U.M.S. Costa

Inertial Effects on Fluid Flow through Disordered Porous Media

We investigate the origin of the deviations from the classical Darcy law by numerical simulation of the Navier-Stokes equations in two-dimensional disordered porous media. We apply the Forchheimer equation as a phenomenological model to correlate the variations of the friction factor for different porosities and flow conditions. At sufficiently high Reynolds numbers, when inertia becomes relevant, we observe a transition from linear to nonlinear behavior which is typical of experiments. We find that such a transition can be understood and statistically characterized in terms of the spatial distribution of kinetic energy in the system. [S0031-9007(99)09541-1]

An improved description of the dielectric breakdown in oxides based on a generalized Weibull distribution

In this work, we address modal parameter fluctuations in statistical distributions describing charge-to-breakdown (QBD) and/or time-to-breakdown (tBD) during the dielectric breakdown regime of ultra-thin oxides, which are of high interest for the advancement of electronic technology. We reobtain a generalized Weibull distribution (q-Weibull), which properly describes (tBD) data when oxide thickness fluctuations are present, in order to improve reliability assessment of ultra-thin oxides by time-to-breakdown (tBD) extrapolation and area scaling. The incorporation of fluctuations allows a physical interpretation of the q-Weibull distribution in connection with the Tsallis statistics. In support to our results, we analyze tBD data of SiO2-based MOS devices obtained experimentally and theoretically through a percolation model, demonstrating an advantageous description of the dielectric breakdown by the q-Weibull distribution.

Critical behavior of a three-state Potts model on a Voronoi lattice

We use the single-histogram technique to study the critical behavior of the three-state Potts model on a (random) Voronoi-Delaunay lattice with size ranging from 250 to 8 000 sites. We consider the effect of an exponential decay of the interactions with the distance, J(r) = J0 exp (-ar), with a > 0, and observe that this system seems to have critical exponents γ and ν which are different from the respective exponents of the three-state Potts model on a regular square lattice. However, the ratio γ/ν remains essentially the same. We find numerical evidences (although not conclusive, due to the small range of system size) that the specific heat on this random system behaves as a power-law for a=0 and as a logarithmic divergence for a=0.5 and a=1.0

The ferromagnetic Ising model on a Voronoi–Delaunay lattice

We investigate the two-dimensional ferromagnetic Ising model in the Voronoi–Delaunay tesselation. In this study, we assume that the coupling factor J varies with the distance r between the first neighbors as J(r)∝e−αr, with α⩾0. The disordered system is simulated applying the single-cluster Monte Carlo update algorithm and the reweighting technique. We calculate the critical point exponents γ/ν,β/ν and ν for this model and find that this random system belongs to the same universality class as the pure two-dimensional ferromagnetic Ising model.

The role of inertia on fluid flow through disordered porous media

We study the fluid flow through disordered porous media by numerically solving the complete set of the Navier–Stokes equations in a two-dimensional lattice with a spatially random distribution of solid obstacles (plaquettes). We simulate viscous and non-viscous flow through these idealized pore spaces to determine the origin of the deviations from the classical Darcys law behavior. Due to the nonlinear contribution of inertia to the transport of momentum at the pore scale, we observe a typical departure from Darcys law at sufficiently high Reynolds numbers. Moreover, we show that the classical Forchheimer equation provides a valid phenomenological model to correlate the variations of the friction factor of the porous media over a wide range of Reynolds conditions.

Self-organized percolation growth in regular and disordered lattices

The self-organized percolation process (SOP) is a growth model in which a critical percolation state is reached through self-organization. By controlling the number of sites or bonds in the growth front of the aggregate, the system is spontaneously driven to a stationary state that corresponds to approximately the percolation threshold of the lattice topology and percolation process. The SOP model is applied here to site and bond percolation in several regular lattices in two and three dimensions (triangular, honeycomb and simple cubic), as well as in a disordered network (Voronoi–Delaunai). Based on these results, we propose the use of this growth algorithm as a plausible model to describe the dynamics and the anomalous geometrical properties of some natural processes.

Turbulent effects on fluid flow through disordered porous media

The influence of turbulent effects on a fluid flow through a (pseudo) porous media is studied by numerically solving the set of Reynolds-averaged Navier-Stokes equations with the κ–e model for turbulence. The spatial domains are two-dimensional rectangular grids with different porosities obtained by the random placing of rigid obstacles. The objective of the simulations is to access the behavior of the generalized friction factor with varying Reynolds number. A good agreement with the Forchheimers equation is observed. The flow distribution at both low and high Reynolds conditions is also analyzed.

Fluctuation of energy in the generalized thermostatistics

We calculate the fluctuation of a systems energy in Tsallis statistics following the finite heat bath canonical ensemble approach. We obtain this fluctuation as the second derivative of the logarithm of the partition function plus an additional term. We also find an explicit expression for the relative fluctuation as related to the number of degrees of freedom of the bath and the composite system.

Transport theory in the context of the normalized generalized statistics

In this work assuming that the equipartition theorem is valid and using the normalized q-expectation value, we obtain, until first-order approximation, the hydrodynamics equation for the generalized statistics. These equations are different from those obtained in the context of the Boltzmann–Gibbs statistics. This difference is that now appears two transport coefficients that depend on the parameter q.

Critical behavior of the S = 1 / 2 Heisenberg ferromagnet: A Handscomb quantum Monte Carlo study

We investigate the critical relaxational dynamics of the S=1/2 Heisenberg ferromagnet on a simple cubic lattice within the Handscomb prescription on which it is a diagrammatic series expansion of the partition function that is computed by means of a Monte Carlo procedure. Using a phenomenological renormalization group analysis of graph quantities related to the spin susceptibility and order parameter, we obtain precise estimates for the critical exponents relations