Linear Fractal Dimension Research Articles

Identifying the drivers of structural complexity on Hawaiian coral reefs

Habitat structural complexity is created by biotic and abiotic processes that operate over a range of scales. This can be seen clearly on coral reefs, where corals and reef geomorphology create structure from mm to km scales. Here, we quantified the relative contribution of biotic and abiotic structures to habitat complexity using ‘Structure from Motion’, a technology that allows accurate 3D models of environments to be reconstructed from overlapping photographs. We calculated the linear fractal dimension of these models using a virtual analogue of a profile gauge. By adjusting the spacing between profile gauge rods, we partitioned structural complexity into a series of scale intervals. We identified scales that were most indicative of coral cover (0.5-16 cm) and reef geomorphology (16-256 cm). We found that reefs in the Main Hawaiian Islands have more complexity at finer scales than reefs in the Northwest Hawaiian Islands, which we attribute to the latitudinal gradient in coral cover along the archipelago. At coarser scales, islands at each end of the archipelago have sites with high structural complexity, with less complexity in the center of the archipelago. These differences are consistent with geologic factors shaping island uplift, subsidence, and reef formation. In addition, we found that different coral genera and morphologies display unique patterns of fractal dimension, with branchingPoritescorals creating the greatest amount of habitat structure at nearly all scales. This study demonstrates how multi-scale approaches can be used to identify the processes responsible for reef structural complexity and changes in structure over time.

Soil structure changes due to different land-use practices in the central Zagruos region, Iran

In this study, the effect of land-use treatments and the feasibility of fractal dimension to quantify soil aggregate stability were investigated in the central Zagrous, Iran. For this purpose, the non-linear fractal dimension (Dnl), linear fractal dimension (Dl) and the mean weight diameter (MWD) of aggregates were compared. Soil samples from three sites with four adjacent land-use types, namely: forest area (F), cultivated lands adjacent to forest (CAF), pasture (P) and cultivated lands adjacent to pasture (CAP) were collected. Results showed that soils under cultivated lands had higher bulk density (BD) (1.30–1.38 Mg m−3) compared to the adjacent soils under forest (1.19 Mg m−3) and pasture (1.21 Mg m−3). In the 0–15 cm layer, soil organic matter (SOM) content in the cultivated plots were respectively 30% and 31% lower compared to the forest and pasture soils. The lowest CVs belonged to Dnl (5–8%) demonstrating that Dnl was more accurate than Dl (8–14%) and MWD (30–53%) methods. CAP had the largest value of Dnl, while P had the smallest value of Dnl. Difference of Dnl between forest and pasture was not significant, whereas both of them significantly differed from CAF and CAP. Dl did not differ significantly between forest and CAF. There were significant differences between forest and pasture for the measured MWD. Both fractal dimensions had negative correlation with MWD, SOM, hydraulic conductivity (HC) and macroaggregates (>0.25 mm) and positive correlation with BD and total porosity (TP).

Modification of Dual Phase Filler by Electron Beam Irradiation: Physical Characterization

Abstract Electron beam modification of carbon black (N220) and carbon-silica dual phase filler affects the microstructure of carbon black. This is confirmed from X-ray diffraction studies. The scanning electron microscopy /energy dispersive X-ray analysis reveals surface oxidation, which is further corroborated from nitrogen and iodine adsorptions. Transmission electron microscopy studies show the aggregation of fillers upon electron beam irradiation. Linear fractal dimension calculated by image analysis increases upon irradiation, due to the formation of filler aggregates.

A New Model to Calculate Three-Phase Relative Permeabilities: Application and Validation for a Sandstone

Three-phase flow in a porous medium is usually described by the Stone model (1970). This model is based on two-phase data and relies on empirical correlations. It is valid only under strong water wettability and recognized as being a poor predictor. The goal of the present study is to develop a mathematical model for three-phase flow avoiding any empirical correlations. In this paper, only strong water-wet and spreading conditions are considered. However the model could be relatively easily extended to oil-wet or even mixed-wet conditions. The model is based on a physically relevant description of phase distribution and flow mechanisms at the pore scale. The porous medium is described as a set of fractal pores, whose linear fractal dimension and size distributions are derived from a mercury intrusion capillary pressure curve. The fluids are allowed to flow together in the same fractal pore, gas in the center, water near the walls and oil in an intermediate phase. The relative permeabilities are evaluated by calculating the flow of each fluid applying Poiseuille's law. The model results are compared to relative permeabilities obtained by history matching of gas injection experiments. The same experiments are also simulated using Stone's model and laboratory measured two-phase data.

Fractal geometry of root systems: Field observations of contrasting genotypes of common bean ( Phaseolus vulgaris L.) grown under different phosphorus regimes

Root growth and architecture are important for phosphorus acquisition due to the relative immobility of P in the soil. Fractal geometry is a potential new approach to the analysis of root architecture. Substantial genetic variation in root growth and architecture has been observed in common bean. Common bean (Phaseolus vulgaris L.) genotypes with contrasting root architecture were grown under moderate and low P conditions in a field experiment. Linear and planar fractal dimension were measured by tracing root intercepts with vertical planes. Linear fractal dimension increased over time in efficient genotypes, but remained fairly constant over time in inefficient genotypes. Planar fractal dimension increased over time for all genotypes, but was higher in efficient than inefficient genotypes at the end of the experiment. Planar fractal dimension of medium P plants was found to correlate with shoot P content indicating fractal dimension to be a possible indicator for root P uptake. The increasing fractal dimension over time indicates that fractal analysis is a sensitive measure of root branching intensity. A less destructive method for acquisition of data that allows for continuous analysis of fractal geometry and thereby screening for more P efficient genotypes in the field is suggested. This method will allow the researcher to conduct fractal analysis and still complete field trials with final yield evaluation.