Dynamics of diffusive rough interfaces in inhomogeneous systems

We investigate the dynamics of interfaces growth in inhomogeneous systems. The description of the kinetics is based on the mean field master equation in terms of lattice gas model. The existence of repulsive interactions between nearest-neighbour particles creates an order in the system. We show that the order extension has an influence on the localisation of the diffusive interface called "the diffusion front" which delimits disordered region from ordered one. We analyze the time evolution of diffusion fronts by dynamic scaling approach and we find that the scaling behavior of these interfaces is characterized by anomalously large exponents which agree with the experimental and theoretical results.We investigate the dynamics of interfaces growth in inhomogeneous systems. The description of the kinetics is based on the mean field master equation in terms of lattice gas model. The existence of repulsive interactions between nearest-neighbour particles creates an order in the system. We show that the order extension has an influence on the localisation of the diffusive interface called "the diffusion front" which delimits disordered region from ordered one. We analyze the time evolution of diffusion fronts by dynamic scaling approach and we find that the scaling behavior of these interfaces is characterized by anomalously large exponents which agree with the experimental and theoretical results

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

Scaling behaviour in driven diffusive systems: The example of a bi-dimensional system

The investigations consider a driven lattice gas of interacting particles with open boundaries within a mean field treatment. We confirm the result obtained by J. Krug that the external conditions induce a phase transition. In the case of a square lattice with repulsive interactions, the phase transition is an order-disorder one which leads to the coexistence of ordered and disordered domains. The dynamical phase transition consists in the break down of the lattice occupation symmetry then in a rapid relaxation of the order parameter. The latter regime is characterised by the growth of the available space for the superstructure tilt the saturation of the maximal value of the order parameter. The onset of this steady state leads to the dynamical phase diagram to approach the statistical one except around critical points. A preliminary study of the interface delimiting the ordered and disordered regions is also given. We show that the transition influences the localisation of the interface called: “the diffusion front “.The investigations consider a driven lattice gas of interacting particles with open boundaries within a mean field treatment. We confirm the result obtained by J. Krug that the external conditions induce a phase transition. In the case of a square lattice with repulsive interactions, the phase transition is an order-disorder one which leads to the coexistence of ordered and disordered domains. The dynamical phase transition consists in the break down of the lattice occupation symmetry then in a rapid relaxation of the order parameter. The latter regime is characterised by the growth of the available space for the superstructure tilt the saturation of the maximal value of the order parameter. The onset of this steady state leads to the dynamical phase diagram to approach the statistical one except around critical points. A preliminary study of the interface delimiting the ordered and disordered regions is also given. We show that the transition influences the localisation of the interface called: “the diffusion front “

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,