On the fluctuations of jamming coverage upon random sequential adsorption on homogeneous and heterogeneous media

The fluctuations of the jamming coverage upon Random Sequential Adsorption (RSA) are studied using both analytical and numerical techniques. Our main result shows that these fluctuations (characterized by $\sigma_{\theta_J}$) decay with the lattice size according to the power-law $\sigma_{\theta_J} \propto L^{-1/ \nu}$. The exponent $\nu$ depends on the dimensionality $D$ of the substrate and the fractal dimension of the set where the RSA process actually takes place ($d_f$) according to $\nu = 2 / (2D - d_f)$.This theoretical result is confirmed by means of extensive numerical simulations applied to the RSA of dimers on homogeneous and stochastic fractal substrates. Furthermore, our predictions are in excellent agreement with different previous numerical results. It is also shown that, studying correlated stochastic processes, one can define various fluctuating quantities designed to capture either the underlying physics of individual processes or that of the whole system. So, subtle differences in the definitions may lead to dramatically different physical interpretations of the results. Here, this statement is demonstrated for the case of RSA of dimers on binary alloys.Comment: 20 pages, 8 figure

Universality in diffusion front growth dynamics

We have studied the scaling properties of diffusion fronts by numerical calculations based on the mean field approach in the context of a lattice gas model, performed in a triangular lattice. We find that the height-height correlation function scales with time t and length l as $C(l,t)\approx l^{\alpha} f(t/l^{\alpha/\beta})$ with $\alpha=0.62\pm 0.01$ and $\beta =0.39\pm 0.02$. These exponent values are identical to those characterising the roughness of the diffusion fronts evolving through a square lattice [1,2], thus confirming their universality

Dynamic scaling and self-organized criticality in diffusion fronts growth

PACS. 05.50.+q Lattice theory and statistics (Ising, Potts, etc.) - 05.60.-k Transport processes - 68.35.Fx Diffusion; interface formation,