On the fractal scaling of soil data. Particle-size distributions

Millán, H.; González-Posada, M.; Aguilar, Miguel Ángel; Domínguez, José Ferreirós; Céspedes, L.

doi:10.1016/s0016-7061(03)00138-1

Cited by 106 publications

(88 citation statements)

References 26 publications

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“…A large number of studies reported the multifractal behavior of soil particle size distribution [56,[88][89][90][91][92][93][94][95]. Most of the studies used soil particle size distributions measured using laser diffraction.…”

Section: Multifractal Analysismentioning

confidence: 99%

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Application of Multifractal and Joint Multifractal Analysis in Examining Soil Spatial Variation: A Review

Biswas¹,

Cresswell²,

Bing³

2012

Fractal Analysis and Chaos in Geosciences

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Section: Multifractal Analysismentioning

confidence: 99%

“…Most of the studies used soil particle size distributions measured using laser diffraction. One of the studies also used a piece-wise fractal model for very fine and coarse particle sizes [95]. Multifractal behavior of soil particles sizes at different land can be used to characterize soil physical health and its quality [90].…”

Section: Multifractal Analysismentioning

confidence: 99%

Application of Multifractal and Joint Multifractal Analysis in Examining Soil Spatial Variation: A Review

Biswas¹,

Cresswell²,

Bing³

2012

Fractal Analysis and Chaos in Geosciences

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“…It could result in the best quantification of land use effects on soil structure. Apparently the fractal nature of soils produces a fractal behavior of aggregates which does support the FR model to better characterize the WASD (Millan et al 2003). The FL and R models were better than the N model for 65 and 30% of soils, respectively.…”

Section: Resultsmentioning

confidence: 81%

Evaluation of models for description of wet aggregate size distribution from soils of different land uses

Tirgarsoltani

Gorji

Mohammadi

et al. 2014

Soil Science and Plant Nutrition

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A proper description of aggregate size distribution (ASD) with an optimum mathematical model would be useful in modeling and monitoring land use effect. The objective of this study was to evaluate the suitability of six cumulative distribution models, namely, Jaky, normal, log-normal, Rosin-Rammler, Fredlund and a mass-based fractal model with wet aggregate size distribution (WASD) data sets from a given range of soil structural properties. The models were tested on wet sieving data of samples that had been collected from a number of different land use types (dry farmland, rangeland and forestland). Three statistical criteria, namely, coefficient of determination (R 2 ), Mallows statistics (C p ), and Akaike's information criterion (AIC), were used for evaluating model performance, based on the least sum of square error and number of fitting parameters. Analysis of R 2 showed that the Fredlund three-parameter model showed the best performance in all of the soils apart from the number of parameters. The log-normal model gave a good fit on WASD from rangeland and forestland; it was the best especially in dry farmland. The normal model provided a good description of WASD from the rangeland and forest. However, it failed in dry farmland. According to C p and AIC as the evaluation criteria, the fractal model was the optimum to describe WASD for all of the land uses. The Fredlund, log-normal, Jaky and Rosin-Rammler models ranked next in the given order.

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“…On the view of the natural organization of the PSDs, it is assumed that there might exist a critical value r c to partition the whole distribution into two intervals of particle diameter over which the fractal dimensions are different (Millán et al 2003). The fractal size distribution function in Equation (26) …”

Section: Piecewise Fractal Modelmentioning

confidence: 99%

Fractal analysis in particle dissolution: a review

Bao

Long

et al. 2014

Reviews in Chemical Engineering

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Abstract:Fractal is a geometric language to describe the objects, the systems, and the phenomenon spatially and temporally. This paper reviews the literature on fractal models developed to describe the dissolution of particles. Dissolution, the process by which a solid forms a homogeneous mixture with a solution, is the behavior of a population of particles rather than a single one in most of the cases. The fractal models developed for the particle population are reviewed on the basis of two key particle surface properties, namely, the surface fractal nature and the chemical reactivity of particle surfaces. In terms of the surface fractal nature, fractals have been used to describe the change in the superficial roughness of particles, surface area-particle size relation, and particle size distribution (PSD). In terms of the reactive fractal dimensions, the models that describe the dissolution process have been developed to obtain the empirical noninteger exponent, the reactive fractal dimension that can dictate the chemical reactivity of a solid surface. The comparison between the surface fractal dimension and the reactive fractal dimension provides the dissolution mechanisms in many aspects of surface morphology. Further research is necessary to modify the current models to coincide with the real industrial processes and production and to develop the specific models for a better understanding of many processes involving the dissolution of particles encountered in many areas, including pharmaceutical and chemical applications and hydrometallurgy.

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On the fractal scaling of soil data. Particle-size distributions

Cited by 106 publications

References 26 publications

Application of Multifractal and Joint Multifractal Analysis in Examining Soil Spatial Variation: A Review

Application of Multifractal and Joint Multifractal Analysis in Examining Soil Spatial Variation: A Review

Evaluation of models for description of wet aggregate size distribution from soils of different land uses

Fractal analysis in particle dissolution: a review

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