Debris flows in essence are the process of mass transportation controlled by the constitution featured by a wide-ranged distribution of grain size. Debris-flow samples of different densities collected from different r...Debris flows in essence are the process of mass transportation controlled by the constitution featured by a wide-ranged distribution of grain size. Debris-flow samples of different densities collected from different regions and gullies reveal that cumulative curve of grain composition, in particular for debris flows of high density, ρ5〉2 g/cm^3, can be fitted well by exponential function with exponents varying with regions and gullies. Debris flows fall into a narrow-valued domain of the exponent, as evidenced by Jiangjiagou Gully （JJG） with high occurrence frequency of debris flows. Furthermore, fractality of grain composition and porosity have been derived from cumulative curves in a certain size range, a range that determines the upper limit of grains constituting the matrix of debris flows. One can conclude that fractal structure of porosity plays crucial roles in soil fluidization that initiates debris flows, and debris flows occur at some range of fractal dimension, in coincidence with field observations.展开更多
On the basis of the basic model of the kinetic theory of aging of living systems,mathematical modeling of various characteristics of aging of mankind,state,generation,human body,organs and cells has been carried out.T...On the basis of the basic model of the kinetic theory of aging of living systems,mathematical modeling of various characteristics of aging of mankind,state,generation,human body,organs and cells has been carried out.These results are compared with experimental and calculated data of other authors.The analysis of the works presented here and those carried out earlier gave reason to believe that the basic mathematical model of the evolution of aging of living dynamic systems of various hierarchical levels and nature is the invariant differential equation of the kinetic theory of aging,as a manifestation of the fractality property of living systems.展开更多
<strong>Background:</strong> The basal metabolic rate has a scaling by tumor mass on the exponent of 3/4, while a simple surface-supplied volume of the mass would have a lower exponent, 2/3. The higher exp...<strong>Background:</strong> The basal metabolic rate has a scaling by tumor mass on the exponent of 3/4, while a simple surface-supplied volume of the mass would have a lower exponent, 2/3. The higher exponent can be explained by optimizing the overall energy distribution in the tumor, assuming that the target is four-dimensional. There are two possible ways of approximating the metabolic rate of the malignant tumor: 1) the volume blood-supply remains, but the surface and the length of the vessel network are modified;or 2) assuming that the malignant cell clusters try to maximize their metabolic rate to energize their proliferation by the longer length of the vessels. Our objective is to study how vascular fractality changes due to the greater demand for nutrients due to the proliferation of cancerous tissue. <strong>Results: </strong>It is shown that when a malignant tumor remains in expected four-dimensional volumetric conditions, it has a lower metabolic rate than the maximal metabolic potential in the actual demand of the proliferating cancer tissue. By maximizing the metabolic rate in malignant conditions, the allometric exponent will be smaller than 3/4, so the observed “dimensionality” of the metabolic rate versus mass becomes greater than four. The first growing period is exponential and keeps the “four-dimensional volume”, but the growth process turns to the sigmoidal phase in higher metabolic demand, and the tumor uses other optimizing strategies, further lowering the scaling exponent of metabolic rate. <strong>Conclusion:</strong> It is shown that a malignant cellular cluster changes its metabolic scaling exponent when maximizing its energy intake in various alimentary conditions.展开更多
We applied the Koch snowflake fractal antenna in planning calibration of the Five-hundred-meter Aperture Spherical radio Telescope(FAST), hypothesizing second-order fractal primary reflectors can optimize the orientat...We applied the Koch snowflake fractal antenna in planning calibration of the Five-hundred-meter Aperture Spherical radio Telescope(FAST), hypothesizing second-order fractal primary reflectors can optimize the orientated sensitivity of the telescope. Meanwhile, on the grounds of NASA Science Working Group Report in 1984, we reexamine the strategy of Search for Extraterrestrial Intelligence(SETI).A mathematical analysis of the radar equation will be performed in the first section, aiming to make it convenient to design a receiver system that can detect activities of an extraterrestrial civilization, according to the observable region of the narrowband. Taking advantage of the inherent potential of FAST, we simulate the theoretical detection of a Kardashev Type I civilization by a snowflake-selected reflecting area(Drake et al.).展开更多
Pores among particles provide the main space for the storage and migration of deep underground fluids(such as oil,gas,groundwater,and unconventional natural gas).The pores form a pore structure with complex morphology...Pores among particles provide the main space for the storage and migration of deep underground fluids(such as oil,gas,groundwater,and unconventional natural gas).The pores form a pore structure with complex morphology which is mainly dominated by the shape and distribution of particles.Therefore,the reconstruction of the pore structure or granular porous media and the evaluation of particle roundness have become an important foundation for the study of fluid flow through deep underground rock mass.This research proposes a novel approach for the multi-scale model with angular vertexes.The fractal topology theory and Voronoi space segmentation technology are combinedly used for the reconstruction of fractal granular porous media.The angular shapes are smoothed by using a modified B-spline technique and the particles with varying degrees of roundness are generated.To validate the superiority of our approach,the roundness based on the Wadell roundness calculation method is calculated and compared with the roundness obtained from particles smoothed using the vertex rounding substitution method.Results show that the roundness of particles smoothed with the modified B-spline technique closely aligns with the corresponding set rounded level(a nondimensional variable).Conversely,the vertex rounding substitution method is limited to a single dimensionally rounded radius.This innovative approach can offer a new method for the construction of granular porous media for the fluid flow study in deep underground rock mass.展开更多
Fracability is a critical indicator for evaluating the exploration and development potential of coalbed methane reservoirs and assessing the effectiveness of hydraulic fracturing stimulation operations.Its core functi...Fracability is a critical indicator for evaluating the exploration and development potential of coalbed methane reservoirs and assessing the effectiveness of hydraulic fracturing stimulation operations.Its core function is to characterize the complexity of the induced fracture network and the resulting effective stimulated volume.In this study,we quantified fracture area and geometric complexity using true triaxial fracturing experiments and computed tomography three-dimensional(3D)reconstruction technology,combined with the box-counting method to calculate the 3D fractal dimension of the fracture surfaces.The results revealed that the total fracture surface area per unit volume of the stimulated reservoir effectively characterized reservoir fracability;specifically,both a larger total fracture surface area and a higher fractal dimension corresponded to better reservoir fracability.Fracture complexity was enhanced by a decrease in the horizontal principal stress difference or an increase in the injection rate.Under optimal conditions of a 3 MPa stress difference and an injection rate of 60 mL/min,fracability improved by 27.6%.Furthermore,liquid carbon dioxide(CO_(2))improved fracability by 50.7%compared to using water as the fracturing fluid,a result attributed to its low viscosity and strong diffusion capacity,which activated a greater number of natural fractures.A fracability evaluation model integrating brittleness,fracture toughness,and dimensionless net pressure was developed using regression analysis,which demonstrated high reliability with a strong determination coefficient(R^(2))of 0.9019.This study clarifies the logical relationships among fracture area,complexity,and fractal dimension,providing a novel method for evaluating the fracability of coal reservoirs.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
This study presents a comprehensive theoretical investigation of the electronic and structural properties of a series of fractal molecular architectures derived from benzene and progressively extended toward circumcor...This study presents a comprehensive theoretical investigation of the electronic and structural properties of a series of fractal molecular architectures derived from benzene and progressively extended toward circumcoronene-like graphene analogues.Molecular geometries were constructed using GaussView 6,while all quantum-chemical calculations were carried out within the Gaussian 09 package using density functional theory(DFT)at the B3LYP/6-31G level,ensuring a reliable balance between computational accuracy and efficiency.The gradual expansion of the hexagonal framework resulted in a systematic reduction in the energy gap between the highest occupied molecular orbital(HOMO)and the lowest unoccupied molecular orbital(LUMO),indicating enhanced electronic delocalization and improved charge-transport characteristics in higher-order fractal structures.Electron density contour maps revealed an increasedπ-electron symmetry in the central regions of the larger systems,whereas smaller units exhibited an edge-localized electron density,consistent with the development of extendedπ–πconjugation.In addition,the density of states(DOS)spectra demonstrated a pronounced broadening of both occupied and virtual states with an increasing structural size,confirming the strong correlation between the fractal growth and electronic transport behavior.Furthermore,the analysis of the HOMO and LUMO distributions showed an orbital broadening and enhanced spatial symmetry in advanced fractal geometries,accounting for the observed reduction in the energy gap.These results indicate that coronene-based fractal structures exhibit significant potential for applications in conductive nanomaterials and molecular electronics,as their electronic and structural properties can be finely tuned through controlled fractal branching,enabling tailored performance in next-generation nanoscale devices.展开更多
To investigate the pore structure of graphene oxide modified polymer cement mortar(GOPM)under salt-freeze-thaw(SFT)coupling effects and its impact on deterioration,this study modifies polymer cement mortar(EMCM)with g...To investigate the pore structure of graphene oxide modified polymer cement mortar(GOPM)under salt-freeze-thaw(SFT)coupling effects and its impact on deterioration,this study modifies polymer cement mortar(EMCM)with graphene oxide(GO).The micro-pore structure of GOPM is characterized using LF-NMR and SEM.Fractal theory is applied to calculate the fractal dimension of pore volume,and the deterioration patterns are analyzed based on the evolution characteristics of capillary pores.The experimental results indicate that,after 25 salt-freeze-thaw cycles(SFTc),SO2-4 ions penetrate the matrix,generating corrosion products that fill existing pores and enhance the compactness of the specimen.As the number of cycles increases,the ongoing formation and expansion of corrosion products within the matrix,combined with persistent freezing forces,and result in the degradation of the pore structure.Therefore,the mass loss rate(MLR)of the specimens shows a trend of first decreasing and then increasing,while the relative dynamic elastic modulus(RDEM)initially increases and then decreases.Compared to the PC group specimens,the G3PM group specimens show a 28.71% reduction in MLR and a 31.42% increase in RDEM after 150 SFTc.The fractal dimensions of the transition pores,capillary pores,and macropores in the G3PM specimens first increase and then decrease as the number of SFTc increases.Among them,the capillary pores show the highest correlation with MLR and RDEM,with correlation coefficients of 0.97438 and 0.98555,respectively.展开更多
Driven by advancements in mobile internet technology,images have become a crucial data medium.Ensuring the security of image information during transmission has thus emerged as an urgent challenge.This study proposes ...Driven by advancements in mobile internet technology,images have become a crucial data medium.Ensuring the security of image information during transmission has thus emerged as an urgent challenge.This study proposes a novel image encryption algorithm specifically designed for grayscale image security.This research introduces a new Cantor diagonal matrix permutation method.The proposed permutation method uses row and column index sequences to control the Cantor diagonal matrix,where the row and column index sequences are generated by a spatiotemporal chaotic system named coupled map lattice(CML).The high initial value sensitivity of the CML system makes the permutation method highly sensitive and secure.Additionally,leveraging fractal theory,this study introduces a chaotic fractal matrix and applies this matrix in the diffusion process.This chaotic fractal matrix exhibits selfsimilarity and irregularity.Using the Cantor diagonal matrix and chaotic fractal matrix,this paper introduces a fast image encryption algorithm involving two diffusion steps and one permutation step.Moreover,the algorithm achieves robust security with only a single encryption round,ensuring high operational efficiency.Experimental results show that the proposed algorithm features an expansive key space,robust security,high sensitivity,high efficiency,and superior statistical properties for the ciphered images.Thus,the proposed algorithm not only provides a practical solution for secure image transmission but also bridges fractal theory with image encryption techniques,thereby opening new research avenues in chaotic cryptography and advancing the development of information security technology.展开更多
Internal structural defects in engineering rock masses vary in size,exhibit complex shapes,and are unevenly distributed.Dominant fractures within a rock mass often play a critical to its mechanical behavior,directly a...Internal structural defects in engineering rock masses vary in size,exhibit complex shapes,and are unevenly distributed.Dominant fractures within a rock mass often play a critical to its mechanical behavior,directly affecting the macromechanical properties and failure modes.These fractures affect the instability and failure of the surrounding rock,significantlyimpacting the overall stability of engineering structures.Herein,sand-powder three-dimensional(3D)printing technology was used to prepare rock-like specimens with internal fracture networks.Triaxial compression testing,post-failure fracture mapping,and fractal dimension analysis of the fracture surfaces were conducted to investigate the effects of dominant fracture angles on the strength and deformation of rocks with internal fracture networks under triaxial stress.The results indicate that the dominant fracture angle has a pronounced effect on the mechanical behavior of rock.With increasing angle,both compressive strength and elastic modulus exhibit an initial decline followed by an increase.Moreover,higher confiningpressure significantlyimproves the compressive strength of fractured rock.This enhancement weakens as the confiningpressure further increases.Moreover,with increasing confiningpressure,the differences between the maximum and minimum values of elastic moduli and lateral strain ratios in fractured rock gradually decrease.Thus,the impact of the dominant fracture angle on rock mass deformation decreases with increasing confiningpressure.This research elucidates the effects of dominant fracture angles on the mechanical and failure properties of complex fractured rock masses and the influenceof the confiningpressure on these relationships.It provides valuable theoretical insights and practical guidance for stability analyses in engineering rock masses.展开更多
The pore structure of shale oil reservoir significantly affects the occurrence and mobility of hydrocarbons.The potential of a new type of alkaline lake shale oil has been demonstrated,but there are few reports on the...The pore structure of shale oil reservoir significantly affects the occurrence and mobility of hydrocarbons.The potential of a new type of alkaline lake shale oil has been demonstrated,but there are few reports on the pore system of alkaline lake shale,which restricts the efficient exploration and development of shale oil.This study investigates the Fengcheng Formation shale in the Mahu sag of the Junggar Basin,employing methods such as low-temperature nitrogecn adsorption(LTNA),mercury intrusion capillary pressure(MICP),and nuclear magnetic resonance(NMR)to quantitatively characterize the multi-scale pore structure and fractal characteristics of shale,while evaluating the applicability of these methods.Based on a comprehensive analysis of material composition,different pore types,and fractal dimensions,the controlling factors for the development of different pore types and their seepage capacity are discussed.The results indicate that inorganic mineral pores are the main development in alkaline lake shale,with the pore morphology being characterized by slit-like and ink-bottle shapes.The multi-scale pore size distribution(PSD)shows that Ⅱ-micropores(10-100 nm)and mesopores(100–1000 nm)are the main contributors to the pore system.The development of Ⅱ-micropores is associated with feldspar and calcareous minerals,the development of Ⅰ-micropores(<10 nm)and mesopores is related to quartz content,while large pores are mainly found in interlayer fissures of clay minerals.The development of Ⅰ-micropores increases the roughness of pore surface and enhances the adsorption capacity of the pores,while the development of Ⅱ-micropores associated with calcareous minerals hinders pore seepage capacity.Mesopores and macropores(>1000 nm)exhibit good flowability.The high content of siliceous minerals plays a positive role in the pore system of alkaline lake shale.The shale with higher fractal dimension Dmin exhibits greater adsorption capacity,which hinders the accumulation of free-state shale oil.Different types of pore space play different roles in the occurrence of shale oil,with free-state shale oil primarily occurring in micro-fractures and inorganic mineral pores,and the pore size is exceeding 10 nm.展开更多
Quantifying two-phase fluid flow in fractured rocks is essential for resource reutilization in abandoned mines,subsurface energy recovery and underground waste isolation.This study develops a mathematical framework fo...Quantifying two-phase fluid flow in fractured rocks is essential for resource reutilization in abandoned mines,subsurface energy recovery and underground waste isolation.This study develops a mathematical framework for predicting the permeability of rough fracture networks by integrating fractal geometry with single-phase and two-phase seepage theory.A permeability model for rough fracture networks is first established,and its sensitivity to key geometric parameters is analyzed.A second model is then formulated to relate water-phase saturation to measurable variables,enabling the estimation of two-phase permeability from Reynolds number and aperture.Model predictions show deviations of less than 10%from numerical simulations for both single-phase and two-phase flow,demonstrating the accuracy and robustness of the proposed approach.The results highlight the dominant roles of fracture number,tortuosity and aperture in controlling permeability,as well as the influence of flow regimes on relative permeability.The proposed framework provides a practical and physically based method for analyzing multiphase seepage in fractured rock and offers a foundation for further applications to field-scale fractured systems.展开更多
Mine filling materials urgently need to improve mechanical properties and achieve low-carbon transformation.This study explores the mechanism of the synergistic effect of optimizing aggregate fractal grading and intro...Mine filling materials urgently need to improve mechanical properties and achieve low-carbon transformation.This study explores the mechanism of the synergistic effect of optimizing aggregate fractal grading and introducing CO_(2)nanobubble technology to improve the performance of cement-fly ash-based backfill materials(CFB).The properties including fluidity,setting time,uniaxial compressive strength,elastic modulus,porosity,microstructure and CO_(2)storage performance were systematically studied through methods such as fluidity evaluation,time test,uniaxial compression test,mercury intrusion porosimetry(MIP),scanning electron microscopy-energy dispersive spectroscopy analysis(SEM-EDS),and thermogravimetric-differential thermogravimetric analysis(TG-DTG).The experimental results show that the density and strength of the material are significantly improved under the synergistic effect of fractal dimension and CO_(2)nanobubbles.When the fractal dimension reaches 2.65,the mass ratio of coarse and fine aggregates reaches the optimal balance,and the structural density is greatly improved at the same time.At this time,the uniaxial compressive strength and elastic modulus reach their peak values,with increases of up to 13.46%and 27.47%,respectively.CO_(2)nanobubbles enhance the material properties by promoting hydration reaction and carbonization.At the microscopic level,CO_(2)nanobubble water promotes the formation of C-S-H(hydrated calcium silicate),C-A-S-H(hydrated calcium aluminium silicate)gel and CaCO_(3),which is the main way to enhance the performance.Thermogravimetric studies have shown that when the fractal dimension is 2.65,the dehydration of hydration products and the decarbonization process of CaCO_(3)are most obvious,and CO_(2)nanobubble water promotes the carbonization reaction,making it surpass the natural state.The CO_(2)sequestration quality of cement-fly ash-based materials treated with CO_(2)nanobubble water at different fractal dimensions increased by 12.4wt%to 99.8wt%.The results not only provide scientific insights for the design and implementation of low-carbon filling materials,but also provide a solid theoretical basis for strengthening green mining practices and promoting sustainable resource utilization.展开更多
Extensive engineering experience and research findings suggest that rock mass instability is typically attributed to human engineering activities and natural disturbances,resulting in general dynamic mechanical proper...Extensive engineering experience and research findings suggest that rock mass instability is typically attributed to human engineering activities and natural disturbances,resulting in general dynamic mechanical properties.This is attributed to external interference resulting from the extensive use of the mechanical and blasting techniques necessary for mineral extraction.Quantifying the impact of dynamic disturbances on rock deformation behavior is essential for comprehending the long-term response of surrounding rock during excavation.This study placed the rock to sustained pressure and investigated the impact of varying hammer heights and dry and wet(W-D)damage on its shear failure behavior.This study investigated the fatigue disturbance studies on W-D damaged sandstone samples via W-D equipment,a disturbance creep device,digital image correlation(DIC),and acoustic emission(AE)technology.The experimental findings suggest that acoustic emission sensors can be utilized to quantify the internal damage of rock samples during cyclic impact,whereas DIC technology(optical measurement)is capable of capturing the surface crack propagation of samples.Under repeated impact and the combined action of W-D conditions,the bearing capacity of sandstone decreases,whereas the deformation capacity increases.Furthermore,the W-D cycles and impact strength are inversely related to the fatigue life.The intensity of W-D damage and disturbances further accelerates the development and propagation of cracks under cyclic disturbances.The research results are of preventive significance to ensure the safety and sustainable development of engineering construction.展开更多
In the classic theory of fracture mechanics,expressions for calculating the stresses and displacements in the vicinity of the crack tip are deduced on the basis of the assumption that a fracture surface is a smooth su...In the classic theory of fracture mechanics,expressions for calculating the stresses and displacements in the vicinity of the crack tip are deduced on the basis of the assumption that a fracture surface is a smooth surface or that a crack is a smooth crack.In fact,the surface of a crack formed during the fracture is usually very irregular.So the real asymptotic form of the stress and displacement fields at the crack tip is different from the classic one.Considering the irregularity of a real fracture surface or a real crack profile,the crack is taken as a fractal one,and then the real asymptotic form at the crack tip is developed by applying Griffith's energy balance principle and fractal geometry.Through the developed asymptotic form,it is discovered that the fractality of the crack reduces the stress singularity at the crack tip.展开更多
To investigate the effects of the maximum principal stress direction(θ)and cross-section shape on the failure characteristics of sandstone,true-triaxial compression experiments were conducted using cubic samples with...To investigate the effects of the maximum principal stress direction(θ)and cross-section shape on the failure characteristics of sandstone,true-triaxial compression experiments were conducted using cubic samples with rectangular,circular,and D-shaped holes.Asθincreases from 0°to 60°in the rectangular hole,the left failure location shifts from the left corner to the left sidewall,the left corner,and then the floor,while the right failure location shifts from the right corner to the right sidewall,right roof corner,and then the roof.Furthermore,the initial failure vertical stress first decreases and then increases.In comparison,the failure severity in the rectangular hole decreases for variousθvalues as 30°>45°>60°>0°.With increasingθ,the fractal dimension(D)of rock slices first increases and then decreases.For the rectangular and D-shaped holes,whenθ=0°,30°,and 90°,D for the rectangular hole is less than that of the D-shaped hole.Whenθ=45°and 60°,D for the rectangular hole is greater than that of the D-shaped hole.Theoretical analysis indicates that the stress concentration at the rectangular and D-shaped corners is greater than the other areas.The failure location rotates with the rotation ofθ,and the failure occurs on the side with a high concentration of compressive stress,while the side with the tensile and compressive stresses remains relatively stable.Therefore,the fundamental reason for the rotation of failure location is the rotation of stress concentration,and the external influencing factor is the rotation ofθ.展开更多
The high-temperature dissolution behavior of primary carbides in samples taken from GCr15 continuous-casting bloom was observed in-situ by confocal laser scanning microscopy.Equations were fitted to the dissolution ki...The high-temperature dissolution behavior of primary carbides in samples taken from GCr15 continuous-casting bloom was observed in-situ by confocal laser scanning microscopy.Equations were fitted to the dissolution kinetics of primary carbides during either heating or soaking.Dissolution of carbides proceeded in three stages(fast→slow→faster)as either temperature or holding time was increased.During the heating process and during the first and third stages of the soaking process,the original size of the carbides determined the steepness of the slope,but during the middle(“slow”)stage of the soaking process,the slope remained zero.The initial size of the carbides varied greatly,but their final dissolution temperature fell within the narrow range of 1210-1235℃,and the holding time remained within 50 min.Fractal analysis was used to study the morphological characteristics of small and medium-sized carbides during the dissolution process.According to changes in the fractal dimension before and after soaking,the carbides tended to evolve towards a more regular morphology.展开更多
Understanding the mesoscopic tensile fracture damage of rock is the basis of evaluating the deterioration process of mechanical properties of heat-damaged rock. For this, tensile tests of rocks under high-temperature ...Understanding the mesoscopic tensile fracture damage of rock is the basis of evaluating the deterioration process of mechanical properties of heat-damaged rock. For this, tensile tests of rocks under high-temperature treatment were conducted with a ϕ75 mm split Hopkinson tension bar (SHTB) to investigate the mesoscopic fracture and damage properties of rock. An improved scanning electron microscopy (SEM) experimental method was used to analyze the tensile fracture surfaces of rock samples. Qualitative and quantitative analyses were performed to assess evolution of mesoscopic damage of heat-damaged rock under tensile loading. A constitutive model describing the mesoscopic fractal damage under thermo-mechanical coupling was established. The results showed that the high temperatures significantly reduced the tensile strength and fracture surface roughness of the red sandstone. The three-dimensional (3D) reconstruction of the fracture surface of the samples that experienced tensile failure at 900 °C showed a flat surface. The standard deviation of elevation and slope angle of specimen fracture surface first increased and then decreased with increasing temperature. The threshold for brittle fracture of the heat-damaged red sandstone specimens was 600 °C. Beyond this threshold temperature, local ductile fracture occurred, resulting in plastic deformation of the fracture surface during tensile fracturing. With increase of temperature, the internal meso-structure of samples was strengthened slightly at first and then deteriorated gradually, which was consistent with the change of macroscopic mechanical properties of red sandstone. The mesoscopic characteristics, such as the number, mean side length, maximum area, porosity, and fractal dimension of crack, exhibited an initial decline, followed by a gradual increase. The development of microcracks in samples had significant influence on mesoscopic fractal dimension. The mesoscopic fractal characteristics were used to establish a mesoscopic fractal damage constitutive model for red sandstone, and the agreement between the theoretical and experimental results validated the proposed model.展开更多
基金N ationalN aturalScience Foundation ofChina,N o.40101001N o.40025103
文摘Debris flows in essence are the process of mass transportation controlled by the constitution featured by a wide-ranged distribution of grain size. Debris-flow samples of different densities collected from different regions and gullies reveal that cumulative curve of grain composition, in particular for debris flows of high density, ρ5〉2 g/cm^3, can be fitted well by exponential function with exponents varying with regions and gullies. Debris flows fall into a narrow-valued domain of the exponent, as evidenced by Jiangjiagou Gully （JJG） with high occurrence frequency of debris flows. Furthermore, fractality of grain composition and porosity have been derived from cumulative curves in a certain size range, a range that determines the upper limit of grains constituting the matrix of debris flows. One can conclude that fractal structure of porosity plays crucial roles in soil fluidization that initiates debris flows, and debris flows occur at some range of fractal dimension, in coincidence with field observations.
文摘On the basis of the basic model of the kinetic theory of aging of living systems,mathematical modeling of various characteristics of aging of mankind,state,generation,human body,organs and cells has been carried out.These results are compared with experimental and calculated data of other authors.The analysis of the works presented here and those carried out earlier gave reason to believe that the basic mathematical model of the evolution of aging of living dynamic systems of various hierarchical levels and nature is the invariant differential equation of the kinetic theory of aging,as a manifestation of the fractality property of living systems.
文摘<strong>Background:</strong> The basal metabolic rate has a scaling by tumor mass on the exponent of 3/4, while a simple surface-supplied volume of the mass would have a lower exponent, 2/3. The higher exponent can be explained by optimizing the overall energy distribution in the tumor, assuming that the target is four-dimensional. There are two possible ways of approximating the metabolic rate of the malignant tumor: 1) the volume blood-supply remains, but the surface and the length of the vessel network are modified;or 2) assuming that the malignant cell clusters try to maximize their metabolic rate to energize their proliferation by the longer length of the vessels. Our objective is to study how vascular fractality changes due to the greater demand for nutrients due to the proliferation of cancerous tissue. <strong>Results: </strong>It is shown that when a malignant tumor remains in expected four-dimensional volumetric conditions, it has a lower metabolic rate than the maximal metabolic potential in the actual demand of the proliferating cancer tissue. By maximizing the metabolic rate in malignant conditions, the allometric exponent will be smaller than 3/4, so the observed “dimensionality” of the metabolic rate versus mass becomes greater than four. The first growing period is exponential and keeps the “four-dimensional volume”, but the growth process turns to the sigmoidal phase in higher metabolic demand, and the tumor uses other optimizing strategies, further lowering the scaling exponent of metabolic rate. <strong>Conclusion:</strong> It is shown that a malignant cellular cluster changes its metabolic scaling exponent when maximizing its energy intake in various alimentary conditions.
基金supported by the National Natural Science Foundation of China(Grant No.11929301)National Key R&D Program of China(2017YFA0402600)。
文摘We applied the Koch snowflake fractal antenna in planning calibration of the Five-hundred-meter Aperture Spherical radio Telescope(FAST), hypothesizing second-order fractal primary reflectors can optimize the orientated sensitivity of the telescope. Meanwhile, on the grounds of NASA Science Working Group Report in 1984, we reexamine the strategy of Search for Extraterrestrial Intelligence(SETI).A mathematical analysis of the radar equation will be performed in the first section, aiming to make it convenient to design a receiver system that can detect activities of an extraterrestrial civilization, according to the observable region of the narrowband. Taking advantage of the inherent potential of FAST, we simulate the theoretical detection of a Kardashev Type I civilization by a snowflake-selected reflecting area(Drake et al.).
基金Natural Science Foundation of Henan Province of China,Grant/Award Number:232300420438Fundamental Research Funds for the Universities of Henan Province,Grant/Award Numbers:NSFRF220427,NSFRF220204+2 种基金National Natural Science foundation of China,Grant/Award Number:41972175Excellent Youth Foundation of Henan Scientific Committee,Grant/Award Number:232300421025Doctoral Foundation of Henan Polytechnic University,Grant/Award Number:B2021-78。
文摘Pores among particles provide the main space for the storage and migration of deep underground fluids(such as oil,gas,groundwater,and unconventional natural gas).The pores form a pore structure with complex morphology which is mainly dominated by the shape and distribution of particles.Therefore,the reconstruction of the pore structure or granular porous media and the evaluation of particle roundness have become an important foundation for the study of fluid flow through deep underground rock mass.This research proposes a novel approach for the multi-scale model with angular vertexes.The fractal topology theory and Voronoi space segmentation technology are combinedly used for the reconstruction of fractal granular porous media.The angular shapes are smoothed by using a modified B-spline technique and the particles with varying degrees of roundness are generated.To validate the superiority of our approach,the roundness based on the Wadell roundness calculation method is calculated and compared with the roundness obtained from particles smoothed using the vertex rounding substitution method.Results show that the roundness of particles smoothed with the modified B-spline technique closely aligns with the corresponding set rounded level(a nondimensional variable).Conversely,the vertex rounding substitution method is limited to a single dimensionally rounded radius.This innovative approach can offer a new method for the construction of granular porous media for the fluid flow study in deep underground rock mass.
基金supported by the Natural Science Foundation of China(Grant No.52574047 and Grant No.52374045)Key Project of Sichuan Provincial Joint Fund for Science Technology and Education,China(Grant No.2025NSFSC2008).
文摘Fracability is a critical indicator for evaluating the exploration and development potential of coalbed methane reservoirs and assessing the effectiveness of hydraulic fracturing stimulation operations.Its core function is to characterize the complexity of the induced fracture network and the resulting effective stimulated volume.In this study,we quantified fracture area and geometric complexity using true triaxial fracturing experiments and computed tomography three-dimensional(3D)reconstruction technology,combined with the box-counting method to calculate the 3D fractal dimension of the fracture surfaces.The results revealed that the total fracture surface area per unit volume of the stimulated reservoir effectively characterized reservoir fracability;specifically,both a larger total fracture surface area and a higher fractal dimension corresponded to better reservoir fracability.Fracture complexity was enhanced by a decrease in the horizontal principal stress difference or an increase in the injection rate.Under optimal conditions of a 3 MPa stress difference and an injection rate of 60 mL/min,fracability improved by 27.6%.Furthermore,liquid carbon dioxide(CO_(2))improved fracability by 50.7%compared to using water as the fracturing fluid,a result attributed to its low viscosity and strong diffusion capacity,which activated a greater number of natural fractures.A fracability evaluation model integrating brittleness,fracture toughness,and dimensionless net pressure was developed using regression analysis,which demonstrated high reliability with a strong determination coefficient(R^(2))of 0.9019.This study clarifies the logical relationships among fracture area,complexity,and fractal dimension,providing a novel method for evaluating the fracability of coal reservoirs.
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.
文摘This study presents a comprehensive theoretical investigation of the electronic and structural properties of a series of fractal molecular architectures derived from benzene and progressively extended toward circumcoronene-like graphene analogues.Molecular geometries were constructed using GaussView 6,while all quantum-chemical calculations were carried out within the Gaussian 09 package using density functional theory(DFT)at the B3LYP/6-31G level,ensuring a reliable balance between computational accuracy and efficiency.The gradual expansion of the hexagonal framework resulted in a systematic reduction in the energy gap between the highest occupied molecular orbital(HOMO)and the lowest unoccupied molecular orbital(LUMO),indicating enhanced electronic delocalization and improved charge-transport characteristics in higher-order fractal structures.Electron density contour maps revealed an increasedπ-electron symmetry in the central regions of the larger systems,whereas smaller units exhibited an edge-localized electron density,consistent with the development of extendedπ–πconjugation.In addition,the density of states(DOS)spectra demonstrated a pronounced broadening of both occupied and virtual states with an increasing structural size,confirming the strong correlation between the fractal growth and electronic transport behavior.Furthermore,the analysis of the HOMO and LUMO distributions showed an orbital broadening and enhanced spatial symmetry in advanced fractal geometries,accounting for the observed reduction in the energy gap.These results indicate that coronene-based fractal structures exhibit significant potential for applications in conductive nanomaterials and molecular electronics,as their electronic and structural properties can be finely tuned through controlled fractal branching,enabling tailored performance in next-generation nanoscale devices.
基金Funded by the National Natural Science Foundation of China(Nos.5226804252468035)。
文摘To investigate the pore structure of graphene oxide modified polymer cement mortar(GOPM)under salt-freeze-thaw(SFT)coupling effects and its impact on deterioration,this study modifies polymer cement mortar(EMCM)with graphene oxide(GO).The micro-pore structure of GOPM is characterized using LF-NMR and SEM.Fractal theory is applied to calculate the fractal dimension of pore volume,and the deterioration patterns are analyzed based on the evolution characteristics of capillary pores.The experimental results indicate that,after 25 salt-freeze-thaw cycles(SFTc),SO2-4 ions penetrate the matrix,generating corrosion products that fill existing pores and enhance the compactness of the specimen.As the number of cycles increases,the ongoing formation and expansion of corrosion products within the matrix,combined with persistent freezing forces,and result in the degradation of the pore structure.Therefore,the mass loss rate(MLR)of the specimens shows a trend of first decreasing and then increasing,while the relative dynamic elastic modulus(RDEM)initially increases and then decreases.Compared to the PC group specimens,the G3PM group specimens show a 28.71% reduction in MLR and a 31.42% increase in RDEM after 150 SFTc.The fractal dimensions of the transition pores,capillary pores,and macropores in the G3PM specimens first increase and then decrease as the number of SFTc increases.Among them,the capillary pores show the highest correlation with MLR and RDEM,with correlation coefficients of 0.97438 and 0.98555,respectively.
基金supported by the National Natural Science Foundation of China(62376106)The Science and Technology Development Plan of Jilin Province(20250102212JC).
文摘Driven by advancements in mobile internet technology,images have become a crucial data medium.Ensuring the security of image information during transmission has thus emerged as an urgent challenge.This study proposes a novel image encryption algorithm specifically designed for grayscale image security.This research introduces a new Cantor diagonal matrix permutation method.The proposed permutation method uses row and column index sequences to control the Cantor diagonal matrix,where the row and column index sequences are generated by a spatiotemporal chaotic system named coupled map lattice(CML).The high initial value sensitivity of the CML system makes the permutation method highly sensitive and secure.Additionally,leveraging fractal theory,this study introduces a chaotic fractal matrix and applies this matrix in the diffusion process.This chaotic fractal matrix exhibits selfsimilarity and irregularity.Using the Cantor diagonal matrix and chaotic fractal matrix,this paper introduces a fast image encryption algorithm involving two diffusion steps and one permutation step.Moreover,the algorithm achieves robust security with only a single encryption round,ensuring high operational efficiency.Experimental results show that the proposed algorithm features an expansive key space,robust security,high sensitivity,high efficiency,and superior statistical properties for the ciphered images.Thus,the proposed algorithm not only provides a practical solution for secure image transmission but also bridges fractal theory with image encryption techniques,thereby opening new research avenues in chaotic cryptography and advancing the development of information security technology.
基金supported by the National Key Research and Development Program Young Scientist Project(Grant No.2024YFC2911000)the National Natural Science Foundation of China(Grant No.52474103)the Major Basic Research Project of the Natural Science Foundation of Shandong Province(Grant No.ZR2024ZD22).
文摘Internal structural defects in engineering rock masses vary in size,exhibit complex shapes,and are unevenly distributed.Dominant fractures within a rock mass often play a critical to its mechanical behavior,directly affecting the macromechanical properties and failure modes.These fractures affect the instability and failure of the surrounding rock,significantlyimpacting the overall stability of engineering structures.Herein,sand-powder three-dimensional(3D)printing technology was used to prepare rock-like specimens with internal fracture networks.Triaxial compression testing,post-failure fracture mapping,and fractal dimension analysis of the fracture surfaces were conducted to investigate the effects of dominant fracture angles on the strength and deformation of rocks with internal fracture networks under triaxial stress.The results indicate that the dominant fracture angle has a pronounced effect on the mechanical behavior of rock.With increasing angle,both compressive strength and elastic modulus exhibit an initial decline followed by an increase.Moreover,higher confiningpressure significantlyimproves the compressive strength of fractured rock.This enhancement weakens as the confiningpressure further increases.Moreover,with increasing confiningpressure,the differences between the maximum and minimum values of elastic moduli and lateral strain ratios in fractured rock gradually decrease.Thus,the impact of the dominant fracture angle on rock mass deformation decreases with increasing confiningpressure.This research elucidates the effects of dominant fracture angles on the mechanical and failure properties of complex fractured rock masses and the influenceof the confiningpressure on these relationships.It provides valuable theoretical insights and practical guidance for stability analyses in engineering rock masses.
基金financially supported by the National Natural Science Foundation of China(Nos.42272137,42202160)AAPG Foundation Grants-in-Aid and the Strategic Cooperation Technology Projecti of CNPC and CUPB(No.ZLZX2020-01-05)。
文摘The pore structure of shale oil reservoir significantly affects the occurrence and mobility of hydrocarbons.The potential of a new type of alkaline lake shale oil has been demonstrated,but there are few reports on the pore system of alkaline lake shale,which restricts the efficient exploration and development of shale oil.This study investigates the Fengcheng Formation shale in the Mahu sag of the Junggar Basin,employing methods such as low-temperature nitrogecn adsorption(LTNA),mercury intrusion capillary pressure(MICP),and nuclear magnetic resonance(NMR)to quantitatively characterize the multi-scale pore structure and fractal characteristics of shale,while evaluating the applicability of these methods.Based on a comprehensive analysis of material composition,different pore types,and fractal dimensions,the controlling factors for the development of different pore types and their seepage capacity are discussed.The results indicate that inorganic mineral pores are the main development in alkaline lake shale,with the pore morphology being characterized by slit-like and ink-bottle shapes.The multi-scale pore size distribution(PSD)shows that Ⅱ-micropores(10-100 nm)and mesopores(100–1000 nm)are the main contributors to the pore system.The development of Ⅱ-micropores is associated with feldspar and calcareous minerals,the development of Ⅰ-micropores(<10 nm)and mesopores is related to quartz content,while large pores are mainly found in interlayer fissures of clay minerals.The development of Ⅰ-micropores increases the roughness of pore surface and enhances the adsorption capacity of the pores,while the development of Ⅱ-micropores associated with calcareous minerals hinders pore seepage capacity.Mesopores and macropores(>1000 nm)exhibit good flowability.The high content of siliceous minerals plays a positive role in the pore system of alkaline lake shale.The shale with higher fractal dimension Dmin exhibits greater adsorption capacity,which hinders the accumulation of free-state shale oil.Different types of pore space play different roles in the occurrence of shale oil,with free-state shale oil primarily occurring in micro-fractures and inorganic mineral pores,and the pore size is exceeding 10 nm.
基金supported by the National Natural Science Foundation of China(Nos.52504155 and 52374147)National Key Research and Development Program of China(No.2023YFC3804204)+1 种基金China Postdoctoral Science Foundation(No.2024M753531)Jiangsu Funding Program for Excellent Postdoctoral Talent(No.2024ZB853).
文摘Quantifying two-phase fluid flow in fractured rocks is essential for resource reutilization in abandoned mines,subsurface energy recovery and underground waste isolation.This study develops a mathematical framework for predicting the permeability of rough fracture networks by integrating fractal geometry with single-phase and two-phase seepage theory.A permeability model for rough fracture networks is first established,and its sensitivity to key geometric parameters is analyzed.A second model is then formulated to relate water-phase saturation to measurable variables,enabling the estimation of two-phase permeability from Reynolds number and aperture.Model predictions show deviations of less than 10%from numerical simulations for both single-phase and two-phase flow,demonstrating the accuracy and robustness of the proposed approach.The results highlight the dominant roles of fracture number,tortuosity and aperture in controlling permeability,as well as the influence of flow regimes on relative permeability.The proposed framework provides a practical and physically based method for analyzing multiphase seepage in fractured rock and offers a foundation for further applications to field-scale fractured systems.
基金financially supported by the China Scholarship Council(CSC)。
文摘Mine filling materials urgently need to improve mechanical properties and achieve low-carbon transformation.This study explores the mechanism of the synergistic effect of optimizing aggregate fractal grading and introducing CO_(2)nanobubble technology to improve the performance of cement-fly ash-based backfill materials(CFB).The properties including fluidity,setting time,uniaxial compressive strength,elastic modulus,porosity,microstructure and CO_(2)storage performance were systematically studied through methods such as fluidity evaluation,time test,uniaxial compression test,mercury intrusion porosimetry(MIP),scanning electron microscopy-energy dispersive spectroscopy analysis(SEM-EDS),and thermogravimetric-differential thermogravimetric analysis(TG-DTG).The experimental results show that the density and strength of the material are significantly improved under the synergistic effect of fractal dimension and CO_(2)nanobubbles.When the fractal dimension reaches 2.65,the mass ratio of coarse and fine aggregates reaches the optimal balance,and the structural density is greatly improved at the same time.At this time,the uniaxial compressive strength and elastic modulus reach their peak values,with increases of up to 13.46%and 27.47%,respectively.CO_(2)nanobubbles enhance the material properties by promoting hydration reaction and carbonization.At the microscopic level,CO_(2)nanobubble water promotes the formation of C-S-H(hydrated calcium silicate),C-A-S-H(hydrated calcium aluminium silicate)gel and CaCO_(3),which is the main way to enhance the performance.Thermogravimetric studies have shown that when the fractal dimension is 2.65,the dehydration of hydration products and the decarbonization process of CaCO_(3)are most obvious,and CO_(2)nanobubble water promotes the carbonization reaction,making it surpass the natural state.The CO_(2)sequestration quality of cement-fly ash-based materials treated with CO_(2)nanobubble water at different fractal dimensions increased by 12.4wt%to 99.8wt%.The results not only provide scientific insights for the design and implementation of low-carbon filling materials,but also provide a solid theoretical basis for strengthening green mining practices and promoting sustainable resource utilization.
基金supported by National Natural Science Foundation of China(Grant Nos.52364004 and 52264006)The Youth Talent Growth Project of Guizhou Provincial Department of Education(Grant No.QianJiaoJi[2024]18).
文摘Extensive engineering experience and research findings suggest that rock mass instability is typically attributed to human engineering activities and natural disturbances,resulting in general dynamic mechanical properties.This is attributed to external interference resulting from the extensive use of the mechanical and blasting techniques necessary for mineral extraction.Quantifying the impact of dynamic disturbances on rock deformation behavior is essential for comprehending the long-term response of surrounding rock during excavation.This study placed the rock to sustained pressure and investigated the impact of varying hammer heights and dry and wet(W-D)damage on its shear failure behavior.This study investigated the fatigue disturbance studies on W-D damaged sandstone samples via W-D equipment,a disturbance creep device,digital image correlation(DIC),and acoustic emission(AE)technology.The experimental findings suggest that acoustic emission sensors can be utilized to quantify the internal damage of rock samples during cyclic impact,whereas DIC technology(optical measurement)is capable of capturing the surface crack propagation of samples.Under repeated impact and the combined action of W-D conditions,the bearing capacity of sandstone decreases,whereas the deformation capacity increases.Furthermore,the W-D cycles and impact strength are inversely related to the fatigue life.The intensity of W-D damage and disturbances further accelerates the development and propagation of cracks under cyclic disturbances.The research results are of preventive significance to ensure the safety and sustainable development of engineering construction.
基金Supported by the National Natural Science Foundation of China(Grant Nos.50539030,50539010,50539110 and 50579010)the National Science and Technology Supporting Program(Grant No.2006BAC14B03)the National Science Foundation of Hohai University(Grant No.2008426811)
文摘In the classic theory of fracture mechanics,expressions for calculating the stresses and displacements in the vicinity of the crack tip are deduced on the basis of the assumption that a fracture surface is a smooth surface or that a crack is a smooth crack.In fact,the surface of a crack formed during the fracture is usually very irregular.So the real asymptotic form of the stress and displacement fields at the crack tip is different from the classic one.Considering the irregularity of a real fracture surface or a real crack profile,the crack is taken as a fractal one,and then the real asymptotic form at the crack tip is developed by applying Griffith's energy balance principle and fractal geometry.Through the developed asymptotic form,it is discovered that the fractality of the crack reduces the stress singularity at the crack tip.
基金supported by the National Natural Science Foundation of China (Grant Nos.52304227 and 52104133)Scientific and Technological Research Platform for Disaster Prevention and Control of Deep Coal Mining (Anhui University of Science and Technology) (Grant No.DPDCM2208).
文摘To investigate the effects of the maximum principal stress direction(θ)and cross-section shape on the failure characteristics of sandstone,true-triaxial compression experiments were conducted using cubic samples with rectangular,circular,and D-shaped holes.Asθincreases from 0°to 60°in the rectangular hole,the left failure location shifts from the left corner to the left sidewall,the left corner,and then the floor,while the right failure location shifts from the right corner to the right sidewall,right roof corner,and then the roof.Furthermore,the initial failure vertical stress first decreases and then increases.In comparison,the failure severity in the rectangular hole decreases for variousθvalues as 30°>45°>60°>0°.With increasingθ,the fractal dimension(D)of rock slices first increases and then decreases.For the rectangular and D-shaped holes,whenθ=0°,30°,and 90°,D for the rectangular hole is less than that of the D-shaped hole.Whenθ=45°and 60°,D for the rectangular hole is greater than that of the D-shaped hole.Theoretical analysis indicates that the stress concentration at the rectangular and D-shaped corners is greater than the other areas.The failure location rotates with the rotation ofθ,and the failure occurs on the side with a high concentration of compressive stress,while the side with the tensile and compressive stresses remains relatively stable.Therefore,the fundamental reason for the rotation of failure location is the rotation of stress concentration,and the external influencing factor is the rotation ofθ.
基金supported by Independent Research Project of State Key Laboratory of Advanced Special Steel,Shanghai Key Laboratory of Advanced Ferrometallurgy,Shanghai University(SKLASS-2023-Z13)the Science and Technology Commission of Shanghai Municipality(No.19DZ2270200)+1 种基金A portion of the work was performed at US National High Magnetic Field Laboratory,which is supported by the National Science Foundation(Cooperative Agreement No.DMR-1157490 and DMR-1644779)the State of Florida.Thanks also to Mary Tyler for editing.
文摘The high-temperature dissolution behavior of primary carbides in samples taken from GCr15 continuous-casting bloom was observed in-situ by confocal laser scanning microscopy.Equations were fitted to the dissolution kinetics of primary carbides during either heating or soaking.Dissolution of carbides proceeded in three stages(fast→slow→faster)as either temperature or holding time was increased.During the heating process and during the first and third stages of the soaking process,the original size of the carbides determined the steepness of the slope,but during the middle(“slow”)stage of the soaking process,the slope remained zero.The initial size of the carbides varied greatly,but their final dissolution temperature fell within the narrow range of 1210-1235℃,and the holding time remained within 50 min.Fractal analysis was used to study the morphological characteristics of small and medium-sized carbides during the dissolution process.According to changes in the fractal dimension before and after soaking,the carbides tended to evolve towards a more regular morphology.
基金supported by The National Natural Science Foundation of China(Grant Nos.12272411 and 42007259).
文摘Understanding the mesoscopic tensile fracture damage of rock is the basis of evaluating the deterioration process of mechanical properties of heat-damaged rock. For this, tensile tests of rocks under high-temperature treatment were conducted with a ϕ75 mm split Hopkinson tension bar (SHTB) to investigate the mesoscopic fracture and damage properties of rock. An improved scanning electron microscopy (SEM) experimental method was used to analyze the tensile fracture surfaces of rock samples. Qualitative and quantitative analyses were performed to assess evolution of mesoscopic damage of heat-damaged rock under tensile loading. A constitutive model describing the mesoscopic fractal damage under thermo-mechanical coupling was established. The results showed that the high temperatures significantly reduced the tensile strength and fracture surface roughness of the red sandstone. The three-dimensional (3D) reconstruction of the fracture surface of the samples that experienced tensile failure at 900 °C showed a flat surface. The standard deviation of elevation and slope angle of specimen fracture surface first increased and then decreased with increasing temperature. The threshold for brittle fracture of the heat-damaged red sandstone specimens was 600 °C. Beyond this threshold temperature, local ductile fracture occurred, resulting in plastic deformation of the fracture surface during tensile fracturing. With increase of temperature, the internal meso-structure of samples was strengthened slightly at first and then deteriorated gradually, which was consistent with the change of macroscopic mechanical properties of red sandstone. The mesoscopic characteristics, such as the number, mean side length, maximum area, porosity, and fractal dimension of crack, exhibited an initial decline, followed by a gradual increase. The development of microcracks in samples had significant influence on mesoscopic fractal dimension. The mesoscopic fractal characteristics were used to establish a mesoscopic fractal damage constitutive model for red sandstone, and the agreement between the theoretical and experimental results validated the proposed model.
