Variation Of Fractal Dimension Research Articles

FRACTAL-BASED ANALYSIS OF THE RELATIONSHIP BETWEEN THE SURFACE FINISH OF WORKPIECE AND CHIP FORMATION IN MILLING OPERATION

Surface finish is one of the most important issues that is discussed in machining of materials. In fact, reaching the required surface finish is the key scale in analysis of the quality of machined workpiece. Chip formation is an important factor that highly affects the surface finish of machined workpiece. In this research, we analyze the relationship between surface finish and chip formation by fractal analysis of their surfaces. Since both patterns have complex structures, we calculate their fractal dimension in case of different experiments in which machining parameters change. The result of analysis indicates that the variations of fractal dimension of machined surface show a reverse pattern compared to the fractal dimension of chip surface in case of variations of depth of cut and feed rate. However, in case of variations of spindle speed, the variations of fractal dimension of machined surface show a similar pattern with the fractal dimension of chip surface. Therefore, it can be said that the complexity of machined surface is linked to the complexity of chip surface. The method of analysis used in this research can be further applied to other manufacturing operations.

Coastline Fractal Dimension of Mainland, Island, and Estuaries Using Multi-temporal Landsat Remote Sensing Data from 1978 to 2018: A Case Study of the Pearl River Estuary Area

The Pearl River Estuary Area was selected for this study. For the past 40 years, it has been one of the most complex coasts in China, yet few studies have analyzed the complexity and variations of the area’s different coastlines. In this investigation, the coastlines of the Pearl River Estuary Area were extracted from multi-temporal Landsat remote sensing data from 1978, 1988, 1997, 2008, and 2018. The coastline of this area was classified into mainland, island, and estuarine. To obtain more detailed results of the mainland and island, we regarded this area as the main body, rezoned into different parts. The box-counting dimension was applied to compute the bidimensional (2D) fractal dimension. Coastline length and the fractal dimension of different types of coastline and different parts of the main body were calculated and compared. The fractal dimension of the Pearl River Estuary Area was found to have increased significantly, from 1.228 to 1.263, and coastline length also increased during the study period. The island and mainland showed the most complex coastlines, while estuaries showed the least complexity during the past forty years. A positive correlation was found between length and 2D-fractal dimension in some parts of the study area. Land reclamation had the strongest influence on fractal dimension variations.

Preparation, characterization and discussion of glass ceramic foam material: Analysis of glass phase, fractal dimension and self-foaming mechanism

Resource utilization of waste has always been the focus attention due to the increased environmental problems. In this work, glass ceramic foam was prepared using coal gangue, fly ash and silica sand as raw materials without addition agent. The pore morphology, microstructure and some physical properties of the samples with different silica sand contents were investigated. In addition, the fractal dimension was introduced to quantitatively describe the variation in pore morphology. The results illustrated that the addition of silica sand in the samples is beneficial to form a unique close-pore construction which endows the prepared material with good performance for using as a lightweight wall material in the construction field. Discussion indicated that the introduction of silica sand was found to promote the formation of glass phase, which possibly was the Si–Al–O glass system. The variation of fractal dimension inferred that the co-existence of large and small pores formed in samples with high content silica sand may be originated from the interaction of the two glass phases. The analysis of self-foaming mechanism revealed that only the gases released after glass phase formation were effective to build pore structure. This study provides a highly efficient and clean utilization route for recycling solid waste by preparing lightweight glass ceramic foam.

Investigation of fractality and variation of fractal dimension in germinating seed

The fractal analysis has now been recognized as a potential mathematical tool in analyzing complex structures. The present work reports not only the fractal nature of Vigna radiata seed analyzed with the help of Field Emission Scanning Electron Microscopic images but also the variation of fractal dimension (FD) in a germinating seed. The variation of FD during germination in different media—water, salt, and diesel soot with carbon nanoparticles (CNPs)—is studied using the box-counting technique. The study is the first report of the fractality of seed. Irrespective of the media, the FD attains a maximum value on the day of germination and decreases after that. The time (T) for achieving maximum FD varies with the nature of stress. In the study, when the CNPs of diesel soot lower the T value, the salt raises the T value with respect to the control set. The Fourier Transform Infrared analysis of the seeds germinating in different media shows an increased rate of protein formation during the initial stage of germination and a steady state after that. In conjunction with the literature, the variation in the amino nitrogen, soluble nucleotide—RNA, and protein content of the seed during the initial days of germination gets reflected in its FD.

Complexity-based decoding of brain-skin relation in response to olfactory stimuli

Background and ObjectiveHuman body is covered with skin in different parts. In fact, skin reacts to different changes around human. For instance, when the surrounding temperature changes, human skin will react differently. It is known that the activity of skin is regulated by human brain. In this research, for the first time we investigate the relation between the activities of human skin and brain by mathematical analysis of Galvanic Skin Response (GSR) and Electroencephalography (EEG) signals. MethodFor this purpose, we employ fractal theory and analyze the variations of fractal dimension of GSR and EEG signals when subjects are exposed to different olfactory stimuli in the form of pleasant odors. ResultsBased on the obtained results, the complexity of GSR signal changes with the complexity of EEG signal in case of different stimuli, where by increasing the molecular complexity of olfactory stimuli, the complexity of EEG and GSR signals increases. The results of statistical analysis showed the significant effect of stimulation on variations of complexity of GSR signal. In addition, based on effect size analysis, fourth odor with greatest molecular complexity had the greatest effect on variations of complexity of EEG and GSR signals. ConclusionTherefore, it can be said that human skin reaction changes with the variations in the activity of human brain. The result of analysis in this research can be further used to make a model between the activities of human skin and brain that will enable us to predict skin reaction to different stimuli.

Perfluorooctanoic Acid Exposure Assessment on Common Carp Liver through Image and Ultrastructural Investigation.

Perfluorooctanoic acid (PFOA) poses particular concern as an emerging pollutant in both surface and ground waters. Fish, as a natural inhabitant of these waters and being highly representative of vertebrates, represents an ideal animal model to assess the toxic effects of PFOA. Hereby, liver microscopic texture was comparatively evaluated in individuals of common carp subchronically exposed to PFOA using grayscale differential box counting, a fractal analysis method. Furthermore, liver cytoplasmic glycogen areas and ultrastructure were also evaluated and compared to the image analysis findings. Redundancy Analysis was performed to assess, in summary, how much the variation of fractal dimension and lacunarity was explained by the concentration of PFOA in liver, the mass of liver and the number of proliferating cell nuclear antigen (PCNA)-immunoreactive nuclei. Treatment group ordination was better determined by fractal dimension than lacunarity. Interestingly, a significant complexity increase was associated with the modification of liver microscopic texture due to PFOA exposure. This complexity increase was related to “cloudy swelling”, possibly representing a primarily adaptive strategy against PFOA challenge, rather than a slight, reversible form of degeneration as traditionally proposed. The occurrence of endoplasmic reticulum stress, unfolded protein reaction and hormetic response was proposed and discussed.

Experimental Study on Pore-fracture Evolution Law in the Thermal Damage Process of Coal

ABSTRACT High temperature causes thermal damage to coal, alters its pore-fracture structure, and then influences its permeability and spontaneous combustion characteristics. In this paper, to study the evolution law of coal pore-fracture in the thermal damage process and the influence mechanism of thermal damage on pore-fracture development, the microfracture evolution characteristics and pore morphology of coal samples treated under different temperatures were qualitatively studied by susing a scanning electron microscope (SEM). Besides, the evolution of coal pore structure as a function of temperatures in the heating process was quantitatively studied based on Nuclear magnetic resonance (NMR) technique. In addition, the pore structure of coal samples was quantitatively characterized in combination with the fractal theory, and the variation of fractal dimension of coal sample pore structure with heat treatment temperature was obtained. The results show that after heat treatment, the development of fractures of coal was promoted, and the connectivity between the fractures was effectively enhanced. Moreover, the higher the temperature is, the more favorable it is for the development, expansion, and connectivity of fractures and for the formation of microfracture networks in coal. The high-temperature thermal damage changes the pore structure of coal, increases the pore volume and porosity of coal and enhances the pore connectivity. Moreover, after high-temperature heat treatment, the pore structure of DL coal with low metamorphism changed more significantly than that of XG coal. The porosity of DL coal and XG coal increased with the rising temperature, while the pore fractal dimension DmNMR, DMNMR, and DNMR of the two kinds coal samples show the opposite trend. Furthermore, the variation amplitude of DmNMR is significantly larger than that of DMNMR, and the variation of three fractal dimensions of DL coal is larger than that of XG coal. The research results can support a reference for coal fire prevention.

Fractal analysis of pore structures in graphene oxide-carbon nanotube based cementitious pastes under different ultrasonication

Abstract Nano cement additive using a hybrid of graphene oxide (GO) and multi-walled carbon nanotubes (MWCNTs) combines the excellent affinity of GO and the superior mechanical properties of MWCNTs. Ultrasonication is the key process to disperse the GO/MWCNTs and further optimizes the pore structures of cement-based pastes. Fractal dimension can effectively and quantitatively characterize the pore structures of cementitious composites. The present study investigates the fractal dimensions of pore structures of GO/MWCNT-OPC pastes under power- and time-controlled ultrasonication based on the mercury intrusion porosimetry (MIP) tests data. The finding of this study shows that comparing to calculating the fractal dimension of the overall pore size range, assessing the variations of fractal dimension of individual pore size range is more effective in evaluating the pore characteristic. The fractal dimension of larger capillary pores $$\left( {{D}_{>{{10}^{4}}nm}} \right)$$can be use to describe the change of pore structure of GO/MWCNT-OPC pastes under ultrasonication treatment with sufficient accuracy as higher value of $${{D}_{>{{10}^{4}}nm}}$$indicates better pore characteristics. The fractal dimension change trend of mesopores is always opposite to that of bigger capillary pores. Modest increment in both power- and time-controlled ultrasonication seems to result in the increase of the fractal dimension of capillary pores and lead to better reinforcement effects. Prolongation of ultrasonication time slightly influences the pore structure of the specimens, while nano cement additives exposed to excess ultrasonication power fail to afford adequate reinforcing effect and finally cause the deterioration of the pore structures. The findings of this study can provide helpful information of GO/MWCNT-OPC pastes and ultrasonication treatment in the future.

Micro-fracture mechanism of polycrystalline CBN grain during single grain scratching tests based on fractal dimension analysis

The wear phenomenon is an important issue that affects the grinding performance of polycrystalline cubic boron nitride (PCBN) grinding wheel. To explore the wear mechanism, single grain scratching tests were conducted on the nickel-based superalloy Inconel 718. Fractal theory was applied to evaluate the grain wear process, and the influences of undeformed chip thickness agmax and grinding wheel speed vs on grain wear were analysed. The variation in fractal dimension, grinding force and grinding force ratio were discussed. Results show that the micro-fracture is caused by the crack, and the adhered grinding chip leads to the attrition wear of PCBN grain. The average specific material removal volume of monocrystalline CBN grain is approximately 10.7% that of PCBN grain when macro-fracture occurs. The effect of agmax on grain macro-fracture is stronger than that of vs. Furthermore, the grinding parameters should be set as follows: vs of 80 m/s and agmax in the range of 0.1–0.67 μm. These settings help improve the grain micro-fracture phenomenon in high-speed grinding.

Investigation into the diversity in the fractal dimensions of arterioles and venules in a microvascular network – A quantitative analysis

Fractal dimension is a robust fractal parameter for estimating the morphology of vascular networks. It reflects the property of vascular networks that may vary and thus, differentiate between individual networks and/or identify physiological and pathological conditions. As such, fractal dimension differs also between arteriolar and venular compartments, yet the underlying reason is so far unclear. In order to understand the mechanisms behind these differences, we quantitatively analyzed the impacts of vessel attributes on the fractal dimension. Fractal dimension and vessel attributes given by vessel density (VD), vessel length density (VL), and diameter index (DI=VD/VL) were analyzed in three microvascular networks of the rat mesentery, which were reconstructed from experimental data. The results show that differences in diameter between arterioles and venules are primarily responsible for arterio-venous differences in fractal dimension. Moreover, multiple linear regression analysis demonstrates that the sensitivity of the variation of fractal dimension to vessel length and diameter varies with the type of the vessels. While the change of vessel length contributes 57.8 ± 3.4% to the variation of arteriolar dimension, vessel diameter contributes 63.9 ± 4.8% to the variation of venular dimension. The present study provides an explanation for the different fractal dimension and dimension variation in arteriolar and venular compartments. It highlights the importance of estimating the fractal dimensions of arterioles and venules separately, which will enhance the ability of feature extraction by fractal analysis in physiological and clinical application.

Small-angle X-ray scattering study on the fractal structure of solid products of bituminous coal at different carbonization temperatures

ABSTRACTCarbonization is one of the main methods for comprehensive utilization of bituminous coal. Bituminous coal and its solid products from carbonization, namely char and coke, have complex pore structures, which can be characterized by fractals. We performed a study on the fractal structure of the solid products prepared from the bituminous coal of Shuiyu mine in Shanxi Province, China, at different carbonization temperatures (25°C∼1000°C) by synchrotron radiation small-angle X-ray scattering (SAXS). The results show that the bituminous coal has a surface fractal structure during the whole carbonization process. The variation of fractal dimension with carbonization temperature illustrates the different stages of the carbonization process.

Fractal Properties of Greenland Isolines

The shape of Earth’s surface topography is determined by numerous competing processes that act to either roughen or smoothen the surface. Hence, calculating topographic roughness is a useful technique for understanding the relative importance of these processes. This study analyzes the relative surface roughness of the Greenland Ice Sheet by calculating the fractal dimension of surface elevation isolines. It is shown that the fractal dimension of isolines decreases at higher elevations for nearly all the ice sheet catchments. However, the magnitude of fractality, which represents the relative complexity or roughness of the surface, is spatially variable. Catchments in the central-east of the ice sheet have the highest fractal dimension, and the north catchment has the lowest fractal dimension. Multi-fractality at lower elevations for several catchments is observed including the southeast catchment, indicating that these catchments have variable dominant forcings at different length scales. Exploring the local variation of fractal dimensions shows that the majority of isolines with high fractal dimension are clustered in the central-east region and persist in contours up to 2500 m elevation. However, it is shown that local fractal dimensions are related to surface elevation, bed elevation, and ice thickness. It is also shown that local fractal dimensions are correlated with the ruggedness of basal topography (defined as the difference between the highest and lowest elevation in a window of $$3\times 3$$ pixels on a 150 m grid). This analysis serves as a qualitative approach for investigating the processes that control the geometry of ice caps on other terrestrial planets.

FracVAL: An improved tunable algorithm of cluster–cluster aggregation for generation of fractal structures formed by polydisperse primary particles

In this study, the tunable algorithm of cluster–cluster aggregation developed by Filippov et al. (2000) for generating fractal aggregates formed by monodisperse spherical primary particles is extended to polydisperse primary particles. This new algorithm, termed FracVAL, is developed by using an innovative aggregation strategy. The algorithm is able to preserve the prescribed fractal dimension (Df) and prefactor (kf) for each aggregate, regardless of its size, with negligible error for lognormally distributed primary particles with the geometric standard deviation σp,geo being as large as 3. In contrast, for polydisperse primary particles the direct use of Filippov et al. (2000) method, as is done by Skorupski et al. (2014), does not ensure the preservation of Df and kf for individual aggregates and it is necessary to generate a large number of aggregates to achieve the prescribed Df and kf on an ensemble basis. The performance of FracVAL is evaluated for aggregates consisting of 500 and 1000 monomers and for fractal dimension variation over the entire range of Df between 1 and 3 and kf between 0.1 and 2.7. Aggregates consisting of 500 monomers are generated on average in less than 2.4 min on a common laptop, illustrating the efficiency of the proposed algorithm. Program summaryProgram Title: FracVALProgram Files doi:http://dx.doi.org/10.17632/mgf8wdcsfb.1Licensing provisions: GNU General Public License v3Programming language: Fortran 90Nature of problem: Generation of fractal-like aggregates, consisting of point-touching, polydisperse primary particlesSolution method: Hierarchical cluster–cluster random aggregationAdditional comments including restrictions and unusual features: Possible combinations of fractal dimension and prefactor depend on monomers polydispersity

The role of gangue on the mitigation of mining-induced hazards and environmental pollution: An experimental investigation

Gangue, produced from coal mining and washing process, is a serious threat to the ground environment. Gangue backfilling mining method can solve this problem and reduce mining-induced hazards, e.g., controlling surface subsidence and preventing water inrush from seeping into goaf by cracks in overlying strata. In this paper, effects of the original particle size distribution (PSD) and water content on the particle crushing behavior and seepage properties of granular gangues were investigated. Experimental results show that the crushing behavior can promote the compaction of gangue particles; the variation of PSD after crushing reveals distinct fractal characteristics. With the increasing compression stress, the particle crushing ratio and fractal dimension increase, while the permeability decreases. Due to the rearrangement of particles and newly generated fine particles filled the gap among larger particles, it is difficult to reduce the permeability by increasing the compressive stress. In addition, the variation of fractal dimensions is similar to the crushing ratio, so the particle crushing can be illustrated by fractal dimensions. The relationship between porosity and permeability established by the Kozeny-Carman equation can model the effect of particle crushing in this research. The reliability of the equation is verified by the comparison of model result and experimental data. To increase the mitigation rate of mining-induced hazards and environmental pollution by GBM method, granular gangues can be crushed into smaller particles and dehydrated before backfilling.

Raman spectroscopic and fractal analysis of blood samples of dengue fever patients.

The limitations of the existing techniques for the early detection of dengue fever necessitate the development of a powerful optical technique. The present work is a study of Raman spectral modifications of blood on dengue infection and thereby to develop a spectroscopic method for its early detection. The images of the samples are subjected to fractal analysis to find the variation of fractal dimensions on dengue infection. Correlation of platelet counts of dengue infected blood with Raman spectrum modification and fractal dimension. The effect of lowering of blood platelet count due to dengue infection is found to show some interesting changes in the spectrum. The full width at half maximum (FWHM) of the two bands in the region 950-1200cm-1 increase with the decrease of blood platelet count. The increase in fractal dimension gives an indication of the decrease of platelet count and hence the dengue infection. Raman spectrum and fractal analysis can effectively be used as potential techniques for the early detection of dengue infection.

A study of fractal dimension as a quality indicator of hairtail (Trichiurus haumela) samples during frozen storage

Hairtail fish samples were stored at different freezing temperatures of −5 °C, −20 °C, −40 °C and −80 °C. To establish an effective quality evaluation approach for hairtail samples during frozen storage, fractal dimension was used to observe the porous microstructure that resulted from the ice crystal formation in frozen hairtail meat. The results showed that the initial value of fractal dimension of all the samples was 1.968. After frozen storage, the fractal dimension of samples at −5 °C, −20 °C, −40 °C and −80 °C decreased to 1.539, 1.682, 1.856 and 1.896, respectively. Traditional quality indicators such as water activity, color and textural properties (i.e., hardness, springiness and chewiness) also exhibited a similar decreasing trend, and the rate of change decreased with a decrease in storage temperature. The relationships were analyzed, and these traditional quality indicators were correlated with the fractal dimension with determined correlation coefficients within ±0.900. Moreover, based on the fractal dimension model, the first-order kinetic equation of fractal dimension variation during storage was {{bf{d}}}_{{bf{t}}}={bf{1.968}},{{bf{e}}}^{{boldsymbol{-}}{bf{0.928}}{bf{t}}{{bf{e}}}^{{boldsymbol{-}}{bf{1431.396}}/{bf{T}}}}, which can be used to predict the shelf life of preserved hairtails at different storage temperatures. The results demonstrated fractal dimension was a novel and feasible method to evaluate the quality of hairtails in frozen storage.

Effect of slurry concentration on erosion wear behavior of AISI 5117 steel and high-chromium white cast iron

PurposeThis paper aims to investigate the influence of slurry concentration on the erosion behavior of AISI 5117 steel and high-chromium white cast iron by using a whirling-arm rig. In this study, the slurry erosion mechanism with particle concentration has been studied.Design/methodology/approachThe tests were carried out with particle concentrations in the range of 1-7 Wt.%, and the impact velocity of slurry stream was 15 m/s. Silica sand with a nominal size range of 500-710 µm was used as an erodent. The study revealed that the failure mode was independent of concentration.FindingsThe results showed that the erosion rate decreases with the increase in particle concentration and the variation in the reduction depends on the material. It was found that the variation of fractal dimension calculated from slope of linearized power spectral density of eroded surface image for different concentrations can be used to characterize the slurry erosion intensity in a similar manner to the erosion rate. It was also found that the variation of fractal dimension versus concentration of sand has a general trend that does not depend on magnification factor.Originality/valueUsing the gravitational measurement and image analysis, the variation of the wear with slurry concentration has been analyzed to investigate the implicated mechanisms of erosion during the process.

Fractal-Based Pattern Extraction From Time-Series NDVI Data for Feature Identification

The spatial coarseness of time-series satellite data (≥250 m) and land cover mixing within a pixel poses difficulties in identifying a unique reference profile for each land cover class in regional level mapping. This problem is exaggerated further in a hilly terrain with different topographic, climatic, environmental conditions, and landscape composition. In this regard, this study aims to evaluate the usefulness of two reference-independent fractal dimension (FD) estimation techniques (box counting and rescaled range) for identifying land cover classes from the MODIS (MOD13Q1-v5) 16-day interval time-series normalized difference vegetation index profile at the pixel level. We have analyzed the FD images from each technique using Welch's t -statistics to evaluate the interclass mean FD variations in Himachal Pradesh—a mountainous state in Northern India. Furthermore, a support vector machine-based classification is performed using time-series principal components in conjunction with FD measures to assess the effectiveness of FD images in improving the accuracy of land use and land cover classification. The experiments revealed that the use of FD images has considerably increased the user accuracy and helped in accurately detecting mixed pixels which are dominated by agriculture class.

Characterizing Factors Associated with Built-Up Land Expansion in Urban and Non-Urban Areas from a Morphological Perspective

In this paper, built-up land expansion patterns and the associated factors were characterized in urban and non-urban areas across the Wen-Tai region of eastern China. Fractal dimension can be used as a reliable indicator of the complexity of built-up land form, and the increasing trend of fractal dimension indicated a more complex, dispersed pattern of built-up land in urban areas. Spatial regression models were quantitatively implemented to identify the indicators influencing the variation of fractal dimensions. Our findings suggested that the fractal dimension of built-up land forms was positively correlated to the patch density and elevation when built-up land expansion was more concentrated. Both landscape shape index and Gross Domestic Product (GDP) were positively correlated with fractal dimension in urban areas, and total edge, edge density, and connective index had impacts on fractal dimension in non-urban areas. Slope and agricultural population also showed an influence on fractal dimension. This study provided a new way for urban studies in interpreting the complex interactions between fractal dimension and related factors. The combined approach of fractal dimension and spatial analysis can provide the government planners with valuable information that can be efficiently used to realize the influences of land use policies in urban and non-urban areas.

Viscoelastic phase separation of polystyrene/poly(vinyl methyl ether) blends with different dynamic asymmetry

Viscoelastic phase separation (VPS) can be induced in dynamically asymmetric polystyrene/poly(vinyl methyl ether) (PS/PVME) blend in which there is a large difference between glass transition temperature of the components (about 125 °C). In this study, the effect of molecular weight of the slower component, PS, on VPS mechanism is investigated. The correlation between the time evolution of the phase-separating morphologies and their linear and nonlinear rheological behavior is studied for blends with three different PSs. Rheological measurements and morphological observations are carried out at quench depth of 14 °C. While it was previously found that depending on composition of blend, three different types of VPS behavior can be observed due to self-induced stresses in the early stage of phase separation—(i) the transient gel induced VPS (TG-VPS), (ii) coalescence induced VPS (C-VPS), and (iii) aggregating nucleation and growth (ANG)—in this study, we show that different types of VPS can be observed for a single composition by changing the molecular weight of PS. In other words, dynamic asymmetry between PS-rich and PVME-rich phases decreases with a decrease of molecular weight of PS which results in weaker transient gel in the early stage of phase separation. Consequently, the phase separation mechanism changes for 10/90 blend from TG-VPS to C-VPS and, for 5/95 blend from C-VPS to ANG or NNG (normal nucleation and growth). Furthermore, the variation of fractal dimension by phase separation is studied for 10/90 blends containing PS with different molecular weights.