Fractal Behaviour and Irregularity of Wetting Fronts in Heterogeneous Porous Media

The wetting front is the zone where water invades and advances into an initially dry porous material and it plays a crucial role in solute transport through the unsaturated zone. Water is an essential part of the physiological process of all plants. Through water, necessary minerals are moved from the roots to the parts of the plants that require them. Water moves chemicals from one part of the plant to another. It is also required for photosynthesis, for metabolism and for transpiration. The leaching of chemicals by wetting fronts is influenced by two major factors, namely: the irregularity of the fronts and heterogeneity in the distribution of chemicals, both of which have been described by using fractal techniques. Soil structure can significantly modify infiltration rates and flow pathways in soils. Relations between features of soil structure and features of infiltration could be elucidated from the velocities and the structure of wetting fronts. When rainwater falls onto soil, it doesn?t just pool on surfaces. Water ?or another fluid- acts differently on porous surfaces. If the surface is permeable (porous) it seeps down through layers of soil, filling that layer to capacity. Once that layer is filled, it moves down into the next layer. In sandy soil, water moves quickly, while it moves much slower through clay soil. The movement of water through soil layers is called the the wetting front. Our research concerns the motion of a liquid into an initially dry porous medium. Our work presents a theoretical framework for studying the physical interplay between a stationary wetting front of fractal dimension D with different porous materials. The aim was to model the mass geometry interplay by using the fractal dimension D of a stationary wetting front. The plane corresponding to the image is divided in several squares (the minimum correspond to the pixel size) of size length ". We acknowledge the help of Prof. M. García Velarde and the facilities offered by the Pluri-Disciplinary Institute of the Complutense University of Madrid. We also acknowledge the help of European Community under project Multi-scale complex fluid flows and interfacial phenomena (PITN-GA-2008-214919). Thanks are also due to ERCOFTAC (PELNoT, SIG 14)

3D Soil Images Structure Quantification using Relative Entropy

Soil voids manifest the cumulative effect of local pedogenic processes and ultimately influence soil behavior - especially as it pertains to aeration and hydrophysical properties. Because of the relatively weak attenuation of X-rays by air, compared with liquids or solids, non-disruptive CT scanning has become a very attractive tool for generating three-dimensional imagery of soil voids. One of the main steps involved in this analysis is the thresholding required to transform the original (greyscale) images into the type of binary representation (e.g., pores in white, solids in black) needed for fractal analysis or simulation with Lattice?Boltzmann models (Baveye et al., 2010). The objective of the current work is to apply an innovative approach to quantifying soil voids and pore networks in original X-ray CT imagery using Relative Entropy (Bird et al., 2006; Tarquis et al., 2008). These will be illustrated using typical imagery representing contrasting soil structures. Particular attention will be given to the need to consider the full 3D context of the CT imagery, as well as scaling issues, in the application and interpretation of this index.

A packing computational method relating fractal particle size distribution and void fraction in granular media

The study of granular systems is of great interest to many fields of science and technology. The packing of particles affects to the physical properties of the granular system. In particular, the crucial influence of particle size distribution (PSD) on the random packing structure increase the interest in relating both, either theoretically or by computational methods. A packing computational method is developed in order to estimate the void fraction corresponding to a fractal-like particle size distribution.

Computer simulation of the interplay between fractal structures and surrounding heterogeneous multifractal distributions. Applications

In a large number of physical, biological and environmental processes interfaces with high irregular geometry appear separating media (phases) in which the heterogeneity of constituents is present. In this work the quantification of the interplay between irregular structures and surrounding heterogeneous distributions in the plane is made For a geometric set image and a mass distribution (measure) image supported in image, being image, the mass image gives account of the interplay between the geometric structure and the surrounding distribution. A computation method is developed for the estimation and corresponding scaling analysis of image, being image a fractal plane set of Minkowski dimension image and image a multifractal measure produced by random multiplicative cascades. The method is applied to natural and mathematical fractal structures in order to study the influence of both, the irregularity of the geometric structure and the heterogeneity of the distribution, in the scaling of image. Applications to the analysis and modeling of interplay of phases in environmental scenarios are given.

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&

A Packing Computational Method Relating Fractal Particle Size Distribution and Void Fraction in Granular Media

The study of granular systems is of great interest to many fields of science and technology. The packing of particles affects to the physical properties of the granular system. In particular, the crucial influence of particle size distribution (PSD) on the random packing structure increase the interest in relating both, either theoretically or by computational methods. A packing computational method is developed in order to estimate the void fraction corresponding to a fractal-like particle size distribution.

Geometrical characterization of undisturbed soil samples using X-ray computed tomography image analysis. Effect of soil management on soil structure

El estudio de la estructura del suelo es de vital importancia en diferentes campos de la ciencia y la tecnología. La estructura del suelo controla procesos físicos y biológicos importantes en los sistemas suelo-planta-microorganismos. Estos procesos están dominados por la geometría de la estructura del suelo, y una caracterización cuantitativa de la heterogeneidad de la geometría del espacio poroso es beneficiosa para la predicción de propiedades físicas del suelo. La tecnología de la tomografía computerizada de rayos-X (CT) nos permite obtener imágenes digitales tridimensionales del interior de una muestra de suelo, proporcionando información de la geometría de los poros del suelo y permitiendo el estudio de los poros sin destruir las muestras. Las técnicas de la geometría fractal y de la morfología matemática se han propuesto como una poderosa herramienta para analizar y cuantificar características geométricas. Las dimensiones fractales del espacio poroso, de la interfaz poro-sólido y de la distribución de tamaños de poros son indicadores de la complejidad de la estructura del suelo. Los funcionales de Minkowski y las funciones morfológicas proporcionan medios para medir características geométricas fundamentales de los objetos geométricos tridimensionales. Esto es, volumen, superficie, curvatura media de la superficie y conectividad. Las características del suelo como la distribución de tamaños de poros, el volumen del espacio poroso o la superficie poro-solido pueden ser alteradas por diferentes practicas de manejo de suelo. En este trabajo analizamos imágenes tomográficas de muestras de suelo de dos zonas cercanas con practicas de manejo diferentes. Obtenemos un conjunto de medidas geométricas, para evaluar y cuantificar posibles diferencias que el laboreo pueda haber causado en el suelo. ABSTRACT The study of soil structure is of vital importance in different fields of science and technology. Soil structure controls important physical and biological processes in soil-plant-microbial systems. Those processes are dominated by the geometry of soil pore structure, and a quantitative characterization of the spatial heterogeneity of the pore space geometry is beneficial for prediction of soil physical properties. The technology of X-ray computed tomography (CT) allows us to obtain three-dimensional digital images of the inside of a soil sample providing information on soil pore geometry and enabling the study of the pores without disturbing the samples. Fractal geometry and mathematical morphological techniques have been proposed as powerful tools to analyze and quantify geometrical features. Fractal dimensions of pore space, pore-solid interface and pore size distribution are indicators of soil structure complexity. Minkowski functionals and morphological functions provide means to measure fundamental geometrical features of three-dimensional geometrical objects, that is, volume, boundary surface, mean boundary surface curvature, and connectivity. Soil features such as pore-size distribution, pore space volume or pore-solid surface can be altered by different soil management practices. In this work we analyze CT images of soil samples from two nearby areas with contrasting management practices. We performed a set of geometrical measures, some of them from mathematical morphology, to assess and quantify any possible difference that tillage may have caused on the soil.

On the possibility of coherently stimulated recombination and cosmological structure generation: recombination instability.

Possible instabilities during cosmological recombination may produce an epoch of nonlinear density growth and fractal-like structural patterns out to the horizon scale at that epoch (approximately 200 Mpc today). With this motivation, we examine the consequences of the change in effective radiative recombination reaction rate coefficients produced by intense stimulated emission. The proton-electron recombination is considered as a natural laser, leading to the formation of spatially nonuniform distributions of neutral matter earlier than the recombination epoch.

On the possibility of coherently stimulated recombination and cosmological structure generation: cosmological consequences.

Given a specific physical mechanism for instabilities during cosmological recombination discussed in an earlier paper, we examine the nonlinear growth of density structures to form fractal-like structural patterns out to the horizon scale at that epoch (approximately 200 Mpc today). A model for such fractal patterns is presented. Such effects could explain observed large-scale structure patterns and the formation of objects at high z, while keeping microwave background anisotropies at the observed minimal levels. We also discuss possible microwave background implications of such a transition and note a potentially observable spectral signature at lambda approximately 0.18 mm as well as a weak line near the peak in the microwave background.

Analysis of the spectral response of fractal antennas related with its geometry and current paths

Fractal antennas have been proposed to improve the bandwidth of resonant structures and optical antennas. Their multiband characteristics are of interest in radiofrequency and microwave technologies. In this contribution we link the geometry of the current paths built-in the fractal antenna with the spectral response. We have seen that the actual currents owing through the structure are not limited to the portion of the fractal that should be geometrically linked with the signal. This fact strongly depends on the design of the fractal and how the different scales are arranged within the antenna. Some ideas involving materials that could actively respond to the incoming radiation could be of help to spectrally select the response of the multiband design.

Fractal analysis of pyramidal cells in the visual cortex of the galago (Otolemur garnetti): Regional variation in dendritic branching patterns between visual areas

Previously it has been shown that the branching pattern of pyramidal cells varies markedly between different cortical areas in simian primates. These differences are thought to influence the functional complexity of the cells. In particular, there is a progressive increase in the fractal dimension of pyramidal cells with anterior progression through cortical areas in the occipitotemporal (OT) visual stream, including the primary visual area (V1), the second visual area (V2), the dorsolateral area (DL, corresponding to the fourth visual area) and inferotemporal cortex (IT). However, there are as yet no data on the fractal dimension of these neurons in prosimian primates. Here we focused on the nocturnal prosimian galago (Otolemur garnetti). The fractal dimension (D), and aspect ratio (a measure of branching symmetry), was determined for I I I layer III pyramidal cells in V1, V2, DL and IT. We found, as in simian primates, that the fractal dimension of neurons increased with anterior progression from V1 through V2, DL, and IT. Two important conclusions can be drawn from these results: (1) the trend for increasing branching complexity with anterior progression through OT areas was likely to be present in a common primate ancestor, and (2) specialization in neuron structure more likely facilitates object recognition than spectral processing.

Fractal PBG assisted co-planar waveguides

In general, conventional electromagnetic bandgap (PBGs) with uniform distribution show spurious ripples in pass-band and poor stop-band responses. This paper presents a detailed investigation in terms of pass-band and stop-band characteristics of uniplanar transmission line loaded with fractal shape PBGs. (c) 2005 Wiley Periodicals, Inc.

On Parabolic Subgroups and Hecke Algebras of some Fractal Groups

* The authors thank the “Swiss National Science Foundation” for its support.

Fractal Analysis for Cancer Research: Case Study and Simulation of Fractals

2010 Mathematics Subject Classification: 65D18.

Estudo de arranjos de antenas de microfita com Patch quase-fractal para comunicações sem fio

In this dissertation, are presented two microstrip antennas and two arrays for applications in wireless communication systems multiband. Initially, we studied an antenna and a linear array consisting of two elements identical to the patch antenna isolated. The shape of the patch used in both structures is based on fractal geometry and has multiband behavior. Next a new antenna is analyzed and a new array such as initial structure, but with the truncated ground plane, in order to obtain better bandwidths and return loss. For feeding the structures, we used microstrip transmission line. In the design of planar structures, was used HFSS software for the simulation. Next were built and measures electromagnetic parameters such as input impedance and return loss, using vector network analyzer in the telecommunications laboratory of Federal University of Rio Grande do Norte. The experimental results were compared with the simulated and showed improved return loss for the first array and also appeared a fourth band and increased directivity compared with the isolated antenna. The first two benefits are not commonly found in the literature. For structures with a truncated ground planes, the technique improved impedance matching, bandwidth and return loss when compared to the initial structure with filled ground planes. Moreover, these structures exhibited a better distribution of frequency, facilitating the adjustment of frequencies. Thus, it is expected that the planar structures presented in this study, particularly arrays may be suitable for specific applications in wireless communication systems when frequency multiband and wideband transmission signals are required.