Results Of Fractal Dimension Research Articles

Micro-expansion performance and microstructure of hardened cement slurry with calcined carbide slag capsules

This work studies the micro-expansion performance of hardened cement slurry with calcined carbide slag (CS) capsules (P/CS). The free expansion (FE), compressive strength (fc), and flexural strength (ff) of mortar with P/CS were measured at different CS contents of 0–6 %. Meanwhile, the calcium hydroxyl (CH) content, porosity, and pore size of mortar with P/CS were studied before 28 d. Results demonstrated that the FE of mortar with P/CS promptly increased with curing time before 3 d followed by slowly increasing. At the same time, the FE of mortar with P/CS increased with P/CS content and remained higher than that of mortar without P/CS. The fc and ff of mortar with P/CS decreased with the P/CS content and were lower than those of mortar without P/CS. Moreover, the CH content of mortar with P/CS was higher than that of mortar without P/CS at the corresponding age. For mortar containing P/CS-4 %, the porosity and proportion of large pores (>50 nm) were improved, compared to mortar without P/CS. In parallel, the results of fractal dimensions indicated that the addition of P/CS weakened the pore structure of the mortar.

The Suitability of Trabecular Patterns in the Assessment of Dental Implant Osseointegration Process through 2D Digital and 3D CBCT Radiographs.

The research aims to determine the suitability of the trabecular pattern in the assessment of the dental implant osseointegration process through two-dimensional (2D) digital and three-dimensional (3D) cone-beam computed tomography (CBCT) radiographs. This is a correlation description that explains the relationship between variables. The population consisted of 24 data points on 3D CBCT and 2D digital radiographs from the procedure after dental implants were inserted into the tibia of a New Zealand white rabbit (Oryctolagus cuniculus) on days 3, 14, and 28. The radiograph was selected based on the region of interest (ROI), which covers the peri-implant area with a width of 1 mm and length following the height of the implant. The ROI was analyzed for trabecular thickness (Tb.Th), separation (Tb.Sp), number (Tb.N), and fractal dimension. The intraclass correlation coefficient (ICC) was used to statistically test the data to assess the consistency of intraobserver measurements and the r value (Pearson's correlation coefficient). This determines the correlation between trabecular patterns in both radiographic modalities and the Bland-Altman plot to observe the limits of acceptable discrepancies. The ICC test showed high intraobserver consistency in trabecular pattern measurements on 2D digital radiographs and 3D CBCT. The trabecular space pattern and number showed an r value of 0.88 with radiographic modalities of 0.72 mm and 0.018, respectively. Additionally, the trabecular thickness and fractal dimension had an insignificant correlation, with an r value of 0.22, and the mean of the 2D radiograph was lower than that of CBCT. The 2D radiograph and 3D CBCT showed correlations in the trabecular number and space results but had no correlation in the trabecular thickness and fractal dimension results. Based on intraclass correlation analysis, 3D CBCT appeared to be more reliable for measuring trabecular patterns (Tb.Th, Tb.Sp, Tb.N, and fractal dimension) than 2D radiograph.

Fractal Characteristic Analysis of Urban Land-Cover Spatial Patterns with Spatiotemporal Remote Sensing Images in Shenzhen City (1988–2015)

Understanding the urban land-cover spatial patterns is of particular significance for sustainable development planning. Due to the nonlinear characteristics related to the spatial pattern for land cover, it is essential to provide a new analysis method to analyze them across remote sensing imagery. This paper is devoted to exploring the fractals and fractal dimension properties of land-cover spatial patterns in Shenzhen city, China. Land-cover information was extracted using a supervised classification method with ArcGIS technology from cloud-free Landsat TM/ETM+/OLI imagery, covering 1988–2015. The box-counting method and the least squares regression method are combined to estimate fractal dimensions of the land-cover spatial pattern. The information entropy was used to verify our fractal dimension results. The results show the fractal dimension changes for each land cover type from 1988 to 2015: (1) the land-cover spatial form of Shenzhen city has a clear fractal structure, but fractal dimension values vary in different land cover types; (2) the fractal dimension of build-up land increases and reaches a stable value, while grassland and cultivated land decrease; The fractal structure of grassland and bare land showed a bifractals trend increasing year by year; (3) the information entropy dimension growth is approaching its maximum capacity before 2011. We integrated the information entropy index and fractal dimension to analyze the complexity in land-cover spatial evolution from space-filling, space balance, and space complexity. It can be concluded that driven by policies, the land-cover spatial form in Shenzhen experienced a process from a hierarchical spatial structure with a low evolution intensity to a higher evolution intensity with multiscale differential development. The fractal dimension has been becoming better through self-organization, and its land resources are reaching the growth limits.

Relationship between multifractal characteristics of particle-size distribution and hydraulic conductivity of unsaturated soils

In order to study the relationship between multifractal characteristics of particle-size distribution (PSD) and unsaturated hydraulic conductivity, taking the Hunan clay as the research object, we analysed the particle composition of the whole particle size range by a laser particle size analyser, and discussed the multifractal characteristics of PSD by using the fractal theory. The soil–water characteristic curve (SWCC) and unsaturated hydraulic conductivity were measured by the pressure plate instrument and instantaneous profile method, and the unsaturated hydraulic conductivity was predicted by the fractal model. The results show that the fractal dimension D is not a fixed value for the Hunan clay with the whole particle size range, which exhibits obvious multifractal characteristics. The value of fractal dimension D is closely related to the investigated particle size range. The larger the particles in the particle size range, the larger the corresponding fractal dimension D. By comparing the measured and predicted values of the unsaturated hydraulic conductivity, it is found that the prediction results of fractal dimension D for unsaturated hydraulic conductivity with different particle size ranges are quite different, and that those results with larger particle size ranges are more reasonable.

Dendritic surface patterns from Bénard‐Marangoni instabilities upon evaporation of a reactive ZnO nanofluid droplet: A fractal dimension analysis

We present a box counting fractal dimension (FD) analysis of the dendritic patterns obtained under conditions far from equilibrium via rapid evaporation of a sessile drop containing reactive ZnO nanoparticles. These dendrites were manifestations of solidified Bénard-Marangoni (BM) instability convection cells, and we previously noted that their complex hierarchical morphologies were superficially analogous to the foliage of red algae, Spanish dagger, or spider plant. The fractal dimension of the Bénard-Marangoni dendrites was found to vary in the range of 1.77–1.89 and also depend on the size of the Bénard-Marangoni cells. These fractal dimension results were correlated with the morphological details of the Bénard-Marangoni cells and ZnO particle characteristics, providing a quantitative description of such complex surface patterns emerging from the dynamic process of the Bénard-Marangoni instability.

Effect of Hybridization of Carboxyl‐Terminated Acrylonitrile Butadiene Liquid Rubber and Alumina Nanoparticles on the Fracture Toughness of Epoxy Nanocomposites

The aim of this work was to study the effect of carboxyl‐terminated acrylonitrile butadiene (CTBN) liquid rubber and alumina nanoparticles (Al2O3) on the fracture toughness of an epoxy resin. Hybrid nanocomposite samples were prepared by the inclusion of the optimum concentration of CTBN (15 phr) and 0–10 phr Al2O3 into the epoxy matrix. Samples were examined using Fourier transform infrared spectroscopy, scanning electron microscopy, and fracture toughness test. Fractal dimension values were also estimated from the edge of the fracture surfaces for the hybrid samples. The maximum value of critical stress intensity factor, K IC, was found for the non‐hybrid sample containing 15 phr CTBN and the G IC values showed an increasing trend as it was expected from the increase in K IC values and decrease in Young's modulus. The maximum K IC for the hybrid samples was obtained for the one containing 7 phr Al2O3 and an almost similar trend was observed for G IC, accompanied with the significant changes in the fracture surface morphology. These were consistent with the fractal dimension results, where the sample containing 7 phr Al2O3 exhibited the maximum roughness. Therefore, the hybrid system of epoxy/CTBN (15 phr)/Al2O3 (7 phr) was found to be the optimum formulation. POLYM. COMPOS., 40:2700–2711, 2019. © 2018 Society of Plastics Engineers

An Analysis of COVID-19 using X-ray Image Segmentation based Graph Cut and Box Counting Fractal Dimension

COVID-19 is a disease that spreads relatively quickly. So that many victims are infected by this virus. There are various ways to diagnose the body's infection with the coronavirus. One of them with X-ray results. Detecting COVID-19 with the help of an X-ray sometimes has problems determining the location of the lesion because it is possible because of the large amount of noise in the image. Therefore, the X-ray results will be segmented images using the graph cut algorithm to analyze normal lungs and lungs infected with COVID-19. After obtaining the segmentation results in the form of binary images, the next step is to analyze using the box-counting method's fractal dimensions. From the fractal Dimension results, normal lungs have an average dimension of 1.7890, and lungs infected with COVID-19 have an average dimension of 1.5834. Normal lungs have dimensions larger than lungs infected with the coronavirus due to the lungs' covering by lesions or abnormal conditions in body tissues. This is what causes COVID-19 patients to have complaints of difficulty breathing.

Studies of physico-chemical properties and fractal dimensions of MgB2 superconductor surface

The porous structure of MgB2 has been investigated using atomic force microscopy (AFM) and sorption techniques. The fractal dimension and surface roughness parameters were evaluated from (AFM) and nitrogen adsorption–desorption isotherms measured at −196 °C for MgB2 sample. Adsorption capacity, specific surface area, and fractal dimensions were determined from adsorption–desorption isotherms. The sorption isotherms of MgB2 samples were S-shaped and belong to type II according to the IUPAC classification. The results of fractal dimensions of MgB2 surface determined on the basis sorptometry and AFM data are compared.

Comparison of Three Models of Polymer Erosion — in vivo, in vitro and Computer Simulation — Using Fractal Analysis

Polyurethane foam has been examined extensively because of its use in many implantable devices. The influence of different environments on polymer structure has been investigated via a number of clinical studies, animal models, in vitro experiments and mathematical models to predict biomaterial behavior. In this work, we employed image analysis and fractal geometry in three models of polymer degradation. In the in vivo and in vitro degradation models, we observed structural collapse and thinning of the polymer backbone, which resulted in a decrease of fractal dimension. Also, an original graphic model was developed. This computer-simulated erosion model was generated by pixel withdrawal from images. A relative degree of erosion is attributed each time an erosion process is applied. Thus, these degrees of erosion can be associated with a general time-related operation. With the computer-simulated erosion model, an unambiguous relationship was demonstrated between the estimation of fractal dimension and the relative degree of erosion. Since such models are based on a loss of mass, the results of fractal dimension were plotted against image surface, allowing us to compare the three different sets of experiments. In all three models, a proportional relationship was found between fractal dimension and image surface. Indeed, the erosion process was well-characterized by decreased fractal dimension since it is a mass dimension. Finally, we showed that the combination of a graphic computer model and a box-counting algorithm is reliable for the quantification of surface erosion.

Fractal analysis on the fatigue fracture surface along the crack propagation direction

The fractal dimension along the crack propagation direction on the fatigue fracture surface of a dual‐phase steel was investigated by both vertical section profile method and secondary electron line scanning method. Results from the vertical section profile method showed that during the crack propagation, the fractal dimension of the fracture surface increases with increasing stress intensity factor, however, the secondary electron line scanning method presented somewhat different results of fractal dimension and was proved not feasible in all kinds of fracture surfaces, so this method is not suggested in calculating the fractal dimension of the fracture surface.