Based on fractal super fibers and binary fractal fibers, the following objectives are approached in this paper： First, the concept of multiple-cell elements is induced and abstracted. Second, through multiple-cell el...Based on fractal super fibers and binary fractal fibers, the following objectives are approached in this paper： First, the concept of multiple-cell elements is induced and abstracted. Second, through multiple-cell elements, the constructability of regular multifractals with strict self-similarities is confirmed, and the universality of the con- struction mode for regular multifractals is proved. Third, through the construction mode and multiple-cell elements, regular multifractals are demonstrated to be equivalent to generalized regular single fractals with multilayer fine structures. On the basis of such equivalence, the dimension formula of the regular single fractal is extended to that of the regular multifractal, and the geometry of regular single fractals is extended to that of regular multifractals. Fourth, through regular multifractals, a few golden fractals are constructed.展开更多
The strategy of ore prospection is made on the basis of raw exploratory data which are the products of coupled geological processes and random natural reformation. This decision-making system is extraordinary risky an...The strategy of ore prospection is made on the basis of raw exploratory data which are the products of coupled geological processes and random natural reformation. This decision-making system is extraordinary risky and needs to be supported by various statistical sciences. In this paper, geostatistics and multifractals are jointly employed to delineate the complexity of mineralization and to provide important guidelines for future ore prospecting. The geostatistical analysis indicates the mineralization in granite domain is more homogenous than that in wallrocks, and the exploratory spacing in these two lithological units should be different when taking into consideration the range of variogram. The multifractal analysis shows the spatial variation of mineralization homogeneity. The mineralization in the southwest of this region is much more heterogeneous than that in the granite. The schemes of borehole design are specified based on the combination of abovementioned analytical results. The joint application of geostatistics and multifractal proposed in this study can excavate the exploratory data and output mathematic models in an intuitive and quantitative way, assisting in decision-making and risk avoidance of mining industry.展开更多
As an important component of secondary aerosols,sulfate plays a crucial role in regulating atmospheric radiative balance and influencing the secondary formation of ozone(O_(3)).In real atmosphere,atmospheric oxidants ...As an important component of secondary aerosols,sulfate plays a crucial role in regulating atmospheric radiative balance and influencing the secondary formation of ozone(O_(3)).In real atmosphere,atmospheric oxidants NO_(2)and O_(3)can promote the oxidation of SO_(2)to form sulfate(SO_(4)^(2−))through multiphase chemistry that occur at different time scales.Due to the combined impact of meteorology,pollution sources,atmospheric chemistry,etc.,time-scale dependence of SO_(2)-SO_(4)^(2−)conversion makes the impact of NO_(2)/O_(3)on it more complex.In this study,based on long-term time series(2013-2020)of air pollution variables from seven stations in Hong Kong,the Multifractal Detrended Cross-Correlation Analysis(MFDCCA)method has been employed to quantify the cross-correlations between SO_(2)and SO_(4)^(2−)in real atmosphere at different time scales,for examining the time-scale dependence of SO_(2)-SO_(4)^(2−)conversion efficiency.Furthermore,the Pearson correlation analysis has been used to study the influence of NO_(2)/O_(3)on SO_(2)-SO_(4)^(2−)conversion,and the regional and seasonal differences have been analyzed by considering factors such as meteorology,pollution sources,and regional transport.Changes in the main components of secondary aerosols are closely linked with the co-control of regional PM_(2.5)and O_(3).Therefore,the exploration of the impact of co-existing NO_(2)/O_(3)gases on the secondary formation of sulfates in real atmosphere is significant.展开更多
Understanding the rate-dependent shear behavior of rough joints is crucial.This study explores the ratedependent shear behavior of rough joints through direct shear tests conducted under constant normal stiffness(CNS)...Understanding the rate-dependent shear behavior of rough joints is crucial.This study explores the ratedependent shear behavior of rough joints through direct shear tests conducted under constant normal stiffness(CNS)boundary conditions,with the shear failure process monitored using acoustic emission(AE)technology.As the shear rate increases,both the peak and ultimate shear stresses of rough joints exhibit a decrease,highlighting a pronounced rate-dependent behavior.Asperity degradation under different shear rates is effectively characterized by normalized AE counts,exhibiting a three-stage Sshaped trend:Stage I(quiescent),Stage II(growth),and Stage III(stable).The simultaneous occurrence of the lowest AE b-value and the highest AE amplitude closely aligns with the moment of peak shear stress.This synchronization suggests that AE events of significant energy are predominantly clustered around the peak shear stress,which critically influences the overall progression of failure.Three failure modes of asperities were categorized,including the biting-off failure mode(BFM),the climbing-sliding failure mode(CFM),and the hybrid biting-off and climbing-sliding failure mode(HFM).Analysis of the multifractal spectra reveals that both the multifractal spectrum width(Δα)and the fractal dimension variability(Δf)diminish as the shear rate increases,suggesting that the complexity of the failure modes is inversely related to the shear rate.With increasing shear rates,the dominant failure mode evolves from BFM to CFM.The research findings facilitate a comprehensive understanding of the ratedependent shear behavior of rough joints,providing valuable guidance for rational support in underground engineering.展开更多
Unveiling the underlying physical mechanisms governing the fracture of brittle rocks is imperative for preventing rockbursts.The novelty of this study lies in the analysis of the dynamic response process of rock three...Unveiling the underlying physical mechanisms governing the fracture of brittle rocks is imperative for preventing rockbursts.The novelty of this study lies in the analysis of the dynamic response process of rock three-dimensional(3D)deformation under true triaxial stress,and the surge behavior of timedependent multifractal spectrum has been successfully used to warn of progressive failure inside the rock.Firstly,this study analyzed the dynamic adjustment trajectory of rock deformation,specifically lateral strain,within the framework of the Poisson effect.This analysis highlighted the intricate dependence of rock mechanical properties on the intermediate principal stress.Secondly,by defining the crack interval function(ICF),this study compared the disparities between the two crack growth stages(strengthening stage and weakening stage)under varying stress levels.It was found that the fracture activity of granite system has significant multifractal characteristics.Notably,the multifractal spectrum emerges as a valuable tool for characterizing the distinct fracture properties of rocks,encompassing both the crack scale and the associated energy.Finally,a quantitative criterion grounded in the multifractal parameters of the acoustic emission(AE)time series was formulated,and it indicates that the abrupt changes observed in the time-dependent fractal spectra can serve as precursor indicators for the progressive development of rockbursts.展开更多
Disordered ferromagnets with a domain structure that exhibit a hysteresis loop when driven by the external magnetic field are essential materials for modern technological applications.Therefore,the understanding and p...Disordered ferromagnets with a domain structure that exhibit a hysteresis loop when driven by the external magnetic field are essential materials for modern technological applications.Therefore,the understanding and potential for controlling the hysteresis phenomenon in thesematerials,especially concerning the disorder-induced critical behavior on the hysteresis loop,have attracted significant experimental,theoretical,and numerical research efforts.We review the challenges of the numerical modeling of physical phenomena behind the hysteresis loop critical behavior in disordered ferromagnetic systems related to the non-equilibriumstochastic dynamics of domain walls driven by external fields.Specifically,using the extended Random Field Ising Model,we present different simulation approaches and advanced numerical techniques that adequately describe the hysteresis loop shapes and the collective nature of the magnetization fluctuations associated with the criticality of the hysteresis loop for different sample shapes and varied parameters of disorder and rate of change of the external field,as well as the influence of thermal fluctuations and demagnetizing fields.The studied examples demonstrate how these numerical approaches reveal newphysical insights,providing quantitativemeasures of pertinent variables extracted from the systems’simulated or experimentally measured Barkhausen noise signals.The described computational techniques using inherent scale-invariance can be applied to the analysis of various complex systems,both quantum and classical,exhibiting non-equilibrium dynamical critical point or self-organized criticality.展开更多
An empirical test on long memory between price and trading volume of China metals futures market was given with MF-DCCA method. The empirical results show that long memory feature with a certain period exists in price...An empirical test on long memory between price and trading volume of China metals futures market was given with MF-DCCA method. The empirical results show that long memory feature with a certain period exists in price-volume correlation and a fittther proof was given by analyzing the source of multifractal feature. The empirical results suggest that it is of important practical significance to bring the fractal market theory and other nonlinear theory into the analysis and explanation of the behavior in metal futures market.展开更多
Using a simple multifractal model based on the model De Wijs, various geochemical map patterns for element concentration values are being simulated. Each pattern is self-similar on the average in that a similar patter...Using a simple multifractal model based on the model De Wijs, various geochemical map patterns for element concentration values are being simulated. Each pattern is self-similar on the average in that a similar pattern can be derived by application of the multiplicative cascade model used to any small subarea on the pattern. In other experiments, the original, self-similar pattern is distorted by superimposing a 2-dimensional trend pattern and by mixing it with a constant concentration value model. It is investigated how such distortions change the multifractal spectrum estimated by means of the 3-step method of moments. Discrete and continuous frequency distribution models are derived for patterns that satisfy the model of De Wijs. These simulated patterns satisfy a discrete frequency distribution model that as upper bound has a continuous frequency distribution to which it approaches in form when the subdivisions of the multiplicative cascade model are repeated indefinitely. This limiting distribution is lognormal in the center and has Pareto tails. Potentially, this approach has important implications in mineral and oil resource evaluation.展开更多
The purpose of this contribution is to highlight four topics of regional and worldwide mineral resource prediction:(1)use of the jackknife for bias elimination in regional mineral potential assessments;(2)estimating t...The purpose of this contribution is to highlight four topics of regional and worldwide mineral resource prediction:(1)use of the jackknife for bias elimination in regional mineral potential assessments;(2)estimating total amounts of metal from mineral potential maps;(3)fractal/multifractal modeling of mineral deposit density data in permissive areas;and(4)worldwide and large-areas metal size-frequency distribution modeling.The techniques described in this paper remain tentative because they have not been widely researched and applied in mineral potential studies.Although most of the content of this paper has previously been published,several perspectives for further research are suggested.展开更多
AIMTo characterize the human retinal vessel arborisation in normal and amblyopic eyes using multifractal geometry and lacunarity parameters.METHODSMultifractal analysis using a box counting algorithm was carried out f...AIMTo characterize the human retinal vessel arborisation in normal and amblyopic eyes using multifractal geometry and lacunarity parameters.METHODSMultifractal analysis using a box counting algorithm was carried out for a set of 12 segmented and skeletonized human retinal images, corresponding to both normal (6 images) and amblyopia states of the retina (6 images).RESULTSIt was found that the microvascular geometry of the human retina network represents geometrical multifractals, characterized through subsets of regions having different scaling properties that are not evident in the fractal analysis. Multifractal analysis of the amblyopia images (segmented and skeletonized versions) show a higher average of the generalized dimensions (D<sub>q</sub>) for q=0, 1, 2 indicating a higher degree of the tree-dimensional complexity associated with the human retinal microvasculature network whereas images of healthy subjects show a lower value of generalized dimensions indicating normal complexity of biostructure. On the other hand, the lacunarity analysis of the amblyopia images (segmented and skeletonized versions) show a lower average of the lacunarity parameter Λ than the corresponding values for normal images (segmented and skeletonized versions).CONCLUSIONThe multifractal and lacunarity analysis may be used as a non-invasive predictive complementary tool to distinguish amblyopic subjects from healthy subjects and hence this technique could be used for an early diagnosis of patients with amblyopia.展开更多
We investigate the approximating capability of Markov modulated Poisson processes (MMPP) for modeling multifractal Internet traffic. The choice of MMPP is motivated by its ability to capture the variability and correl...We investigate the approximating capability of Markov modulated Poisson processes (MMPP) for modeling multifractal Internet traffic. The choice of MMPP is motivated by its ability to capture the variability and correlation in moderate time scales while being analytically tractable. Important statistics of traffic burstiness are described and a customized moment-based fitting procedure of MMPP to traffic traces is presented. Our methodology of doing this is to examine whether the MMPP can be used to predict the performance of a queue to which MMPP sample paths and measured traffic traces are fed for comparison respectively, in addition to the goodness-of-fit test of MMPP. Numerical results and simulations show that the fitted MMPP can approximate multifractal traffic quite well, i.e. accurately predict the queueing performance.展开更多
A new kind of multifractal is constructed by fractional Fourier transform of Cantor sets. The wavelet transform modulus maxima method is applied to calculate the singularity spectrum under an operational definition of...A new kind of multifractal is constructed by fractional Fourier transform of Cantor sets. The wavelet transform modulus maxima method is applied to calculate the singularity spectrum under an operational definition of multifractal. In particular, an analysing procedure to determine the spectrum is suggested for practice. Nonanalyticities of singularity spectra or phase transitions are discovered, which are interpreted as some indications on the range of Boltzmann temperature q, on which the scaling relation of partition function holds.展开更多
The manuscript attempts to explore the periodicity in the distribution of galaxies in the recently reported Saraswati supercluster and the Stripe 82 region containing it as an example.The report of 120 Mpc periodicity...The manuscript attempts to explore the periodicity in the distribution of galaxies in the recently reported Saraswati supercluster and the Stripe 82 region containing it as an example.The report of 120 Mpc periodicity in the Abell galaxy clusters by power spectrum analysis is the motivation behind the study.The power spectral analysis across the central part of the Stripe 82 region shows a periodic variation of 3.09°or 71 Mpc in fractal dimension whereas an average angular periodicity of 3.45°or 94 Mpc is observed across the Stripe 82 region.This refers to the periodicity of complexity or cluster density of galaxy distribution.The texture of the distribution pattern understood through lacunarity analysis indicates a near symmetric distribution.Fractal dimensions like box-counting dimension,information dimension and correlation dimension are also found through multifractal analysis.While the information dimension tells about the distribution density of galactic points,the correlation dimension details the distribution of galaxies in the neighbourhood.展开更多
We have investigated the Nu Calm Transcutaneous Vagus Nerve Stimulation device of the NuCalm Solace Lifesciences founding that it gives a multifractal output. A diminishing fractal/multifractal HRV is consistently rep...We have investigated the Nu Calm Transcutaneous Vagus Nerve Stimulation device of the NuCalm Solace Lifesciences founding that it gives a multifractal output. A diminishing fractal/multifractal HRV is consistently reported in literature as related to a serious Autonomic Nervous System (ANS) dysfunction that of course we observe in several psychological and psychiatric disorders. Therefore, we suggest the investigators to apply such a device in subjects affected from anxiety, depression and stress using the method of inducing tVNS stimulation.展开更多
Pore structure characteristics are important to oil and gas exploration in complex low-permeability reservoirs. Using multifractal theory and nuclear magnetic resonance （NMR）, we studied the pore structure of low-pe...Pore structure characteristics are important to oil and gas exploration in complex low-permeability reservoirs. Using multifractal theory and nuclear magnetic resonance （NMR）, we studied the pore structure of low-permeability sandstone rocks from the 4th Member （Es4） of the Shahejie Formation in the south slope of the Dongying Sag. We used the existing pore structure data from petrophysics, core slices, and mercury injection tests to classify the pore structure into three categories and five subcategories. Then, the T2 spectra of samples with different pore structures were interpolated, and the one- and three-dimensional fractal dimensions and the multifractal spectrum were obtained. Parameters a （intensity of singularity） andf（a） （density of distribution） were extracted from the multifractal spectra. The differences in the three fractal dimensions suggest that the pore structure types correlate with a andf（a）. The results calculated based on the multifractal spectrum is consistent with that of the core slices and mercury injection. Finally, the proposed method was applied to an actual logging profile to evaluate the pore structure of low-permeability sandstone reservoirs.展开更多
Shale gas resources have been regarded as a viable energy source, and it is of great significance to characterize the shale composition of different cements, such as quartz and dolomite. In this research, chemical ana...Shale gas resources have been regarded as a viable energy source, and it is of great significance to characterize the shale composition of different cements, such as quartz and dolomite. In this research, chemical analysis and the multifractal method have been used to study the mineral compositions and petrophysical structures of cements in shale samples from the Longmaxi Formation, China. X-ray diffraction, electron microprobe, field emission scanning electron microscopy, cathodoluminescence microscopy and C-O isotope analyses confirmed that cements in the Longmaxi Formation shales are mainly composed of Fe-bearing dolomite and quartz. Fe-bearing dolomite cements concentrate around dolomite as annuli, filling micron-sized inorganic primary pores. Quartz cements in the form of nanoparicles fill primary inter-crystalline pores among clay minerals. Theoretical calculation shows that the Fe-bearing dolomite cements formed slightly earlier than the quartz cements, but both were related to diagenetic illitization of smectite. Moreover, multifractal analysis reveals that the quartz cements are more irregularly distributed in pores than the Fe-bearing dolomite cements. These results suggest that the plugging effect of the quartz cements on the primary inoraganic pore structures is the dominant factor resulting in low interconnected porosity of shales, which are unfavorable for the enrichment of shale gas.展开更多
A series of element concentrations sampled from four drill cores with a length about 1000 m into different skarn-type deposits were selected from the Shizishan orefield, central Tongling, southeastern part of Anhui Pr...A series of element concentrations sampled from four drill cores with a length about 1000 m into different skarn-type deposits were selected from the Shizishan orefield, central Tongling, southeastern part of Anhui Province. Using the multifractal method, the distribution and migration characteristics of the major and trace elements are analyzed. The multifractal spectrum of the major elements is left-skewed, whereas the spectrum of the trace elements is right-skewed, which shows that in the process of skarn formation, the trace elements were enriched only locally, and major elements transported within a much larger range. The correlation coefficients of the multifractal parameters Aa （width of the multifractal spectrum） of the four drill cores are relatively low, but the correlation coefficients of the multifractal parameters R （spectrum symmetry parameter） and Af are relatively higher, indicating that although the non-homogeneous intensity of the distribution of elements is inconsistent, their spatial accumulation patterns are almost the same during the ore-forming process. The statistics of the mnltifractal parameters of various elements in the different locations show that the ore-forming processes and element migration pattern in the Shizishan orefield are consistent, and that the migrations of trace elements and major elements exhibit some differences.展开更多
When exploring the temporal and spatial change law of ocean environment, the most common method used is using smaller-scale observed data to derive the change law for a larger-scale system. For instance, using 30-year...When exploring the temporal and spatial change law of ocean environment, the most common method used is using smaller-scale observed data to derive the change law for a larger-scale system. For instance, using 30-year observation data to derive 100-year return period design wave height. Therefore, the study of inherent self-similarity in ocean hydrological elements becomes increasingly important to the study of multi-year return period design wave height derivation. In this paper, we introduced multifractal to analyze the statistical characteristics of wave height series data observed from oceanic hydrological station. An improvement is made to address the existing problems of the multifractal detrended fluctuation analysis (MF-DFA) method, where trend function showed a discontinuity between intervals. The improved MFDFA method is based on signal mode decomposition, replacing piecewise polynomial fitting used in the original method. We applied the proposed method to the wave height data collected at Chaolian Island, Shandong, China, from 1963 to 1989 and was able to conclude the wave height sequence presented weak multi-fractality. This result provided strong support to the past research on the derivation of multi-year return period design wave height with observed data. Moreover, the new method proposed in this paper also provides a new perspective to explore the intrinsic characteristic of data.展开更多
In order to analyze and compare the differences in pore structures between shale gas and shale oil formations, a few samples from the Longmaxi and Bakken Formations were collected and studied using X-ray diffraction, ...In order to analyze and compare the differences in pore structures between shale gas and shale oil formations, a few samples from the Longmaxi and Bakken Formations were collected and studied using X-ray diffraction, LECO TOC measurement, gas adsorption and field-emission scanning electron microscope. The results show that samples from the Bakken Formation have a higher TOC than those from the Longmaxi Formation. The Longmaxi Formation has higher micropore volume and larger micropore surface area and exhibited a smaller average distribution of microsize pores compared to the Bakken Formation. Both formations have similar meso-macropore volume. The Longmaxi Formation has a much larger meso-macropore surface area, which is corresponding to a smaller average meso-macropore size. CO_2 adsorption data processing shows that the pore size of the majority of the micropores in the samples from the Longmaxi Formation is less than 1 nm, while the pore size of the most of the micropores in the samples from the Bakken Formation is larger than 1 nm. Both formations have the same number of pore clusters in the 2–20 nm range, but the Bakken Formation has two additional pore size groups with mean pore size diameters larger than 20 nm. Multifractal analysis of pore size distribution curves that was derived from gas adsorption indicates that the samples from the Longmaxi Formation have more significant micropore heterogeneity and less meso-macropore heterogeneity. Abundant micropores as well as mesomacropores exist in the organic matter in the Longmaxi Formation, while the organic matter of the Bakken Formation hosts mainly micropores.展开更多
Based on the experiments of nitrogen gas adsorption(N_2 GA) and nuclear magnetic resonance(NMR),the multifractal characteristics of pore structures in shale and tight s andstone from the Chang 7 member of Trias sic Ya...Based on the experiments of nitrogen gas adsorption(N_2 GA) and nuclear magnetic resonance(NMR),the multifractal characteristics of pore structures in shale and tight s andstone from the Chang 7 member of Trias sic Yanchang Formation in Ordos Basin,NW China,are investigated.The multifractal spectra obtained from N2 GA and NMR are analyzed with pore throat structure parameters.The results show that the pore size distributions obtained from N2 GA and NMR are different,and the obtained multifractal characteristics vary from each other.The specific surface and total pore volume obtained by N2 GA experiment have correlations with multifractal characteristics.For the core samples with the similar specific surface,the value of the deviation of multifractal spectra Rd increases with the increase in the proportion of large pores.When the proportion of macropores is small,the Rd value will increase with the increase in specific surface.The multifractal characteristics of pore structures are influenced by specific surface area,average pore size and adsorption volume measured from N2 GA experiment.The multifractal characteristic parameters of tight sandstone measured from NMR spectra are larger than those of shale,which may be caused by the differences in pore size distribution and porosity of shale and tight sandstone.展开更多
基金supported by the National Natural Science Foundation of China (No. 10872114)the Natural Science Foundation of Jiangsu Province (No. BK2008370)
文摘Based on fractal super fibers and binary fractal fibers, the following objectives are approached in this paper： First, the concept of multiple-cell elements is induced and abstracted. Second, through multiple-cell elements, the constructability of regular multifractals with strict self-similarities is confirmed, and the universality of the con- struction mode for regular multifractals is proved. Third, through the construction mode and multiple-cell elements, regular multifractals are demonstrated to be equivalent to generalized regular single fractals with multilayer fine structures. On the basis of such equivalence, the dimension formula of the regular single fractal is extended to that of the regular multifractal, and the geometry of regular single fractals is extended to that of regular multifractals. Fourth, through regular multifractals, a few golden fractals are constructed.
文摘The strategy of ore prospection is made on the basis of raw exploratory data which are the products of coupled geological processes and random natural reformation. This decision-making system is extraordinary risky and needs to be supported by various statistical sciences. In this paper, geostatistics and multifractals are jointly employed to delineate the complexity of mineralization and to provide important guidelines for future ore prospecting. The geostatistical analysis indicates the mineralization in granite domain is more homogenous than that in wallrocks, and the exploratory spacing in these two lithological units should be different when taking into consideration the range of variogram. The multifractal analysis shows the spatial variation of mineralization homogeneity. The mineralization in the southwest of this region is much more heterogeneous than that in the granite. The schemes of borehole design are specified based on the combination of abovementioned analytical results. The joint application of geostatistics and multifractal proposed in this study can excavate the exploratory data and output mathematic models in an intuitive and quantitative way, assisting in decision-making and risk avoidance of mining industry.
基金supported by the National Natural Science Foundation of China(No.52160024)the Natural Science Foundation of Hunan Province,China(No.2022JJ30475)+2 种基金the Innovation Team Funds of China West Normal University(No.KCXTD2023-4)the Natural Science Foundation of Sichuan,China(No.24NSFSC0537)the Fundamental Research Funds of China West Normal University(Nos.22kE015 and 22kE016).
文摘As an important component of secondary aerosols,sulfate plays a crucial role in regulating atmospheric radiative balance and influencing the secondary formation of ozone(O_(3)).In real atmosphere,atmospheric oxidants NO_(2)and O_(3)can promote the oxidation of SO_(2)to form sulfate(SO_(4)^(2−))through multiphase chemistry that occur at different time scales.Due to the combined impact of meteorology,pollution sources,atmospheric chemistry,etc.,time-scale dependence of SO_(2)-SO_(4)^(2−)conversion makes the impact of NO_(2)/O_(3)on it more complex.In this study,based on long-term time series(2013-2020)of air pollution variables from seven stations in Hong Kong,the Multifractal Detrended Cross-Correlation Analysis(MFDCCA)method has been employed to quantify the cross-correlations between SO_(2)and SO_(4)^(2−)in real atmosphere at different time scales,for examining the time-scale dependence of SO_(2)-SO_(4)^(2−)conversion efficiency.Furthermore,the Pearson correlation analysis has been used to study the influence of NO_(2)/O_(3)on SO_(2)-SO_(4)^(2−)conversion,and the regional and seasonal differences have been analyzed by considering factors such as meteorology,pollution sources,and regional transport.Changes in the main components of secondary aerosols are closely linked with the co-control of regional PM_(2.5)and O_(3).Therefore,the exploration of the impact of co-existing NO_(2)/O_(3)gases on the secondary formation of sulfates in real atmosphere is significant.
基金supported by the Nagasaki University Global Human Resource Development Scholarship and the Support for Pioneering Research Initiated by the Next Generation.
文摘Understanding the rate-dependent shear behavior of rough joints is crucial.This study explores the ratedependent shear behavior of rough joints through direct shear tests conducted under constant normal stiffness(CNS)boundary conditions,with the shear failure process monitored using acoustic emission(AE)technology.As the shear rate increases,both the peak and ultimate shear stresses of rough joints exhibit a decrease,highlighting a pronounced rate-dependent behavior.Asperity degradation under different shear rates is effectively characterized by normalized AE counts,exhibiting a three-stage Sshaped trend:Stage I(quiescent),Stage II(growth),and Stage III(stable).The simultaneous occurrence of the lowest AE b-value and the highest AE amplitude closely aligns with the moment of peak shear stress.This synchronization suggests that AE events of significant energy are predominantly clustered around the peak shear stress,which critically influences the overall progression of failure.Three failure modes of asperities were categorized,including the biting-off failure mode(BFM),the climbing-sliding failure mode(CFM),and the hybrid biting-off and climbing-sliding failure mode(HFM).Analysis of the multifractal spectra reveals that both the multifractal spectrum width(Δα)and the fractal dimension variability(Δf)diminish as the shear rate increases,suggesting that the complexity of the failure modes is inversely related to the shear rate.With increasing shear rates,the dominant failure mode evolves from BFM to CFM.The research findings facilitate a comprehensive understanding of the ratedependent shear behavior of rough joints,providing valuable guidance for rational support in underground engineering.
基金funding support from the National Natural Science Foundation of China(Grant No.U2034207)the Natural Science Foundation of Hebei Province(Grant No.E2021210099).
文摘Unveiling the underlying physical mechanisms governing the fracture of brittle rocks is imperative for preventing rockbursts.The novelty of this study lies in the analysis of the dynamic response process of rock three-dimensional(3D)deformation under true triaxial stress,and the surge behavior of timedependent multifractal spectrum has been successfully used to warn of progressive failure inside the rock.Firstly,this study analyzed the dynamic adjustment trajectory of rock deformation,specifically lateral strain,within the framework of the Poisson effect.This analysis highlighted the intricate dependence of rock mechanical properties on the intermediate principal stress.Secondly,by defining the crack interval function(ICF),this study compared the disparities between the two crack growth stages(strengthening stage and weakening stage)under varying stress levels.It was found that the fracture activity of granite system has significant multifractal characteristics.Notably,the multifractal spectrum emerges as a valuable tool for characterizing the distinct fracture properties of rocks,encompassing both the crack scale and the associated energy.Finally,a quantitative criterion grounded in the multifractal parameters of the acoustic emission(AE)time series was formulated,and it indicates that the abrupt changes observed in the time-dependent fractal spectra can serve as precursor indicators for the progressive development of rockbursts.
基金Djordje Spasojevic and Svetislav Mijatovic acknowledge the support from the Ministry of Science,TechnologicalDevelopment and Innovation of the Republic of Serbia(Agreement No.451-03-65/2024-03/200162)S.J.ibid.(Agreement No.451-03-65/2024-03/200122)Bosiljka Tadic from the Slovenian Research Agency(program P1-0044).
文摘Disordered ferromagnets with a domain structure that exhibit a hysteresis loop when driven by the external magnetic field are essential materials for modern technological applications.Therefore,the understanding and potential for controlling the hysteresis phenomenon in thesematerials,especially concerning the disorder-induced critical behavior on the hysteresis loop,have attracted significant experimental,theoretical,and numerical research efforts.We review the challenges of the numerical modeling of physical phenomena behind the hysteresis loop critical behavior in disordered ferromagnetic systems related to the non-equilibriumstochastic dynamics of domain walls driven by external fields.Specifically,using the extended Random Field Ising Model,we present different simulation approaches and advanced numerical techniques that adequately describe the hysteresis loop shapes and the collective nature of the magnetization fluctuations associated with the criticality of the hysteresis loop for different sample shapes and varied parameters of disorder and rate of change of the external field,as well as the influence of thermal fluctuations and demagnetizing fields.The studied examples demonstrate how these numerical approaches reveal newphysical insights,providing quantitativemeasures of pertinent variables extracted from the systems’simulated or experimentally measured Barkhausen noise signals.The described computational techniques using inherent scale-invariance can be applied to the analysis of various complex systems,both quantum and classical,exhibiting non-equilibrium dynamical critical point or self-organized criticality.
基金Project(13&ZD024)supported by the Major Program of the National Social Science Fund of ChinaProject(71073177)supported by the National Natural Science Foundation of China+3 种基金Project(CX2012B107)supported by the Graduate Student Innovation Project of Hunan Province,ChinaProject(13YJAZH149)supported by the Social Science Fund of Ministry of Education of ChinaProject(2011ZK2043)supported by the Key Program of the Soft Science Research Project of Hunan Province,ChinaProject(12JJ4077)supported by Natural Science Foundation of Hunan Province of China
文摘An empirical test on long memory between price and trading volume of China metals futures market was given with MF-DCCA method. The empirical results show that long memory feature with a certain period exists in price-volume correlation and a fittther proof was given by analyzing the source of multifractal feature. The empirical results suggest that it is of important practical significance to bring the fractal market theory and other nonlinear theory into the analysis and explanation of the behavior in metal futures market.
文摘Using a simple multifractal model based on the model De Wijs, various geochemical map patterns for element concentration values are being simulated. Each pattern is self-similar on the average in that a similar pattern can be derived by application of the multiplicative cascade model used to any small subarea on the pattern. In other experiments, the original, self-similar pattern is distorted by superimposing a 2-dimensional trend pattern and by mixing it with a constant concentration value model. It is investigated how such distortions change the multifractal spectrum estimated by means of the 3-step method of moments. Discrete and continuous frequency distribution models are derived for patterns that satisfy the model of De Wijs. These simulated patterns satisfy a discrete frequency distribution model that as upper bound has a continuous frequency distribution to which it approaches in form when the subdivisions of the multiplicative cascade model are repeated indefinitely. This limiting distribution is lognormal in the center and has Pareto tails. Potentially, this approach has important implications in mineral and oil resource evaluation.
文摘The purpose of this contribution is to highlight four topics of regional and worldwide mineral resource prediction:(1)use of the jackknife for bias elimination in regional mineral potential assessments;(2)estimating total amounts of metal from mineral potential maps;(3)fractal/multifractal modeling of mineral deposit density data in permissive areas;and(4)worldwide and large-areas metal size-frequency distribution modeling.The techniques described in this paper remain tentative because they have not been widely researched and applied in mineral potential studies.Although most of the content of this paper has previously been published,several perspectives for further research are suggested.
文摘AIMTo characterize the human retinal vessel arborisation in normal and amblyopic eyes using multifractal geometry and lacunarity parameters.METHODSMultifractal analysis using a box counting algorithm was carried out for a set of 12 segmented and skeletonized human retinal images, corresponding to both normal (6 images) and amblyopia states of the retina (6 images).RESULTSIt was found that the microvascular geometry of the human retina network represents geometrical multifractals, characterized through subsets of regions having different scaling properties that are not evident in the fractal analysis. Multifractal analysis of the amblyopia images (segmented and skeletonized versions) show a higher average of the generalized dimensions (D<sub>q</sub>) for q=0, 1, 2 indicating a higher degree of the tree-dimensional complexity associated with the human retinal microvasculature network whereas images of healthy subjects show a lower value of generalized dimensions indicating normal complexity of biostructure. On the other hand, the lacunarity analysis of the amblyopia images (segmented and skeletonized versions) show a lower average of the lacunarity parameter Λ than the corresponding values for normal images (segmented and skeletonized versions).CONCLUSIONThe multifractal and lacunarity analysis may be used as a non-invasive predictive complementary tool to distinguish amblyopic subjects from healthy subjects and hence this technique could be used for an early diagnosis of patients with amblyopia.
文摘We investigate the approximating capability of Markov modulated Poisson processes (MMPP) for modeling multifractal Internet traffic. The choice of MMPP is motivated by its ability to capture the variability and correlation in moderate time scales while being analytically tractable. Important statistics of traffic burstiness are described and a customized moment-based fitting procedure of MMPP to traffic traces is presented. Our methodology of doing this is to examine whether the MMPP can be used to predict the performance of a queue to which MMPP sample paths and measured traffic traces are fed for comparison respectively, in addition to the goodness-of-fit test of MMPP. Numerical results and simulations show that the fitted MMPP can approximate multifractal traffic quite well, i.e. accurately predict the queueing performance.
文摘A new kind of multifractal is constructed by fractional Fourier transform of Cantor sets. The wavelet transform modulus maxima method is applied to calculate the singularity spectrum under an operational definition of multifractal. In particular, an analysing procedure to determine the spectrum is suggested for practice. Nonanalyticities of singularity spectra or phase transitions are discovered, which are interpreted as some indications on the range of Boltzmann temperature q, on which the scaling relation of partition function holds.
文摘The manuscript attempts to explore the periodicity in the distribution of galaxies in the recently reported Saraswati supercluster and the Stripe 82 region containing it as an example.The report of 120 Mpc periodicity in the Abell galaxy clusters by power spectrum analysis is the motivation behind the study.The power spectral analysis across the central part of the Stripe 82 region shows a periodic variation of 3.09°or 71 Mpc in fractal dimension whereas an average angular periodicity of 3.45°or 94 Mpc is observed across the Stripe 82 region.This refers to the periodicity of complexity or cluster density of galaxy distribution.The texture of the distribution pattern understood through lacunarity analysis indicates a near symmetric distribution.Fractal dimensions like box-counting dimension,information dimension and correlation dimension are also found through multifractal analysis.While the information dimension tells about the distribution density of galactic points,the correlation dimension details the distribution of galaxies in the neighbourhood.
文摘We have investigated the Nu Calm Transcutaneous Vagus Nerve Stimulation device of the NuCalm Solace Lifesciences founding that it gives a multifractal output. A diminishing fractal/multifractal HRV is consistently reported in literature as related to a serious Autonomic Nervous System (ANS) dysfunction that of course we observe in several psychological and psychiatric disorders. Therefore, we suggest the investigators to apply such a device in subjects affected from anxiety, depression and stress using the method of inducing tVNS stimulation.
基金supported by the National Natural Science Foundation of China(Grant No.41202110)Open Fund of State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation(Southwest Petroleum University)(Grant No.PLN201612)+1 种基金the Applied Basic Research Projects in Sichuan Province(Grant No.2015JY0200)Open Fund Project from Sichuan Key Laboratory of Natural Gas Geology(Grant No.2015trqdz07)
文摘Pore structure characteristics are important to oil and gas exploration in complex low-permeability reservoirs. Using multifractal theory and nuclear magnetic resonance （NMR）, we studied the pore structure of low-permeability sandstone rocks from the 4th Member （Es4） of the Shahejie Formation in the south slope of the Dongying Sag. We used the existing pore structure data from petrophysics, core slices, and mercury injection tests to classify the pore structure into three categories and five subcategories. Then, the T2 spectra of samples with different pore structures were interpolated, and the one- and three-dimensional fractal dimensions and the multifractal spectrum were obtained. Parameters a （intensity of singularity） andf（a） （density of distribution） were extracted from the multifractal spectra. The differences in the three fractal dimensions suggest that the pore structure types correlate with a andf（a）. The results calculated based on the multifractal spectrum is consistent with that of the core slices and mercury injection. Finally, the proposed method was applied to an actual logging profile to evaluate the pore structure of low-permeability sandstone reservoirs.
基金financially funded by the National Key R&D Program of China(No.2016YFC0600501)the Natural Science Foundation of China(Nos.41572315,41872250)the Fundamental Research Funds for the Central Universities,China University of Geosciences(Wuhan)(No.CUG170104)
文摘Shale gas resources have been regarded as a viable energy source, and it is of great significance to characterize the shale composition of different cements, such as quartz and dolomite. In this research, chemical analysis and the multifractal method have been used to study the mineral compositions and petrophysical structures of cements in shale samples from the Longmaxi Formation, China. X-ray diffraction, electron microprobe, field emission scanning electron microscopy, cathodoluminescence microscopy and C-O isotope analyses confirmed that cements in the Longmaxi Formation shales are mainly composed of Fe-bearing dolomite and quartz. Fe-bearing dolomite cements concentrate around dolomite as annuli, filling micron-sized inorganic primary pores. Quartz cements in the form of nanoparicles fill primary inter-crystalline pores among clay minerals. Theoretical calculation shows that the Fe-bearing dolomite cements formed slightly earlier than the quartz cements, but both were related to diagenetic illitization of smectite. Moreover, multifractal analysis reveals that the quartz cements are more irregularly distributed in pores than the Fe-bearing dolomite cements. These results suggest that the plugging effect of the quartz cements on the primary inoraganic pore structures is the dominant factor resulting in low interconnected porosity of shales, which are unfavorable for the enrichment of shale gas.
文摘A series of element concentrations sampled from four drill cores with a length about 1000 m into different skarn-type deposits were selected from the Shizishan orefield, central Tongling, southeastern part of Anhui Province. Using the multifractal method, the distribution and migration characteristics of the major and trace elements are analyzed. The multifractal spectrum of the major elements is left-skewed, whereas the spectrum of the trace elements is right-skewed, which shows that in the process of skarn formation, the trace elements were enriched only locally, and major elements transported within a much larger range. The correlation coefficients of the multifractal parameters Aa （width of the multifractal spectrum） of the four drill cores are relatively low, but the correlation coefficients of the multifractal parameters R （spectrum symmetry parameter） and Af are relatively higher, indicating that although the non-homogeneous intensity of the distribution of elements is inconsistent, their spatial accumulation patterns are almost the same during the ore-forming process. The statistics of the mnltifractal parameters of various elements in the different locations show that the ore-forming processes and element migration pattern in the Shizishan orefield are consistent, and that the migrations of trace elements and major elements exhibit some differences.
基金Supported by the NSFC-Shandong Joint Fund “Study on the DisasterCausing Mechanism and Disaster Prevention Countermeasures of MultiSource Storm Surges”(No.U1706226)the National Natural Science Foundation of China “Coastal Engineering and Risk Assessment Based on a Four-Layer Nested Multi-Objective Probability Model”(No.51379195)+1 种基金the Natural Science Foundation of Shandong Province “Three-Layer Nested Multi-Objective Probability Prediction and Risk Assessment in Coastal Engineering”(No.ZR2013EEM034)the Program of Promotion Plan for Postgraduates’ Educational Quality “Paying More Attention to the Study on the Cultivation Mode of Mathematical Modeling for Engineering Postgraduates”(No.861801232417)
文摘When exploring the temporal and spatial change law of ocean environment, the most common method used is using smaller-scale observed data to derive the change law for a larger-scale system. For instance, using 30-year observation data to derive 100-year return period design wave height. Therefore, the study of inherent self-similarity in ocean hydrological elements becomes increasingly important to the study of multi-year return period design wave height derivation. In this paper, we introduced multifractal to analyze the statistical characteristics of wave height series data observed from oceanic hydrological station. An improvement is made to address the existing problems of the multifractal detrended fluctuation analysis (MF-DFA) method, where trend function showed a discontinuity between intervals. The improved MFDFA method is based on signal mode decomposition, replacing piecewise polynomial fitting used in the original method. We applied the proposed method to the wave height data collected at Chaolian Island, Shandong, China, from 1963 to 1989 and was able to conclude the wave height sequence presented weak multi-fractality. This result provided strong support to the past research on the derivation of multi-year return period design wave height with observed data. Moreover, the new method proposed in this paper also provides a new perspective to explore the intrinsic characteristic of data.
基金the joint support from China Scholarship Council(201406450029)National Natural Science Foundation of China(Grant No.41504108)China Postdoctoral Science Foundation(Grant No.2015M582568)
文摘In order to analyze and compare the differences in pore structures between shale gas and shale oil formations, a few samples from the Longmaxi and Bakken Formations were collected and studied using X-ray diffraction, LECO TOC measurement, gas adsorption and field-emission scanning electron microscope. The results show that samples from the Bakken Formation have a higher TOC than those from the Longmaxi Formation. The Longmaxi Formation has higher micropore volume and larger micropore surface area and exhibited a smaller average distribution of microsize pores compared to the Bakken Formation. Both formations have similar meso-macropore volume. The Longmaxi Formation has a much larger meso-macropore surface area, which is corresponding to a smaller average meso-macropore size. CO_2 adsorption data processing shows that the pore size of the majority of the micropores in the samples from the Longmaxi Formation is less than 1 nm, while the pore size of the most of the micropores in the samples from the Bakken Formation is larger than 1 nm. Both formations have the same number of pore clusters in the 2–20 nm range, but the Bakken Formation has two additional pore size groups with mean pore size diameters larger than 20 nm. Multifractal analysis of pore size distribution curves that was derived from gas adsorption indicates that the samples from the Longmaxi Formation have more significant micropore heterogeneity and less meso-macropore heterogeneity. Abundant micropores as well as mesomacropores exist in the organic matter in the Longmaxi Formation, while the organic matter of the Bakken Formation hosts mainly micropores.
基金supported by the National Natural Science Foundation of China(No.51874320)Scientific Research Foundation of China University of Petroleum,Beijing(No.2462017BJB11)。
文摘Based on the experiments of nitrogen gas adsorption(N_2 GA) and nuclear magnetic resonance(NMR),the multifractal characteristics of pore structures in shale and tight s andstone from the Chang 7 member of Trias sic Yanchang Formation in Ordos Basin,NW China,are investigated.The multifractal spectra obtained from N2 GA and NMR are analyzed with pore throat structure parameters.The results show that the pore size distributions obtained from N2 GA and NMR are different,and the obtained multifractal characteristics vary from each other.The specific surface and total pore volume obtained by N2 GA experiment have correlations with multifractal characteristics.For the core samples with the similar specific surface,the value of the deviation of multifractal spectra Rd increases with the increase in the proportion of large pores.When the proportion of macropores is small,the Rd value will increase with the increase in specific surface.The multifractal characteristics of pore structures are influenced by specific surface area,average pore size and adsorption volume measured from N2 GA experiment.The multifractal characteristic parameters of tight sandstone measured from NMR spectra are larger than those of shale,which may be caused by the differences in pore size distribution and porosity of shale and tight sandstone.
