An introduction to flow and transport in fractal models of porous media: Part I

This special issue gathers together a number of recent papers on fractal geometry and its applications to the modeling of flow and transport in porous media. The aim is to provide a systematic approach for analyzing the statics and dynamics of fluids in fractal porous media by means of theory, modeling and experimentation. The topics covered include lacunarity analyses of multifractal and natural grayscale patterns, random packing's of self-similar pore/particle size distributions, Darcian and non-Darcian hydraulic flows, diffusion within fractals, models for the permeability and thermal conductivity of fractal porous media and hydrophobicity and surface erosion properties of fractal structures.

Fractal parameters of pore space from CT images of soils under contrasting management practices

Soil structure plays an important role in flow and transport phenomena, and a quantitative characterization of the spatial heterogeneity of the pore space geometry is beneficial for prediction of soil physical properties. Morphological features such as pore-size distribution, pore space volume or pore?solid surface can be altered by different soil management practices. Irregularity of these features and their changes can be described using fractal geometry. In this study, we focus primarily on the characterization of soil pore space as a 3D geometrical shape by fractal analysis and on the ability of fractal dimensions to differentiate between two a priori different soil structures. We analyze X-ray computed tomography (CT) images of soils samples from two nearby areas with contrasting management practices. Within these two different soil systems, samples were collected from three depths. Fractal dimensions of the pore-size distributions were different depending on soil use and averaged values also differed at each depth. Fractal dimensions of the volume and surface of the pore space were lower in the tilled soil than in the natural soil but their standard deviations were higher in the former as compared to the latter. Also, it was observed that soil use was a factor that had a statistically significant effect on fractal parameters. Fractal parameters provide useful complementary information about changes in soil structure due to changes in soil management. Read More: http://www.worldscientific.com/doi/abs/10.1142/S0218348X14400118?queryID=%24%7BresultBean.queryID%7D&

Computer simulation of random parckings for self-similar particle size distributions in soil and granular materials: porosity and pore size distribution

A 2D computer simulation method of random packings is applied to sets of particles generated by a self-similar uniparametric model for particle size distributions (PSDs) in granular media. The parameter p which controls the model is the proportion of mass of particles corresponding to the left half of the normalized size interval [0,1]. First the influence on the total porosity of the parameter p is analyzed and interpreted. It is shown that such parameter, and the fractal exponent of the associated power scaling, are efficient packing parameters, but this last one is not in the way predicted in a former published work addressing an analogous research in artificial granular materials. The total porosity reaches the minimum value for p = 0.6. Limited information on the pore size distribution is obtained from the packing simulations and by means of morphological analysis methods. Results show that the range of pore sizes increases for decreasing values of p showing also different shape in the volume pore size distribution. Further research including simulations with a greater number of particles and image resolution are required to obtain finer results on the hierarchical structure of pore space.

Anomalous Consistency in Mild Cognitive Impairment: A Complex Networks Approach

Increased variability in performance has been associated with the emergence of several neurological and psychiatric pathologies. However, whether and how consistency of neuronal activity may also be indicative of an underlying pathology is still poorly understood. Here we propose a novel method for evaluating consistency from non-invasive brain recordings. We evaluate the consistency of the cortical activity recorded with magnetoencephalography in a group of subjects diagnosed with Mild Cognitive Impairment (MCI), a condition sometimes prodromal of dementia, during the execution of a memory task. We use metrics coming from nonlinear dynamics to evaluate the consistency of cortical regions. A representation known as parenclitic networks is constructed, where atypical features are endowed with a network structure, the topological properties of which can be studied at various scales. Pathological conditions correspond to strongly heterogeneous networks, whereas typical or normative conditions are characterized by sparsely connected networks with homogeneous nodes. The analysis of this kind of networks allows identifying the extent to which consistency is affected in the MCI group and the focal points where MCI is especially severe. To the best of our knowledge, these results represent the first attempt at evaluating the consistency of brain functional activity using complex networks theory.

Quantifying the relationship between drainage networks at hillslope scale and particle size distribution at pedon scale

Nowadays, translating information about hydrologic and soil properties and processes across scales has emerged as a major theme in soil science and hydrology, and suitable theories for upscaling or downscaling hydrologic and soil information are being looked forward. The recognition of low-order catchments as self-organized systems suggests the existence of a great amount of links at different scales between their elements. The objective of this work was to research in areas of homogeneous bedrock material, the relationship between the hierarchical structure of the drainage networks at hillslope scale and the heterogeneity of the particle-size distribution at pedon scale. One of the most innovative elements in this work is the choice of the parameters to quantify the organization level of the studied features. The fractal dimension has been selected to measure the hierarchical structure of the drainage networks, while the Balanced Entropy Index (BEI) has been the chosen parameter to quantify the heterogeneity of the particle-size distribution from textural data. These parameters have made it possible to establish quantifiable relationships between two features attached to different steps in the scale range. Results suggest that the bedrock lithology of the landscape constrains the architecture of the drainage networks developed on it and the particle soil distribution resulting in the fragmentation processes.

Quantifying the relationship between drainage networks at hillslope scale and particle size distribution at pedon scale

Nowadays, translating information about hydrologic and soil properties and processes across scales has emerged as a major theme in soil science and hydrology, and suitable theories for upscaling or downscaling hydrologic and soil information are being looked forward. The recognition of low-order catchments as self-organized systems suggests the existence of a great amount of links at different scales between their elements. The objective of this work was to research in areas of homogeneous bedrock material, the relationship between the hierarchical structure of the drainage networks at hillslope scale and the heterogeneity of the particle-size distribution at pedon scale. One of the most innovative elements in this work is the choice of the parameters to quantify the organization level of the studied features. The fractal dimension has been selected to measure the hierarchical structure of the drainage networks, while the Balanced Entropy Index (BEI) has been the chosen parameter to quantify the heterogeneity of the particle-size distribution from textural data. These parameters have made it possible to establish quantifiable relationships between two features attached to different steps in the scale range. Results suggest that the bedrock lithology of the landscape constrains the architecture of the drainage networks developed on it and the particle soil distribution resulting in the fragmentation processes.