Implementação da rotina de unfolding para determinação de distribuição de tamanho de grãos esféricos via distribuição de interceptos lineares e de área de seção

Na unfolding method of linear intercept distributions and secction área distribution was implemented for structures with spherical grains. Although the unfolding routine depends on the grain shape, structures with spheroidal grains can also be treated by this routine. Grains of non-spheroidal shape can be treated only as approximation. A software was developed with two parts. The first part calculates the probability matrix. The second part uses this matrix and minimizes the chi-square. The results are presented with any number of size classes as required. The probability matrix was determined by means of the linear intercept and section area distributions created by computer simulation. Using curve fittings the probability matrix for spheres of any sizes could be determined. Two kinds of tests were carried out to prove the efficiency of the Technique. The theoretical tests represent ideal cases. The software was able to exactly find the proposed grain size distribution. In the second test, a structure was simulated in computer and images of its slices were used to produce the corresponding linear intercept the section area distributions. These distributions were then unfolded. This test simulates better reality. The results show deviations from the real size distribution. This deviations are caused by statistic fluctuation. The unfolding of the linear intercept distribution works perfectly, but the unfolding of section area distribution does not work due to a failure in the chi-square minimization. The minimization method uses a matrix inversion routine. The matrix generated by this procedure cannot be inverted. Other minimization method must be used

Fluxo de fluído através de um meio poroso fractal desordenado. Análise das tensões de cisalhamento e efeito de escala na estimativa das forças viscosas

In this work we have investigated some aspects of the two-dimensional flow of a viscous Newtonian fluid through a disordered porous medium modeled by a random fractal system similar to the Sierpinski carpet. This fractal is formed by obstacles of various sizes, whose distribution function follows a power law. They are randomly disposed in a rectangular channel. The velocity field and other details of fluid dynamics are obtained by solving numerically of the Navier-Stokes and continuity equations at the pore level, where occurs actually the flow of fluids in porous media. The results of numerical simulations allowed us to analyze the distribution of shear stresses developed in the solid-fluid interfaces, and find algebraic relations between the viscous forces or of friction with the geometric parameters of the model, including its fractal dimension. Based on the numerical results, we proposed scaling relations involving the relevant parameters of the phenomenon, allowing quantifying the fractions of these forces with respect to size classes of obstacles. Finally, it was also possible to make inferences about the fluctuations in the form of the distribution of viscous stresses developed on the surface of obstacles.

Distribuição e uso de habitat por peixes recifais em um gradiente ambiental: estudo de caso em recifes areníticos

There are several abiotic factors reported in the literature as regulators of the distribution of fish species in marine environments. Among them stand out structural complexity of habitat, benthic composition, depth and distance from the coast are usually reported as positive influencers in the diversity of difentes species, including reef fish. These are dominant elements in reef systems and considered high ecological and socioeconomic importance. Understanding how the above factors influence the distribution and habitat use of reef fish communities are important for their management and conservation. Thus, this study aims to evaluate the influence of these variables on the community of reef fishes along an environmental gradient of depth and distance from shore base in sandstone reefs in the coast of state of Rio Grande do Norte, Brazil. These variables are also used for creating a simple predictive model reef fish biomass for the environment studied. Data collection was performed through visual surveys in situ, and recorded environmental data (structural complexity of habitat, type of coverage of the substrate, benthic invertebrates) and ecological (wealth, abundance and reef fish size classes). As a complement, information on the diet were raised through literature and the biomass was estimated from the length-weight relationship of each species. Overall, the reefs showed a low coverage by corals and the Shallow reefs, Intermediate I and II dominated by algae and the Funds by algae and sponges. The complexity has increased along the gradient and positively influenced the species richness and abundance. Both attributes influenced in the structure of the reef fish community, increasing the richness, abundance and biomass of fish as well as differentiating the trophic structure of the community along the depth gradient and distance from the coast. Distribution and use of habitat by recifas fish was associated with food availability. The predictor model identified depth, roughness and coverage for foliose algae, calcareous algae and soft corals as the most significant variables influencing in the biomass of reef fish. In short, the description and understanding of these patterns are important steps to elucidate the ecological processes. In this sense, our approach provides a new understanding of the structure of the reef fish community of Rio Grande do Norte, allowing understand a part of a whole and assist future monitoring actions, evaluation, management and conservation of these and other reefs of Brazil.

Implementação da rotina de unfolding para determinação de distribuição de tamanho de grãos esféricos via distribuição de interceptos lineares e de área de seção

Na unfolding method of linear intercept distributions and secction área distribution was implemented for structures with spherical grains. Although the unfolding routine depends on the grain shape, structures with spheroidal grains can also be treated by this routine. Grains of non-spheroidal shape can be treated only as approximation. A software was developed with two parts. The first part calculates the probability matrix. The second part uses this matrix and minimizes the chi-square. The results are presented with any number of size classes as required. The probability matrix was determined by means of the linear intercept and section area distributions created by computer simulation. Using curve fittings the probability matrix for spheres of any sizes could be determined. Two kinds of tests were carried out to prove the efficiency of the Technique. The theoretical tests represent ideal cases. The software was able to exactly find the proposed grain size distribution. In the second test, a structure was simulated in computer and images of its slices were used to produce the corresponding linear intercept the section area distributions. These distributions were then unfolded. This test simulates better reality. The results show deviations from the real size distribution. This deviations are caused by statistic fluctuation. The unfolding of the linear intercept distribution works perfectly, but the unfolding of section area distribution does not work due to a failure in the chi-square minimization. The minimization method uses a matrix inversion routine. The matrix generated by this procedure cannot be inverted. Other minimization method must be used