Murilo P. Almeida

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]

Giant saltation on Mars

Saltation, the motion of sand grains in a sequence of ballistic trajectories close to the ground, is a major factor for surface erosion, dune formation, and triggering of dust storms on Mars. Although this mode of sand transport has been matter of research for decades through both simulations and wind tunnel experiments under Earth and Mars conditions, it has not been possible to provide accurate measurements of particle trajectories in fully developed turbulent flow. Here we calculate the motion of saltating grains by directly solving the turbulent wind field and its interaction with the particles. Our calculations show that the minimal wind velocity required to sustain saltation on Mars may be surprisingly lower than the aerodynamic minimal threshold measurable in wind tunnels. Indeed, Mars grains saltate in 100 times higher and longer trajectories and reach 5-10 times higher velocities than Earth grains do. On the basis of our results, we arrive at general expressions that can be applied to calculate the length and height of saltation trajectories and the flux of grains in saltation under various physical conditions, when the wind velocity is close to the minimal threshold for saltation.

Generalized entropies from first principles

A derivation of power law canonical distributions from first principle statistical mechanics, including the exponential distribution as a particular case is presented. It is shown that these distributions arise naturally, and that the heat capacity of the heat bath is the condition that determines its type. As a consequence, a physical interpretation for the parameter q of the generalized entropy is given.

Aeolian transport layer

We investigate the airborne transport of particles on a granular surface by the saltation mechanism through numerical simulation of particle motion coupled with turbulent flow. We determine the saturated flux q(s) and show that its behavior is consistent with classical empirical relations obtained from wind tunnel measurements. Our results also allow one to propose and explain a new relation valid for small fluxes, namely, q(s) = a(u*-u(t))alpha, where u* and u(t) are the shear and threshold velocities of the wind, respectively, and the scaling exponent is alpha approximately 2. We obtain an expression for the velocity profile of the wind distorted by the particle motion due to the feedback and discover a novel dynamical scaling relation. We also find a new expression for the dependence of the height of the saltation layer as a function of the wind velocity.

Tsallis thermostatistics for finite systems: a Hamiltonian approach

The derivation of the Tsallis generalized canonical distribution from the traditional approach of the Gibbs microcanonical ensemble is revisited (Phys. Lett. A 193 (1994) 140). We show that finite systems whose Hamiltonians obey a generalized homogeneity relation rigorously follow the nonextensive thermostatistics of Tsallis. In the thermodynamical limit, however, our results indicate that the Boltzmann–Gibbs statistics is always recovered, regardless of the type of potential among interacting particles. This approach provides, moreover, a one-to-one correspondence between the generalized entropy and the Hamiltonian structure of a wide class of systems, revealing a possible origin for the intrinsic nonlinear features present in the Tsallis formalism that lead naturally to power-law behavior. Finally, we confirm these exact results through extensive numerical simulations of the Fermi–Pasta–Ulam chain of anharmonic oscillators.

Displacement operator for quantum systems with position-dependent mass

A translation operator is introduced to describe the quantum dynamics of a position-dependent mass particle in a null or constant potential. From this operator, we obtain a generalized form of the momentum operator as well as a unique commutation relation for x and p{sub {gamma}}. Such a formalism naturally leads to a Schroedinger-like equation that is reminiscent of wave equations typically used to model electrons with position-dependent (effective) masses propagating through abrupt interfaces in semiconductor heterostructures. The distinctive features of our approach are demonstrated through analytical solutions calculated for particles under null and constant potentials like infinite wells in one and two dimensions and potential barriers.

Brazilian elections: voting for a scaling democracy

The proportional elections held in Brazil in 1998 and 2002 display identical statistical signatures. In particular, the distribution of votes among candidates includes a power-law regime. We suggest that the rationale behind this robust scaling invariance is a multiplicative process in which the voters choice for a candidate is governed by a product of probabilities.

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

Heat transport through rough channels

We investigate the two-dimensional transport of heat through viscous flow between two parallel rough interfaces with a given fractal geometry. The flow and heat transport equations are solved through direct numerical simulations, and for different conduction–convection conditions. Compared with the behavior of a channel with smooth interfaces, the results for the rough channel at low and moderate values of the Peclet number indicate that the effect of roughness is almost negligible on the efficiency of the heat transport system. This is explained here in terms of Makarovs theorem, using the notion of active zone in Laplacian transport. At sufficiently high Peclet numbers, where convection becomes the dominant mechanism of heat transport, the role of the interface roughness is to generally increase both the heat flux across the wall as well as the active length of heat exchange, when compared with the smooth channel. Finally, we show that this last behavior is closely related with the presence of recirculation zones in the re-entrant regions of the fractal geometry.

Thermodynamical entropy (and its additivity) within generalized thermodynamics

This is an analysis of the thermodynamical entropy of systems with finite heat baths and of its additivity. It is presented an expression for the physical entropy of weakly interacting ergodic systems, and it is shown how it relates to the traditional entropies of the micro-canonical (constant energy), the canonical Boltzmann–Gibbs (infinite heat bath) and the Tsallis (finite heat bath) ensembles. This physical entropy contains one term that is a variant of the Tsallis entropy, and it becomes an additive function after a suitable choice of additive constants, in a procedure reminiscent to the solution presented by Gibbs to the paradox bearing his name.This is an analysis of the additivity of the entropy of thermodynamical systems with finite heat baths. It is presented an expression for the physical entropy of weakly interacting ergodic systems, and it is shown that it is valid for both the microcanonical (constant energy), the Boltzmann-Gibbs canonical (infinite heat bath) and the Tsallis (finite heat bath) ensembles. This physical entropy may be written as a variant of Tsallis entropy. It becomes an additive function after a suitable choice of additive constants, in a procedure reminiscent to the solution presented by Gibbs to the paradox bearing his name.