Multifractal and joint multifractal analysis of the spatial variability of CO2 emission and other soil properties

<p>Soil is a major source and also a sink of CO<sub>2</sub>. Agricultural management practices influence soil  carbon sequestration. Identification of CO<sub>2</sub> emission hotspots may be instrumental in implemented strategies for managing carbon cycling in agricultural soils. We used multifractal analysis to assess the spatial variability of both, soil CO<sub>2</sub> emissions and associated soil physico-chemical attributes. The objectives of this study were: i) to characterize patterns of spatial variability of CO<sub>2</sub> emissions and related soil properties using single multifractal spectra, and ii) to compare the scale‐dependent relationship between soil CO<sub>2</sub> emissions and selected soil attributes by joint multifractal analysis. The study site was an experimental field managed as a sylvopastoral system, located in Selviria, South Mato Grosso state, Brazil. The soil was an Oxisol developed over basalt. Soil CO<sub>2 </sub>emission, soil water content and soil temperature were measured at 128 points every meter. In addition<strong>, </strong>soil was sampled at the marked points to analyze clay content, macro and microporosity, air free porosity, magnetic susceptibility, bulk density, and humification index of soil organic matter in absolute values and relative to organic carbon content. The generalized dimension, D<sub>q</sub> versus q, and singularity spectra, f(α) versus α, of the spatial distributions of the 11 variables studied showed various degrees of multifractality. In general, the amplitude of the generalized dimension and singularity spectra was much higher for negative than for positive q order statistical moments. Joint multifractal spectra show a positive relationship between the scaling indices of the spatial distributions of CO<sub>2</sub> and all of the other soil variables studied. However, contour plots were diagonally oriented for higher values of scaling indices and showed no distinct trend for the lower ones. Joint multifractal analysis corroborates different degrees of association between the scaling indices of CO<sub>2</sub> and all of the remaining variables studied. It also showed that CO<sub>2</sub> was stronger correlated at multiple scales than at the observation scale. Therefore, single scale analysis may not be sufficient to fully describe relationships between soil testing methods.Our study suggests that soil factors and processes driven the spatial variability of CO<sub>2</sub> and the associated variables studied may be not very different.</p><p> </p>

Multifractal characteristics of shale and tight sandstone pore structures with nitrogen adsorption and nuclear magnetic resonance

Based on the experiments of nitrogen gas adsorption (N2GA) and nuclear magnetic resonance (NMR), the multifractal characteristics of pore structures in shale and tight sandstone from the Chang 7 member of Triassic Yanchang Formation in Ordos Basin, NW China, are investigated. The multifractal spectra obtained from N2GA and NMR are analyzed with pore throat structure parameters. The results show that the pore size distributions obtained from N2GA and NMR are different, and the obtained multifractal characteristics vary from each other. The specific surface and total pore volume obtained by N2GA experiment have correlations with multifractal characteristics. For the core samples with the similar specific surface, the value of the deviation of multifractal spectra Rd increases with the increase in the proportion of large pores. When the proportion of macropores is small, the Rd value will increase with the increase in specific surface. The multifractal characteristics of pore structures are influenced by specific surface area, average pore size and adsorption volume measured from N2GA experiment. The multifractal characteristic parameters of tight sandstone measured from NMR spectra are larger than those of shale, which may be caused by the differences in pore size distribution and porosity of shale and tight sandstone.

Small-Angle Scattering and Multifractal Analysis of DNA Sequences

The arrangement of A, C, G and T nucleotides in large DNA sequences of many prokaryotic and eukaryotic cells exhibit long-range correlations with fractal properties. Chaos game representation (CGR) of such DNA sequences, followed by a multifractal analysis, is a useful way to analyze the corresponding scaling properties. This approach provides a powerful visualization method to characterize their spatial inhomogeneity, and allows discrimination between mono- and multifractal distributions. However, in some cases, two different arbitrary point distributions, may generate indistinguishable multifractal spectra. By using a new model based on multiplicative deterministic cascades, here it is shown that small-angle scattering (SAS) formalism can be used to address such issue, and to extract additional structural information. It is shown that the box-counting dimension given by multifractal spectra can be recovered from the scattering exponent of SAS intensity in the fractal region. This approach is illustrated for point distributions of CGR data corresponding to Escherichia coli, Phospholamban and Mouse mitochondrial DNA, and it is shown that for the latter two cases, SAS allows extraction of the fractal iteration number and the scaling factor corresponding to “ACGT” square, or to recover the number of bases. The results are compared with a model based on multiplicative deterministic cascades, and respectively with one which takes into account the existence of forbidden sequences in DNA. This allows a classification of the DNA sequences in terms of random and deterministic fractals structures emerging in CGR.

Study of the structural degradation of steel 15Kh5M upon continuous duty

Structural degradation of the material upon long-term thermal and force impacts is a complex process which includes migration of the grain boundaries, diffusion of the active elements of the external and technological environment, hydrogen embrittlement, aging, grain boundary corrosion and other mechanisms. Application of the fractal and multifractal formalism to the description of microstructures opens up wide opportunities for quantitative assessment of the structural arrangement of the material, clarifies and reveals new aspects of the known mechanisms of structural transformations. Multifractal parameterization allows us to study the processes of structural degradation from the images of microstructures and identify structural changes that are hardly distinguishable visually. Any quantitative structural indicator can be used to calculate the multifractal spectra of the microstructure, but the most preferable is that provides the maximum range of variation in the numerical values of the multifractal components. The results of studying structural degradation of steel 15Kh5M upon continuous duty are presented. It is shown that structural degradation of steel during operation under high temperatures and stresses is accompanied by enlargement of the microstructural objects, broadening of the grain boundaries and allocation of the dispersed particles which are represented as point objects in the images. The processes of structural degradation lead to an increase in the range of changes in the components of the multifractal spectra. High values of complex indicators of structural arrangement indicate to an increase in heterogeneity and randomness at the micro-scale level, but at the same time, to manifestation of the ordered combinations of individual submicrostructures. Those structural transformations adapt the material to external impacts and provide the highest reliability and fracture resistance of the material.