This work proposes a fractal Hilbert curve-based low-cost, easy-to-fabricate, highly sensitive, and noninvasive microwave sensor for the dielectric characterization of liquids. The sensor's design ...comprises the second iteration of Hilbert curve fractal geometry and is fabricated on low-cost FR-4 material with an overall dimension of <inline-formula> <tex-math notation="LaTeX">0.28\,\,\lambda _{{0}} \times 0.224\,\,\lambda _{{0}} \times 0.012\,\,\lambda _{{0}} </tex-math></inline-formula>. The liquid-under test (LUT) is placed in a closed vicinity of the high electric field region to achieve better sensitivity. The central operating frequency of the sensor is 3.035 GHz for air, and the variation in resonant frequencies of a range of liquids is observed to determine their respective dielectric characteristics. A maximum shift of 1.68 GHz in the resonant frequency was observed for deionized water, and a maximum <inline-formula> <tex-math notation="LaTeX">{Q} </tex-math></inline-formula>-factor of 283.14 was observed for ethanol. The curve fitting technique determines the values of the dielectric constant and loss tangent. For various considered cases in the dielectric permittivity range of 1-79, the root-mean-square errors of retrieved parameters are found to be less than 0.1%. Our proposed design with affordability, compact footprint, and ease of operation exhibits superior performance over the state-of-the-art in terms of sensitivity for the characterization of a wide range of liquid materials.
Abstract
In cold regions, progressive cracking, caused by freeze–thaw cycles, plays an important role in deteriorating engineering rock mass. Employing central cracked Brazilian disks (CCBDs) of ...sandstone, this paper aims at investigating the variations of falling rate among different modes of fracture toughness exposed to freeze–thaw cycles and the applicability of fracture criterion in predictions. Results revealed that different modes of fracture toughness exhibited comparable descending trends after varied freeze–thaw cycles. There was an agreement between the predictions via the generalized maximum tangential stress criterion (GMTS) and the test results. In specified conditions, the GMTS criterion incorporating fracture process zone of 0 freeze–thaw cycle can be applied to estimations for different freeze–thaw cycles. With increasing freeze–thaw cycles the fractal dimensions of mode I and mixed‐mode I–II fracture surfaces displayed a growing trend, indicating that the fracture surfaces became rougher and more complicated.
Highlights
Falling rates of fracture toughness of sandstone after freeze–thaw cycles were studied.
The generalized maximum tangential stress criterion offered viable predictions.
Fracture process zone had limited effects on fracture locus in specified conditions.
Mode I and mixed‐mode I–II surfaces became rougher with growing freeze–thaw cycles.
Glaucoma is one of the leading causes of vision loss worldwide. It leads to reduced quality of life for individuals and substantial economic loss for society. This problem can be reduced by the early ...and reliable diagnosis of glaucoma. The traditional instrument-based methods are nonautomated and laborious. Recently, many computer-based approaches have been proposed for glaucoma detection. However, none of the existing approaches can be efficiently used for the classification of glaucoma stages. In this study, we proposed a novel method to classify the glaucoma stages (healthy, early-stage, and advanced-stage) using a 2-D compact variational mode decomposition (2-D-C-VMD) algorithm. In this work, the preprocessed input images are first decomposed into several variational modes (VMs) employing 2-D-C-VMD. Next, various features, namely, Kapur entropy (KE), Renyi entropy (RE), Shannon entropy (SE), Yager entropy (YE), energy (En), and fractal dimension (FD) features, which are extracted from the first VM. Then, linear discriminant analysis (LDA) has been used for dimensionality reduction. Finally, a trained multiclass least-squares-support vector machine (MC-LS-SVM) classifier has been utilized for classification purpose. The proposed approach has been tested on two different public glaucoma database. Our method achieved the highest classification accuracy of 98.11% with tenfold cross-validation. The experimental results show that the proposed approach performed far better as compared to state-of-the-art approaches.
As there is a great demand of 2D metal networks, especially out of gold for a plethora of applications we show a universal synthetic method via phase boundary gelation which allows the fabrication of ...networks displaying areas of up to 2 cm2. They are transferred to many different substrates: glass, glassy carbon, silicon, or polymers such as PDMS. In addition to the standardly used web thickness, the networks are parametrized by their fractal dimension. By variation of experimental conditions, we produced web thicknesses between 4.1 nm and 14.7 nm and fractal dimensions in the span of 1.56 to 1.76 which allows to tailor the structures to fit for various applications. Furthermore, the morphology can be tailored by stacking sheets of the networks. For each different metal network, we determined its optical transmission and sheet resistance. The obtained values of up to 97 % transparency and sheet resistances as low as 55.9 Ω/sq highlight the great potential of the obtained materials.
Stacked fractals: 2D gold mesh‐like gels with areas of up to 2 cm2 are synthesized via phase boundary gelation. The structures are described as fractals. By variation of experimental details, web thicknesses between 4.1 nm and 14.7 nm are achieved. The networks can be stacked or transferred to different substrates.
Neuro-degenerative diseases influence significantly the gait behavior and the ability to move. To explore the etiology of neuro-degenerative disease, it would be useful to characterize gait dynamics. ...The purpose of this study is to classify different neuro-degenerative diseases using fractal geometry. We use Gait Dynamics in Neuro-Degenerative Disease Data Base including recordings from patients with Parkinson's disease (n = 15), Huntington's disease (n = 20), or amyotrophic lateral sclerosis (n = 13) and 16 healthy control subjects are also included (Hausdorff JM et al., 2000). The vibration analysis using power spectral densities (PSD) method has been carried out to discover whether some type of power-law scaling exists for various statistical moments at different scales of these databases. Using Discrete Wavelet Transform (DWT) and Wavelet Leader Multifractal (WLM) analysis, we explore the possibility that these recordings belong to the class of multifractal process for which a large number of scaling exponents are required to characterize their scaling structures. A non-linear analysis called the Fractal Dimension (FD) using Higuchi algorithm has been performed to quantify the fractal complexity of recordings. According to our results, we noticed that neither the power spectral densities nor the Higuchi algorithm to find the fractal dimension alone were sufficient to separate different classes of patients and healthy people. In addition, when multifractal analysis and scaling exponent were used as a classifier, the three classes could not be well separated. However, this study revealed that we have a wide range of exponents for some of the gait recordings which indicates they have multifractal structure and they need to be indexed by different exponents as we decompose them into different subsets. In other words, these multifractal subjects require much more exponents to characterize their scaling properties compared to monofractal gait recordings which their spectrum displays a narrow width of scaling exponent. Another important outcome from our multifractal analysis is recognizing obvious changes in the shape of D(h) curves for some of the gait recordings which is crucial in finding the best strategies to better controlling the gait mechanisms in different neuro-degenerative diseases. Although the vibration analysis, fractal dimension and multifractal analysis may not be able to classify gait recordings, however, they can be used as comprehensive frameworks to further analysis, characterize and compare the complexity and fractal behavior of gait recordings and data structures of different neuro-degenerative diseases in clinical database. Likewise, beside the Higuchi algorithm to find the fractal dimension as a complexity measure for the gait recordings, it will require much more efforts and further clinical analysis to find a specific threshold which make the fractal dimension to be considered as a biomarker and diagnosis tool for different neuro-degenerative diseases.
•Neuro-degenerative diseases influence significantly the gait behavior and the ability to move. To explore the etiology of neuro-degenerative disease, it would be useful to characterize gait dynamics.•The purpose of this study is to classify different neuro-degenerative diseases using fractal geometry.•The vibration analysis using power spectral densities (PSD) method has been carried out to discover whether some type of power-law scaling exists for various statistical moments at different scales of these databases.•Using Discrete Wavelet Transform (DWT), we explore the possibility that these recordings belong to the class of multifractal process with a large number of scaling exponents required to characterize their scaling structures.•A non-linear analysis called the Fractal Dimension (FD) using Higuchi algorithm has been performed to quantify the fractal complexity of recordings.
To reveal the influence of pore structure of coal on the characteristics of coal dust generation during roadheader cutting, a self-developed coal cutting system was used to generate dust. A low field ...nuclear magnetic resonance was utilized to measure the pore system of coal. Results show that the porosity had negative correlations with the cumulative proportions of both respirable dust and fine particulate matter (PM2.5), but the positive influence on the mass ratio of dust generation (MRD) of total dust and slight effect on MRD of respirable dust and PM2.5 were observed. The correlations of the fractal dimension (Df) of pore structure on dust generation were inverse compared with that of porosity. The negative relationship between porosity and Df was the reason for the opposite correlations. This study can provide basic support for the estimate of dust hazard and the development of dust control technologies.
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•Pore structure of coal sample was tested by a low field nuclear magnetic resonance.•The cumulative proportion of respirable dust reduced with increasing porosity.•The amount of total dust generation grew with increasing porosity.•The effect of fractal dimension of pore on dust generation is contrary to porosity.
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•A fractal model considering crack area to calculate the total surface area of fragments was proposed.•The fractal characteristics of coal particles using different crushing methods ...were discussed.•Three classical comminution laws were examined by the experimental results.•The surface energy of the coal particles from Yaojie coal mine calculated by different methods was obtained.
The crushing energy of coal plays an important role in mining, gas extraction, occurrence of outburst accidents, and coal pulverisation engineering. To calculate the crushing energy of coal, a fractal model considering the crack area was established. The fractal fragmentation distribution and the fractal crack distribution, with their fractal dimensions (Df and Ds) calculated from the particle size distribution, were used to calculate the new specific surface area (SSA) of coal after crushing. Two different experimental methods, quasi-static compression on a single particle (strain rate: 0.0005–0.001 s−1) and dynamic impact on particles (strain rate: 300 s−1), were used to crush coal particles to particle size of 2–3 mm. The experimental results show that Df for coal particles under quasi-static compression (QSC) and dynamic impact (DI) are 1.44–1.85 and 1.9–2.74, respectively. Df increases significantly with the crushing ratio, and there is a limit value, which is defined as Ds. Ds measured by QSC and DI were 1.87 and 2.75, respectively. The SSA of a single particle obtained by the proposed fractal model increases with the decrease in the particle size, which can be highly consistent with the BET SSA by fitting. The surface energy of coal particles under QSC and DI calculated by the traditional theory, which does not take into account the crack area, is 240.10 J/m2 and 180.92 J/m2, respectively, independent of the crushing ratio. The surface energy calculated by the fractal model is 3.55 J/m2, taking into account the frictional heat.
To investigate the static mechanical properties and failure characteristics of damaged rocks after impact under realistic in-situ stress, dynamic triaxial compression tests with different strain ...rates and confining pressures were conducted on diorite by a modified split Hopkinson pressure bar. The damage factor was calculated according to the change of the longitudinal wave velocity of rocks before and after the impact, and the residual strengths of the damaged diorite were obtained by uniaxial compression and Brazilian tensile tests. In addition, three brittleness indexes based on the residual strength were adopted to evaluate the brittleness of damaged specimens, and fractal dimension was introduced to study the fragmentation characteristics. The results show that the dynamic peak stress, strain, elastic modulus, damage factor and plastic deformation of diorite all increase with increasing strain rate, i.e., rate dependence, and the increasing rate decreases with increasing confining pressure. The increment in confining pressure leads to the increase of dynamic peak stress, elastic modulus, static residual strength and brittleness, and the increasing rate increases with increasing strain rate, while other physio-mechanical parameters decrease with confining pressure. The post-peak behavior of dynamic stress-strain curves is divided into two classes according to the strain rate and fracture state of rocks under dynamic loading. Upon the strain rate increases above 87 s−1, the brittleness of damaged specimens generally decreases to moderately brittle or even low brittle, and the corresponding drillability becomes much easier. The fractal dimension of damaged specimens increases with the increase of confining pressure and decreases linearly with the increase of strain rate.
A microchannel reactor with porous surface for hydrogen production can enhance fluid flow and heat transfer characteristics. To improve the fluid flow and heat transfer characteristics of a ...microreactor with a porous surface, a numerical model is proposed based on fractal geometry. The porous surface in the microreactor is fabricated using a layered powder sintering and dissolution method with NaCl particles, in which two sizes of NaCl particles (180–280 μm and 280–450 μm) are utilized. For the construction of the porous surface, these two types of fabricated surfaces are measured and the fractal dimensions are characterized as 1.905 and 1.849, respectively. Subsequently, a numerical model based on fractal geometry for a microchannel reactor with porous surface is developed to study the fluid flow and heat transfer characteristics. This is followed by the microchannel reactor fabrication and experimental testing. Both model calculation and experimental results demonstrate that a microreactor with a porous surface can enhance the heat transfer performances compared with that with a non-porous surface, and that a microchannel reactor fabricated with larger NaCl particles (280–450 μm) has better heat transfer characteristics compared with a microreactor with small NaCl particles (180–280 μm). Thus, the developed numerical model based on fractal geometry can be used to accurately predict the fluid flow and heat transfer characteristics of the microreactor for hydrogen production.
•A numerical model based on fractal geometry was proposed.•The porous surface can enhance the heat transfer performance.•The microreactor with larger NaCl particles has better heat transfer performance.
Rock burst is a serious geological hazard in deep underground mines affecting progress of mining operations. Although rock burst is a complex process, a distribution law of fractal characteristics ...can explain the rock failure mechanism. Using a servo-controlled testing system, uniaxial cyclic loading tests on coal rock specimens were conducted to investigate the fractal characteristics of the fragments under different loading rates. To comprehensively characterize the coal fragments of different sizes, samples were divided into four groups of different size: particles, fine, medium-size, and coarse fragments. The distribution of the fragments under uniaxial cyclic loading conditions was then investigated based on the theory of fractal geometry, and the relationships between fractal dimensions and loading rates. Under uniaxial cyclic loading and unloading conditions, most of the fragments are irregular wedges and bulks, exhibiting obvious shape characteristics. Under various loading rates, the length-quantity fractal dimensions of the coal fragments ranged from 0.74 to 1.44, the width-quantity fractal dimensions range from 0.44 to 1.65, and the thickness-cumulative mass fractal dimensions range from 1.0 to 1.33. The coal rock’s crushing size-mass fractal dimensions under different loading rates were 2.27, 2.30, 2.32, and 2.35, respectively. Under a small loading rate, the dimension-quantity fractal dimensions are relatively small, suggesting that the coal rock was less crushed, with large fragments differing greatly in length, width, and thickness. The results show that the coal rock fragments exhibit certain shape characteristics after the cyclic loading, like irregular shapes and wedges. Under a larger loading rate, the fragments showed greater fractal dimensions of both size and mass; the coal samples crushed more thoroughly with more uniform fragments in length, width, thickness and mass. The conclusions obtained in this study confirm the classification and fractal characteristics of coal rock fragments by uniaxial cyclic loading conditions in laboratory test and provide the basis for further study on the mechanism of rock burst. This study is helpful for us to make a thorough inquiry the danger degree of rock burst in coal mine by using fractal geometry, understand the effects of methane to coal and the evolution mechanism of cracks, and it can be applied to the research on occurrence mechanism and early warning of rock burst.
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