Gas-liquid two-phase flow in fractal porous media is pivotal for engineering applications,yet it remains challenging to be accurately characterized due to complex microstructure-flow interactions.This study establishe...Gas-liquid two-phase flow in fractal porous media is pivotal for engineering applications,yet it remains challenging to be accurately characterized due to complex microstructure-flow interactions.This study establishes a pore-scale numerical framework integratingMonte Carlo-generated fractal porousmedia with Volume of Fluid(VOF)simulations to unravel the coupling among pore distribution characterized by fractal dimension(Df),flow dynamics,and displacement efficiency.A pore-scale model based on the computed tomography(CT)microstructure of Berea sandstone is established,and the simulation results are compared with experimental data.Good agreement is found in phase distribution,breakthrough behavior,and flow path morphology,confirming the reliability of the numerical simulation method.Ten fractal porous media models with Df ranging from 1.25~1.7 were constructed using a Monte-Carlo approach.The gas-liquid two-phase flow dynamics was characterized using the VOF solver across gas injection rates of 0.05-5m/s,inwhich the time-resolved two-phase distribution patternswere systematically recorded.The results reveal that smaller fractal dimensions(Df=1.25~1.45)accelerate fingering breakthrough(peak velocity is 1.73 m/s at Df=1.45)due to a bimodal pore size distribution dominated by narrow channels.Increasing Df amplifies vorticity generation by about 3 times(eddy viscosity is 0.033 Pa⋅s at Df=1.7)through reduced interfacial curvature,while tortuosity-driven pressure differentials transition from sharp increases(0.4~6.3 Pa at Df=1.25~1.3)to inertial plateaus(4.8 Pa at Df=1.7).A nonlinear increase in equilibrium gas volume fraction(fav=0.692 at Df=1.7)emerges from residual gas saturation and turbulence-enhanced dispersion.This behavior is further modulated by flow velocity,with fav peaking at 0.72 under capillary-dominated conditions(0.05 m/s),but decreasing to 0.65 in the inertial regime(0.5 m/s).The work quantitatively links fractal topology to multiphase flow regimes,demonstrating the critical role of Df in governing preferential pathways,energy dissipation,and phase distribution.展开更多
The Black–Scholes equation is one of the most important partial differential equations governing the value of financial derivatives in financial markets.The Black–Scholes model for pricing stock options has been app...The Black–Scholes equation is one of the most important partial differential equations governing the value of financial derivatives in financial markets.The Black–Scholes model for pricing stock options has been applied to various payoff structures,and options trading is based on Black and Scholes’principle of dynamic hedging to estimate and assess option prices over time.However,the Black–Scholes model requires severe constraints,assumptions,and conditions to be applied to real-life financial and economic problems.Several methods and approaches have been developed to approach these conditions,such as fractional Black–Scholes models based on fractional derivatives.These fractional models are expected since the Black–Scholes equation is derived using Ito’s lemma from stochastic calculus,where fractional derivatives play a leading role.Hence,a fractional stochastic model that includes the basic Black–Scholes model as a special case is expected.However,these fractional financial models require computational tools and advanced analytical methods to solve the associated fractional Black–Scholes equations.Nevertheless,it is believed that the fractal nature of economic processes permits to model economical and financial markets problems more accurately compared to the conventional model.The relationship between fractional calculus and fractals is well-known in the literature.This study introduces a generalized Black–Scholes equation in fractal dimensions and discusses its role in financial marketing.In our analysis,we consider power-laws properties for volatility,interest rated,and dividend payout,which emerge in several empirical regularities in quantitative finance and economics.We apply our model to study the problem of pricing barrier option and we estimate the values of fractal dimensions in both time and in space.Our model can be used to obtain the prices of many pay-off models.We observe that fractal dimensions considerably affect the solutions of the Black–Scholes equation and that,for fractal dimensions much smaller than unity,the call option increases significantly.We prove that fractal dimensions are a powerful tool to obtain new results.Further details are analyzed and discussed.展开更多
Fire detection has held stringent importance in computer vision for over half a century.The development of early fire detection strategies is pivotal to the realization of safe and smart cities,inhabitable in the futu...Fire detection has held stringent importance in computer vision for over half a century.The development of early fire detection strategies is pivotal to the realization of safe and smart cities,inhabitable in the future.However,the development of optimal fire and smoke detection models is hindered by limitations like publicly available datasets,lack of diversity,and class imbalance.In this work,we explore the possible ways forward to overcome these challenges posed by available datasets.We study the impact of a class-balanced dataset to improve the fire detection capability of state-of-the-art(SOTA)vision-based models and propose the use of generative models for data augmentation,as a future work direction.First,a comparative analysis of two prominent object detection architectures,You Only Look Once version 7(YOLOv7)and YOLOv8 has been carried out using a balanced dataset,where both models have been evaluated across various evaluation metrics including precision,recall,and mean Average Precision(mAP).The results are compared to other recent fire detection models,highlighting the superior performance and efficiency of the proposed YOLOv8 architecture as trained on our balanced dataset.Next,a fractal dimension analysis gives a deeper insight into the repetition of patterns in fire,and the effectiveness of the results has been demonstrated by a windowing-based inference approach.The proposed Slicing-Aided Hyper Inference(SAHI)improves the fire and smoke detection capability of YOLOv8 for real-life applications with a significantly improved mAP performance over a strict confidence threshold.YOLOv8 with SAHI inference gives a mAP:50-95 improvement of more than 25%compared to the base YOLOv8 model.The study also provides insights into future work direction by exploring the potential of generative models like deep convolutional generative adversarial network(DCGAN)and diffusion models like stable diffusion,for data augmentation.展开更多
The FeCrA1 fiber was used to prepare porous metal materials with air-laid technology, and then followed by sintering at 1300 ℃ for a holding period of 2 h in the vacuum. In addition, a novel fractal soft, which was d...The FeCrA1 fiber was used to prepare porous metal materials with air-laid technology, and then followed by sintering at 1300 ℃ for a holding period of 2 h in the vacuum. In addition, a novel fractal soft, which was developed based on the fractal theory and the computer image processing technology, was explored to describe the pore structure of porous metal materials. Furthermore, the fractal dimension of pore structure was calculated by the soft and the effects of magnification and porosity on ffactal dimension were also discussed. The results show that the fractal dimension decreases with increase in the magnification, while it increases continuously with the porosity enhancing. The interrelationship between the fractal dimension and the magnification or porosity can be presented by the equation of D=α_0exp（-x/α_1）＋α_2和D=k_2-（k_1-k_2）/[1＋exp（（θ-k_0）/k_3）], respectively.展开更多
Surface electromyogram （EMG） signals were identified by fractal dimension.Two patterns of surface EMG signals were acquired from 30 healthy volunteers＇ right forearm flexor respectively in the process of forearm su...Surface electromyogram （EMG） signals were identified by fractal dimension.Two patterns of surface EMG signals were acquired from 30 healthy volunteers＇ right forearm flexor respectively in the process of forearm supination （FS） and forearm pronation （FP）.After the raw action surface EMG （ASEMG） signal was decomposed into several sub-signals with wavelet packet transform （WPT）,five fractal dimensions were respectively calculated from the raw signal and four sub-signals by the method based on fuzzy self-similarity.The results show that calculated from the sub-signal in the band 0 to 125 Hz,the fractal dimensions of FS ASEMG signals and FP ASEMG signals distributed in two different regions,and its error rate based on Bayes decision was no more than 2.26%.Therefore,the fractal dimension is an appropriate feature by which an FS ASEMG signal is distinguished from an FP ASEMG signal.展开更多
[Objective] The aim was to discuss the spatial pattern changes of land use in Tianjin new coastal area based on fractal dimensions.[Method] By dint of remote and geographic information system technology to obtain the ...[Objective] The aim was to discuss the spatial pattern changes of land use in Tianjin new coastal area based on fractal dimensions.[Method] By dint of remote and geographic information system technology to obtain the data of urban land use in new coastal area from 1993 to 2008,the boundary dimension,radius dimension and information dimension of each land use type were calculated based on fractal dimension.In addition,the revealed land use spatial dimension changes characteristics were analyzed.[Result] The spatial distribution of each land use type in new costal area had distinct fractal characteristics.And,the amount and changes of three types of dimension values effectively revealed the changes of complicatedness,centeredness and evenness of spatial pattern of land use in the study area.The boundary dimension of unused land and salty earth increased incessantly,which suggested its increasing complicatedness.The boundary of the port and wharf and shoal land was getting simpler.The radius dimension of the cultivated land was larger than 2,which suggested that its area spread from center to the surroundings;the one in salty land and waters distributed evenly within different radius space to the center of the city;the one in other land use types reduced gradually from center to the surroundings.The information dimension value in the woodland and orchard land,unused land and shoal land was small,and was in obvious concentrated distribution;the spatial distribution of cultivated and salty land concentrated in the outside area;the construction area in the port and wharf spread gradually on the basis of original state;the spatial distribution of waters and residents and mines were even.[Conclusion] Applying fractal dimensions to the study of spatial pattern changes of urban land use can make up for some disadvantages in classical urban spatial pattern quantitative research,which has favorable practical value.展开更多
The split-Hopkinson pressure bar(SHPB)and digital image correlation(DIC)techniques are combined to analyze the dynamic compressive failure process of coal samples,and the box fractal dimension is used to quantitativel...The split-Hopkinson pressure bar(SHPB)and digital image correlation(DIC)techniques are combined to analyze the dynamic compressive failure process of coal samples,and the box fractal dimension is used to quantitatively analyze the dynamic changes in the coal sample cracks under impact load conditions with different loading rates.The experimental results show that the fractal dimension can quantitatively describe the evolution process of coal fractures under dynamic load.During the dynamic compression process,the evolution of the coal sample cracks presents distinct stages.In the crack propagation stage,the fractal dimension increases rapidly with the progress of loading,and in the crack widening stage,the fractal dimension increases slowly with the progress of loading.The initiation of the crack propagation phase of the coal samples gradually occurs more quickly with increasing loading rate;the initial cracks appear earlier.At the same loading time point,when the loading rate is greater,the fractal dimension of the cracks observed in the coal sample is greater.展开更多
Fractal geometry is an important method in soil science,and many studies have used fractal theory to examine soil properties and the relationships with other eco-environmental factors.However,there have been few studi...Fractal geometry is an important method in soil science,and many studies have used fractal theory to examine soil properties and the relationships with other eco-environmental factors.However,there have been few studies examining soil particle volume fractal dimension in alpine grasslands.To study the volume fractal dimension of soil particles （D） and its relationships with soil salt,soil nutrient and plant species diversity,we conducted an experiment on an alpine grassland under different disturbance degrees：non-disturbance （N0）,light disturbance （L）,moderate disturbance （M） and heavy disturbance （H）.The results showed that （1） Ds varied from 2.573 to 2.635 among the different disturbance degrees and increased with increasing degrees of disturbance.（2） Shannon-Wiener diversity index,Pielou＇s evenness index and Margalef richness index reached their highest values at the M degree,indicating that moderate disturbance is beneficial to the increase of plant species diversity.（3） In the L and M degrees,there was a significant positive correlation between D and clay content and a significant negative correlation between D and soil organic matter （SOM）.In the H degree,D was significantly and positively correlated with total salt （TS）.The results suggested that to a certain extent,D can be used to characterize the uniformity of soil texture in addition to soil fertility characteristics.（4） For the L degree,there was a significant negative correlation between D and the Shannon-Wiener diversity index; while for the M degree,there was a significant negative correlation between D and Pielou＇s evenness index.展开更多
Food dye Brilliant Blue was introduced as the tracer in a dye-tracing experiment to obtain dye profile patterns of sandy loam soil, aeolian sandy soil, percolating paddy soil and permeable paddy soil. The dyed soil pr...Food dye Brilliant Blue was introduced as the tracer in a dye-tracing experiment to obtain dye profile patterns of sandy loam soil, aeolian sandy soil, percolating paddy soil and permeable paddy soil. The dyed soil profiles were then photographed and the photos were scanned into a computer. Edited with certain software, only the dyed areas were left on the profile photos, which indicted the preferential flow paths for water and solute transport. Fractal dimensions of the dye patterns were calculated according to Arnold's function. Soil particle size distribution was analyzed by pipette method. The regression analysis showed that there was significant relationship between soil clay content and fractal dimension D of the dye pattern of soil profile. Based on the experiment results, the possibility of introducing fractal dimension to estimation of soil sensitivity to preferential flow is discussed.展开更多
In the research of fractal cities, the fractal dimension is very important. It is used to describe the fractal character of the city. The authors have designed two approaches to calculate the fractal dimension by the ...In the research of fractal cities, the fractal dimension is very important. It is used to describe the fractal character of the city. The authors have designed two approaches to calculate the fractal dimension by the box-counting method through an example of Beijing, which are called the vector method and the grid method, respectively. The former calculates the fractal dimension through an intersecting analysis in ArcView; and the latter is carried out by programming in Matlab. They are compared from three aspects： the calculating process, the limits in use, and the results. As a result, the conclusion is made that there are merits and faults on both methods, and they should be chosen to use properly in practical situation.展开更多
Based on the geological conditions of coal mining face No.15-14120 at No.8 mine of Pingdingshan coal mining group,the real-time evolution of coal-roof crack network with working face advancing was collected with the h...Based on the geological conditions of coal mining face No.15-14120 at No.8 mine of Pingdingshan coal mining group,the real-time evolution of coal-roof crack network with working face advancing was collected with the help of intrinsically safe borehole video instrument.And according to the geology of this working face,a discrete element model was calculated by UDEC.Combining in situ experimental data with numerical results,the relationship between the fractal dimension of boreholes'wall and the distribution of advanced abutment pressure was studied under the condition of mining advance.The results show that the variation tendency of fractal dimension and the abutment pressure has the same characteristic value.The distance between working face and the peak value of the abutment pressure has a slight increasing trend with the advancing of mining-face.When the working face is set as the original point,the trend of fractal dimension from the far place to the origin can be divided into three phases:constant,steady increasing and constant.And the turning points of these phases are the max-influencing distance(50 m)and peak value(15 m)of abutment pressure.展开更多
The characteristics of broken surfaces were r esearched by a scanning electron microscope (SEM) and a reflection microscope, a nd the fractal dimensions of broken surfaces were measured by the Slit Island me thod. Th...The characteristics of broken surfaces were r esearched by a scanning electron microscope (SEM) and a reflection microscope, a nd the fractal dimensions of broken surfaces were measured by the Slit Island me thod. The experimental results indicate that the broken surface of aluminum elec tric porcelain is a fractal body in statistics, and the fractal dimensions of br oken surfaces are different with the different amplification multiple value.In a ll of measured fractal dimensions,both of values measured in 100× under reflect ion microscope and in 500× under SEM are maximum, whereas the values measur ed in 63× under reflection microscope and in 2000× under SEM are obviously min imum. The fractal dimensions of broken surfaces are also affected by the degrees of gray comparison and the kinds of measuring methods. The relationships betwee n the fractal dimensions of broken surfaces and porcelain bend strengths are tha t they are in positive correlation on the low multiples and in negative correlat ion on the high multiples.展开更多
As the scale of residual oil treatment increases and cleaner production improves in China,slurry bubble column reactors face many challenges and opportunities for residual oil hydrogenation technology.The internals de...As the scale of residual oil treatment increases and cleaner production improves in China,slurry bubble column reactors face many challenges and opportunities for residual oil hydrogenation technology.The internals development is critical to adapt the long-term stable operation.In this paper,the volumetric mass transfer coefficient,gas holdup and bubble size in a gas-liquid up-flow column are studied with two kinds of internals.The gas holdup and volumetric mass transfer coefficient increase by 120% and 42% when the fractal dimension of bubbles increases from 0.56 to 2.56,respectively.The enhanced mass transfer processing may improve the coke suppression ability in the slurry reactor for residual oil treatment.The results can be useful for the exploration of reacting conditions,scale-up strategies,and oil adaptability.This work is valuable for the design of reactor systems and technological processes.展开更多
The fractal dimension（FD） of surfaces has been widely used to characterize the properties of materials.However,most of the previous researches were concentrated on the correlation between the FD of surfaces and mech...The fractal dimension（FD） of surfaces has been widely used to characterize the properties of materials.However,most of the previous researches were concentrated on the correlation between the FD of surfaces and mechanical properties of materials,such as impact energy and fracture toughness,etc.The aim of this paper is to characterize the spheroidization grade and strength of 15CrMo steel through determination of FD of cementite phase on the basis of two-dimension microstructural image.Two methods,namely slit-island method（SIM） and box-counting method（BCM）,are used to determine the value of FD.It is found that the FD value evaluated by using BCM is generally higher than that evaluated by SIM.This phenomenon may be due to the difference in the principles used in different methods.Whether SIM or BCM is used,the spheroidization grade in 15CrMo steel linearly increases with decreasing the value of FD.The relationship between the FD value,D,and spheroidization grade,Sg,can be approximately expressed as D≌-0.11Sg＋A,where A is a constant value which is depended on the evaluation method.Both the ultimate strength and the yielding strength of 15CrMo steel increase with increasing FD of cementite phase.There may be a common relationship between the FD of cementite phase and strength of 15CrMo steel.When the FD of cementite phase in 15CrMo steel is determined,the strength of this steel can be evaluated.The present paper can provide a novel method to evaluate the strength and spheroidization grade of carbon steel through determination of fractal dimension（FD） of cementite phase.展开更多
The fractal dimension is one important parameter that characterizes waveforms. In this paper, we derive a new method to calculate fractal dimension of digital voice-signal waveforms. We show that fractal dimension is ...The fractal dimension is one important parameter that characterizes waveforms. In this paper, we derive a new method to calculate fractal dimension of digital voice-signal waveforms. We show that fractal dimension is an efficient tool for speaker recognition or speech recognition. It can be used to identify different speakers or distinguish speech. We apply our results to Chinese speaker recognition and numerical experiment shows that fractal dimension is an efficient parameter to characterize individual Chinese speakers. We have developed a semiautomatic voiceprint analysis system based on the theory of this paper and former researches.展开更多
The impact of harmful algal blooms （HABs） on public health and related economics have been increasing in many coastal regions of the world. Sedimentation of algal cells through flocculation with clay particles is a ...The impact of harmful algal blooms （HABs） on public health and related economics have been increasing in many coastal regions of the world. Sedimentation of algal cells through flocculation with clay particles is a promising strategy for controlling HABs. Previous studies found that removal efficiency （RE） was influenced by many factors, including clay type and concentration, algal growth stage, and physiological aspects of HAB cells. To estimate the effect of morphological characteristics of the aggregates on HAB cell removal, fractal dimensions were measured and the RE of three species of HAB organism, Heterosigma akashiwo, Alexandrium tamarense, and Skeletonema eostatum, by original clay and modified clay, was determined. For all HAB species, the modified clay had a higher RE than original clay. For the original clay, the two-dimensional fractal dimension （D2） was 1.92 and three-dimensional ffactal dimension （D3） 2.81, while for the modified clay, D2 was 1.84 and D3 was 2.50. The addition of polyaluminum chloride （PAC1） lead to a decrease of the repulsive barrier between clay particles, and resulted in lower D2 and D3. Due to the decrease of D3, and the increase of the effective sticking coefficient, the flocculation rate between modified clay particles and HAB organisms increased, and thus resulted in a high RE. The fractal dimensions of flocs differed in HAB species with different cell morphologies. For example, Alexandrium tamarense cells are ellipsoidal, and the D3 and D2 of flocs were the highest, while for Skeletonema costatum, which has filamentous cells, the D3 and D2 of flocs were the lowest.展开更多
A fractal pore structure model of combustible cartridge cases was established by virtue of the fractal geometry. Pore structure information, such as backbone fractal dimension and pore fractal dimension, of four kinds...A fractal pore structure model of combustible cartridge cases was established by virtue of the fractal geometry. Pore structure information, such as backbone fractal dimension and pore fractal dimension, of four kinds of combustible cartridge case were obtained by mercury intrusion porosimetry (MIP) . The formation mechanism of fractal pore structure of combustible cartridge was studied. The results show that the backbone fractal dimension consists of the component and influenced by the component number and size of components; the pore percolation fractal dimension reflects the pore structures of components; and the fractal dimension of pore structure is positively relative to the tensile strength of combustible cartridge case.展开更多
This article extends a signal-based approach formerly proposed by the authors, which utilizes the fractal dimension of time frequency feature （FDTFF） of displacements, for earthquake damage detection of moment resis...This article extends a signal-based approach formerly proposed by the authors, which utilizes the fractal dimension of time frequency feature （FDTFF） of displacements, for earthquake damage detection of moment resist frame （MRF）, and validates the approach with shaking table tests. The time frequency feature （TFF） of the relative displacement at measured story is defined as the real part of the coefficients of the analytical wavelet transform. The fractal dimension （FD） is to quantify the TFF within the fundamental frequency band using box counting method. It is verified that the FDTFFs at all stories of the linear MRF are identical with the help of static condensation method and modal superposition principle, while the FDTFFs at the stories with localized nonlinearities due to damage will be different from those at the stories without nonlinearities using the reverse-path methodology. By comparing the FDTFFs of displacements at measured stories in a structure, the damage-induced nonlinearity of the structure under strong ground motion can be detected and localized. Finally shaking table experiments on a 1：8 scale sixteen-story three-bay steel MRF with added frictional dampers, which generate local nonlinearities, are conducted to validate the approach.展开更多
This study investigates the spatial and temporal variation of fractal dimension and b-value for the eastern part of the Himalaya and adjoining area(26°N–31°N and 87°E–98°E).The analysis is carrie...This study investigates the spatial and temporal variation of fractal dimension and b-value for the eastern part of the Himalaya and adjoining area(26°N–31°N and 87°E–98°E).The analysis is carried out on the earthquake dataset of 1373 events(Mc=4.0)by sliding window technique for the period 1964 to 2020.The region is divided into three sub regions A(87°E–92°E),B(92°E–94°E)and C(94°E–98°E).The b-value computed for the region A comprising eastern Nepal is smaller compared to other two regions which infers the possible high stress and asperities in the region.High spatial fractal dimension(Dc>1.5)and low temporal fractal dimension(Dt<0.31)are computed for the regions.High spatial fractal dimension may indicate that fractures generating earthquakes are approaching a 2D structure and low temporal fractal dimension implies high clustering of earthquake’s epicenters.The b value shows a weak negative correlation with Dc for regions A and C while a weak positive correlation is observed for the region B.Based on b-value and fractal dimension,this study explains the frequency of earthquakes and heterogeneity of the seismogenic structure in this part of the Himalaya.展开更多
The paper proposes a new multiple-factor clustering method(NMFCM)with consideration of both box fractal dimension(BFD)and orientation of joints.This method assumes that the BFDs of different clusters were uneven,and c...The paper proposes a new multiple-factor clustering method(NMFCM)with consideration of both box fractal dimension(BFD)and orientation of joints.This method assumes that the BFDs of different clusters were uneven,and clustering was performed by redistributing the joints near the boundaries of clusters on a polar map to maximize an index for estimating the difference of the BFD(DBFD).Three main aspects were studied to develop the NMFCM.First,procedures of the NMFCM and reasonableness of assumptions were illustrated.Second,main factors affecting the NMFCM were investigated by numerical simulations with disk joint models.Finally,two different sections of a rock slope were studied to verify the practicability of the NMFCM.The results demonstrated that:(1)The NMFCM was practical and could effectively alleviate the problem of hard boundary during clustering;(2)The DBFD tended to increase after the improvement of clustering accuracy;(3)The improvement degree of the NMFCM clustering accuracy was mainly influenced by three parameters,namely,the number of clusters,number of redistributed joints,and total number of joints;and(4)The accuracy rate of clustering could be effectively improved by the NMFCM.展开更多
基金funded by the National Key R&D Program of China,China(Grant No.2023YFB4005500)National Natural Science Foundation of China,China(Grant Nos.52379113 and 52379114).
文摘Gas-liquid two-phase flow in fractal porous media is pivotal for engineering applications,yet it remains challenging to be accurately characterized due to complex microstructure-flow interactions.This study establishes a pore-scale numerical framework integratingMonte Carlo-generated fractal porousmedia with Volume of Fluid(VOF)simulations to unravel the coupling among pore distribution characterized by fractal dimension(Df),flow dynamics,and displacement efficiency.A pore-scale model based on the computed tomography(CT)microstructure of Berea sandstone is established,and the simulation results are compared with experimental data.Good agreement is found in phase distribution,breakthrough behavior,and flow path morphology,confirming the reliability of the numerical simulation method.Ten fractal porous media models with Df ranging from 1.25~1.7 were constructed using a Monte-Carlo approach.The gas-liquid two-phase flow dynamics was characterized using the VOF solver across gas injection rates of 0.05-5m/s,inwhich the time-resolved two-phase distribution patternswere systematically recorded.The results reveal that smaller fractal dimensions(Df=1.25~1.45)accelerate fingering breakthrough(peak velocity is 1.73 m/s at Df=1.45)due to a bimodal pore size distribution dominated by narrow channels.Increasing Df amplifies vorticity generation by about 3 times(eddy viscosity is 0.033 Pa⋅s at Df=1.7)through reduced interfacial curvature,while tortuosity-driven pressure differentials transition from sharp increases(0.4~6.3 Pa at Df=1.25~1.3)to inertial plateaus(4.8 Pa at Df=1.7).A nonlinear increase in equilibrium gas volume fraction(fav=0.692 at Df=1.7)emerges from residual gas saturation and turbulence-enhanced dispersion.This behavior is further modulated by flow velocity,with fav peaking at 0.72 under capillary-dominated conditions(0.05 m/s),but decreasing to 0.65 in the inertial regime(0.5 m/s).The work quantitatively links fractal topology to multiphase flow regimes,demonstrating the critical role of Df in governing preferential pathways,energy dissipation,and phase distribution.
基金Rami Ahmad El-Nabulsi has received funding from the Czech National Agency of Agricultural 533 Research,project QK22020134“Innovative fisheries management of a large reservoir”.
文摘The Black–Scholes equation is one of the most important partial differential equations governing the value of financial derivatives in financial markets.The Black–Scholes model for pricing stock options has been applied to various payoff structures,and options trading is based on Black and Scholes’principle of dynamic hedging to estimate and assess option prices over time.However,the Black–Scholes model requires severe constraints,assumptions,and conditions to be applied to real-life financial and economic problems.Several methods and approaches have been developed to approach these conditions,such as fractional Black–Scholes models based on fractional derivatives.These fractional models are expected since the Black–Scholes equation is derived using Ito’s lemma from stochastic calculus,where fractional derivatives play a leading role.Hence,a fractional stochastic model that includes the basic Black–Scholes model as a special case is expected.However,these fractional financial models require computational tools and advanced analytical methods to solve the associated fractional Black–Scholes equations.Nevertheless,it is believed that the fractal nature of economic processes permits to model economical and financial markets problems more accurately compared to the conventional model.The relationship between fractional calculus and fractals is well-known in the literature.This study introduces a generalized Black–Scholes equation in fractal dimensions and discusses its role in financial marketing.In our analysis,we consider power-laws properties for volatility,interest rated,and dividend payout,which emerge in several empirical regularities in quantitative finance and economics.We apply our model to study the problem of pricing barrier option and we estimate the values of fractal dimensions in both time and in space.Our model can be used to obtain the prices of many pay-off models.We observe that fractal dimensions considerably affect the solutions of the Black–Scholes equation and that,for fractal dimensions much smaller than unity,the call option increases significantly.We prove that fractal dimensions are a powerful tool to obtain new results.Further details are analyzed and discussed.
基金supported by a grant from R&D Program Development of Rail-Specific Digital Resource Technology Based on an AI-Enabled Rail Support Platform,grant number PK2401C1,of the Korea Railroad Research Institute.
文摘Fire detection has held stringent importance in computer vision for over half a century.The development of early fire detection strategies is pivotal to the realization of safe and smart cities,inhabitable in the future.However,the development of optimal fire and smoke detection models is hindered by limitations like publicly available datasets,lack of diversity,and class imbalance.In this work,we explore the possible ways forward to overcome these challenges posed by available datasets.We study the impact of a class-balanced dataset to improve the fire detection capability of state-of-the-art(SOTA)vision-based models and propose the use of generative models for data augmentation,as a future work direction.First,a comparative analysis of two prominent object detection architectures,You Only Look Once version 7(YOLOv7)and YOLOv8 has been carried out using a balanced dataset,where both models have been evaluated across various evaluation metrics including precision,recall,and mean Average Precision(mAP).The results are compared to other recent fire detection models,highlighting the superior performance and efficiency of the proposed YOLOv8 architecture as trained on our balanced dataset.Next,a fractal dimension analysis gives a deeper insight into the repetition of patterns in fire,and the effectiveness of the results has been demonstrated by a windowing-based inference approach.The proposed Slicing-Aided Hyper Inference(SAHI)improves the fire and smoke detection capability of YOLOv8 for real-life applications with a significantly improved mAP performance over a strict confidence threshold.YOLOv8 with SAHI inference gives a mAP:50-95 improvement of more than 25%compared to the base YOLOv8 model.The study also provides insights into future work direction by exploring the potential of generative models like deep convolutional generative adversarial network(DCGAN)and diffusion models like stable diffusion,for data augmentation.
基金Project(2011CB610302) supported by the National Basic Research Program of ChinaProjects(51074130,51134003) supported by the National Natural Science Foundation of ChinaProject(20110491699) supported by the National Science Foundation for Post-doctoral Scientists of China
文摘The FeCrA1 fiber was used to prepare porous metal materials with air-laid technology, and then followed by sintering at 1300 ℃ for a holding period of 2 h in the vacuum. In addition, a novel fractal soft, which was developed based on the fractal theory and the computer image processing technology, was explored to describe the pore structure of porous metal materials. Furthermore, the fractal dimension of pore structure was calculated by the soft and the effects of magnification and porosity on ffactal dimension were also discussed. The results show that the fractal dimension decreases with increase in the magnification, while it increases continuously with the porosity enhancing. The interrelationship between the fractal dimension and the magnification or porosity can be presented by the equation of D=α_0exp（-x/α_1）＋α_2和D=k_2-（k_1-k_2）/[1＋exp（（θ-k_0）/k_3）], respectively.
基金The National Natural Science Foundation of China(No.60171006)the National Basic Research Programof China (973 Pro-gram) (No.2005CB724303).
文摘Surface electromyogram （EMG） signals were identified by fractal dimension.Two patterns of surface EMG signals were acquired from 30 healthy volunteers＇ right forearm flexor respectively in the process of forearm supination （FS） and forearm pronation （FP）.After the raw action surface EMG （ASEMG） signal was decomposed into several sub-signals with wavelet packet transform （WPT）,five fractal dimensions were respectively calculated from the raw signal and four sub-signals by the method based on fuzzy self-similarity.The results show that calculated from the sub-signal in the band 0 to 125 Hz,the fractal dimensions of FS ASEMG signals and FP ASEMG signals distributed in two different regions,and its error rate based on Bayes decision was no more than 2.26%.Therefore,the fractal dimension is an appropriate feature by which an FS ASEMG signal is distinguished from an FP ASEMG signal.
基金Supported by National Natural Science Fund Program(40705038)~~
文摘[Objective] The aim was to discuss the spatial pattern changes of land use in Tianjin new coastal area based on fractal dimensions.[Method] By dint of remote and geographic information system technology to obtain the data of urban land use in new coastal area from 1993 to 2008,the boundary dimension,radius dimension and information dimension of each land use type were calculated based on fractal dimension.In addition,the revealed land use spatial dimension changes characteristics were analyzed.[Result] The spatial distribution of each land use type in new costal area had distinct fractal characteristics.And,the amount and changes of three types of dimension values effectively revealed the changes of complicatedness,centeredness and evenness of spatial pattern of land use in the study area.The boundary dimension of unused land and salty earth increased incessantly,which suggested its increasing complicatedness.The boundary of the port and wharf and shoal land was getting simpler.The radius dimension of the cultivated land was larger than 2,which suggested that its area spread from center to the surroundings;the one in salty land and waters distributed evenly within different radius space to the center of the city;the one in other land use types reduced gradually from center to the surroundings.The information dimension value in the woodland and orchard land,unused land and shoal land was small,and was in obvious concentrated distribution;the spatial distribution of cultivated and salty land concentrated in the outside area;the construction area in the port and wharf spread gradually on the basis of original state;the spatial distribution of waters and residents and mines were even.[Conclusion] Applying fractal dimensions to the study of spatial pattern changes of urban land use can make up for some disadvantages in classical urban spatial pattern quantitative research,which has favorable practical value.
基金Projects(51822403,51827901)supported by the National Natural Science Foundation of ChinaProject(2019ZT08G315)supported by the Department of Science and Technology of Guangdong Province,China。
文摘The split-Hopkinson pressure bar(SHPB)and digital image correlation(DIC)techniques are combined to analyze the dynamic compressive failure process of coal samples,and the box fractal dimension is used to quantitatively analyze the dynamic changes in the coal sample cracks under impact load conditions with different loading rates.The experimental results show that the fractal dimension can quantitatively describe the evolution process of coal fractures under dynamic load.During the dynamic compression process,the evolution of the coal sample cracks presents distinct stages.In the crack propagation stage,the fractal dimension increases rapidly with the progress of loading,and in the crack widening stage,the fractal dimension increases slowly with the progress of loading.The initiation of the crack propagation phase of the coal samples gradually occurs more quickly with increasing loading rate;the initial cracks appear earlier.At the same loading time point,when the loading rate is greater,the fractal dimension of the cracks observed in the coal sample is greater.
基金financially supported by the National Basic Research Program of China(2009CB825103)
文摘Fractal geometry is an important method in soil science,and many studies have used fractal theory to examine soil properties and the relationships with other eco-environmental factors.However,there have been few studies examining soil particle volume fractal dimension in alpine grasslands.To study the volume fractal dimension of soil particles （D） and its relationships with soil salt,soil nutrient and plant species diversity,we conducted an experiment on an alpine grassland under different disturbance degrees：non-disturbance （N0）,light disturbance （L）,moderate disturbance （M） and heavy disturbance （H）.The results showed that （1） Ds varied from 2.573 to 2.635 among the different disturbance degrees and increased with increasing degrees of disturbance.（2） Shannon-Wiener diversity index,Pielou＇s evenness index and Margalef richness index reached their highest values at the M degree,indicating that moderate disturbance is beneficial to the increase of plant species diversity.（3） In the L and M degrees,there was a significant positive correlation between D and clay content and a significant negative correlation between D and soil organic matter （SOM）.In the H degree,D was significantly and positively correlated with total salt （TS）.The results suggested that to a certain extent,D can be used to characterize the uniformity of soil texture in addition to soil fertility characteristics.（4） For the L degree,there was a significant negative correlation between D and the Shannon-Wiener diversity index; while for the M degree,there was a significant negative correlation between D and Pielou＇s evenness index.
基金Project supported by the National Key Basic Research Support FOundation(NKBRSF) of China(No.G19990ll708) and the Guangxi Uni,rsitv Science funds China(No.1701).
文摘Food dye Brilliant Blue was introduced as the tracer in a dye-tracing experiment to obtain dye profile patterns of sandy loam soil, aeolian sandy soil, percolating paddy soil and permeable paddy soil. The dyed soil profiles were then photographed and the photos were scanned into a computer. Edited with certain software, only the dyed areas were left on the profile photos, which indicted the preferential flow paths for water and solute transport. Fractal dimensions of the dye patterns were calculated according to Arnold's function. Soil particle size distribution was analyzed by pipette method. The regression analysis showed that there was significant relationship between soil clay content and fractal dimension D of the dye pattern of soil profile. Based on the experiment results, the possibility of introducing fractal dimension to estimation of soil sensitivity to preferential flow is discussed.
文摘In the research of fractal cities, the fractal dimension is very important. It is used to describe the fractal character of the city. The authors have designed two approaches to calculate the fractal dimension by the box-counting method through an example of Beijing, which are called the vector method and the grid method, respectively. The former calculates the fractal dimension through an intersecting analysis in ArcView; and the latter is carried out by programming in Matlab. They are compared from three aspects： the calculating process, the limits in use, and the results. As a result, the conclusion is made that there are merits and faults on both methods, and they should be chosen to use properly in practical situation.
基金financial support from the State Key Basic Research Program of China(Nos.2011CB201201and 2010CB226802)the National Natural Science Foundation of China(No.51204112)
文摘Based on the geological conditions of coal mining face No.15-14120 at No.8 mine of Pingdingshan coal mining group,the real-time evolution of coal-roof crack network with working face advancing was collected with the help of intrinsically safe borehole video instrument.And according to the geology of this working face,a discrete element model was calculated by UDEC.Combining in situ experimental data with numerical results,the relationship between the fractal dimension of boreholes'wall and the distribution of advanced abutment pressure was studied under the condition of mining advance.The results show that the variation tendency of fractal dimension and the abutment pressure has the same characteristic value.The distance between working face and the peak value of the abutment pressure has a slight increasing trend with the advancing of mining-face.When the working face is set as the original point,the trend of fractal dimension from the far place to the origin can be divided into three phases:constant,steady increasing and constant.And the turning points of these phases are the max-influencing distance(50 m)and peak value(15 m)of abutment pressure.
基金Funded by the Natural Science Foundation of Shaanxi Province(No.2003E225)
文摘The characteristics of broken surfaces were r esearched by a scanning electron microscope (SEM) and a reflection microscope, a nd the fractal dimensions of broken surfaces were measured by the Slit Island me thod. The experimental results indicate that the broken surface of aluminum elec tric porcelain is a fractal body in statistics, and the fractal dimensions of br oken surfaces are different with the different amplification multiple value.In a ll of measured fractal dimensions,both of values measured in 100× under reflect ion microscope and in 500× under SEM are maximum, whereas the values measur ed in 63× under reflection microscope and in 2000× under SEM are obviously min imum. The fractal dimensions of broken surfaces are also affected by the degrees of gray comparison and the kinds of measuring methods. The relationships betwee n the fractal dimensions of broken surfaces and porcelain bend strengths are tha t they are in positive correlation on the low multiples and in negative correlat ion on the high multiples.
基金the National Natural Science Foundation of China(51678238,51722806,51608325,21908057)National Key R&D Program of China(2018YFC1802704,2018YFC1801904)+1 种基金China Postdoctoral Science Foundation funded project(2018M641942)Shanghai Sailing Program(19YF1411800)for financial support.
文摘As the scale of residual oil treatment increases and cleaner production improves in China,slurry bubble column reactors face many challenges and opportunities for residual oil hydrogenation technology.The internals development is critical to adapt the long-term stable operation.In this paper,the volumetric mass transfer coefficient,gas holdup and bubble size in a gas-liquid up-flow column are studied with two kinds of internals.The gas holdup and volumetric mass transfer coefficient increase by 120% and 42% when the fractal dimension of bubbles increases from 0.56 to 2.56,respectively.The enhanced mass transfer processing may improve the coke suppression ability in the slurry reactor for residual oil treatment.The results can be useful for the exploration of reacting conditions,scale-up strategies,and oil adaptability.This work is valuable for the design of reactor systems and technological processes.
基金supported by National Natural Science Foundations ofChina (Grant Nos. 50835003,50805047,10972078)National Hi-tech Research and Development Program of China (863 Program,Grant No.2009AA04Z421)
文摘The fractal dimension（FD） of surfaces has been widely used to characterize the properties of materials.However,most of the previous researches were concentrated on the correlation between the FD of surfaces and mechanical properties of materials,such as impact energy and fracture toughness,etc.The aim of this paper is to characterize the spheroidization grade and strength of 15CrMo steel through determination of FD of cementite phase on the basis of two-dimension microstructural image.Two methods,namely slit-island method（SIM） and box-counting method（BCM）,are used to determine the value of FD.It is found that the FD value evaluated by using BCM is generally higher than that evaluated by SIM.This phenomenon may be due to the difference in the principles used in different methods.Whether SIM or BCM is used,the spheroidization grade in 15CrMo steel linearly increases with decreasing the value of FD.The relationship between the FD value,D,and spheroidization grade,Sg,can be approximately expressed as D≌-0.11Sg＋A,where A is a constant value which is depended on the evaluation method.Both the ultimate strength and the yielding strength of 15CrMo steel increase with increasing FD of cementite phase.There may be a common relationship between the FD of cementite phase and strength of 15CrMo steel.When the FD of cementite phase in 15CrMo steel is determined,the strength of this steel can be evaluated.The present paper can provide a novel method to evaluate the strength and spheroidization grade of carbon steel through determination of fractal dimension（FD） of cementite phase.
文摘The fractal dimension is one important parameter that characterizes waveforms. In this paper, we derive a new method to calculate fractal dimension of digital voice-signal waveforms. We show that fractal dimension is an efficient tool for speaker recognition or speech recognition. It can be used to identify different speakers or distinguish speech. We apply our results to Chinese speaker recognition and numerical experiment shows that fractal dimension is an efficient parameter to characterize individual Chinese speakers. We have developed a semiautomatic voiceprint analysis system based on the theory of this paper and former researches.
基金Supported by the Fund for Creative Research Groups by National Natural Science Foundation of China (No. 40821004)the National Natural Science Foundation of China (No. 40906055)the National Basic Research Program of China (973 Program) (No. 2010CB428706)
文摘The impact of harmful algal blooms （HABs） on public health and related economics have been increasing in many coastal regions of the world. Sedimentation of algal cells through flocculation with clay particles is a promising strategy for controlling HABs. Previous studies found that removal efficiency （RE） was influenced by many factors, including clay type and concentration, algal growth stage, and physiological aspects of HAB cells. To estimate the effect of morphological characteristics of the aggregates on HAB cell removal, fractal dimensions were measured and the RE of three species of HAB organism, Heterosigma akashiwo, Alexandrium tamarense, and Skeletonema eostatum, by original clay and modified clay, was determined. For all HAB species, the modified clay had a higher RE than original clay. For the original clay, the two-dimensional fractal dimension （D2） was 1.92 and three-dimensional ffactal dimension （D3） 2.81, while for the modified clay, D2 was 1.84 and D3 was 2.50. The addition of polyaluminum chloride （PAC1） lead to a decrease of the repulsive barrier between clay particles, and resulted in lower D2 and D3. Due to the decrease of D3, and the increase of the effective sticking coefficient, the flocculation rate between modified clay particles and HAB organisms increased, and thus resulted in a high RE. The fractal dimensions of flocs differed in HAB species with different cell morphologies. For example, Alexandrium tamarense cells are ellipsoidal, and the D3 and D2 of flocs were the highest, while for Skeletonema costatum, which has filamentous cells, the D3 and D2 of flocs were the lowest.
基金Sponsored by Young Fund Programs of Explosives&Propellants ( HYZ08010202-4)
文摘A fractal pore structure model of combustible cartridge cases was established by virtue of the fractal geometry. Pore structure information, such as backbone fractal dimension and pore fractal dimension, of four kinds of combustible cartridge case were obtained by mercury intrusion porosimetry (MIP) . The formation mechanism of fractal pore structure of combustible cartridge was studied. The results show that the backbone fractal dimension consists of the component and influenced by the component number and size of components; the pore percolation fractal dimension reflects the pore structures of components; and the fractal dimension of pore structure is positively relative to the tensile strength of combustible cartridge case.
基金National Natural Science Foundation under Grant No.51161120359Ministry of Education under Grant No.20112302110050Special Fund for Earthquake Scientific Research in the Public Interest under Grant No.201308003
文摘This article extends a signal-based approach formerly proposed by the authors, which utilizes the fractal dimension of time frequency feature （FDTFF） of displacements, for earthquake damage detection of moment resist frame （MRF）, and validates the approach with shaking table tests. The time frequency feature （TFF） of the relative displacement at measured story is defined as the real part of the coefficients of the analytical wavelet transform. The fractal dimension （FD） is to quantify the TFF within the fundamental frequency band using box counting method. It is verified that the FDTFFs at all stories of the linear MRF are identical with the help of static condensation method and modal superposition principle, while the FDTFFs at the stories with localized nonlinearities due to damage will be different from those at the stories without nonlinearities using the reverse-path methodology. By comparing the FDTFFs of displacements at measured stories in a structure, the damage-induced nonlinearity of the structure under strong ground motion can be detected and localized. Finally shaking table experiments on a 1：8 scale sixteen-story three-bay steel MRF with added frictional dampers, which generate local nonlinearities, are conducted to validate the approach.
基金University Grants Commission(UGC),Nepal for providing financial support。
文摘This study investigates the spatial and temporal variation of fractal dimension and b-value for the eastern part of the Himalaya and adjoining area(26°N–31°N and 87°E–98°E).The analysis is carried out on the earthquake dataset of 1373 events(Mc=4.0)by sliding window technique for the period 1964 to 2020.The region is divided into three sub regions A(87°E–92°E),B(92°E–94°E)and C(94°E–98°E).The b-value computed for the region A comprising eastern Nepal is smaller compared to other two regions which infers the possible high stress and asperities in the region.High spatial fractal dimension(Dc>1.5)and low temporal fractal dimension(Dt<0.31)are computed for the regions.High spatial fractal dimension may indicate that fractures generating earthquakes are approaching a 2D structure and low temporal fractal dimension implies high clustering of earthquake’s epicenters.The b value shows a weak negative correlation with Dc for regions A and C while a weak positive correlation is observed for the region B.Based on b-value and fractal dimension,this study explains the frequency of earthquakes and heterogeneity of the seismogenic structure in this part of the Himalaya.
基金funded by the National Natural Science Foundation of China(Grant Nos.41972264 and 52078093)Liaoning Revitalization Talents Program,China(Grant No.XLYC1905015)。
文摘The paper proposes a new multiple-factor clustering method(NMFCM)with consideration of both box fractal dimension(BFD)and orientation of joints.This method assumes that the BFDs of different clusters were uneven,and clustering was performed by redistributing the joints near the boundaries of clusters on a polar map to maximize an index for estimating the difference of the BFD(DBFD).Three main aspects were studied to develop the NMFCM.First,procedures of the NMFCM and reasonableness of assumptions were illustrated.Second,main factors affecting the NMFCM were investigated by numerical simulations with disk joint models.Finally,two different sections of a rock slope were studied to verify the practicability of the NMFCM.The results demonstrated that:(1)The NMFCM was practical and could effectively alleviate the problem of hard boundary during clustering;(2)The DBFD tended to increase after the improvement of clustering accuracy;(3)The improvement degree of the NMFCM clustering accuracy was mainly influenced by three parameters,namely,the number of clusters,number of redistributed joints,and total number of joints;and(4)The accuracy rate of clustering could be effectively improved by the NMFCM.
