Ascânio D. Araújo

Wind velocity and sand transport on a barchan dune

We present measurements of wind velocity and sand flux performed on the windward side of a large barchan dune in Jericoacoara, northeastern Brazil. From the measured profile, we calculate the air shear stress using an analytical approximation and treat the problem of flow separation by an heuristic model. We find that the results from this approach agree well with our field data. Moreover, using the calculated shear velocity, we predict the sand flux according to well-known equilibrium relations and with a phenomenological continuum saltation model that includes saturation transients and thus allows for nonequilibrium conditions. Based on the field data and theoretical predicted results, we indicate the principal differences between saturated and nonsaturated sand flux models. Finally, we show that the measured dune moves with invariant shape and predict its velocity from our data and calculations.

Numerical modeling of the wind flow over a transverse dune

Transverse dunes, which form under unidirectional winds and have fixed profile in the direction perpendicular to the wind, occur on all celestial objects of our solar system where dunes have been detected. Here we perform a numerical study of the average turbulent wind flow over a transverse dune by means of computational fluid dynamics simulations. We find that the length of the zone of recirculating flow at the dune lee — the separation bubble — displays a surprisingly strong dependence on the wind shear velocity, u*: it is nearly independent of u* for shear velocities within the range between 0.2 m/s and 0.8 m/s but increases linearly with u* for larger shear velocities. Our calculations show that transport in the direction opposite to dune migration within the separation bubble can be sustained if u* is larger than approximately 0.39 m/s, whereas a larger value of u* (about 0.49 m/s) is required to initiate this reverse transport.

Periodic Neural Activity Induced by Network Complexity

We study a model for neural activity on the small-world topology of Watts and Strogatz and on the scale-free topology of Barabási and Albert. We find that the topology of the network connections may spontaneously induce periodic neural activity, contrasting with nonperiodic neural activities exhibited by regular topologies. Periodic activity exists only for relatively small networks and occurs with higher probability when the rewiring probability is larger. The average length of the periods increases with the square root of the network size.

Distribution of local fluxes in diluted porous media.

We study the distributions of channel openings, local fluxes, and velocities in a two-dimensional random medium of nonoverlapping disks. We present theoretical arguments supported by numerical data of high precision and find scaling laws as functions of the porosity. For the channel openings we observe a crossover to a highly correlated regime at small porosities. The distribution of velocities through these channels scales with the square of the porosity. The fluxes turn out to be the convolution of velocity and channel width corrected by a geometrical factor. Furthermore, while the distribution of velocities follows a Gaussian form, the fluxes are distributed according to a stretched exponential with exponent 1/2. Finally, our scaling analysis allows us to express the tortuosity and pore shape factors from the Kozeny-Carman equation as direct average properties from microscopic quantities related to the geometry as well as the flow through the disordered porous medium.

Invasion percolation between two sites

We investigate the process of invasion percolation between two sites (injection and extraction sites) separated by a distance r in two-dimensional lattices of size L. Our results for the nontrapping invasion percolation model indicate that the statistics of the mass of invaded clusters is significantly dependent on the local occupation probability (pressure) Pe at the extraction site. For Pe = 0, we show that the mass distribution of invaded clusters P(M) follows a power-law P(M) approximately M(-alpha) for intermediate values of the mass M, with an exponent alpha = 1.39+/-0.03. When the local pressure is set to Pe = Pc, where Pc corresponds to the site percolation threshold of the lattice topology, the distribution P(M) still displays a scaling region, but with an exponent alpha = 1.02+/-0.03. This last behavior is consistent with previous results for the cluster statistics in standard percolation. In spite of these differences, the results of our simulations indicate that the fractal dimension of the invaded cluster does not depend significantly on the local pressure Pe and it is consistent with the fractal dimension values reported for standard invasion percolation. Finally, we perform extensive numerical simulations to determine the effect of the lattice borders on the statistics of the invaded clusters and also to characterize the self-organized critical behavior of the invasion percolation process.

Nonequilibrium model on Apollonian networks.

We investigate the majority-vote model with two states (-1,+1) and a noise parameter q on Apollonian networks. The main result found here is the presence of the phase transition as a function of the noise parameter q. Previous results on the Ising model in Apollonian networks have reported no presence of a phase transition. We also studied the effect of redirecting a fraction p of the links of the network. By means of Monte Carlo simulations, we obtained the exponent ratio γ/ν, β/ν, and 1/ν for several values of rewiring probability p. The critical noise q{c} and U were also calculated. Therefore, the results presented here demonstrate that the majority-vote model belongs to a different universality class than equilibrium Ising model on Apollonian network.

Statistics of the critical percolation backbone with spatial long-range correlations.

We study the statistics of the backbone cluster between two sites separated by distance r in two-dimensional percolation networks subjected to spatial long-range correlations. We find that the distribution of backbone mass follows the scaling ansatz, P(M(B)) approximately M(-(alpha+1))(B)f(M(B)/M(0)), where f(x)=(alpha+etax(eta))exp(-x(eta)) is a cutoff function and M0 and eta are cutoff parameters. Our results from extensive computational simulations indicate that this scaling form is applicable to both correlated and uncorrelated cases. We show that the exponent alpha can be directly related to the fractal dimension of the backbone d(B), and should therefore depend on the imposed degree of long-range correlations.

Dynamics of enzymatic digestion of elastic fibers and networks under tension.

We study the enzymatic degradation of an elastic fiber under tension using an anisotropic random-walk model coupled with binding-unbinding reactions that weaken the fiber. The fiber is represented by a chain of elastic springs in series along which enzyme molecules can diffuse. Numerical simulations show that the fiber stiffness decreases exponentially with two distinct regimes. The time constant of the first regime decreases with increasing tension. Using a mean field calculation, we partition the time constant into geometrical, chemical and externally controllable factors, which is corroborated by the simulations. We incorporate the fiber model into a multiscale network model of the extracellular matrix and find that network effects do not mask the exponential decay of stiffness at the fiber level. To test these predictions, we measure the force relaxation of elastin sheets stretched to 20% uniaxial strain in the presence of elastase. The decay of force is exponential and the time constant is proportional to the inverse of enzyme concentration in agreement with model predictions. Furthermore, the fragment mass released into the bath during digestion is linearly related to enzyme concentration that is also borne out in the model. We conclude that in the complex extracellular matrix, feedback between the local rate of fiber digestion and the force the fiber carries acts to attenuate any spatial heterogeneity of digestion such that molecular processes manifest directly at the macroscale. Our findings can help better understand remodeling processes during development or in disease in which enzyme concentrations and/or mechanical forces become abnormal.

Optimal array of sand fences

Sand fences are widely applied to prevent soil erosion by wind in areas affected by desertification. Sand fences also provide a way to reduce the emission rate of dust particles, which is triggered mainly by the impacts of wind-blown sand grains onto the soil and affects the Earth’s climate. Many different types of fence have been designed and their effects on the sediment transport dynamics studied since many years. However, the search for the optimal array of fences has remained largely an empirical task. In order to achieve maximal soil protection using the minimal amount of fence material, a quantitative understanding of the flow profile over the relief encompassing the area to be protected including all employed fences is required. Here we use Computational Fluid Dynamics to calculate the average turbulent airflow through an array of fences as a function of the porosity, spacing and height of the fences. Specifically, we investigate the factors controlling the fraction of soil area over which the basal average wind shear velocity drops below the threshold for sand transport when the fences are applied. We introduce a cost function, given by the amount of material necessary to construct the fences. We find that, for typical sand-moving wind velocities, the optimal fence height (which minimizes this cost function) is around 50 cm, while using fences of height around 1.25 m leads to maximal cost.

Entropy Production and the Pressure-Volume Curve of the Lung.

We investigate analytically the production of entropy during a breathing cycle in healthy and diseased lungs. First, we calculate entropy production in healthy lungs by applying the laws of thermodynamics to the well-known transpulmonary pressure–volume (P–V) curves of the lung under the assumption that lung tissue behaves as an entropic spring similar to rubber. The bulk modulus, B, of the lung is also derived from these calculations. Second, we extend this approach to elastic recoil disorders of the lung such as occur in pulmonary fibrosis and emphysema. These diseases are characterized by particular alterations in the P–V relationship. For example, in fibrotic lungs B increases monotonically with disease progression, while in emphysema the opposite occurs. These diseases can thus be mimicked simply by making appropriate adjustments to the parameters of the P–V curve. Using Clausiuss formalism, we show that entropy production, ΔS, is related to the hysteresis area, ΔA, enclosed by the P–V curve during a breathing cycle, namely, ΔS=ΔA∕T, where T is the body temperature. Although ΔA is highly dependent on the disease, such formula applies to healthy as well as diseased lungs, regardless of the disease stage. Finally, we use an ansatz to predict analytically the entropy produced by the fibrotic and emphysematous lungs.