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

Is it really possible to grow isotropic on-lattice diffusion-limited aggregates?

In a recent paper (Bogoyavlenskiy V A 2002 \JPA \textbf{35} 2533), an algorithm aiming to generate isotropic clusters of the on-lattice diffusion-limited aggregation (DLA) model was proposed. The procedure consists of aggregation probabilities proportional to the squared number of occupied sites ($k^2$). In the present work, we analyzed this algorithm using the noise reduced version of the DLA model and large scale simulations. In the noiseless limit, instead of isotropic patterns, a $45^\circ$ ($30^\circ$) rotation in the anisotropy directions of the clusters grown on square (triangular) lattices was observed. A generalized algorithm, in which the aggregation probability is proportional to $k^\nu$, was proposed. The exponent $\nu$ has a nonuniversal critical value $\nu_c$, for which the patterns generated in the noiseless limit exhibit the original (axial) anisotropy for $\nu<\nu_c$ and the rotated one (diagonal) for $\nu>\nu_c$. The values $\nu_c = 1.395\pm0.005$ and $\nu_c = 0.82\pm 0.01$ were found for square and triangular lattices, respectively. Moreover, large scale simulations show that there are a nontrivial relation between noise reduction and anisotropy direction. The case $\nu=2$ (\bogo's rule) is an example where the patterns exhibit the axial anisotropy for small and the diagonal one for large noise reduction.Comment: 12 pages, 8 figure

3D gravity and non-linear cosmology

By the inclusion of an additional term, non-linear in the scalar curvature $R$, it is tested if dark energy could rise as a geometrical effect in 3D gravitational formulations. We investigate a cosmological fluid obeying a non-polytropic equation of state (the van der Waals equation) that is used to construct the energy-momentum tensor of the sources, representing the hypothetical inflaton in gravitational interaction with a matter contribution. Following the evolution in time of the scale factor, its acceleration, and the energy densities of constituents it is possible to construct the description of an inflationary 3D universe, followed by a matter dominated era. For later times it is verified that, under certain conditions, the non-linear term in $R$ can generate the old 3D universe in accelerated expansion, where the ordinary matter is represented by the barotropic limit of the van der Waals constituent.Comment: 7 pages, to appear in Mod. Phys. Let

Morphological transition between diffusion-limited and ballistic aggregation growth patterns

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 $\lambda$, which assumes the value $\lambda=0$ (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 $\lambda \ne 0$, the patterns are fractal on the small length scales, but homogeneous on the large ones. We evaluated the mean density of particles $\bar{\rho}$ in the region defined by a circle of radius $r$ centered at the initial seed. As a function of $r$, $\bar{\rho}$ reaches the asymptotic value $\rho_0(\lambda)$ following a power law $\bar{\rho}=\rho_0+Ar^{-\gamma}$ with a universal exponent $\gamma=0.46(2)$, independent of $\lambda$. The asymptotic value has the behavior $\rho_0\sim|1-\lambda|^\beta$, where $\beta= 0.26(1)$. The characteristic crossover length that determines the transition from DLA- to BA-like scaling regimes is given by $\xi\sim|1-\lambda|^{-\nu}$, where $\nu=0.61(1)$, while the cluster mass at the crossover follows a power law $M_\xi\sim|1 -\lambda|^{-\alpha}$, where $\alpha=0.97(2)$. We deduce the scaling relations \beta=\n u\gamma and $\beta=2\nu-\alpha$ between these exponents.Comment: 7 pages, 8 figure

Decrease in carbon stocks in an oxisol due to land use and cover change in southwestern Amazon.

This study presents data on the influence of the land cover type on soil carbon stocks in an Oxisol in southwestern Amazon, Acre, Brazil, under three land cover types: mature forest, pasture and rubber tree plantation. Total soil carbon was calculated using carbon concentration in soil and soil bulk density. Accumulated soil carbon stock up to 1 m depth was greater in mature forest (96 Mg ha-1), followed by pasture (79.7 Mg ha-1) and then by rubber tree plantation (56.3 Mg ha-1); also the greatest carbon accumulation in the surface layers was in pasture. Such results demonstrate that we need not only carbon stocks information by soil type, but also precise information on the land cover classification within a region in order to generate better soil carbon stocks estimations. Also, it is important to notice that mature forest conversion to other land covers can be the source to the atmosphere of about 20 to 40% of the carbon stocked in the soil previously

Non-linear terms in 2D cosmology

In this work we investigate the behavior of two-dimensional (2D) cosmological models, starting with the Jackiw-Teitelboim (JT) theory of gravitation. A geometrical term, non-linear in the scalar curvature $R$, is added to the JT dynamics to test if it could play the role of dark energy in a 2D expanding universe. This formulation makes possible, first, the description of an early (inflationary) 2D universe, when the van der Waals (vdW) equation of state is used to construct the energy-momentum tensor of the gravitational sources. Second, it is found that for later times the non-linear term in $R$ can generate an old 2D universe in accelerated expansion, where an ordinary matter dominated era evolves into a decelerated/accelerated transition, giving to the dark energy effects a geometrical origin. The results emerge through numerical analysis, following the evolution in time of the scale factor, its acceleration, and the energy densities of constituents.Comment: tex file plus figures in two zipped files. To appear in Europhys. Let

Immersion Anomaly of Dirac Operator on Surface in R^3

In previous report (J. Phys. A (1997) 30 4019-4029), I showed that the Dirac field confined in a surface immersed in $R^3$ by means of a mass type potential is governed by the Konopelchenko-Kenmotsu-Weierstrass-Enneper equation. In this article, I quantized the Dirac field and calculated the gauge transformation which exhibits the gauge freedom of the parameterization of the surface. Then using the Ward-Takahashi identity, I showed that the expectation value of the action of the Dirac field is expressed by the Willmore functional and area of the surface.Comment: AMS-Tex Us

Universal fluctuations in radial growth models belonging to the KPZ universality class

We investigate the radius distributions (RD) of surfaces obtained with large-scale simulations of radial clusters that belong to the KPZ universality class. For all investigated models, the RDs are given by the Tracy-Widom distribution of the Gaussian unitary ensemble, in agreement with the conjecture of the KPZ universality class for curved surfaces. The quantitative agreement was also confirmed by two-point correlation functions asymptotically given by the covariance of the Airy$_2$ process. Our simulation results fill the last lacking gap of the conjecture that had been recently verified analytically and experimentally.Comment: 5 pages, 5 figure

Palms use a bluffing strategy to avoid seed predation by rats in Brazil.

The goal of this study was to ascertain why the production of variable seediness is advantageous for Attalea phalerata palms. Our hypothesis was that variation reduces seed predation by the spiny rats Thrichomys pachyurus and Clyomys laticeps. Although there is a positive correlation between endocarp size and number of seeds, endocarps sometimes contain more or fewer seeds than expected; palms bluff about the number of seed per endocarp. Therefore, rats do not know how many seeds an endocarp contains. To model rats? predating behavior, we applied Charnov?s Marginal Value Theorem. The model shows that rats attack endocarps only when the energy gain is higher than the energy available in the habitat. Hence, it is not advantageous to eat all the seeds inside an endocarp. This explains why 45 percent of forest endocarps and 35 percent of savanna endocarps were still viable after predation. We then applied the model to two simulated endocarp populations with less variability in the number of seeds per endocarp size and determined that viable diaspores after predation were reduced to 15 percent. With less variability, palms cannot bluff about the number of seeds inside endocarps and predators can predict accurately how many seeds they should try to eat. Uncertainty about the number of seeds diminished predation but gave selective advantage to multiseeded fruits. Therefore, the bluffing strategy would be evolutionarily stable only if it were counterbalanced by other forces. Otherwise, predators would win the bluffing game