Kinetic roughening with anysotropic growth rules

Inspired by the chemical etching processes, where experiments show that growth rates depending on the local environment might play a fundamental role in determining the properties of the etched surfaces, we study here a model for kinetic roughening which includes explicitly an anisotropic effect in the growth rules. Our model introduces a dependence of the growth rules on the local environment conditions, i.e. on the local curvature of the surface. Variables with different local curvatures of the surface, in fact, present different quenched disorder and a parameter $p$ (which could represent different experimental conditions) is introduced to account for different time scales for the different classes of variables. We show that the introduction of this {\em time scale separation} in the model leads to a cross-over effect on the roughness properties. This effect could explain the scattering in the experimental measurements available in the literature. The interplay between anisotropy and the cross-over effect and the dependence of critical properties on parameter $p$ is investigated as well as the relationship with the known universality classes.Comment: 11 pages, 21 figures. submitted to PR

Fractal Growth from Local Instabilities

We study, both with numerical simulations and theoretical methods, a cellular automata model for continuum equations describing growth processes in the presence of an external flux of particles. As a result of local instabilities we find a fractal regime of growth for small external fluxes. The growing tip is selected with probability proportional to the curvature in the point. A parameter $p$ gives the probability of lateral growth on the tip. The value of $p$ determines the fractal dimension of the aggregate. Furthermore, for each value of $p$ a cross-over between two different fractal dimensions is observed. Instead, the roughness exponent $\chi$ of the aggregates does not depend on $p$ ($\chi \simeq 0.5$). Fixed scale transformation approach is applied to compute theoretically the fractal dimension for one of the branches of the structure.Comment: 7 pages, 5 figures, submitted to EP

Damaging and Cracks in Thin Mud Layers

We present a detailed study of a two-dimensional minimal lattice model for the description of mud cracking in the limit of extremely thin layers. In this model each bond of the lattice is assigned to a (quenched) breaking threshold. Fractures proceed through the selection of the part of the material with the smallest breaking threshold. A local damaging rule is also implemented, by using two different types of weakening of the neighboring sites, corresponding to different physical situations. Some analytical results are derived through a probabilistic approach known as Run Time Statistics. In particular, we find that the total time to break down the sample grows with the dimension $L$ of the lattice as $L^2$ even though the percolating cluster has a non trivial fractal dimension. Furthermore, a formula for the mean weakening in time of the whole sample is obtained.Comment: 10 pages, 7 figures (9 postscript files), RevTe

Study of the disordered one-dimensional contact process

New theoretical and numerical analysis of the one-dimensional contact process with quenched disorder are presented. We derive new scaling relations, different from their counterparts in the pure model, which are valid not only at the critical point but also away from it due to the presence of generic scale invariance. All the proposed scaling laws are verified in numerical simulations. In addition we map the disordered contact process into a Non-Markovian contact process by using the so called Run Time Statistic, and write down the associated field theory. This turns out to be in the same universality class as one derived by Janssen for the quenched system with a Gaussian distribution of impurities. Our findings here support the lack of universality suggested by the field theoretical analysis: generic power-law behaviors are obtained, evidence is shown of the absence of a characteristic time away from the critical point, and the absence of universality is put forward. The intermediate sublinear regime predicted by Bramsom et al. is also found.Comment: 18 Figures (fig. 1 and 9 not available), Late

Theory of Boundary Effects in Invasion Percolation

We study the boundary effects in invasion percolation with and without trapping. We find that the presence of boundaries introduces a new set of surface critical exponents, as in the case of standard percolation. Numerical simulations show a fractal dimension, for the region of the percolating cluster near the boundary, remarkably different from the bulk one. We find a logarithmic cross-over from surface to bulk fractal properties, as one would expect from the finite-size theory of critical systems. The distribution of the quenched variables on the growing interface near the boundary self-organises into an asymptotic shape characterized by a discontinuity at a value $x_c=0.5$, which coincides with the bulk critical threshold. The exponent $\tau^{sur}$ of the boundary avalanche distribution for IP without trapping is $\tau^{sur}=1.56\pm0.05$; this value is very near to the bulk one. Then we conclude that only the geometrical properties (fractal dimension) of the model are affected by the presence of a boundary, while other statistical and dynamical properties are unchanged. Furthermore, we are able to present a theoretical computation of the relevant critical exponents near the boundary. This analysis combines two recently introduced theoretical tools, the Fixed Scale Transformation (FST) and the Run Time Statistics (RTS), which are particularly suited for the study of irreversible self-organised growth models with quenched disorder. Our theoretical results are in rather good agreement with numerical data.Comment: 11 pages, 13 figures, revte

A driven two-dimensional granular gas with Coulomb friction

We study a homogeneously driven granular gas of inelastic hard particles with rough surfaces subject to Coulomb friction. The stationary state as well as the full dynamic evolution of the translational and rotational granular temperatures are investigated as a function of the three parameters of the friction model. Four levels of approximation to the (velocity-dependent) tangential restitution are introduced and used to calculate translational and rotational temperatures in a mean field theory. When comparing these theoretical results to numerical simulations of a randomly driven mono-layer of particles subject to Coulomb friction, we find that already the simplest model leads to qualitative agreement, but only the full Coulomb friction model is able to reproduce/predict the simulation results quantitatively for all magnitudes of friction. In addition, the theory predicts two relaxation times for the decay to the stationary state. One of them corresponds to the equilibration between the translational and rotational degrees of freedom. The other one, which is slower in most cases, is the inverse of the common relaxation rate of translational and rotational temperatures.Comment: 23 pages, 17 figure

Mean Field theory for a driven granular gas of frictional particles

We propose a mean field (MF) theory for a homogeneously driven granular gas of inelastic particles with Coulomb friction. The model contains three parameters, a normal restitution coefficient $r_n$, a maximum tangential restitution coefficient $r_t^m$, and a Coulomb friction coefficient $\mu$. The parameters can be tuned to explore a wide range of physical situations. In particular, the model contains the frequently used $\mu \to \infty$ limit as a special case. The MF theory is compared with the numerical simulations of a randomly driven monolayer of spheres for a wide range of parameter values. If the system is far away from the clustering instability ($r_n \approx 1$), we obtain a good agreement between mean field and simulations for $\mu=0.5$ and $r_t^m=0.4$, but for much smaller values of $r_n$ the agreement is less good. We discuss the reasons of this discrepancy and possible refinements of our computational scheme.Comment: 6 pages, 3 figures (10 *.eps files), elsart style (macro included), in Proceedings of the International Conference "Statistical Mechanics and Strongly Correlated Systems", University of Rome "La Sapienza" (Italy), 27-29 September 199

Dynamics of Fractures in Quenched Disordered Media

We introduce a model for fractures in quenched disordered media. This model has a deterministic extremal dynamics, driven by the energy function of a network of springs (Born Hamiltonian). The breakdown is the result of the cooperation between the external field and the quenched disorder. This model can be considered as describing the low temperature limit for crack propagation in solids. To describe the memory effects in this dynamics, and then to study the resistance properties of the system we realized some numerical simulations of the model. The model exhibits interesting geometric and dynamical properties, with a strong reduction of the fractal dimension of the clusters and of their backbone, with respect to the case in which thermal fluctuations dominate. This result can be explained by a recently introduced theoretical tool as a screening enhancement due to memory effects induced by the quenched disorder.Comment: 7 pages, 9 Postscript figures, uses revtex psfig.sty, to be published on Phys. Rev.

Two-dimensional Granular Gas of Inelastic Spheres with Multiplicative Driving

We study a two-dimensional granular gas of inelastic spheres subject to multiplicative driving proportional to a power $|v(\vec{x})|^{\delta}$ of the local particle velocity $v(\vec{x})$. The steady state properties of the model are examined for different values of $\delta$, and compared with the homogeneous case $\delta=0$. A driving linearly proportional to $v(\vec{x})$ seems to reproduce some experimental observations which could not be reproduced by a homogeneous driving. Furthermore, we obtain that the system can be homogenized even for strong dissipation, if a driving inversely proportional toComment: 4 pages, 5 figures (accepted as Phys. Rev. Lett.

Association between Vitamin D Receptor Gene Polymorphisms and Periodontal Bacteria: A Clinical Pilot Study

Abstract: Background: Periodontitis is an inflammatory disease caused by microorganisms involving the supporting tissues of the teeth. Gene variants may influence both the composition of the biofilm in the oral cavity and the host response. The objective of the study was to investigate the potential correlations between the disease susceptibility, the presence and the quantity of periodontopathogenic oral bacterial composition and the VDR gene polymorphisms. Methods: Fifty (50) unrelated periodontal patients and forty-one (41) healthy controls were selected for genomic DNA extraction. DNA concentration was measured and analyzed. The periodontopathogenic bacterial species were identified and quantified using a Real Time PCR performed with species-specific primers and probes. Results: Genotype distribution showed a different distribution between the groups for BsmI rs1544410 genotypes (p = 0.0001) with a prevalence of the G(b) allele in periodontal patients (p = 0.0003). Statistical significance was also found for VDR TaqI rs731236 (p ≤ 0.00001) with a prevalence of the T(T) allele in periodontal patients (p ≤ 0.00001). The average bacterial copy count for the periodontitis group was significantly higher than that of control group. Dividing patients into two groups based on high or low bacterial load, FokI rs2228570 T allele (f) was statistically more represented in patients with high bacterial load. Conclusions: The findings of the study suggest the involvement of the VDR gene BsmI and TaqI polymorphisms in periodontal disease, while FokI and BsmI may be involved in determining an increased presence of periodontopathogens