Let X^H(u)(u)={X^H(u)(u);u∈R^N+}be linear multifractional stable sheets with index functional H(u),where H(u)=(H1(u),…,HN(u))is a function with values in(0;1)N.Based on some assumptions of H(u),we obtain the existen...Let X^H(u)(u)={X^H(u)(u);u∈R^N+}be linear multifractional stable sheets with index functional H(u),where H(u)=(H1(u),…,HN(u))is a function with values in(0;1)N.Based on some assumptions of H(u),we obtain the existence of the local times of X^H(u)(u)and establish its joint continuity and the Holder regularity.These results generalize the corresponding results about fractional stable sheets to multifractional stable sheets.展开更多
In this paper, we prove that two-parameter Volterra multifractional process can be approximated in law in the topology of the anisotropic Besov spaces by the family of processes {Bn（s, t）}n∈N defined by Bn（s,t）=...In this paper, we prove that two-parameter Volterra multifractional process can be approximated in law in the topology of the anisotropic Besov spaces by the family of processes {Bn（s, t）}n∈N defined by Bn（s,t）=∫0^s∫0^tKa（s）（s,u）Kβ（t）（t,v）θn（u,u）dudu,where {θn（u, v））,n∈N is a family of processes, converging in law to a Brownian sheet as n -＊ oo, based on the well known Donsker＇s theorem.展开更多
This article proposes an innovative method for modeling financial markets using multifractional Brownian motion(mBm).Unlike traditional fractional Brownian motion,mBm offers variable local memory,providing a more accu...This article proposes an innovative method for modeling financial markets using multifractional Brownian motion(mBm).Unlike traditional fractional Brownian motion,mBm offers variable local memory,providing a more accurate representation of the multifractal volatility and long-range dependencies found in financial time series.We present a precise mathematical formulation of mBm,sophisticated techniques for estimating the Hurst function,efficient numerical simulation algorithms,and a detailed empirical study covering several major stock indices.The results indicate that mBm more accurately reflects price dynamics,significantly improves risk analysis,and provides more precise pricing of exotic options compared to traditional models.展开更多
In this paper,we prove approximations of multifractional Brownian motions with moving-average representations and of those with harmonizable representations in the space of continuous functions on [0,1]. These approxi...In this paper,we prove approximations of multifractional Brownian motions with moving-average representations and of those with harmonizable representations in the space of continuous functions on [0,1]. These approximations are constructed by Poisson processes.展开更多
The main goal of this paper is to study the sample path properties for the harmonisable-type N-parameter multifractional Brownian motion, whose local regularities change as time evolves. We provide the upper and lower...The main goal of this paper is to study the sample path properties for the harmonisable-type N-parameter multifractional Brownian motion, whose local regularities change as time evolves. We provide the upper and lower bounds on the hitting probabilities of an （N, d）-multifractional Brownian motion. Moreover, we determine the Hausdorff dimension of its inverse images, and the Hausdorff and packing dimensions of its level sets.展开更多
Presently,financial portfolio managers lack a solid basis for building a reliable risk management strategy for green debt instrument investments due to the lack of compelling growth and resilience data.Therefore,this ...Presently,financial portfolio managers lack a solid basis for building a reliable risk management strategy for green debt instrument investments due to the lack of compelling growth and resilience data.Therefore,this study assesses the role of green bonds in financial markets by assessing and correlating their complex scaling behaviors across multiple periods with those of key benchmark assets(e.g.,conventional bonds,high-yield bonds,Euro-Dollar exchange,Dow Jones Industrial Index,Bitcoin,and Gold).Specifically,we explore linear and nonlinear correlation patterns using crosscorrelation tests and the dynamic conditional correlation model,focusing on bond interactions under various degrees of freedom.Our analysis reveals that although most assets exhibit nonlinear correlations,Bitcoin uniquely aligns linearly with U.S.bonds under certain conditions.Green bonds,however,display nonlinear correlations with Bitcoin and stand out for their distinct upward financial persistence.We find also that green bonds are primary drivers in the financial domain,highlighted by their pronounced interactions and the consistent cross-correlation with the Euro-Dollar exchange rate.Moreover,green bonds have the lowest multifractality,showing persistent upward trends and antipersistent downward trends,rendering them quite resilient during periods of high volatility.These results imply that green bonds may be advantageous to portfolio risk management strategies,especially during crises when diversification and hedging tactics are needed.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
This study investigates the relationships between agricultural spot markets and external uncertainties through multifractal detrending moving-average cross-correlation analysis(MF-X-DMA).The dataset contains the Grain...This study investigates the relationships between agricultural spot markets and external uncertainties through multifractal detrending moving-average cross-correlation analysis(MF-X-DMA).The dataset contains the Grains&Oilseeds Index(GOI)and its five subindices for wheat,maize,soyabeans,rice,and barley.Moreover,we use three uncertainty proxies,namely,economic policy uncertainty(EPU),geopolitical risk(GPR),and Volatility Index(VIX).We observe multifractal cross-correlations between agricultural markets and uncertainties.Furthermore,statistical tests reveal that maize has intrinsic joint multifractality with all the uncertainty proxies,highly sensitive to external shocks.Additionally,intrinsic multifractality among GOI-GPR,wheat-GPR,and soyabeans-VIX is illustrated.However,other series have apparent multifractal crosscorrelations with high probabilities.Moreover,our analysis suggests that among the three types of external uncertainties,GPR has the strongest association with grain prices,excluding maize and soyabeans.展开更多
The carbonate-rich shale of the Permian Wujiaping Formation in Sichuan Basin exhibits significant heterogeneity in its lithology and pore structure,which directly influence its potential for shale gas extraction.This ...The carbonate-rich shale of the Permian Wujiaping Formation in Sichuan Basin exhibits significant heterogeneity in its lithology and pore structure,which directly influence its potential for shale gas extraction.This study assesses the factors that govern pore heterogeneity by analyzing the mineral composition of the shale,as well as its pore types and their multifractal characteristics.Three primary shale facies-siliceous,mixed,and calcareous-are identified based on mineralogy,and their multifractal characteristics reveal strongly heterogeneous pore structures.The brittleness of siliceous shale,rich in quartz and pyrite,is favorable for hydraulic fracturing;while calcareous shale,with higher levels of calcite,exhibits reduced brittleness.Multifractal analysis,using nitrogen adsorption isotherms,reveals complex pore structures across different shale facies,with siliceous shale showing better pore connectivity and uniformity.The types of pores in shales include organic matter pores,interparticle pores,and intraparticle pores,among which organic matter pores are the most abundant.Pore size distribution and connectivity are notably higher in siliceous shale compared to calcareous shale,which exhibit a predominance of micropores and more isolated pore structures.Pore heterogeneity of the carbonate-rich shale in the Wujiaping Formation is primarily governed by its intrinsic mineral composition,carbonate diagenesis,mechanical compaction,and its subsequent thermal maturation with the micro-migration of organic matter.This study highlights the importance of mineral composition,especially the presence of dolomite and calcite,in shaping pore heterogeneity.These findings emphasize the critical role of shale lithofacies and pore structure in optimizing shale gas extraction methods.展开更多
Biotite content critically influences rock mechanical behavior and threatens underground engineering stability.Uniaxial compression tests with acoustic emission(AE)monitoring were conducted on granite pegmatite sample...Biotite content critically influences rock mechanical behavior and threatens underground engineering stability.Uniaxial compression tests with acoustic emission(AE)monitoring were conducted on granite pegmatite samples having varying biotite content.Peak frequency distribution analysis,rise angleaverage frequency(RA-AF)analysis,multifractal theory,and a dynamic multifractal algorithm were applied to explore the relationship between damage evolution and AE characteristics.Results indicate that increased biotite content reduces uniaxial compressive strength and elastic modulus,enhances plastic deformation,and increases the proportion of shear cracks.The segmented evolution of the dynamic multifractal parameter Δα_(m) is biotite-dependent.Oscillations during the elastic phase signify localized shear crack initiation and propagation;their attenuation in the plastic phase reflects frictional closure along biotite cleavage planes,promoting elastic energy storage and delaying release.AE-based damage models and time-varying signals characterize rock damage progression.Stress concentrations around biotite minerals foster localized shear band formation,leading to concentrated shear failure at lower damage levels.Higher biotite content accelerates crack propagation,while smooth cleavage planes lower the fracture energy threshold,reducing strength and stiffness.These findings enhance understanding of biotite-influenced progressive rock damage and underpin stability monitoring and early-warning systems for underground engineering.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
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
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
文摘Let X^H(u)(u)={X^H(u)(u);u∈R^N+}be linear multifractional stable sheets with index functional H(u),where H(u)=(H1(u),…,HN(u))is a function with values in(0;1)N.Based on some assumptions of H(u),we obtain the existence of the local times of X^H(u)(u)and establish its joint continuity and the Holder regularity.These results generalize the corresponding results about fractional stable sheets to multifractional stable sheets.
基金partially supported by National Natural Science Foundation of China(Grant Nos.1140131311771209)+6 种基金partially supported by National Natural Science Foundation of China(Grant No.11426036)Natural Science Foundation of Jiangsu Province(Grant No.BK20161579)China Postdoctoral Science Foundation(Grant Nos.2014M5603682015T80475)2014 Qing Lan ProjectNatural Science Foundation of Anhui Province(Grant No.1408085QA10)Key Natural Science Foundation of Anhui Education Commission(Grant No.KJ2016A453)
文摘In this paper, we prove that two-parameter Volterra multifractional process can be approximated in law in the topology of the anisotropic Besov spaces by the family of processes {Bn（s, t）}n∈N defined by Bn（s,t）=∫0^s∫0^tKa（s）（s,u）Kβ（t）（t,v）θn（u,u）dudu,where {θn（u, v））,n∈N is a family of processes, converging in law to a Brownian sheet as n -＊ oo, based on the well known Donsker＇s theorem.
文摘This article proposes an innovative method for modeling financial markets using multifractional Brownian motion(mBm).Unlike traditional fractional Brownian motion,mBm offers variable local memory,providing a more accurate representation of the multifractal volatility and long-range dependencies found in financial time series.We present a precise mathematical formulation of mBm,sophisticated techniques for estimating the Hurst function,efficient numerical simulation algorithms,and a detailed empirical study covering several major stock indices.The results indicate that mBm more accurately reflects price dynamics,significantly improves risk analysis,and provides more precise pricing of exotic options compared to traditional models.
基金supported by National Natural Science Foundation of China (Grant No. 10901054)
文摘In this paper,we prove approximations of multifractional Brownian motions with moving-average representations and of those with harmonizable representations in the space of continuous functions on [0,1]. These approximations are constructed by Poisson processes.
基金Supported by Zhejiang Provincial Natural Science Foundation of China (Grant No. Y6100663)
文摘The main goal of this paper is to study the sample path properties for the harmonisable-type N-parameter multifractional Brownian motion, whose local regularities change as time evolves. We provide the upper and lower bounds on the hitting probabilities of an （N, d）-multifractional Brownian motion. Moreover, we determine the Hausdorff dimension of its inverse images, and the Hausdorff and packing dimensions of its level sets.
基金Benjamin M.Tabak(Grant no.305485/2022-9)gratefully acknowledges financial support from the CNPq foundation and CAPES Foundation。
文摘Presently,financial portfolio managers lack a solid basis for building a reliable risk management strategy for green debt instrument investments due to the lack of compelling growth and resilience data.Therefore,this study assesses the role of green bonds in financial markets by assessing and correlating their complex scaling behaviors across multiple periods with those of key benchmark assets(e.g.,conventional bonds,high-yield bonds,Euro-Dollar exchange,Dow Jones Industrial Index,Bitcoin,and Gold).Specifically,we explore linear and nonlinear correlation patterns using crosscorrelation tests and the dynamic conditional correlation model,focusing on bond interactions under various degrees of freedom.Our analysis reveals that although most assets exhibit nonlinear correlations,Bitcoin uniquely aligns linearly with U.S.bonds under certain conditions.Green bonds,however,display nonlinear correlations with Bitcoin and stand out for their distinct upward financial persistence.We find also that green bonds are primary drivers in the financial domain,highlighted by their pronounced interactions and the consistent cross-correlation with the Euro-Dollar exchange rate.Moreover,green bonds have the lowest multifractality,showing persistent upward trends and antipersistent downward trends,rendering them quite resilient during periods of high volatility.These results imply that green bonds may be advantageous to portfolio risk management strategies,especially during crises when diversification and hedging tactics are needed.
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 National Social Science Fund Major Projects(22&ZD160).
文摘This study investigates the relationships between agricultural spot markets and external uncertainties through multifractal detrending moving-average cross-correlation analysis(MF-X-DMA).The dataset contains the Grains&Oilseeds Index(GOI)and its five subindices for wheat,maize,soyabeans,rice,and barley.Moreover,we use three uncertainty proxies,namely,economic policy uncertainty(EPU),geopolitical risk(GPR),and Volatility Index(VIX).We observe multifractal cross-correlations between agricultural markets and uncertainties.Furthermore,statistical tests reveal that maize has intrinsic joint multifractality with all the uncertainty proxies,highly sensitive to external shocks.Additionally,intrinsic multifractality among GOI-GPR,wheat-GPR,and soyabeans-VIX is illustrated.However,other series have apparent multifractal crosscorrelations with high probabilities.Moreover,our analysis suggests that among the three types of external uncertainties,GPR has the strongest association with grain prices,excluding maize and soyabeans.
基金supported by research projects P23057 and JKK4624004 of Jianghan Oilfield Company,SINOPEC.
文摘The carbonate-rich shale of the Permian Wujiaping Formation in Sichuan Basin exhibits significant heterogeneity in its lithology and pore structure,which directly influence its potential for shale gas extraction.This study assesses the factors that govern pore heterogeneity by analyzing the mineral composition of the shale,as well as its pore types and their multifractal characteristics.Three primary shale facies-siliceous,mixed,and calcareous-are identified based on mineralogy,and their multifractal characteristics reveal strongly heterogeneous pore structures.The brittleness of siliceous shale,rich in quartz and pyrite,is favorable for hydraulic fracturing;while calcareous shale,with higher levels of calcite,exhibits reduced brittleness.Multifractal analysis,using nitrogen adsorption isotherms,reveals complex pore structures across different shale facies,with siliceous shale showing better pore connectivity and uniformity.The types of pores in shales include organic matter pores,interparticle pores,and intraparticle pores,among which organic matter pores are the most abundant.Pore size distribution and connectivity are notably higher in siliceous shale compared to calcareous shale,which exhibit a predominance of micropores and more isolated pore structures.Pore heterogeneity of the carbonate-rich shale in the Wujiaping Formation is primarily governed by its intrinsic mineral composition,carbonate diagenesis,mechanical compaction,and its subsequent thermal maturation with the micro-migration of organic matter.This study highlights the importance of mineral composition,especially the presence of dolomite and calcite,in shaping pore heterogeneity.These findings emphasize the critical role of shale lithofacies and pore structure in optimizing shale gas extraction methods.
基金provided by the National Key R&D Program of China(No.2024YFC3012605)the State Key Laboratory of Geohazard Prevention and Geoenvironment Protection Independent Research Project(Nos.SKLGP2022Z001,SKLGP2023Z029 and SKLGP2022K027)。
文摘Biotite content critically influences rock mechanical behavior and threatens underground engineering stability.Uniaxial compression tests with acoustic emission(AE)monitoring were conducted on granite pegmatite samples having varying biotite content.Peak frequency distribution analysis,rise angleaverage frequency(RA-AF)analysis,multifractal theory,and a dynamic multifractal algorithm were applied to explore the relationship between damage evolution and AE characteristics.Results indicate that increased biotite content reduces uniaxial compressive strength and elastic modulus,enhances plastic deformation,and increases the proportion of shear cracks.The segmented evolution of the dynamic multifractal parameter Δα_(m) is biotite-dependent.Oscillations during the elastic phase signify localized shear crack initiation and propagation;their attenuation in the plastic phase reflects frictional closure along biotite cleavage planes,promoting elastic energy storage and delaying release.AE-based damage models and time-varying signals characterize rock damage progression.Stress concentrations around biotite minerals foster localized shear band formation,leading to concentrated shear failure at lower damage levels.Higher biotite content accelerates crack propagation,while smooth cleavage planes lower the fracture energy threshold,reducing strength and stiffness.These findings enhance understanding of biotite-influenced progressive rock damage and underpin stability monitoring and early-warning systems for underground engineering.
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.
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.
