arXiv subjects
Publications and source records attributed to S. C. Ferreira Jr..
We review some computer algorithms for the simulation of off-lattice clusters grown from a seed, with emphasis on the diffusion-limited aggregation, ballistic aggregation and Eden models. Only those methods which can be immediately extended to distinct off-lattice aggregation processes are discussed. The computer efficiencies of the distinct algorithms are compared.
The self-affinity of growing systems with radial symmetry, from tumors to grain-grain displacement, has devoted increasing interest in the last decade. In this work, we analyzed features about the interface scaling of these clusters through large scale simulations (up to $3\times 10^7$ particles) of two-dimensional growth processes with special emphasis on the off-lattice Eden model. The central objective is to discuss an important pitfall associated to the evaluation of the growth exponent $β$ of these systems. We show that the $β$ value depends on the choice of the origin used to determine the interface width. We considered two strategies frequently used. When the width is evaluated in relation to the center of mass (CM) of the border, the exponent obtained for the Eden model was $β_{CM}=0.404\pm0.013$, in very good agreement with previous reported values. However, if the border CM is replaced by the initial seed position (a static origin), the exponent $β_0=0.333\pm 0.010$, in complete agreement with the KPZ value $β_{KPZ}=1/3$, was found. The difference between $β_{CM}$ and $β_{0}$ was explained through the border CM fluctuations that grow faster than the overall interface fluctuations. Indeed, we show that the exponents $β_0$ and $β_{CM}$ characterize large and small wavelength fluctuations of the interface, respectively. These finds were also observed in three distinct lattice models, in which the lattice-imposed anisotropy is absent.
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 $λ\ne 0$, the patterns are fractal on the small length scales, but homogeneous on the large ones. We evaluated the mean density of particles $\barρ$ in the region defined by a circle of radius $r$ centered at the initial seed. As a function of $r$, $\barρ$ reaches the asymptotic value $ρ_0(λ)$ following a power law $\barρ=ρ_0+Ar^{-γ}$ with a universal exponent $γ=0.46(2)$, independent of $λ$. The asymptotic value has the behavior $ρ_0\sim|1-λ|^β$, where $β= 0.26(1)$. The characteristic crossover length that determines the transition from DLA- to BA-like scaling regimes is given by $ξ\sim|1-λ|^{-ν}$, where $ν=0.61(1)$, while the cluster mass at the crossover follows a power law $M_ξ\sim|1 -λ|^{-α}$, where $α=0.97(2)$. We deduce the scaling relations $β=\n uγ$ and $β=2ν-α$ between these exponents.
Recent experiments involving CdTe films grown on Si(111) substrates by hot wall epitaxy revealed features not previously observed [S. O. Ferreira \textit{et al.}, J. Appl. Phys. \textbf{93}, 1195 (2003)]. This system, which follows the Volmer-Weber growth mode with nucleation of isolated 3D islands for less than one monolayer of evaporated material, was described by a peculiar behavior of the quantum dot (QD) size distributions. In this work, we proposed a kinetic deposition model to reproduce these new features. The model, which includes thermally activated diffusion and evaporation of CdTe, qualitatively reproduced the experimental QD size distributions. Moreover, the model predicts a transition from Stranski-Krastanow growth mode at lower temperatures to Volmer-Weber growth mode at higher ones characterized through the QD width distributions.
One of the most promising strategies to treat cancer is attacking it with viruses. Virus can kill tumor cells specifically or act as carriers that deliver normal genes into cancer cells. A model for virus therapy of cancer is investigated and some of its predictions are in agreement with results obtained from experimental tumors. Furthermore, the model reveals an oscillatory (periodic or aperiodic) response of tumor cells and virus populations which may difficult clinical prognosis. These results suggest the need for new \textit{in vivo} and \textit{in vitro} experiments aiming to detect this oscillatory response.
Recently, we have proposed a nutrient-limited model for the avascular growth of tumors including cell proliferation, motility and death \cite{jr}, that, qualitatively reproduces commonly observed morphologies for carcinomas {\it in situ}. In the present work, we analyze the effects of distinct chemotherapeutic strategies on the patterns, scaling and growth laws obtained for such nutrient-limited model. Two kinds of chemotherapeutic strategies were considered, namely, those that kill cancer cells and those that block cell mitosis but allows the cell to survive for some time. Depending on the chemotherapeutic schedule used, the tumors are completely eliminated, reach a stationary size or grow following power laws. The model suggests that the scaling properties of the tumors are not affected by the mild cytotoxic treatments, although a reduction in growth rates and an increase in invasiveness are observed. For the strategies based on antimitotic drugs a morphological transition in which compact tumors become more fractal under aggressive treatments was seen.