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Fractal Behaviour (fractal + behaviour)

Distribution by Scientific Domains

Earth and Environmental Science	33%

Selected Abstracts

Suspended sediment load estimation and the problem of inadequate data sampling: a fractal view

EARTH SURFACE PROCESSES AND LANDFORMS, Issue 4 2006
Bellie Sivakumar
Abstract Suspended sediment load estimation at high resolutions is an extremely difficult task, because: (1) it depends on the availability of high-resolution water discharge and suspended sediment concentration measurements, which are often not available; (2) any errors in the measurements of these two components could significantly influence the accuracy of suspended sediment load estimation; and (3) direct measurements are very expensive. The purpose of this study is to approach this sampling problem from a new perspective of fractals (or scaling), which could provide important information on the transformation of suspended sediment load data from one scale to another. This is done by investigating the possible presence of fractal behaviour in the daily suspended sediment load data for the Mississippi River basin (at St. Louis, Missouri). The presence of fractal behaviour is investigated using five different methods, ranging from general to specific and from mono-fractal to multi-fractal: (1) autocorrelation function; (2) power spectrum; (3) probability distribution function; (4) box dimension; and (5) statistical moment scaling function. The results indicate the presence of multi-fractal behaviour in the suspended sediment load data, suggesting the possibility of transformation of data from one scale to another using a multi-dimensional model. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Scaling analysis of water retention curves for unsaturated sandy loam soils by using fractal geometry

EUROPEAN JOURNAL OF SOIL SCIENCE, Issue 3 2010
C. Fallico
Fractal geometry was deployed to analyse water retention curves (WRC). The three models used to estimate the curves were the general pore-solid fractal (PSF) model and two specific cases of the PSF model: the Tyler & Wheatcraft (TW) and the Rieu & Sposito (RS) models. The study was conducted on 30 undisturbed, sandy loam soil samples taken from a field and subjected to laboratory analysis. The fractal dimension, a non-variable scale factor characterizing each water retention model proposed, was estimated by direct scaling. The method for determining the fractal dimension proposed here entails limiting the analysis to the interval between an upper and lower pressure head cut-off on a log-log plot, and defining the dimension itself as the straight regression line that interpolates the points in the interval with the largest coefficient of determination, R2. The scale relative to the cut-off interval used to determine the fractal behaviour in each model used is presented. Furthermore, a second range of pressure head values was analysed to approximate the fractal dimension of the pore surface. The PSF model exhibited greater spatial variation than the TW or RS models for the parameter values typical of a sandy loam soil. An indication of the variability of the fractal dimension across the entire area studied is also provided. [source]

Influence of pore size and geometry on peat unsaturated hydraulic conductivity computed from 3D computed tomography image analysis

HYDROLOGICAL PROCESSES, Issue 21 2010
F. Rezanezhad
Abstract In organic soils, hydraulic conductivity is related to the degree of decomposition and soil compression, which reduce the effective pore diameter and consequently restrict water flow. This study investigates how the size distribution and geometry of air-filled pores control the unsaturated hydraulic conductivity of peat soils using high-resolution (45 µm) three-dimensional (3D) X-ray computed tomography (CT) and digital image processing of four peat sub-samples from varying depths under a constant soil water pressure head. Pore structure and configuration in peat were found to be irregular, with volume and cross-sectional area showing fractal behaviour that suggests pores having smaller values of the fractal dimension in deeper, more decomposed peat, have higher tortuosity and lower connectivity, which influences hydraulic conductivity. The image analysis showed that the large reduction of unsaturated hydraulic conductivity with depth is essentially controlled by air-filled pore hydraulic radius, tortuosity, air-filled pore density and the fractal dimension due to degree of decomposition and compression of the organic matter. The comparisons between unsaturated hydraulic conductivity computed from the air-filled pore size and geometric distribution showed satisfactory agreement with direct measurements using the permeameter method. This understanding is important in characterizing peat properties and its heterogeneity for monitoring the progress of complex flow processes at the field scale in peatlands. Copyright © 2010 John Wiley & Sons, Ltd. [source]

Is a chaotic multi-fractal approach for rainfall possible?

HYDROLOGICAL PROCESSES, Issue 6 2001
Bellie Sivakumar
Abstract An Erratum has been published for this article in Hydrological Processes 15 (12) 2001, 2381,2382. Applications of the ideas gained from fractal theory to characterize rainfall have been one of the most exciting areas of research in recent times. The studies conducted thus far have nearly unanimously yielded positive evidence regarding the existence of fractal behaviour in rainfall. The studies also revealed the insufficiency of the mono-fractal approaches to characterizing the rainfall process in time and space and, hence, the necessity for multi-fractal approaches. The assumption behind multi-fractal approaches for rainfall is that the variability of the rainfall process could be directly modelled as a stochastic (or random) turbulent cascade process, since such stochastic cascade processes were found to generically yield multi-fractals. However, it has been observed recently that multi-fractal approaches might provide positive evidence of a multi-fractal nature not only in stochastic processes but also in, for example, chaotic processes. The purpose of the present study is to investigate the presence of both chaotic and fractal behaviours in the rainfall process to consider the possibility of using a chaotic multi-fractal approach for rainfall characterization. For this purpose, daily rainfall data observed at the Leaf River basin in Mississippi are studied, and only temporal analysis is carried out. The autocorrelation function, the power spectrum, the empirical probability distribution function, and the statistical moment scaling function are used as indicators to investigate the presence of fractal, whereas the presence of chaos is investigated by employing the correlation dimension method. The results from the fractal identification methods indicate that the rainfall data exhibit multi-fractal behaviour. The correlation dimension method yields a low dimension, suggesting the presence of chaotic behaviour. The existence of both multi-fractal and chaotic behaviours in the rainfall data suggests the possibility of a chaotic multi-fractal approach for rainfall characterization. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Large-scale cosmic homogeneity from a multifractal analysis of the PSCz catalogue

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2000
Jun Pan
We investigate the behaviour of galaxy clustering on large scales using the PSCz catalogue. In particular, we ask whether there is any evidence of large-scale fractal behaviour in this catalogue. We find the correlation dimension in this survey varies with scale, consistent with other analyses. For example, our results on small and intermediate scales are consistent those obtained from the QDOT sample, but the larger PSCz sample allows us to extend the analysis out to much larger scales. We find firm evidence that the sample becomes homogeneous at large scales; the correlation dimension of the sample is D2=2.992±0.003 for r>30 h,1 Mpc. This provides strong evidence in favour of a universe that obeys the cosmological principle. [source]