Phase separation was studied by the optical microscopy in blends of nylon 6 (PA6) with sodium salt of ethylene/methacrylic acid copolymer (PEMA).The image collecting technology was used to keep track of the developme...Phase separation was studied by the optical microscopy in blends of nylon 6 (PA6) with sodium salt of ethylene/methacrylic acid copolymer (PEMA).The image collecting technology was used to keep track of the development of blends at a certain temperature.The fractal dimension of phase separation was calculated by the image solving technology according to the fractal theory and the self similarity behavior of the process was proved.The relationship of the fractal behavior with composition and experimental temperature was discussed.The fractal behavior of the crystallization development of the crystal phase of PA6 in blends was also discussed and the fractal behavior calculated.展开更多
The present study shows that naturally developed fracture surfaces in rocks display the properties of self-affine fractals. Surface roughness can be quantitatively characterized by fractal dimension D and the intercep...The present study shows that naturally developed fracture surfaces in rocks display the properties of self-affine fractals. Surface roughness can be quantitatively characterized by fractal dimension D and the intercept A on the log-log plot of variance: the former describes the irregularity and the later is statistically analogues to the slopes of asperities. In order to confirm the effects of these fractalparameters on the properties and mechanical behavior of rock joints, which have been observed in experiments under both normal andshear loadings, a theoretic model of rock joint is proposed on the basis of contact mechanics. The shape of asperity at contact is assumed to have a sinusoidal form in its representative scale r, with fractal dimension D and the intercept A. The model considers different local contact mechanisms, such as elastic deformation, frictional sliding and tensile fracture of the asperity. The empirical evolution law of surface damage developed in experiment is implemented into the model to up-date geometry of asperity in loading history. The effects of surface roughness characterized by D, A and re on normal and shear deformation of rock joint have been elaborated.展开更多
The paper reports the effects of surface fractal structures on the rheological behavior and combustion kinetics of raw brown coal and three modified coal water slurries （CWSs）. The results show that the fractal stru...The paper reports the effects of surface fractal structures on the rheological behavior and combustion kinetics of raw brown coal and three modified coal water slurries （CWSs）. The results show that the fractal structures and physicochemical properties of samples are dependent on various modification processes. The apparent viscosities of the coal water slurries increase with increasing surface fractal dimensions （D）, especially with decreasing shear rates. Fur- thermore, it has been proved that the ignition temperatures and apparent activation energies of modified CWSs are lower than that of raw coal water slurry. Compared with the traditional qualitative analysis of the effect of pore structures on CWSs properties, D can more efficiently indicate the quantificational effect of pore structures on the rheological behavior and combustion kinetics of CWSs.展开更多
Comminution of coal to ultrafine sizes by high-pressure waterjet provides a novel method for preparation of coal-water fuels for next generation,near-zero emission electric power generation.The particle size distribut...Comminution of coal to ultrafine sizes by high-pressure waterjet provides a novel method for preparation of coal-water fuels for next generation,near-zero emission electric power generation.The particle size distribution(PSD)of ground coal is a key parameter in the preparation of slurries as it determines the settling behavior of the particles and viscosity of the coal-water mixture.There are several methods available for representation and evaluation of particle size analysis data.However,fractal theory provides a means by which the entire PSD of comminuted materials can be quantified by using of a specific and exact value.In this paper,a volume-based fractal model was deduced to characterize the PSD of the coal which is ground in a specially designed comminution cell.During the size reduction process,the inlet pressures up to 276 MPa were used.展开更多
Sixty-six cells were examined for chromosome length change, with half of them (33) in the early-metaphase and the other half in the pre-metaphase. The 22 couples of chromosomes (excluding sex chromosomes) in each cell...Sixty-six cells were examined for chromosome length change, with half of them (33) in the early-metaphase and the other half in the pre-metaphase. The 22 couples of chromosomes (excluding sex chromosomes) in each cell were analyzed. The differences of chromosome length between the two phases were demonstrated and the correlation dimension of each chromosome was calculated. It was suggested that the mitosis of human chromosome possessed the feature of chaotic decrease. This offers a new approach to the research of the dynamic process of the mitosis.展开更多
The fractal model of rock comminution is presented with Mandelbrot's fractal geometry.The results show that it is difficult for those with only a linear similarity ratio to fit practical situations.The comminution...The fractal model of rock comminution is presented with Mandelbrot's fractal geometry.The results show that it is difficult for those with only a linear similarity ratio to fit practical situations.The comminution prob ability of the central part should be considered so the geometric meaning of the constant in Gaudin-Schuhmann's distribution function can be explained more clearly.展开更多
With a new projective equation, a series of solutions of the （2-J-1）-dimensional dispersive long-water wave system （LWW） is derived. Based on the derived solitary wave solution, we obtain some special fractal loca...With a new projective equation, a series of solutions of the （2-J-1）-dimensional dispersive long-water wave system （LWW） is derived. Based on the derived solitary wave solution, we obtain some special fractal localized structures and chaotic patterns.展开更多
To investigate the instability mechanisms of heterogeneous geological structures in goaf area roofs,three-point bending tests(TPBT)and numerical simulations are performed on composite coal-rock(CCR).Acoustic emission(...To investigate the instability mechanisms of heterogeneous geological structures in goaf area roofs,three-point bending tests(TPBT)and numerical simulations are performed on composite coal-rock(CCR).Acoustic emission(AE)monitoring is employed to analyze key parameters,establishing a multiparameter quantitative system for CCR fracture processes.The impact of lithological homogeneity on fracture evolution and energy migration is examined.Results show that CCR exhibits a three-stage mechanical response:weak contact,strong contact,and post-peak stages,each with distinct crack evolution patterns.A positive correlation is found between lithological homogeneity and tensile crack proportion.No significant correlation is observed between AE average frequency(AF)and AE counts across different lithological CCR;however,peak frequency(PF)displays clear lithology-dependent characteristics.The regulatory effect of the rock homogeneity coefficient(φ)on crack deriva tion mechanisms is quantfied,yielding mathematical relationships between fracture strength(f),crack propagation path angle(β),crack fractal dimension(D),andφ.The study highlights how different fracture modes alter energy migration pathways,confirming the coupling effect of grain distribution on mechanical response and crack propagation,and the influence of parameterφon critical energy release zones.These findings offer new insights into CCR failure mechanisms for mining safety.展开更多
For inhomogeneous lattices we generalize the classical Gaussian model, i.e. it is proposed that the Gaussian type distribution constant and the external magnetic field of site i in this model depend on the coordinatio...For inhomogeneous lattices we generalize the classical Gaussian model, i.e. it is proposed that the Gaussian type distribution constant and the external magnetic field of site i in this model depend on the coordination number qi of site i, and that the relation $b_{q_i}/b_{q_j} = q{_i}/q{_j}$ holds among bq's, where bq is the Gaussian type distribution constant of site j. Using the decimation real-space renormalization group following the spin-rescaling method, the critical points and critical exponents of the Gaussian model are calculated on some Koch type curves and a family of the diamond-type hierarchical (or DH) lattices. At the critical points, it is found that the nearest-neighbor interaction and the magnetic field of site j can be expressed in the form $K^* = b{_q }_{_i } /q{_i } and h_{q_j }^* = 0$ respectively. It is also found that most critical exponents depend on the fractal dimensionality of a fractal system. For the family of the DH lattices, the results are identical with the exact results on translation symmetric lattices, and if the fractal dimensionalityd f=4, the Gaussian model and the mean field theories give the same results.展开更多
The objective of this paper is to investigate the effects of initial particle gradation and rock content on the crushing behavior(i.e.grain size before and after crushing) of weathered phyllite fills.Compaction tests ...The objective of this paper is to investigate the effects of initial particle gradation and rock content on the crushing behavior(i.e.grain size before and after crushing) of weathered phyllite fills.Compaction tests were conducted on weathered phyllite fills with rock contents of 35%,45%,55%,65% and 75%(by weight).First,the particle size distributions(PSDs) were observed before and after compaction,and then the particle breakage of weathered phyllite fills was analyzed by fractal dimension.Relative fractal dimension was proposed to evaluate the effects of initial rock content and initial gradation on the particle breakage.It was found that the fractal dimension method can well characterize the crushing behaviors of the weathered phyllite fills.The finer the fills were,the more they were compacted.That is,after the first compaction,the relative fractal dimension of the weathered phyllite fills increased as the rock content increased,reaching the values of 0.013,0.016,0.024,0.037 and 0.08,respectively.After the second compaction,these relative fractal dimension values,dominated by the initial particle gradation,became 0.059,0.072,0.052,0.095 and 0.118,respectively.In conclusion,the weathered phyllite fills with 55% rock content exhibited the least breakage and were most suitable for filling the subgrade.Findings in this paper will provide significant guidance for the construction of weathered phyllite filling subgrade in future projects.展开更多
This study analyzes the relationship between fracture toughness and the fracture surface fractal dimension for a set of twenty-four CT-type AISI 4340 steel specimens heat treated to a variety of tensile strengths. Spe...This study analyzes the relationship between fracture toughness and the fracture surface fractal dimension for a set of twenty-four CT-type AISI 4340 steel specimens heat treated to a variety of tensile strengths. Specimens were tested in accordance with ASTM E 399. Their respective fracture surfaces were plated, polished, photographed under an SEM in BSE mode and measured according to the Richardson method to obtain fractal dimensions. For brittle materials the limited results are consistent with previous literature: increasing fractal dimension with increasing toughness. For partially or fully ductile materials the results indicate a decrease in fractal dimension with an increase in fracture toughness. The data are modeled using a variation of the function applied to ceramics. Fracture in a ductile mode is characterized by the formation of dimples which exhibit fractal characteristics. The results are discussed in terms of the micromechanisms of fracture.展开更多
The goal of this study is to establish relationships between the hot compression deformation behaviors and the fractal dimension of primary phase morphology of TA15 titanium alloy using the analytical methods of metal...The goal of this study is to establish relationships between the hot compression deformation behaviors and the fractal dimension of primary phase morphology of TA15 titanium alloy using the analytical methods of metallurgical microscope and transmission electron microscope coupled with box-counting dimension method. The hot compression deformation behaviors vary with decreasing fractal dimension owing to the change of microstructure caused by different parameters of the hot compressive deformation.The results indicate that TA15 alloy shows dynamic recrystallization characteristics at deformation temperature lower than 850℃while fractal dimension exhibits a moderate decreasing trend with the temperature increasing,and shows dynamic recovery characteristics at deformation temperature higher than 850℃while fractal dimension reduces rapidly with the temperature increasing.The fractal dimension displays non-linear relationship with fraction of primary phase and with aspect ratio of primary phase.展开更多
The morphological complexity of cells and tissues,whether normal or pathological,is characterized by two primary attributes:Irregularity and self-similarity across different scales.When an object exhibits self-similar...The morphological complexity of cells and tissues,whether normal or pathological,is characterized by two primary attributes:Irregularity and self-similarity across different scales.When an object exhibits self-similarity,its shape remains unchanged as the scales of measurement vary because any part of it resembles the whole.On the other hand,the size and geometric characteristics of an irregular object vary as the resolution increases,revealing more intricate details.Despite numerous attempts,a reliable and accurate method for quantifying the morphological features of gastrointestinal organs,tissues,cells,their dynamic changes,and pathological disorders has not yet been established.However,fractal geometry,which studies shapes and patterns that exhibit self-similarity,holds promise in providing a quantitative measure of the irregularly shaped morphologies and their underlying self-similar temporal behaviors.In this context,we explore the fractal nature of the gastrointestinal system and the potential of fractal geometry as a robust descriptor of its complex forms and functions.Additionally,we examine the practical applications of fractal geometry in clinical gastroenterology and hepatology practice.展开更多
The asymptotic behavior of periodic solutions to fractal nonlinear Burgers equation is considered and the initial data are allowed to be arbitrarily large.The exponential decay estimates of the solutions are obtained ...The asymptotic behavior of periodic solutions to fractal nonlinear Burgers equation is considered and the initial data are allowed to be arbitrarily large.The exponential decay estimates of the solutions are obtained for the power of Laplacian α∈[1/2,1).展开更多
Fractal and chaotic laws of engineering structures are discussed in this paper, it means that the intrinsic essences and laws on dynamic systems which are made from seismic dissipated energy intensity E d and int...Fractal and chaotic laws of engineering structures are discussed in this paper, it means that the intrinsic essences and laws on dynamic systems which are made from seismic dissipated energy intensity E d and intensity of seismic dissipated energy moment I e are analyzed. Based on the intrinsic characters of chaotic and fractal dynamic system of E d and I e, three kinds of approximate dynamic models are rebuilt one by one: index autoregressive model, threshold autoregressive model and local-approximate autoregressive model. The innate laws, essences and systematic error of evolutional behavior I e are explained over all, the short-term behavior predictability and long-term behavior probability of which are analyzed in the end. That may be valuable for earthquake-resistant theory and analysis method in practical engineering structures.展开更多
The characteristics of the nonlinear dynamics in the Heavy Ion Collision (HIC) at intermediate energies have been studied by evaluating the productions of the Generalized Entropy (GE) and the Multifragmentation Entrop...The characteristics of the nonlinear dynamics in the Heavy Ion Collision (HIC) at intermediate energies have been studied by evaluating the productions of the Generalized Entropy (GE) and the Multifragmentation Entropy (ME) as well as the features of the information and fractal dimensions within the Isospin Quantum Molecular Dynamical Model compensated by the lattice methods. Results demonstrate from various views that the existence of deterministic chaos in the dynamical process of reaction.展开更多
In this paper,a novel method for investigating the particle-crushing behavior of breeding particles in a fusion blanket is proposed.The fractal theory and Weibull distribution are combined to establish a theoretical m...In this paper,a novel method for investigating the particle-crushing behavior of breeding particles in a fusion blanket is proposed.The fractal theory and Weibull distribution are combined to establish a theoretical model,and its validity was verified using a simple impact test.A crushable discrete element method(DEM)framework is built based on the previously established theoretical model.The tensile strength,which considers the fractal theory,size effect,and Weibull variation,was assigned to each generated particle.The assigned strength is then used for crush detection by comparing it with its maximum tensile stress.Mass conservation is ensured by inserting a series of sub-particles whose total mass was equal to the quality loss.Based on the crushable DEM framework,a numerical simulation of the crushing behavior of a pebble bed with hollow cylindrical geometry under a uniaxial compression test was performed.The results of this investigation showed that the particle withstands the external load by contact and sliding at the beginning of the compression process,and the results confirmed that crushing can be considered an important method of resisting the increasing external load.A relatively regular particle arrangement aids in resisting the load and reduces the occurrence of particle crushing.However,a limit exists to the promotion of resistance.When the strain increases beyond this limit,the distribution of the crushing position tends to be isotropic over the entire pebble bed.The theoretical model and crushable DEM framework provide a new method for exploring the pebble bed in a fusion reactor,considering particle crushing.展开更多
文摘Phase separation was studied by the optical microscopy in blends of nylon 6 (PA6) with sodium salt of ethylene/methacrylic acid copolymer (PEMA).The image collecting technology was used to keep track of the development of blends at a certain temperature.The fractal dimension of phase separation was calculated by the image solving technology according to the fractal theory and the self similarity behavior of the process was proved.The relationship of the fractal behavior with composition and experimental temperature was discussed.The fractal behavior of the crystallization development of the crystal phase of PA6 in blends was also discussed and the fractal behavior calculated.
文摘The present study shows that naturally developed fracture surfaces in rocks display the properties of self-affine fractals. Surface roughness can be quantitatively characterized by fractal dimension D and the intercept A on the log-log plot of variance: the former describes the irregularity and the later is statistically analogues to the slopes of asperities. In order to confirm the effects of these fractalparameters on the properties and mechanical behavior of rock joints, which have been observed in experiments under both normal andshear loadings, a theoretic model of rock joint is proposed on the basis of contact mechanics. The shape of asperity at contact is assumed to have a sinusoidal form in its representative scale r, with fractal dimension D and the intercept A. The model considers different local contact mechanisms, such as elastic deformation, frictional sliding and tensile fracture of the asperity. The empirical evolution law of surface damage developed in experiment is implemented into the model to up-date geometry of asperity in loading history. The effects of surface roughness characterized by D, A and re on normal and shear deformation of rock joint have been elaborated.
文摘The paper reports the effects of surface fractal structures on the rheological behavior and combustion kinetics of raw brown coal and three modified coal water slurries （CWSs）. The results show that the fractal structures and physicochemical properties of samples are dependent on various modification processes. The apparent viscosities of the coal water slurries increase with increasing surface fractal dimensions （D）, especially with decreasing shear rates. Fur- thermore, it has been proved that the ignition temperatures and apparent activation energies of modified CWSs are lower than that of raw coal water slurry. Compared with the traditional qualitative analysis of the effect of pore structures on CWSs properties, D can more efficiently indicate the quantificational effect of pore structures on the rheological behavior and combustion kinetics of CWSs.
基金supported by the Missouri University of Science and Technology/Waterjet Laboratory and funded by the China Postdoctoral Science Foundation(Grant No.2014M552555XB)Doctoral Program in Xi’an University of Science and Technology(Grant No.2013QDJ039).
文摘Comminution of coal to ultrafine sizes by high-pressure waterjet provides a novel method for preparation of coal-water fuels for next generation,near-zero emission electric power generation.The particle size distribution(PSD)of ground coal is a key parameter in the preparation of slurries as it determines the settling behavior of the particles and viscosity of the coal-water mixture.There are several methods available for representation and evaluation of particle size analysis data.However,fractal theory provides a means by which the entire PSD of comminuted materials can be quantified by using of a specific and exact value.In this paper,a volume-based fractal model was deduced to characterize the PSD of the coal which is ground in a specially designed comminution cell.During the size reduction process,the inlet pressures up to 276 MPa were used.
文摘Sixty-six cells were examined for chromosome length change, with half of them (33) in the early-metaphase and the other half in the pre-metaphase. The 22 couples of chromosomes (excluding sex chromosomes) in each cell were analyzed. The differences of chromosome length between the two phases were demonstrated and the correlation dimension of each chromosome was calculated. It was suggested that the mitosis of human chromosome possessed the feature of chaotic decrease. This offers a new approach to the research of the dynamic process of the mitosis.
基金supported by the National Natural Science Foundation
文摘The fractal model of rock comminution is presented with Mandelbrot's fractal geometry.The results show that it is difficult for those with only a linear similarity ratio to fit practical situations.The comminution prob ability of the central part should be considered so the geometric meaning of the constant in Gaudin-Schuhmann's distribution function can be explained more clearly.
基金Supported by the Natural Science Foundation of Zhejiang Province under Grant Nos.Y604106, Y606128the Scientific Research Fund of Zhejiang Provincial Education Department of China under Grant No.20070568the Natural Science Foundation of Zhejiang Lishui University under Grant No.KY08003
文摘With a new projective equation, a series of solutions of the （2-J-1）-dimensional dispersive long-water wave system （LWW） is derived. Based on the derived solitary wave solution, we obtain some special fractal localized structures and chaotic patterns.
基金support from the National Key Research and Development Plan Project(No.2022YFC3004700)the National Natural Science Foundation of China(No.52374241)+1 种基金Postgraduate Research&Practice Innovation Program of Jiangsu Province(No.KYCX24_2924)Graduate Innovation Program of China University of Mining and Technology(No.2024WLKXJ151).
文摘To investigate the instability mechanisms of heterogeneous geological structures in goaf area roofs,three-point bending tests(TPBT)and numerical simulations are performed on composite coal-rock(CCR).Acoustic emission(AE)monitoring is employed to analyze key parameters,establishing a multiparameter quantitative system for CCR fracture processes.The impact of lithological homogeneity on fracture evolution and energy migration is examined.Results show that CCR exhibits a three-stage mechanical response:weak contact,strong contact,and post-peak stages,each with distinct crack evolution patterns.A positive correlation is found between lithological homogeneity and tensile crack proportion.No significant correlation is observed between AE average frequency(AF)and AE counts across different lithological CCR;however,peak frequency(PF)displays clear lithology-dependent characteristics.The regulatory effect of the rock homogeneity coefficient(φ)on crack deriva tion mechanisms is quantfied,yielding mathematical relationships between fracture strength(f),crack propagation path angle(β),crack fractal dimension(D),andφ.The study highlights how different fracture modes alter energy migration pathways,confirming the coupling effect of grain distribution on mechanical response and crack propagation,and the influence of parameterφon critical energy release zones.These findings offer new insights into CCR failure mechanisms for mining safety.
文摘For inhomogeneous lattices we generalize the classical Gaussian model, i.e. it is proposed that the Gaussian type distribution constant and the external magnetic field of site i in this model depend on the coordination number qi of site i, and that the relation $b_{q_i}/b_{q_j} = q{_i}/q{_j}$ holds among bq's, where bq is the Gaussian type distribution constant of site j. Using the decimation real-space renormalization group following the spin-rescaling method, the critical points and critical exponents of the Gaussian model are calculated on some Koch type curves and a family of the diamond-type hierarchical (or DH) lattices. At the critical points, it is found that the nearest-neighbor interaction and the magnetic field of site j can be expressed in the form $K^* = b{_q }_{_i } /q{_i } and h_{q_j }^* = 0$ respectively. It is also found that most critical exponents depend on the fractal dimensionality of a fractal system. For the family of the DH lattices, the results are identical with the exact results on translation symmetric lattices, and if the fractal dimensionalityd f=4, the Gaussian model and the mean field theories give the same results.
基金supported by the National Natural Science Foundation of China(Grant Nos.51378072 and 51878064)the Special Fund for Basic Scientific Research of the Central College of Chang’an University(Grant No.300102218408)the financial support provided by the China Association of Science and Technology(Grant No.2017CASTQNJL048)for visiting the University of Alberta。
文摘The objective of this paper is to investigate the effects of initial particle gradation and rock content on the crushing behavior(i.e.grain size before and after crushing) of weathered phyllite fills.Compaction tests were conducted on weathered phyllite fills with rock contents of 35%,45%,55%,65% and 75%(by weight).First,the particle size distributions(PSDs) were observed before and after compaction,and then the particle breakage of weathered phyllite fills was analyzed by fractal dimension.Relative fractal dimension was proposed to evaluate the effects of initial rock content and initial gradation on the particle breakage.It was found that the fractal dimension method can well characterize the crushing behaviors of the weathered phyllite fills.The finer the fills were,the more they were compacted.That is,after the first compaction,the relative fractal dimension of the weathered phyllite fills increased as the rock content increased,reaching the values of 0.013,0.016,0.024,0.037 and 0.08,respectively.After the second compaction,these relative fractal dimension values,dominated by the initial particle gradation,became 0.059,0.072,0.052,0.095 and 0.118,respectively.In conclusion,the weathered phyllite fills with 55% rock content exhibited the least breakage and were most suitable for filling the subgrade.Findings in this paper will provide significant guidance for the construction of weathered phyllite filling subgrade in future projects.
文摘This study analyzes the relationship between fracture toughness and the fracture surface fractal dimension for a set of twenty-four CT-type AISI 4340 steel specimens heat treated to a variety of tensile strengths. Specimens were tested in accordance with ASTM E 399. Their respective fracture surfaces were plated, polished, photographed under an SEM in BSE mode and measured according to the Richardson method to obtain fractal dimensions. For brittle materials the limited results are consistent with previous literature: increasing fractal dimension with increasing toughness. For partially or fully ductile materials the results indicate a decrease in fractal dimension with an increase in fracture toughness. The data are modeled using a variation of the function applied to ceramics. Fracture in a ductile mode is characterized by the formation of dimples which exhibit fractal characteristics. The results are discussed in terms of the micromechanisms of fracture.
文摘The goal of this study is to establish relationships between the hot compression deformation behaviors and the fractal dimension of primary phase morphology of TA15 titanium alloy using the analytical methods of metallurgical microscope and transmission electron microscope coupled with box-counting dimension method. The hot compression deformation behaviors vary with decreasing fractal dimension owing to the change of microstructure caused by different parameters of the hot compressive deformation.The results indicate that TA15 alloy shows dynamic recrystallization characteristics at deformation temperature lower than 850℃while fractal dimension exhibits a moderate decreasing trend with the temperature increasing,and shows dynamic recovery characteristics at deformation temperature higher than 850℃while fractal dimension reduces rapidly with the temperature increasing.The fractal dimension displays non-linear relationship with fraction of primary phase and with aspect ratio of primary phase.
文摘The morphological complexity of cells and tissues,whether normal or pathological,is characterized by two primary attributes:Irregularity and self-similarity across different scales.When an object exhibits self-similarity,its shape remains unchanged as the scales of measurement vary because any part of it resembles the whole.On the other hand,the size and geometric characteristics of an irregular object vary as the resolution increases,revealing more intricate details.Despite numerous attempts,a reliable and accurate method for quantifying the morphological features of gastrointestinal organs,tissues,cells,their dynamic changes,and pathological disorders has not yet been established.However,fractal geometry,which studies shapes and patterns that exhibit self-similarity,holds promise in providing a quantitative measure of the irregularly shaped morphologies and their underlying self-similar temporal behaviors.In this context,we explore the fractal nature of the gastrointestinal system and the potential of fractal geometry as a robust descriptor of its complex forms and functions.Additionally,we examine the practical applications of fractal geometry in clinical gastroenterology and hepatology practice.
基金Project supported by the National Natural Science Foundation of China (No. 11071162)the Shanghai Jiao Tong University Innovation Fund for Postgraduates (No. WS3220507101)
文摘The asymptotic behavior of periodic solutions to fractal nonlinear Burgers equation is considered and the initial data are allowed to be arbitrarily large.The exponential decay estimates of the solutions are obtained for the power of Laplacian α∈[1/2,1).
文摘Fractal and chaotic laws of engineering structures are discussed in this paper, it means that the intrinsic essences and laws on dynamic systems which are made from seismic dissipated energy intensity E d and intensity of seismic dissipated energy moment I e are analyzed. Based on the intrinsic characters of chaotic and fractal dynamic system of E d and I e, three kinds of approximate dynamic models are rebuilt one by one: index autoregressive model, threshold autoregressive model and local-approximate autoregressive model. The innate laws, essences and systematic error of evolutional behavior I e are explained over all, the short-term behavior predictability and long-term behavior probability of which are analyzed in the end. That may be valuable for earthquake-resistant theory and analysis method in practical engineering structures.
文摘The characteristics of the nonlinear dynamics in the Heavy Ion Collision (HIC) at intermediate energies have been studied by evaluating the productions of the Generalized Entropy (GE) and the Multifragmentation Entropy (ME) as well as the features of the information and fractal dimensions within the Isospin Quantum Molecular Dynamical Model compensated by the lattice methods. Results demonstrate from various views that the existence of deterministic chaos in the dynamical process of reaction.
基金supported by Anhui Provincial Natural Science Foundation(2408085QA030)Natural Science Research Project of Anhui Educational Committee,China(2022AH050825)+3 种基金Medical Special Cultivation Project of Anhui University of Science and Technology(YZ2023H2C008)the Excellent Research and Innovation Team of Anhui Province,China(2022AH010052)the Scientific Research Foundation for High-level Talents of Anhui University of Science and Technology,China(2021yjrc51)Collaborative Innovation Program of Hefei Science Center,CAS,China(2019HSC-CIP006).
文摘In this paper,a novel method for investigating the particle-crushing behavior of breeding particles in a fusion blanket is proposed.The fractal theory and Weibull distribution are combined to establish a theoretical model,and its validity was verified using a simple impact test.A crushable discrete element method(DEM)framework is built based on the previously established theoretical model.The tensile strength,which considers the fractal theory,size effect,and Weibull variation,was assigned to each generated particle.The assigned strength is then used for crush detection by comparing it with its maximum tensile stress.Mass conservation is ensured by inserting a series of sub-particles whose total mass was equal to the quality loss.Based on the crushable DEM framework,a numerical simulation of the crushing behavior of a pebble bed with hollow cylindrical geometry under a uniaxial compression test was performed.The results of this investigation showed that the particle withstands the external load by contact and sliding at the beginning of the compression process,and the results confirmed that crushing can be considered an important method of resisting the increasing external load.A relatively regular particle arrangement aids in resisting the load and reduces the occurrence of particle crushing.However,a limit exists to the promotion of resistance.When the strain increases beyond this limit,the distribution of the crushing position tends to be isotropic over the entire pebble bed.The theoretical model and crushable DEM framework provide a new method for exploring the pebble bed in a fusion reactor,considering particle crushing.
