffusion-limited aggregate (DLA) clusters using a biased random-walk sampling technique which allows us to measure probabilities of random walkers hitting sections of clusters with unprecedented accuracy; our results include probabilities as small as 10- 80. We find the multifractal D(q) spectrum including regions of small and negative q. Our algorithm allows us to obtain the harmonic measure for clusters more than an order of magnitude larger than those achieved using the method of iterative conformal maps, which is the previous best method. We find a phase transition in the singularity spectrum f(α) at α≈14 and also find a minimum q of D(q), qmin=0.9±0.05

Stretched exponentials and power laws in granular avalanching

We introduce a model for granular avalanching which exhibits both stretched exponential and power law avalanching over its parameter range. Two modes of transport are incorporated, a rolling layer consisting of individual particles and the overdamped, sliding motion of particle clusters. The crossover in behaviour observed in experiments on piles of rice is attributed to a change in the dominant mode of transport. We predict that power law avalanching will be observed whenever surface flow is dominated by clustered motion. Comment: 8 pages, more concise and some points clarified

Scale invariance and universality of force networks in static granular matter

Force networks form the skeleton of static granular matter. They are the key ingredient to mechanical properties, such as stability, elasticity and sound transmission, which are of utmost importance for civil engineering and industrial processing. Previous studies have focused on the global structure of external forces (the boundary condition), and on the probability distribution of individual contact forces. The disordered spatial structure of the force network, however, has remained elusive so far. Here we report evidence for scale invariance of clusters of particles that interact via relatively strong forces. We analyzed granular packings generated by molecular dynamics simulations mimicking real granular matter; despite the visual variation, force networks for various values of the confining pressure and other parameters have identical scaling exponents and scaling function, and thus determine a universality class. Remarkably, the flat ensemble of force configurations--a simple generalization of equilibrium statistical mechanics--belongs to the same universality class, while some widely studied simplified models do not.Comment: 15 pages, 4 figures; to appear in Natur

A Hybrid Monte Carlo Method for Surface Growth Simulations

We introduce an algorithm for treating growth on surfaces which combines important features of continuum methods (such as the level-set method) and Kinetic Monte Carlo (KMC) simulations. We treat the motion of adatoms in continuum theory, but attach them to islands one atom at a time. The technique is borrowed from the Dielectric Breakdown Model. Our method allows us to give a realistic account of fluctuations in island shape, which is lacking in deterministic continuum treatments and which is an important physical effect. Our method should be most important for problems close to equilibrium where KMC becomes impractically slow.Comment: 4 pages, 5 figure

Fractal-based analysis of optical coherence tomography data to quantify retinal tissue damage

BACKGROUND: The sensitivity of Optical Coherence Tomography (OCT) images to identify retinal tissue morphology characterized by early neural loss from normal healthy eyes is tested by calculating structural information and fractal dimension. OCT data from 74 healthy eyes and 43 eyes with type 1 diabetes mellitus with mild diabetic retinopathy (MDR) on biomicroscopy was analyzed using a custom-built algorithm (OCTRIMA) to measure locally the intraretinal layer thickness. A power spectrum method was used to calculate the fractal dimension in intraretinal regions of interest identified in the images. ANOVA followed by Newman-Keuls post-hoc analyses were used to test for differences between pathological and normal groups. A modified p value of <0.001 was considered statistically significant. Receiver operating characteristic (ROC) curves were constructed to describe the ability of each parameter to discriminate between eyes of pathological patients and normal healthy eyes. RESULTS: Fractal dimension was higher for all the layers (except the GCL + IPL and INL) in MDR eyes compared to normal healthy eyes. When comparing MDR with normal healthy eyes, the highest AUROC values estimated for the fractal dimension were observed for GCL + IPL and INL. The maximum discrimination value for fractal dimension of 0.96 (standard error =0.025) for the GCL + IPL complex was obtained at a FD <= 1.66 (cut off point, asymptotic 95% Confidence Interval: lower-upper bound = 0.905-1.002). Moreover, the highest AUROC values estimated for the thickness measurements were observed for the OPL, GCL + IPL and OS. Particularly, when comparing MDR eyes with control healthy eyes, we found that the fractal dimension of the GCL + IPL complex was significantly better at diagnosing early DR, compared to the standard thickness measurement. CONCLUSIONS: Our results suggest that the GCL + IPL complex, OPL and OS are more susceptible to initial damage when comparing MDR with control healthy eyes. Fractal analysis provided a better sensitivity, offering a potential diagnostic predictor for detecting early neurodegeneration in the retina

Fractal to Nonfractal Phase Transition in the Dielectric Breakdown Model

A fast method is presented for simulating the dielectric-breakdown model using iterated conformal mappings. Numerical results for the dimension and for corrections to scaling are in good agreement with the recent RG prediction of an upper critical $\eta_c=4$, at which a transition occurs between branching fractal clusters and one-dimensional nonfractal clusters.Comment: 5 pages, 7 figures; corrections to scaling include

Growth of Patterned Surfaces

During epitaxial crystal growth a pattern that has initially been imprinted on a surface approximately reproduces itself after the deposition of an integer number of monolayers. Computer simulations of the one-dimensional case show that the quality of reproduction decays exponentially with a characteristic time which is linear in the activation energy of surface diffusion. We argue that this life time of a pattern is optimized, if the characteristic feature size of the pattern is larger than $(D/F)^{1/(d+2)}$, where $D$ is the surface diffusion constant, $F$ the deposition rate and $d$ the surface dimension.Comment: 4 pages, 4 figures, uses psfig; to appear in Phys. Rev. Let

Nothing moves a surface: vacancy mediated surface diffusion

We report scanning tunneling microscopy observations, which imply that all atoms in a close-packed copper surface move frequently, even at room temperature. Using a low density of embedded indium `tracer' atoms, we visualize the diffusive motion of surface atoms. Surprisingly, the indium atoms seem to make concerted, long jumps. Responsible for this motion is an ultra-low density of surface vacancies, diffusing rapidly within the surface. This interpretation is supported by a detailed analysis of the displacement distribution of the indium atoms, which reveals a shape characteristic for the vacancy mediated diffusion mechanism that we propose.Comment: 4 pages; for associated movie, see http://www-lion.leidenuniv.nl/sections/cm/groups/interface/projects/therm