Smaller Fractal Dimension Research Articles

Experimental study on fractal characteristics of coarsegrained soil filler for high-speed railway subgrade

This paper takes coarse-grained soil filler of high-speed railway subgrade as object of study, completes a series of coarse grained soil compaction tests under different moisture content with electric heavy compaction apparatus type YX-30, and obtains the granularity fractal distribution curve with coarse-grained granularity fractal model. The result shows that coarse-grained soil filler has obvious fractal characteristics after compaction, and particle breakage fractal dimension between 2.61-2.82. With the increase of fractal dimension, the maximum dry density increases first and then decreases, and the maximum fractal dimension is under the optimum water content. The coarse-grained soil with high clay content has lower particle size and smaller fractal dimension before and after compaction. Water content and clay content are two important factors that affect the crushing of coarse-grained soil. The effect of clay content on particle size is more significant than that of clay content.

Ultrasound driven mound to self-affine surface structure transition in nanostructured films: one-pot route to cubic CuInS2 quantum dots with controlled structure and tunable band gap energy

In the current study, the first method for synthesis of 3D assemblies composed by close-packed QDs of the cubic modification of CuInS2in thin film form is presented. The developed one-pot synthetic approach enables high tunability of materials’ properties by combining ultrasonic irradiation of the reactor with the one-step colloidal chemical approach or by controlled post-deposition annealing of the deposited samples. The average crystal size of the material can be tuned from ~ 1 up to ~ 36 nm. In-depth studies of the structure, surface morphology and optical properties were carried out. Manifestations of size-quantization effects in the optical properties were analyzed in details. Analysis of the second-order statistical properties of thin films’ surfaces has shown that ultrasonically-supported synthesis enables generation of self-affine surfaces, while the colloidal chemical one leads to mounded surfaces. Such change of the surfaces’ character was attributed to heterogeneous sonochemical effects, leading ultimately to more efficient transport of the clusters formed in the bulk liquid and their improved energizing, enabling them to overcome various diffusion barriers on the growing surface. Sonochemically deposited films are characterized by notably larger values of the Hurst exponent than the chemically deposited ones, and an order of magnitude smaller correlation length. Smaller fractal dimensions in sonochemical films are in line with the smoother surfaces generate by ultrasonically-assisted route.

Integrating general principles into mixed-integer programming to optimize schematic network maps

ABSTRACTSchematic maps are popular for the representation of transport networks. Many automated methods have been developed to generate such maps. In these methods, optimization techniques work with various sets of constraints. Most of these constraints govern geometric properties of individual features. A few constraints address relationships among features, but none explicitly deal with the main structure of an entire network. We believe that preservation of main structure is the most important and preservation of relative relations is helpful. This is because human perception follows a global-to-local process. These constraints have recently been formed into four general principles, with two for global structure and two for relativity of features. This study develops an automated method by integrating these principles into the mixed-integer programming (MIP) framework. Experimental evaluations have been conducted with two sets of real-world transit networks. In comparison to the existing method, the proposed method has smaller fractal dimensions, better computational performance and higher scores in terms of clarity, recognition of major lines, visual simplicity and satisfaction. Therefore, it is concluded that the proposed method can generate schematic maps with improved clarity and aesthetics. The idea in this study is also helpful for the design of other visual representations.

Coupling efficiency of a partially coherent collimating laser from turbulent biological tissue to fiber

Abstract We propose a model of the fiber coupling efficiency for a partially coherent collimating laser beam propagating through turbulent biological tissue to fiber. By studying the influence of link parameters on fiber coupling efficiency, we find that there are optimal focal length and transmitting beam radius for specific turbulent tissue. We also find that a larger characteristic length and small length-scale factor, or smaller fractal dimension and strength coefficient of refractive-index fluctuation will lead to larger fiber coupling efficiency. In order to improve the fiber coupling efficiency, we recommend select the optimum focal length, moderate transmitting beam radius, lower aperture diameter of the coupling lens, longer wavelength and higher coherent degree of light source.

Structure and settling performance of aluminum oxide and poly(acrylic acid) flocs in suspension systems

In this work, the flocculation behavior of suspension systems containing poly(acrylic acid) (PAA) with different molecular weights and aluminum oxide particles was studied fundamentally. Correlations were developed among the adsorption of PAAs on the particles, the zeta potential of the aluminum oxide suspensions and the turbidity of the suspensions. The structure of flocs formed between PAA and aluminium oxide particles were comprehensively studied under stirring and non-stirring conditions. The fractal dimension, Df, of the flocs ranged between 1.1 and 2.4 revealing that the flocs generated by PAAs could be considered as fractals. The flocs formed by PAA with molecular weights of 100 kg/mol (PAA-100k) and 450 kg/mol (PAA-450k) were more compact (Df of 1.418), while those formed by PAA with the molecular weight of 1250 kg/mol (PAA-1250k) were larger and random-shaped with loose and porous structure (Df of 1.179). The presence of 3 mg/g of PAA-1250k in aluminum oxide suspension increased the chord length of particles dramatically. Reasonable relationship was developed between settling velocity and chord length of flocs, and flocs with smaller fractal dimension and sediment compactness had faster sediment kinetics.

Reducing Membrane Fouling from Micro-Flocculation in a Humic Acid Ultrafiltration Process

This study investigated the influence of different floc morphologies produced by micro-flocculation process on filtration of a self-constructed polyvinylidene fluoride (PVDF) ultrafiltration membrane. Aluminum sulfate was used as a flocculant and humic acid (HA) and kaolin as raw water. Both the properties of flocs formed during the micro-flocculation process (floc size and distribution, fractal dimension) and the effects of floc formation on membrane flux under different conditions were investigated. The surface morphology of the contaminated membrane was characterized by scanning electron microscopy (SEM) and atomic force microscopy (AFM), and adhesion between the PVDF membrane and organic pollutants was measured to analyze the membrane fouling mechanism. Results showed that the main mechanism during a micro-flocculation process using Al3+ as a flocculant is electrical neutralization to remove organic matter. With an increase in flocculant dosage, floc size increased and the fractal dimension of flocs decreased. The attenuation rate of membrane flux was negatively correlated with floc size. The larger the floc, the lower the membrane flux attenuation rate, and the looser the filter cake layer formed during the ultrafiltration process. Comparatively, membrane fouling caused by flocs with smaller fractal dimension was lighter, and the membrane flux recovery rate was also higher. The interaction force between PVDF and organic matter was positively correlated with the corresponding membrane flux attenuation rate during the initial stage of operation. When dosage of Al3+ was 5 mg·L-1 and initial pH was 7, the HA removal rate was 96.7%, the membrane flux attenuation rate was lowest, and the flux recovery rate reached 88%.

Micro/nanoscale pore structure and fractal characteristics of tight gas sandstone: A case study from the Yuanba area, northeast Sichuan Basin, China

Abstract The pore size distribution (PSD) and fractal dimension are two typical parameters that are used to evaluate the heterogeneous characteristics of unconventional reservoir pores. The micro/nanoscale PSD and pore fractal-dimension characteristics of tight gas sandstones from the Upper Triassic Xujiahe formation in the Yuanba area were investigated by using nuclear magnetic resonance (NMR), nuclear magnetic resonance cryoporometry (NMRC), mercury injection capillary pressure (MICP) and scanning electronic microscopy (SEM) techniques. To date, no other attempts have been made to use NMRC with octamethylcyclotetrasiloxane (OMCTS) as a probe material to describe the pore fractal characteristics of tight gas sandstones. In this study, the fractal dimensions of tight gas sandstones were estimated by processing raw NMRC data with a fractal theoretical model, and the NMRC fractal results were compared to the calculated fractals from the MICP tube model, MICP sphere model and NMR T2 spectrum. The results consistently show that the pore fractal characteristics of tight sandstone samples from the Yuanba area exhibit multiple fractal structures at different pore-size ranges; large pores in the samples are more complex with rougher surfaces, and small pores correspond to smoother surfaces. Sandstones with greater porosity and pore space possess more heterogeneous structures. The PSD and fractal dimensions can be combined and used as an indicator for the presence of gas-bearing and dry formations in the study area. The tight sandstone samples from the dry formations have both lower porosities and smoother pore surfaces with smaller fractal dimensions; these characteristics may not be beneficial for the preservation of hydrocarbon fluids in the target area.

PORE-THROAT STRUCTURE AND FRACTAL CHARACTERISTICS OF SHIHEZI FORMATION TIGHT GAS SANDSTONE IN THE ORDOS BASIN, CHINA

In order to better understand the impact of fractal features of pore-throat structures on effective physical properties of tight gas sandstones, this paper carried out constant-rate mercury injection tests, gas–water permeability analyses, helium-based porosity and nitrogen pulse decay permeability measurements, and SEM and casting thin-section analyses on 20 sandstone samples of the Shihezi Formation from 16 wells of the Sulige Gas Field in the Ordos Basin, China. The fractal dimensions of pores corresponding to two pore radius ranges, namely fractal dimensions [Formula: see text] and [Formula: see text], and those of throats also corresponding to two throat radius ranges, namely fractal dimensions [Formula: see text] and [Formula: see text], were then calculated using the constant-rate mercury injection data. Fractal dimensions [Formula: see text] and [Formula: see text] are negatively correlated with the average pore radius and pore volume as well as quartz content, and they are positively related to contents of clay minerals and lithic fragments. Compared with pore fractal dimensions, throat fractal dimensions have lower correlations with throat structural parameters, and show vague relations with mineral compositions. Although the effects imposed by mineral compositions upon throat structures are similar to those upon pore structures, the flake-like and curved shapes of throats result in irregularity of fractal dimensions. Tight gas sandstones, with smaller fractal dimensions [Formula: see text] and [Formula: see text], have larger effective porosity, indicating that more gas volumes can be replaced by liquids. As for tight gas sandstones with lower fractal dimensions [Formula: see text] and [Formula: see text], the effective gas permeability is relatively high. In such cases, gas can flow more easily through the reservoir.

FRACTAL-BASED ANALYSIS OF THE INFLUENCE OF MUSIC ON HUMAN RESPIRATION

An important challenge in respiration related studies is to investigate the influence of external stimuli on human respiration. Auditory stimulus is an important type of stimuli that influences human respiration. However, no one discovered any trend, which relates the characteristics of the auditory stimuli to the characteristics of the respiratory signal. In this paper, we investigate the correlation between auditory stimuli and respiratory signal from fractal point of view. We found out that the fractal structure of respiratory signal is correlated with the fractal structure of the applied music. Based on the obtained results, the music with greater fractal dimension will result in respiratory signal with smaller fractal dimension. In order to verify this result, we benefit from approximate entropy. The results show the respiratory signal will have smaller approximate entropy by choosing the music with smaller approximate entropy. The method of analysis could be further investigated to analyze the variations of different physiological time series due to the various types of stimuli when the complexity is the main concern.

Airway morphology and inspiratory flow features in the early stages of Chronic Obstructive Pulmonary Disease

BackgroundChronic Obstructive Pulmonary Disease (COPD) is among the leading causes of death worldwide. Inhaled pollutants are the prime risk factor, but the pathogenesis and progression of the diseased is poorly understood. Most studies on the disease onset and trajectory have focused on genetic and molecular biomarkers. Here we investigate the role of the airway anatomy and the consequent respiratory fluid mechanics on the development of COPD. MethodsWe segmented CT scans from a five-year longitudinal study in three groups of smokers (18 subjects each) having: (i) minimal/mild obstruction at baseline with declining lung function at year five; (ii) minimal/mild obstruction at baseline with stable function, and (iii) normal and stable lung function over the five year period. We reconstructed the bronchial trees up to the 7th generation, and for one subject in each group we performed MRI velocimetry in 3D printed models. FindingsThe subjects with airflow obstruction at baseline have smaller airway diameters, smaller child-to-parent diameter ratios, larger length-to-diameter ratios, and smaller fractal dimensions. The differences are more significant for subjects that develop severe decline in pulmonary function. The secondary flows that characterize lateral dispersion along the airways are found to be less intense in the subjects with airflow obstruction. InterpretationThese results indicate that morphology of the conducting airways and inspiratory flow features are correlated with the status and progression of COPD already at an early stage of the disease. This suggests that imaging-based biomarkers may allow a pre-symptomatic diagnosis of disease progression.

Investigation of diamond wheel topography in Elliptical Ultrasonic Assisted Grinding (EUAG) of monocrystal sapphire using fractal analysis method

The wear behaviors of grinding wheel have significant influence on the work-surface topography. However, a comprehensive and quantitative method is lacking for evaluating the wear conditions of grinding wheel. In this paper, a fractal analysis method is used to investigate the wear behavior of resin-bonded diamond wheel in Elliptical Ultrasonic Assisted Grinding (EUAG) of monocrystal sapphire, and a series of experiments on EUAG and conventional grinding (CG) are performed. The results show that the fractal dimension of grinding wheel topography is highly correlated to the wear behavior, i.e., grain fracture, grain pullout, and wheel loading. An increase in cutting edge density on the wheel surface results in an increase of the fractal dimension, but an increase in the grain pullout and wheel loading results in a decrease in the fractal dimension. The wheel topography in EUAG has a higher fractal dimension than that in CG before 60 passes due to better self-sharpening behavior, and then has a smaller fractal dimension because of more serious wheel loadings after 60 passes. By angle-dependent distribution analysis of profile fractal dimensions, the wheel surface topography is transformed from isotropic to anisotropic. These indicated that the fractal analysis method could be further used in monitoring of a grinding wheel performance in EUAG.

Melting behaviors of PCM in porous metal foam characterized by fractal geometry

The fractal Brownian motion is introduced to describe the pore distribution of porous metal foam. By the fractal description, a model of melting heat transfer for the phase change material (PCM) is developed and applied to investigate the melting behaviors in porous metal foam with a particular focus on the role of pore distribution. The dynamic response of temperature and the evolution of melting front are presented. The effects of porosity and fractal dimension on the melting heat transfer are all examined and investigated. In addition, an experiment of melting heat transfer is performed to verify the present model. The results indicate that the porous metal foam is of significance for the enhancement of melting heat transfer. When compared with PCM alone, the melting process in porous metal foam possesses the larger melting rate, the faster evolution of melting front and the higher liquid fraction. Unlike the PCM alone, the melting front is no longer continuous and many independent solid-liquid interfaces are formed inside pores owing to the interstitial heat transfer. Interestingly, the melting phase change is also affected by the fractal dimension even though the porosity is identical. A porous metal foam with smaller fractal dimension is beneficial for the melting heat transfer.

Coal seam porosity and fracture heterogeneity of macrolithotypes in the Hancheng Block, eastern margin, Ordos Basin, China

Heterogeneity in cleats and pore size distribution within coal macrolithotypes (bright, semi-bright, semi-dull, and dull coals, determined from the overall relative luster and percentage of bright components) impact coalbed methane (CBM) extraction. However, few studies have investigated the characteristics of macrolithotypes across multiple length scales. Here, the macrolithotype description was performed for the No. 3, 5, and 11 coal seams in the Hancheng Block of Ordos Basin. The cleats were characterized by optical microscopy and X-ray computed tomography (CT) while pores and their connectivity were determined from mercury intrusion porosimetry, N2 and CO2 adsorption, and low field nuclear magnetic resonance (NMR) of water saturated cores evaluated both cleats and pores. The CH4 adsorption capacity of coal samples scraped from the surface of the macrolithotype layers was also determined. Dull lithotypes (semi-dull and dull) were dominant, followed by bright lithotypes (bright and semi-bright) in these seams. The bright lithotype coal has a higher microfracture density (averaging 339 microcleats per 9cm2, μm–mm), better connectivity, and a larger fractal dimension (averaging 1.7) from optical microscopy. The dull lithotype has a lower average microfracture density (272 microcleats per 9cm2) and a smaller fractal dimension (~1.6). This higher connectivity observation was consistent with X-ray CT observations and low field NMR of the water saturated cores (and the transition upon water removal from the fractures and larger pores). Also the ease of mercury injection from cores also supported higher connectivity in the bright lithotypes. Both the semi-bright and semi-dull lithotypes have equivalent pore proportions micro- to macropores and good apparent connectivity at the nm–μm scale; despite mineral occlusions. Based on the CH4 adsorption capacities of the macrolithotypes, the bright coal has the greatest gas adsorption capacity, due to the largest smaller micropores (<2nm) and a higher specific surface area. These observations aid in understanding the complex behavior observed in CBM extraction and evaluating the impacts of heterogeneity and scale on the degassing behavior.

Strength, fragmentation and fractal properties of mixed flaws

Experiments on Portland cement samples containing mixed flaws are conducted to investigate the strength, fragmentation and fractal properties. Flaw geometry is a new combination of two edge-notched flaws and an imbedded flaw, which is different from those in the previous studies, where parallel or coplanar flaws are used. The physical implications of the shear-box test applied to result to rock slopes are studied. The physical and analytical fragmentation characteristics of preflawed samples are analyzed through the sieve test and fractal theory, respectively. Three different patterns of tensile cracks and shear cracks are observed. A sliding crack model is presented to elucidate the brittle failure flaws. In all of the cases of the shear-box tests, the coalescence is produced by the linkage of shear cracks, and two types of coalescence (Type C1 and Type C2) have been classified, which tend to confirm the observations from the numerical model and field of jointed rock slopes. The shear strength is a function of the flaw geometry and the shear–normal stress ratio. The result of sieve tests indicates that the fragment size distribution of fragments has the fractal property, providing a physical understanding of the fragmentation mechanism. The fragments under the shear-box test have fractal dimensions between 2.2 and 2.6, which are larger than those under the compression test but similar to those in the fault cores. The fragmentation in the case of Type C2 has a smaller fractal dimension, corresponding to a larger shear strength.

Physicochemical Properties and Catalytic Performance of Sulphonic Resins of Various Morphological Types in Ethyl t-Butyl Ether Synthesis

Physicochemical and catalytic properties of sulphonic resins of various morphological types in ethyl t-butyl ether synthesis were studied. We have found that the turnover frequency (TOF) of sulphonated cation-exchange resins reflects the effect of morphology expressed in terms of fractal geometry. The correlation between the catalytic activity of various types of sulphonated resins and their fractal dimension was established. Difference in observed TOF of sulphonic resins of various morphological types is caused by various accessibilities of acid sites. Catalysts of more ordered structure (characterized by smaller fractal dimension) provide the best conditions for the adsorption–desorption of reactants and products resulting in large values of TOF.

Size distribution and particle shape of iron ore powder based on the fractal theory

The size distribution and particle shape of various iron ores are measured in this paper, then the ballability index and compression strength of green pellet of different iron ores are examined. The particle fractal dimensions of particle size distribution and texture are calculated based on fractal theory. Research shows that the size distribution of iron ores has obvious fractal characters. The fractal dimension of size distribution is significantly related with balling index and specific surface area of particle. Particle shape can be characterised by texture fractal dimension. At the same size level, smaller fractal dimension means smoother particle and smaller compression strength of pellet. The relationship between the texture feature parameters and compressive strength of the pellet is obtained.

Comparative Study of Artificial Neural Networks and Wavelet Artificial Neural Networks for Groundwater Depth Data Forecasting with Various Curve Fractal Dimensions

The objective of this study was comparative study of artificial neural networks (ANN) and wavelet artificial neural networks (WANN) for time-series groundwater depth data (GWD) forecasting with various curve fractal dimensions. The paper offered a better method of revealing the change characteristics of GWD. Time series prediction based on ANN algorithms is fundamentally difficult to capture the data change details, when the time-series GWD data changes are more complex. For this purpose, Wavelet analysis and fractal theory methods are proposed to link to ANN models in predicting GWD and analysis the change characteristics. The trend and random components were separated from the original time-series GWD using wavelet methods. The fractal dimension is convenient for quantitatively describing the irregularity or randomness of time series data. Three types of training algorithms for ANN and WANN models using a Mallat decomposition algorithm were investigated as case study at three sites in the Ganzhou region of northwest China to find an optimal model that is suitable for certain characteristics of time-series GWD data. The simulation results indicate that both WANN and ANN models with the Bayesian regularization algorithm are accurate in reproducing GWD at sites with smaller fractal dimensions. However, WANN models alone are suitable for sites at which the fractal dimension of the wavelet decomposition detail components is larger. Prediction error is also greater when the fractal dimension is larger.

Supersonic flow over circular protuberances on a flat plate

The nanotracer planar laser scattering (NPLS) technique is used to test the flow field of Mach 3.0 supersonic flow over circular protuberances. The protuberance heights (H) are 1, 2, and 4 mm, and the diameters (D) are all 4 mm with the Reynolds number of 7.7 × 106/m, while the thickness of the laminar boundary layer (δ) is about 1.2 mm at the mounting position, corresponding to H/δ values of 0.83, 1.67 and 3.33. The fine structures in the symmetrical plane of the flow field around the cylinders are imaged. In the NPLS images, expansion wave, three-dimensional bow-detached shock wave, reattachment shock wave and separation region ahead of the cylinders are clearly visualized. The spatial and temporal evolution characteristics of the vortex structures are analyzed. Special attention is paid to the study of the wake flow and the influence of the height of the protuberances on the wake flow, showing that vortices in the wake flow of the 1-mm high cylinder are isolated and simple, while to the 4-mm high cylinder are complex and mixed-up with less periodicity. After reattachment, the lower cylinder has a relatively longer laminar section as well as transition section. Fractal analysis is done on the wake flow, indicating that higher protuberances tend to have a larger fractal dimension and increasing slope. Based on the average fractal dimension of 50 NPLS images, the 2- and 4-mm cylinders have a close value while the 1-mm cylinder which is submerged in the boundary layer has a much smaller fractal dimension. Streamwise pressure distributions are measured both upstream and downstream, and the results show that the influence extent tends to depend little on the height of the cylinder. While the H/D values only influence on the size of the plateau region and the pressure increasing slope.

Impact of polymer flocculants on coagulation-microfiltration of surface water

Organic polymers are widely used as flocculants in pretreatment for microfiltration. However, their impact on microfiltration system performance was not well understood. In this study, the effects of three types of polymer flocculants on microfiltration permeate water quality and membrane fouling were evaluated using a hollow fiber membrane under two different operation modes, coagulation/flocculation-sedimentation-microfiltration (CFSM) and coagulation/flocculation-microfiltration (CFM). Interestingly, the effect of polymers on membrane fouling did not appear to reflect their impact on dissolved organic matter content or floc particle properties in the membrane feed water. The addition of polymer flocculants resulted in floc particles of larger size and smaller fractal dimension and slightly enhanced the removal of dissolved organic matter, both of which were expected to reduce membrane fouling. However, it significantly aggravated membrane fouling in all cases except when the positively charged poly(diallyldimethylammonium) chloride was used in the CFSM process. In particular, all polymers greatly increased hydraulically irreversible fouling in the CFM mode. The increased fouling in the CFSM mode is attributed to the residual polymer, while that in the CFM mode is attributed to the enhanced irreversible floc particle attachment on the membrane surface. Considering the potential severe membrane fouling and the small improvement in treated water quality when polymers are used, the application of polymers in microfiltration pretreatment needs to be carefully evaluated.

Structural Changes in the Retinal Microvasculature and Renal Function

To evaluate the associations between chronic kidney disease (CKD) and microalbuminuria, and a comprehensive range of retinal microvascular abnormalities including traditional and new retinal vascular measures. This was a population-based, cross-sectional study on 3280 urban Malay adults. The albumin/creatinine ratio (ACR) was calculated from spot urine samples. Estimated glomerular filtration rate (eGFR) was calculated from serum creatinine concentration. Retinal vascular caliber and geometry were quantified from retinal fundus photographs using a semiautomated computer-assisted program. Qualitative changes including focal arteriolar narrowing, arteriovenous nicking, and opacification of the arteriolar wall were assessed by trained graders. In multivariate analyses adjusting for age, sex, hypertension, diabetes, and smoking, narrower retinal arteriolar caliber (P = 0.008), smaller retinal vascular fractal dimensions (P = 0.014), and the presence of AV nicking and opacification (P = 0.005 and P < 0.001, respectively) were significantly associated with lower eGFR. In multivariate adjusted logistic regression analyses, none of the retinal markers was associated with CKD. A smaller fractal dimension (P < 0.001) and the presence of focal arteriolar narrowing, AV nicking and opacification were associated with higher ACR (P < 0.001, P = 0.01, and P = 0.002, respectively). Narrower retinal arterioles (P = 0.041); smaller fractal dimensions (P = 0.006); and focal arteriolar narrowing, AV nicking, and opacification (P = 0.007, P = 0.007, and P = 0.012, respectively) were associated with higher likelihoods of having microalbuminuria. Quantitative changes of the retinal vascular geometry and qualitative changes in the vessel architecture are associated with markers of renal dysfunction and damage.