Massimo Veltri

Usage of infinitesimals in the Menger’s Sponge model of porosity

Abstract The present work concerns the calculation of the infinitesimal porosity by using the Menger’s Sponge model. This computation is based on the grossone theory considering the pore volume estimation for the Menger’s Sponge and afterwards the classical definition of the porosity, given by the ratio between the volume of voids and the total volume (voids plus solid phase). The aim is to investigate the different solutions given by the standard characterization of the porosity and the grossone theory without the direct estimation of the fractal dimension. Once the utility of this procedure had been clarified, the focus moves to possible practical applications in which infinitesimal parts can play a fundamental role. The discussion on this matter still remains open.

A Note on the Fractal Behavior of Hydraulic Conductivity and Effective Porosity for Experimental Values in a Confined Aquifer

Hydraulic conductivity and effective porosity values for the confined sandy loam aquifer of the Montalto Uffugo (Italy) test field were obtained by laboratory and field measurements; the first ones were carried out on undisturbed soil samples and the others by slug and aquifer tests. A direct simple-scaling analysis was performed for the whole range of measurement and a comparison among the different types of fractal models describing the scale behavior was made. Some indications about the largest pore size to utilize in the fractal models were given. The results obtained for a sandy loam soil show that it is possible to obtain global indications on the behavior of the hydraulic conductivity versus the porosity utilizing a simple scaling relation and a fractal model in coupled manner.

Relation between grid, channel, and Peano networks in high‐resolution digital elevation models

The topological interconnection between grid, channel, and Peano networks is investigated by extracting grid and channel networks from high-resolution digital elevation models of real drainage basins, and by using a perturbed form of the equation describing how the average junction degree varies with Horton-Strahler order in Peano networks. The perturbed equation is used to fit the data observed over the Hortonian substructures of real networks. The perturbation parameter, denoted as “uniformity factor,” is shown to indicate the degree of topological similarity between Hortonian and Peano networks. The sensitivities of computed uniformity factors and drainage densities to grid cell size and selected threshold for channel initiation are evaluated. While the topological relation between real and Peano networks may not vary significantly with grid cell size, these networks are found to exhibit the same drainage density only for specific grid cell sizes, which may depend on the selected threshold for channel initiation.