One of the most important issues to be decided in the analysis of time series is to determine their variability and to identify the process of shaping their values. In the classical approach, ...volatility is most often identified with the variance of growth rates. Meanwhile, the nature of risk is not only the variability, but also the predictability of changes, which can be assessed using the fractal dimension. The aim of the article is to present the application of the fractal dimension estimated by the surface division method to evaluate the variability of time series. The paper presents the method of determining the fractal dimension, its interpretation, the significance table and the application example. Specific cases show differences between the use of standard deviation and the fractal dimension for risk assessment. The fractal dimension appears here as a method to assess the degree of stability of variations. This article is an extension of the previously presented method for discrete time series to continuous time series.
Shale matrix pore structure controls the gas storage mechanism and gas transport behaviors. We employed various techniques to characterize the complex pore structures of 12 shale samples collected ...from two marine shale formations in upper Yangtze area (UYA) in China. The characterization techniques include field emission scanning electron microscopy (FE-SEM), high-pressure mercury intrusion porosimetry (MIP), and low-pressure N2/CO2 adsorption. The excess methane adsorption capacity was measured for each sample and the results were modeled using Langmuir model. Based on the FE-SEM image analyses, micro- and meso-pores within organic matter and inter-particle pores between or within clay minerals are the most commonly developed in these shale samples. Both uni- and multi-modal pore size distributions (PSDs) were observed, and a significant portion of pores are in the pore size range between 3 and 100nm. It was also found that the micropore (<2nm) is the major contributor to the overall specific surface area (SSA), whereas most of the pore volume is occupied by mesopores (2–50nm). Two different fractal dimensions, pore surface fractal dimension (D1) and spatial geometry fractal dimension (D2), were estimated from low pressure N2 isotherms, with D1 ranging between 2.469 and 2.682, and D2 ranging between 2.576 and 2.863, indicating that the surface and volume of pore structure are heterogeneous. Samples with higher D1 can provide more adsorption sites for methane and tends to have relatively high adsorption capacity, whereas shales with higher D2 do not influence the gas adsorption and storage capacities. Methane adsorption capacity increases with the increase of both micropore volume and micropore surface area, and this confirms that microporosity is the governing factor on methane adsorption capacity and storage.
•Three types of hybrid nanofluids, composite, Janus and dual nanofluid, have been studied by MD.•The highest TC of composite nanofluids in mono-particle system is attributed to Brownian motion.•Why a ...moderate DOL has a larger TC is discussed.•Enhanced reliability of TC results is achieved from the multi-particle systems including >32 nanoparticles.
More and more applications of hybrid nanofluids are emerging in various fields such as energy engineering, chemical engineering, and automotive engineering. However, the existing literature only employs the term "synergistic effect" to explain the improvement of thermal conductivity of hybrid nanofluids. In order to elucidate the underlying reasons behind the improvement in thermal conductivity of hybrid nanofluids compared to that of conventional ones (mono nanofluids), molecular dynamics simulations were conducted to examine three types of hybrid nanofluids, including Ag-Cu nanocomposites, Au-Cu Janus nanoparticles, and Ag-Cu binary nanoparticles. The results suggest that hybrid nanofluids including Ag-Cu nanocomposites, Au-Cu Janus nanoparticles, and Ag-Cu binary nanoparticles improve the thermal conductivity of 2 vol% nanofluid by 34.3 %, 12.1 %, and 10.4 %, respectively, compared to Cu monofluid. The improvement in thermal conductivity for hybrid nanofluids containing nanocomposites in single-particle systems can be attributed primarily to the stronger Brownian motion, while the improvement in thermal conductivity for hybrid nanofluids containing Au-Cu Janus nanoparticles and Ag-Cu binary nanoparticles is due to the looser aggregation morphology in multi-particle systems. This observation allows us to appreciate the significance of aggregation morphology as a crucial mechanism when considering interactions between nanoparticles. It provides a theoretical basis for the preparation of high-performance nanofluids as heat transfer media.
•Improve fractal dimension estimation by including the color intensities.•Known fractal geometries can be exactly estimated using this proposed method.•There is evidence viruses can be classified ...into families by their fractal dimension.
Current methods of fractal analysis rely on capturing approximations of an images’ fractal dimension by distributing iteratively smaller boxes over the image, counting the set of box and fractal, and using linear regression estimators to estimate the slope of the set count line. To minimize the estimation error in those methods, our aim in this study was to derive a generalized fractal feature that operates without iterative box sizes or any linear regression estimators. To do this, we adapted the Minkowski-Bouligand box counting dimension to a generalized form by fixing the box size to the smallest fundamental unit (the individual pixel) and incorporating each pixel's color channels as components of the intensity measurement. The purpose of this study was twofold; to first validate our novel approach, and to then apply that approach to the classification of detailed, organic images of viruses. When validating our method, we a) computed the fractal dimension of known fractal structures to verify accuracy, and b) tested the results of the proposed method against previously published color fractal structures to assess similarity to comparable existing methods. Finally, we performed a case study of twelve virus transmission electron microscope (TEM) images to investigate the effects of fractal features between viruses and across the factors of family (Orthomyxoviridae, Filoviridae, Paramyxoviridae and Coronaviridae) and physical structure (whole cell, capsid and envelope). Our results show that the presented generalized fractal feature is a) accurate when applied to known fractals and b) shows differing trends to comparable existing methods when performed on color fractals, indicating that the proposed method is indeed a single-scale fractal feature. Finally, results of the analysis of TEM virus images suggest that viruses may be uniquely identified using only their computed fractal features.
Any physical laws are scale-dependent, the same phenomenon might lead to debating theories if observed using different scales. The two-scale thermodynamics observes the same phenomenon using two ...different scales, one scale is generally used in the conventional continuum mechanics, and the other scale can reveal the hidden truth beyond the continuum assumption, and fractal calculus has to be adopted to establish governing equations. Here basic properties of fractal calculus are elucidated, and the relationship between the fractal calculus and traditional calculus is revealed using the two-scale transform, fractal variational principles are discussed for 1-D fluid mechanics. Additionally planet distribution in the fractal solar system, dark energy in the fractal space, and a fractal ageing model are also discussed.
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Rocks are commonly used as building stone and construction materials in many engineering applications. They usually undergo cyclic wetting and drying processes due to the periodical variations in ...moist conditions. In this paper, to understand the deterioration on the tensile strength of sandstone induced by wetting and drying cycles, dynamic Brazilian disc tests were conducted on sandstone specimens after every 10 cycles (for a total of 50 cycles) under a wide range of loading rates using a modified split Hopkinson pressure bar (SHPB) technique. Test results revealed that at the same loading rate, the dynamic tensile strength of specimens decreased with the number of wetting and drying cycles. Microscopic morphological structure on the sandstone surface were also obtained by scanning electron microscope (SEM), the characteristics and fractal analysis indicated that cyclic wetting-drying treatments would result in accumulative crack damage in rock, which was considered as the primary reason for the reduction in strength. Moreover, a decay model considering the effects of loading rate and cyclic wetting and drying deterioration was established to predict the dynamic tensile strength of sandstone after wetting and drying cycles. The forecast data via the decay model matched the trends of the experimental results well, meaning that the decay model was valid and applicable for the strength prediction.
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•The in-situ pore and surface morphological characteristics of coal before and after biodegradation were discovered by SEM.•Pore and molecular structure parameters modified by ...microbes were quantitatively displayed.•Destroying aliphatic side chains and dissociating small molecular clusters cause the modification of coal pore structure.
The aim of microbially-enhanced coalbed methane (MECBM) generation is to replicate the natural process of microbial methane production in coal seams and to increase coalbed methane production. However, a systematic evaluation of the response of coal structure during biogasification is still lacking. Here, alternations of the pore and molecular structures were investigated during the bioconversion of coal to methane using proximate/ultimate analysis, scanning electron microscope, low-field nuclear magnetic resonance (LNMR), low-pressure nitrogen adsorption (LPNA), micro-Fourier transform infrared spectroscopy (FTIR) and X-ray diffraction (XRD) techniques. The results showed that MECBM is a process of carbon enrichment, nitrogen/sulfur fixation and dehydrogenation/deoxygenation. Moreover, microbial modify coal pore structure by destroying aliphatic side chains, dissociating small molecular clusters and reducing the degree of aromaticity. These changes in the coal pore structure result in the “loose” of the coal reservoir spatial structure. We found that micropores (<10 nm) became transition pores (10–100 nm) and mesopores (100–1000 nm) after microbial degradation, which then led to the increase of the average pore width and the reduction of the specific surface area. This process benefits the desorption and transportation of coalbed methane. In addition, the surface fractal dimension decreased, and the volume fractal dimension increased according to the fitting date of LPNA. The fractal dimension of transition pores and mesopores increased of most coal after biotreatment based on NMR. These results led us to draw the hypothesis that the organic compounds formed by biodegradation may adhere to the pores, thus blocking the pores, making the structure of transition pores and mesopores complex, as demonstrated by the SEM images. This phenomenon is thought to be improved by continuous degradation or water movement.
In this study, we have investigated whether fractal dimension is a useful non linear feature for distinguishing electroencephalogram (EEG) of cases with encephalopathy from that of normal healthy ...EEGs. Both Higuchi’s fractal dimension and Katz’s fractal dimension were computed and were statistically analyzed between the normal and disease groups. Both parameters showed significant difference between the normal and encephalopathy groups, though Higuchi’s fractal dimension showed better discriminating ability. Support Vector Machine (SVM) classifier was also applied for the automated diagnosis of encephalopathy based on EEG. It has been found that SVM classifier performed better when Higuchi’s fractal dimension was utilized as feature set than using both Higuchi’s and Katz’s FD together.
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•Water immersion treatment can significantly enhance the wettability of coal dust.•The primary cause for the enhancement in wettability is the increase in hydroxyl content.•The ...fractal dimension of particle size distribution is inadequate to characterize the wettability of coal dust.
In order to enhance the understanding of the wetting mechanism of coal dust and explore additional approaches to improve the wettability of hydrophobic coal dust. Two coal dust samples with different particle sizes were selected and subjected to water immersion treatments. The wetting behavior of coal dust was investigated through a sinking experiment, focusing on the effects of the water immersion process, immersion time, and particle size. Fourier-transform infrared spectroscopy was employed to analyze the changes in functional groups of coal dust during the water immersion process. The results indicated a significant improvement in the wettability of coal dust after a short-term water immersion treatment, and this enhancement effect can be synergistic with the action of surfactants. The increase in hydroxyl content was identified as a crucial factor in enhancing the wettability of coal dust after water immersion. Moreover, the limitations of using the fractal dimension of particle size distribution to characterize the wettability of coal were explored. The results indicated that coal dust with similar fractal dimensions could exhibit significant differences in wettability, suggesting the need for further investigation into the effects of particle size polydispersity and other particle size parameters on coal dust wettability.
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