Narrow Results

X-ray computed tomography (CT) scanning method is the most accurate method to construct digital core, which can reflect the microscopic pore structure of real cores; therefore, it is widely used and researched by experts and scholars all over the world. However, there are few reports about how to select the CT scan core samples at present, and the current practice is to make CT scan samples by visually observing rocks or core columns to select a region that is considered representative or interesting, which can lead to a large difference between the selected sample and the whole rock and a digital core that cannot represent the real rock as a whole. In order to construct the digital cores that can reflect the whole rock structure and reservoir properties, combining with fractal theory, a scientific and reasonable method was proposed to select representative rock samples for digital core modeling. First of all, a core column is scanned by X-ray CT at a certain resolution and CT gray scale images are obtained and stored in the order of scan. Secondly, the fractal dimension (FD) of each image is calculated by box-counting method, and the calculated porosity of each image is achieved by the existing formula. Then, according to the size of the digital core to be constructed, the CT gray scale images are grouped, and the average FD and the average porosity of each combination are calculated by the derived equations. Finally, based on the proposed criteria the best image combination is selected and the preferred sample is determined accordingly. At the same time, a facile experiment was conducted to test the effectiveness of this method. The experimental results show that there are some errors between the subjectively selected cores and the long core in terms of permeability and porosity, and the petrophysical parameters of the core selected by the proposed method are close to those of the long core; as a consequence, the validity of this method was verified and it is feasible and practical to select the representative rock samples for digital core modeling by this method.

Based on the basic principle of the porosity method in image segmentation, considering the relationship between the porosity of the rocks and the fractal characteristics of the pore structures, a new improved image segmentation method was proposed, which uses the calculated porosity of the core images as a constraint to obtain the best threshold. The results of comparative analysis show that the porosity method can best segment images theoretically, but the actual segmentation effect is deviated from the real situation. Due to the existence of heterogeneity and isolated pores of cores, the porosity method that takes the experimental porosity of the whole core as the criterion cannot achieve the desired segmentation effect. On the contrary, the new improved method overcomes the shortcomings of the porosity method, and makes a more reasonable binary segmentation for the core grayscale images, which segments images based on the actual porosity of each image by calculated. Moreover, the image segmentation method based on the calculated porosity rather than the measured porosity also greatly saves manpower and material resources, especially for tight rocks.

Foam fluid has found wide applications in oilfield development, such as profile control, water plugging, gas channeling control, fracturing, and so on. As a non-Newtonian fluid, the successful application of foam is significantly influenced by its structure. The foam texture, however, is complex and irregular, and becomes even more complicated in porous media by the boundary effects. Therefore, the description of dynamic foam structure is crucial and a quantitative description method for foam fluid is worth exploring. In this paper, the fractal characteristics of foam in porous media are verified and combined with foam microdisplacement experiment, and the fractal rule of foam is found. The relationship between fractal dimension and pressure is also discussed. The results show that foam has dynamic fractal characteristics during transport in porous media and the box-counting fractal dimension ranges from 1 to 2. Furthermore, the dynamic change of foam fractal dimension during transport in porous media could be divided into three stages. In the first stage when no foam forms, the fractal dimension is about 2; in the second unsteady foam stage, the fractal dimension is reduced from 1.9 to 1.6; the last one is the steady stage and the fractal dimension is almost constant (about 1.6). Besides, the fractal dimension of foam fluid is closely related to displacement pressure. Low pressure corresponds to higher fractal dimension, and high pressure corresponds to lower fractal dimension. Pressure is negatively linearly correlated with fractal dimension. These results are expected to enrich the understanding of the foam dynamic characteristics in their advanced applications.

The fracture has great impact on the flow behavior in fractured reservoirs. Fracture traces are usually self-similar and scale-independent, which makes the fractal theory become a powerful tool to characterize fracture. To obtain three-dimensional (3D) digital rocks reflecting the properties of fractured reservoirs, we first generate discrete fracture networks by stochastic modeling based on the fractal theory. These fracture networks are then added to the existing digital rocks of rock matrixes. We combine two low-permeable cores as rock matrixes with a group of discrete fracture networks with fractal characteristics. Various types of fractured digital rocks are obtained by adjusting different fracture parameters. Pore network models are extracted from the 3D fractured digital rock. Then the permeability is predicted by Darcy law to investigate the impacts of fracture properties to the absolute permeability. The permeability of fractured rock is subject to exponential increases with fracture aperture. The relationship between the permeability and the fractal dimension of fracture centers is exponential, as well as the relationship between permeability and the fractal dimension of fracture lengths.

Permeability is one of the most important parameters for accurately predicting water flow in reservoirs and quantifying underground water inrush into coal mines. This study developed a predictive permeability model by considering the microstructural parameters and tortuosity effects of low-permeability sandstone. The model incorporates the fractal geometry theory, Darcy’s law, and Poiseuille equation into a multistep inversion framework for systematic interpretation of sandstone scanning electron microscopy (SEM) images. A threshold segmentation algorithm is applied to transform SEM images into binary images. Then, we used an improved statistical algorithm with binary image data to estimate the geometric parameters of each pore, such as the perimeter and area. The fractal parameters of pore microstructure were determined by fitting the data of pore perimeters and areas. Finally, the effects of tortuosity on microscopic percolation were considered, and a conventional model was modified for quantifying the relationship between microscopic pore structures parameters and macroscopic permeability. Eight groups of sandstone samples from the Xingdong coal mine in North China were collected for estimating permeability by the developed inversion framework. A direct permeability measurement was also conducted on each sample with an AP-608 automatic measuring instrument. The measured permeability values were compared with results from theoretical models, and we found that the accuracy of the newly developed predictive model is better than that of a conventional permeability model. The predictive model developed in this study provides a useful tool for estimating permeability in low-permeable sandstone reservoirs.

Supply chain finance is a new financing model tailored for small and medium-sized enterprises, which integrates capital flow into supply chain management, providing commercial trade capital services for enterprises in all aspects of the supply chain and providing new loan financing services for vulnerable enterprises in the supply chain. Fractal originally is a general term for a graph, structure or phenomenon that does not have a feature length but has a statistically significant self-similarity; fractal theory is an emerging edge science that describes the complex system with a random structure and has been widely used in physics, chemistry, geography, economics and many other fields. On the basis of summarizing and analyzing previous published literature works, this paper expounded the research situation and significance of risk measurement in supply chain finance, elaborated the development background, current status and future challenges of fractal theory, proposed the improved fractal volatility model and financial evaluation model, performed risk analysis of supply chain finance through evaluation modeling and elastic fractal dimension, constructed a financial risk measurement model based on fractal theory, and discussed the importance of model parameter estimation, residual test and accuracy examination in risk measurement of supply chain finance. The final empirical analysis shows that the improved fractal volatility model and the proposed financial risk measurement model has better risk measurement ability under different out-of-sample prediction periods, and obtain more accurate conclusion of asymmetry determination of financial assets gains under the common inspection level. The study results of this paper provide a reference for the further researches on risk measurement of supply chain finance based on fractal theory.

Due to the complexity of digital imaging targets and imaging conditions, fractal theory techniques in existing digital imaging systems still have various shortcomings. In this paper, a digital imaging processing method based on fractal theory is proposed for the first time. For X-ray images, the rapid calculation method of H-parameters is derived based on the fractional Brownian random field model. The H-parameters of X-ray images are calculated point by point. After that, all the singular points are connected, which is the edge of the defect in the image. We apply this method to analyze and process the X-ray images with defects such as missing joints, skins and hollows. Secondly, by means of fractal geometry, the contour slice measurement of the digital imaging space of this fractal is studied. The approximate index value is the digital imaging section profile dimension (D1 dimension) and the section shadow dimension (D2 dimension), so that the dimension determines the complexity of the form and detail of digital imaging. Finally, it can be seen from the experimental results that this method is effective and explores a new way for the development of digital imaging technology. At the same time, it is of great significance to the automatic pattern recognition of the application.

Users use the network more and more frequently, and more and more data is published on the network. Therefore, how to find, organize, and use the useful information behind these massive data through effective means, and analyze user intentions is a huge challenge. There are many time series problems in user intentions. Time series have complex characteristics such as randomness and multi-scale variability. Effectively identifying the inherent laws and objective phenomena contained in time series is the purpose of analyzing and processing time series data. Fractal theory provides a new way to analyze time series, and obtains the characteristics and rules of time series from a new perspective. Therefore, this paper introduces the fractal theory to analyze the time series problem, and proposes an improved G-P algorithm to realize the prediction and mining of user intentions. First, the method of array storage instead of repeated calculations is used to improve the method of saturated correlation dimension. Second, the Hurst exponent of the time series is obtained by the variable scale range analysis method. Finally, a fractal model for predicting user intent in short time series is established using the accumulation and transformation method. The experimental results show that the use of fractal theory can effectively describe the relevant characteristics of time series, the development trend of user intentions can be mined from big data, and the prediction model for short time series can be established to achieve information mining of user intentions.

Severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) is the most dangerous type of coronavirus and has infected over 25.3 million people around the world (including causing 848,000 deaths). In this study, we investigated the similarity between the genome walks of coronaviruses in various animals and those of human SARS-CoV-2. Based on the results, although bats show a similar pattern of coronavirus genome walks to that of SARS-CoV-2 in humans, decoding the complex structure of coronavirus genome walks using sample entropy and fractal theory showed that the complexity of the pangolin coronavirus genome walk has a 94% match with the complexity of the SARS-CoV-2 genome walk in humans. This is the first reported study that found a similarity between the hidden characteristics of pangolin coronavirus and human SARS-CoV-2 using complexity-based analysis. The results of this study have great importance for the analysis of the origin and transfer of the virus.

An important research area in physiological and sport sciences is the analysis of the variations of the muscle reaction due to changes in walking speed. In this paper, we investigated the effect of walking speed variations on leg muscle reaction by the analysis of Electromyogram (EMG) signals at different walking inclines. For this purpose, we benefited from fractal theory and sample entropy to analyze how the complexity of EMG signals changes at different walking speeds. According to the results, although fractal theory could not show a clear trend between the variations of the complexity of EMG signals and the variations of the walking speed, however, based on the results, increasing the speed of walking in the case of different inclines is mapped on to the decrement of the sample entropy of EMG signals. Therefore, sample entropy could decode the effect of walking speed on the reaction of leg muscle. This analysis method could be applied to analyze the variations of other physiological signals of humans durin walking.

Analysis of leg muscle activation and gait variability during locomotion is an important area of research in physiological and sport sciences. In this paper, we analyzed the coupling between the alterations of leg muscle activation and gait variability in single-task and dual-task walking. Since leg muscle activation in the form of electromyogram (EMG) signals and gait variability in the form of stride interval time series have complex structures, fractal theory and approximate entropy were used to evaluate their correlation at various walking conditions. Sixty subjects walked at their preferred speed for 10 min under the single-task condition and for 90s under the cognitive dual-task condition, and we evaluated the variations of the fractal dimension and approximate entropy of EMG signals and stride interval time series. According to the results, dual-task walking caused reductions in the complexity of EMG signals and stride interval time series than single-task walking. This technique can be used to evaluate the correlation between other organs during different locomotion.

This paper analyzed the coupling among the reactions of eyes and brain in response to visual stimuli. Since eye movements and electroencephalography (EEG) signals as the features of eye and brain activities have complex patterns, we utilized fractal theory and sample entropy to decode the correlation between them. In the experiment, subjects looked at a dot that moved on different random paths (dynamic visual stimuli) on the screen of a computer in front of them while we recorded their EEG signals and eye movements simultaneously. The results indicated that the changes in the complexity of eye movements and EEG signals are coupled ($r=-0.8043$ in case of fractal dimension and $r=-0.9259$ in case of sample entropy), which reflects the coupling between the brain and eye activities. This analysis could be extended to evaluate the correlation between the activities of other organs versus the brain.

The purpose is to apply the fractal statistical model to analyze tourist flow feature of scenic area, and promote the effective performance of scenic area. Zhangjiajie scenic area is taken as an example. First, its natural resources characteristics, ecological environment and problems in the development of scenic area are analyzed in detail; moreover, fractal theory and fractal dimension calculation method are elaborated; finally, wavelet transform is proposed to analyze the nonlinear transformation characteristics of tourist flow. The results show that the changes of the high-frequency layer $H_1$, $H_2$, $H_3$ and $H_4$ all have cyclical fluctuations in the change of tourist flow. The change range of tourist flow in spring and autumn is relatively large, and the tourist flow in winter is low. Inbound tourism tourist flow has a certain seasonal regularity, with obvious characteristics of low and peak seasons. Wulingyuan scenic spot and Tianmen Mountain scenic spot of Zhangjiajie have three non-scale ranges, which are related to the scale and change of tourist flow. The concentration of inbound tourist flow in the peak season still exists in both scenic spots, and it is more and more serious. Tourist flow of inbound tourists from April to May and from September to October is large, accounting for more than half of the annual tourist flow, while most of the other periods are in the off-season.

The coefficient of vertical permeability is a common filter design criterion for woven slit-film geotextiles. According to the pipe flow theory, a permeability coefficient model has been proposed for predicting the permeability coefficient of woven geotextiles, in which the pore characteristics were described by the Sierpiński carpet fractal theory. The verification of models is performed in 12 woven geotextiles of two types using a digital image method and a vertical water permeability test of the geotextile. The influence of the pore characteristics on the permeability coefficient is further explored using univariate and multivariate analyses. The results show that the porosity model can accurately predict the total percent pore area (POA) and the POA distribution of the woven geotextiles, and the permeability model can accurately predict the permeability coefficient of the geotextiles. The permeability coefficient of geotextiles decreases with the pore area fractal dimension and the minimum pore size under the action of a single factor. The permeability coefficient increases as the maximum pore size increases. POA and maximum pore size are the most significant independent variables affecting the permeability coefficients of geotextile under the action of multifactor.

In this paper, we analyzed the variations in brain activation between different activities. Since Electroencephalogram (EEG) signals as an indicator of brain activation contain information and have complex structures, we employed complexity and information-based analysis. Specifically, we used fractal theory and Shannon entropy for our analysis. Eight subjects performed three different activities (standing, walking, and walking with a brain–computer interface) while their EEG signals were recorded. Based on the results, the complexity and information content of EEG signals have the greatest and smallest values in walking and standing, respectively. Complexity and information-based analysis can be applied to analyze the activations of other organs in different conditions.

Since the brain controls heart activations, there should be a correlation between their activities in different conditions. This study investigates the correlation between heart and brain responses to olfactory stimulation. We employed fractal theory and sample entropy to evaluate the complexity of EEG signals and Heart Rate Variability (HRV) in the form of R–R time series. We applied four different pleasant odors with different molecular complexities to 13 participants and analyzed their EEG and ECG signals. The results demonstrated that the complexities of HRV and EEG signals are strongly correlated; a bigger alteration in the complexity of olfactory stimuli is mapped to a bigger alteration in the complexity of HRV and EEG signals. This investigation can be similarly done to examine the correlation between various organs and the brain by quantifying the complexity of their signals versus brain signals.

One of the important areas of heart research is investigating how heart activity changes during aging. In this research, we employed complexity-based techniques to analyze how heart activity varies based on the age of subjects. For this purpose, the heart rate variability (HRV) of 54 healthy subjects (30 M, 24 F, 28.5–76 years old) in three different age groups was analyzed using fractal theory, sample entropy, and approximate entropy. We showed that the fractal dimension, sample entropy, and approximate entropy of the RR interval time series (as HRV) are related to the age of the subjects. In other words, as subjects get older, the complexity of their RR interval time series decreases. Therefore, we decoded the variations in HRV during aging. The method of analysis that was employed in this research can be used to analyze the variations of other physiological signals (e.g. Electroencephalogram (EEG) signals) during aging.

Due to the increasing growth of economy in the last few years, environmental problems have become a prominent difficulty in Chinese economic growth and social development. Therefore, in order to respond to the environmental protection policy of Anhui Province, all prefecture-level cities need to be evaluated for their environmental efficiency. A study of environmental efficiency in Anhui Province is presented in this paper. The time period is from 2015 to 2020. By exploiting MaxDEA software, the input–output system in different years is taken as the decision-making unit, and slacks-based model (SBM-DEA) which is based on an unexpected output is used to construct the index system by selecting two output indexes and four input indexes, so as to calculate the environmental efficiency of Anhui Province, including 16 prefecture-level cities, under the condition of constant non-radial and non-angle scale benefits. In addition, based on the persistence and anti-persistence theory of fractal theory, in this paper, we have analyzed the future trend of environmental efficiency of prefecture-level cities in Anhui Province by rescaled range analysis (R/S). The results show that Anhui province has 16 prefectures that have not achieved an optimal level of environmental performance and fluctuates downward from 2015 to 2020. The average value of comprehensive efficiency is 0.846. As for technical efficiency, the mean value is 0.954, and scale efficiency has an average value of 0.887. The technical progress of environmental efficiency development in Anhui Province is small and the room for improvement is large. Finally, according to the results of the study, some suggestions on environmental technology are put forward.

Insufficient consideration of the complex morphology of hydraulic fractures (HF) and heterogeneous physical properties of fractured reservoirs in seepage models can result in unreliable well testing analyses. The fractal porosity and permeability (FPP) model provides an effective method for characterizing reservoir heterogeneity in the near-wellbore zone. However, its application to scenarios involving irregularly-shaped hydraulic fracture networks and multiple fracture clusters is challenging due to the lack of spatial symmetry. To address this issue, this paper proposes a combined approach of FPP and conformal mapping (FPP-CM) to transform the region of fractured formation into the exterior of the unit disk domain using numerical conformal mapping. The transient seepage flow model of the vertical fracture well (VFW) is then established by coupling it with the FPP model. The typical curve of pressure transient behavior with the division of flow stages was plotted, and the model verification and sensitivity analysis of parameters were conducted. The results indicate that the fractal dimension primarily affects the formation linear flow stage and its subsequent flow stages; with a decrease in fractal dimension resulting in an increase in the position of the typical curve. For VFW with multiple HF wings, a decrease in the included angle of fracture wings causes an increase in the heterogeneity distribution of microfracture physical properties, resulting in an increase in the position of the pseudo-pressure derivative curve during the late flow stage.

One of the important areas of research in neuroscience is to investigate how brain activity changes during aging. In this research, we employ complexity techniques to analyze how brain activity changes based on the age of subjects during sleep. For this purpose, we analyze the Electroencephalogram (EEG) signals of 22 subjects induced by sleep medication using fractal theory and sample entropy. The analysis showed that the fractal dimension and sample entropy of EEG signals decrease due to aging. Therefore, we concluded that aging causes lower complexity in EEG signals during sleep. The employed method of analysis could be applied to analyze the effect of aging on the variations of the activity of other organs (e.g. heart, muscle) during aging by studying their related physiological signals (e.g. ECG, EMG).