In terms of asymmetrical three-dimensional distribution(ID) of luminous intensity(LI) of light-emitting-diode(LED),a testing system was conducted in this study. Design and principle of the testing system were introduc...In terms of asymmetrical three-dimensional distribution(ID) of luminous intensity(LI) of light-emitting-diode(LED),a testing system was conducted in this study. Design and principle of the testing system were introduced. 31 photometers were placed on a concentric circle,and all of them were used to gather LI data of LED at the same time. The data acquisition card(DAC) was used to gather multichannel data and controlled motor. Experimental results indicated that the testing system had achieved the goal of testing three-dimensional distribution of LI. And each parameter could meet the requirements of industrial production and measurement.展开更多
Asymmetric flames exhibit distinct dynamic characteristics and combustion patterns during combustion,which are crucial for optimizing combustion efficiency and performance.Accurate derivation of three-dimensional temp...Asymmetric flames exhibit distinct dynamic characteristics and combustion patterns during combustion,which are crucial for optimizing combustion efficiency and performance.Accurate derivation of three-dimensional temperature and absorption coefficient distributions in asymmetric flames is essential for real-world flame measurement applications.However,retrieving these data presents a significant challenge,as the process requires solving an ill-posed inverse problem.To tackle this issue,we propose a multi-spectral light field imaging model that utilizes the Monte Carlo ray tracing method to capture these distributions.This model enables the reconstruction of both temperature and absorption coefficients using Tikhonov regularization combined with Bayesian optimization method.Our analysis investigates the uncertainties associated with temperature reconstruction,taking into account factors such as uniform and non-uniform absorption coefficient distributions,the reconstruction technique employed,and the signal-to-noise ratio.Notably,our findings suggest that the absorption properties within the flame have a minimal impact due to the flame medium's optical thickness.Moreover,a comparative assessment between the Tikhonov regularization method and the least-square QR decomposition method reveals that,for comparable accuracy in reconstruction,the Tikhonov method requires a shorter computational time.Ultimately,the uncertainty related to the signal-to-noise ratio emerges as the most influential factor affecting the relative error in the reconstruction of the flame's absorption coefficient.展开更多
Gas diffusion layers(GDLs)are an important component of polymer electrolyte membrane(PEM)fuel cells.They are around 100–400μm thick in typical fuel cell design,which contribute a considerable volume in fuel cell and...Gas diffusion layers(GDLs)are an important component of polymer electrolyte membrane(PEM)fuel cells.They are around 100–400μm thick in typical fuel cell design,which contribute a considerable volume in fuel cell and influence the stack’s volumetric power density.Thus,thin GDLs are considered a viable strategy to increase fuel cell power per volume,which is crucial to fuel cell automobile application.The impacts of the GDL physical processes on cell performance are investigated,with a focus on thin GDLs,through advanced three-dimensional(3-D)non-isothermal two-phase modeling.The 3-D model is based on the conservation equations for mass,momentum,heat,species(oxygen,hydrogen,water,etc.),electron,and proton,coupled with the electrochemical kinetics.It is found that thin GDLs can deteriorate oxygen starvation under the land,reducing local and overall cell performances.In addition,the temperature spatial variation in fuel cell increases when reducing GDL thickness,which can lead to dryout of local GDL and hence electrode in the cathode.For the 25μm thick GDL,the temperature variation can be as high as 17°C at 1.3 A/cm2,raising a major concern of local hot spot formation.Analysis is presented to explain a few important physical processes in GDLs,including the in-plane heat removal by GDL,vapor diffusion driven by temperature gradient,and gas flow in GDLs.The 3-D distributions of reactant and product species and temperature are disclosed,showing that advanced modeling is important to assist thin GDL design for fuel cells.展开更多
Effective isolation between the cement sheath and the sandstone is crucial for the development and production of oil and gas wells in sandstone formations.In this study,a cement-sandstone composite(CSC)was prepared,an...Effective isolation between the cement sheath and the sandstone is crucial for the development and production of oil and gas wells in sandstone formations.In this study,a cement-sandstone composite(CSC)was prepared,and based onμ-CT three-dimensional reconstruction imaging and finite element analysis(FEA)techniques,the stress distribution and potential failure mechanism at the cement-sandstone bonding interface under axial loading were analyzed.The key findings are as follows:(1)stress concentrations are highly likely to form at the gap between the cement and sandstone interface and around interfacial voids,with Von Mises stress reaching critical levels of 18.0-20.0 MPa at these locations,significantly exceeding the stress magnitudes in well-bonded regions;(2)the phenomenon of local stress concentration driven by interfacial defects can be identified as the main basis for predicting damage location in interfacial debonding and continuous shear under axial load;(3)ensuring tight cementation at the cement-sandstone interface and minimizing interfacial voids are paramount for preventing stress-induced failure;(4)the critical Von Mises stress value of 20 MPa at the interface defect can be used as a benchmark for material selection and designed to ensure long-term integrity in oil and gas well applications subjected to similar axial loads.These findings contribute to a more accurate understanding of the failure mechanism of the cement-sandstone interface and to the precise design of material properties,thereby ensuring the long-term integrity of oil and gas well applications subjected to similar axial loads.展开更多
Northwest China is recognized as a main source and a major transport channel of dust aerosols in East Asia.With a fragile ecological environment,this region is quite sensitive to global climate change.Based on the sat...Northwest China is recognized as a main source and a major transport channel of dust aerosols in East Asia.With a fragile ecological environment,this region is quite sensitive to global climate change.Based on the satellite-derived aerosol three-dimensional distribution,the direct radiative effects of dust aerosols over Northwest China are evaluated.Aerosols over Northwest China are mainly distributed in the Tarim Basin,Junggar Basin,Gobi Desert,and Loess Plateau.The aerosol extinction coefficients are greater than 0.36 km-1 over the Tarim Basin and 0.16 km^(-1) over the Gobi Desert and Loess Plateau,decreasing with height.Aerosols over Northwest China are mainly composed of pure dust and polluted dust.These dust aerosols can modify the horizontal temperature gradient,vertical thermodynamic structure,and diurnal temperature range by absorbing and scattering shortwave radiation and emitting longwave radiation.For the column atmosphere,the radiative effect of dust aerosols shows heating effect of approximately 0.3 K day^(-1) during the daytime and cooling effect of approximately-0.4 K day^(-1) at night.In the vertical direction,dust aerosols can heat up the lower atmosphere(0.5–1.5 K day^(-1))and cool down the upper atmosphere(about-1.0 K day^(-1))during the daytime,while they cool down the lower atmosphere(-3 to-1.5 K day^(-1))and heat up the upper atmosphere(1–1.5 K day^(-1))at night.There are also significant lateral and vertical variations in the dust radiative effects corresponding to their spatial distributions.This study provides some scientific basis for reducing uncertainty in the investigation of aerosol radiative effects and provides observation evidence for simulation studies.展开更多
Wind-induced circulation is the main form of lake flow for shallow lakes and plays an important role in algae population distribution.This study constructed a three-dimensional hydrodynamic model(EFDC)of the plateau l...Wind-induced circulation is the main form of lake flow for shallow lakes and plays an important role in algae population distribution.This study constructed a three-dimensional hydrodynamic model(EFDC)of the plateau lake Erhai,China using accuracy wind field observation,runoff data and monthly algae data during 2022–2023.The model successfully reproduced the circulation characteristics of Erhai under prevailing wind directions.The results showed that the lake flow velocity in Lake Erhai is higher in winter than in summer,with lower velocities near shore particularly in the northern and central parts of the lake.There is a negative correlation between algal biomass and flow velocity(FV)in different zones,with lower FV favoring the accumulation of algal biomass,particularly for Microcystis,Dolichospermum,and Peridinium.Additionally,due to buoyancy,cyanobacteria are highly affected by wind direction and tend to accumulate in downwind regions of the prevailing wind direction.This study demonstrates that wind-induced circulation is a crucial factor affecting the spatial distribution of dominant algae populations in shallow plateau lakes with weak hydrodynamic force.Further,the risk of bloom occurrence in Lake Erhai will be higher due to the background of global climate change and the lake’s wind speed decline.In conclusion,we suggest implementing targeted zoning measures to control algal blooms and establishing stricter regulations for nitrogen and phosphorus control to counterbalance the promotion of algal bloom accumulation in low-velocity zones caused by reduced wind speed.展开更多
Tajikistan represents a core region of the biodiversity hotspot in Central Asian mountains and has exceptional vascular plant diversity.However,the species diversity of the country faces urgent conservation challenges...Tajikistan represents a core region of the biodiversity hotspot in Central Asian mountains and has exceptional vascular plant diversity.However,the species diversity of the country faces urgent conservation challenges.There has been a lack of a comprehensive and multidimensional assessment to inform strategic conservation planning.Therefore,this study integrated 4 key biodiversity indices including species richness(SR),phylogenetic diversity(PD),threatened species richness(TSR),and endemic species richness(ESR)to map species diversity distribution patterns,identify conservation gaps,and elucidate their effects of climatic factors.This study revealed that species diversity shows a clear trend of decreasing from the western region to the eastern region of Tajikistan.The central–western mountains(specifically the Gissar-Darvasian and Zeravshanian regions)emerge as irreplaceable biodiversity hotspots.However,we found a severe spatial mismatch between these priority areas and the existing protected areas(PAs).Protection coverage for all hotspots was alarmingly low,ranging from 31.00%to 38.00%.Consequently,a critical 64.80%of integrated priority areas fall outside of the current PAs,representing a major conservation gap.This study identified precipitation seasonality and isothermality as the principal drivers,collectively explaining over 50.00%of the diversity variation and suggesting high vulnerability to hydrological shifts.Furthermore,we detected significant geographic sampling bias in the public biodiversity databases,with the most critical hotspot being systematically under-sampled.This study provides a robust scientific basis for conservation action,highlighting the urgent need to strategically expand PAs in the under-protected southwestern region and to mitigate critical sampling gaps through targeted data digitization and field surveys.These measures are indispensable for securing Tajikistan’s unique biodiversity and achieving the Kunming-Montreal Global Biodiversity Framework Target 3(“30×30 Protection”).展开更多
Nitrogen(N)and phosphorus(P)are essential nutrients and can significantly impact primary productivity of the ecosystem causing water environmental problems.However,their cycling mechanisms are not well understood in a...Nitrogen(N)and phosphorus(P)are essential nutrients and can significantly impact primary productivity of the ecosystem causing water environmental problems.However,their cycling mechanisms are not well understood in alpine mountains with climate change.Hence,94 samples of river water were collected from 2018 to 2020 in the headwaters of the Shule River Basin to assess the nutrients spatiotemporal distribution and combined ap-proach of water quality index to assess water quality and potential sources.The findings depict that high nutrient concentrations were found to coincide with snowmelt and glacial meltwater and rainfall recharge periods,while total flux peaked from June to September due to increased runoff.Notably,total nitrogen(TN)concentrations were significantly higher near the town,primarily attributed to the replenishment of nitrate(NO_(3)^(‒)-N)from live-stock manure.The high total P(TP)was near the glacier,which was attributed to the transportation of glacial sediments into the river,and pH was another critical factor.N was the primary nutrient limiting factor for the growth of phytoplankton in river water.Although the migration and transport of nutrients have altered with climate change,river water quality is good in alpine mountains based on an overall evaluation.These findings contribute to enriching nutrient datasets and highlight the importance of water resource management and water quality assessment in sensitive and fragile alpine mountains.展开更多
Ensuring reliable power supply in urban distribution networks is a complex and critical task.To address the increased demand during extreme scenarios,this paper proposes an optimal dispatch strategy that considers the...Ensuring reliable power supply in urban distribution networks is a complex and critical task.To address the increased demand during extreme scenarios,this paper proposes an optimal dispatch strategy that considers the coordination with virtual power plants(VPPs).The proposed strategy improves systemflexibility and responsiveness by optimizing the power adjustment of flexible resources.In the proposed strategy,theGaussian Process Regression(GPR)is firstly employed to determine the adjustable range of aggregated power within the VPP,facilitating an assessment of its potential contribution to power supply support.Then,an optimal dispatch model based on a leader-follower game is developed to maximize the benefits of the VPP and flexible resources while guaranteeing the power balance at the same time.To solve the proposed optimal dispatch model efficiently,the constraints of the problem are reformulated and resolved using the Karush-Kuhn-Tucker(KKT)optimality conditions and linear programming duality theorem.The effectiveness of the strategy is illustrated through a detailed case study.展开更多
This paper presents a reconstruction model of three-dimensional temperature distribution in furnace based on radiative energy images captured by charge-coupled device （CCD） cameras within the visible wavelength rang...This paper presents a reconstruction model of three-dimensional temperature distribution in furnace based on radiative energy images captured by charge-coupled device （CCD） cameras within the visible wavelength range. Numerical simulation case was used in this study and a zigzag eccentric temperature distribution was assumed to verify the model. Least square QR-factorization （LSQR） method was introduced to deal with reconstruction equation. It is found that the reconstructed temperature distributions in low-temperature areas had some fluctuations and high-temperature areas were reconstructed well. The whole reconstruction relative error was mainly due to errors in low-temperature areas and the relative error for highest-temperature reconstruction was quite small.展开更多
A three-dimensional crustal density model beneath North China is determined using P-wave traveltimes and gravity datum by sequential inversion method in this paper. To improve the uniqueness of the solution, we used a...A three-dimensional crustal density model beneath North China is determined using P-wave traveltimes and gravity datum by sequential inversion method in this paper. To improve the uniqueness of the solution, we used a linear relationship between velocity and density to achieve mutual conversions and constraints between velocity difference and density difference. Algebraic reconstruction technique （ART） was used in density inversion, which highly improved the calculation speed comparing with common least squares method. The inversion results indicate that the crustal density beneath North China is extremely inhomogeneous with its distribution coherent with regional tectonics. The lower crust of Taihang mountain tectonic zone shows an obvious low density characteristic. We proposed that it may be an indicator of upwelling of mantle materials or partial melting of lowermost crust.展开更多
To study the three-dimensional spatial and temporal distributions of dust in tunneling roadways,and to solve the problems of inadequate time and limited number of monitoring points,this paper designs a device for the ...To study the three-dimensional spatial and temporal distributions of dust in tunneling roadways,and to solve the problems of inadequate time and limited number of monitoring points,this paper designs a device for the real-time monitoring and storage of data on the concentrations of dust at multiple measuring points in the same section of a tunnel.The proposed device can measure the total concentration of dust and that of respirable dust in real time at different instances and locations,and using different working procedures.These measurements are used to study the temporal and spatial migration of dust.The results show that there was a sharp fluctuation zone 0–25 m from the heading face,about 25–40 m was high speed subsidence,beyond 40 m was gentle subsidence,The change of respiratory dust is much smoother.At different distances from the heading face,the total dust concentration exhibited a process of“violent oscillation–rapid descent–stable descent,”while the respirable dust exhibited a process of“fluctuating ascent–gradual subsidence.”Changes in the concentrations of total dust and respirable dust dust were consistent at different positions in the same section of the tunnel.The concentration of dust near the wall was low,and those along the sidewalk and air duct of the roadway were slightly higher than in the middle.The concentration of dust farther down the air duct decreased more slowly than that in the remaining lines of measurement.Small amounts of dust featuring large particles settled quickly.High concentrations of dust were observed to be intermittent,and the background value of dust concentration within 100 m of heading face was between 0.5 and 3 mg/m3.展开更多
Objective: We constructed 3D-model of ONFH in computer according to three-dimensional computerized tomography (3D-CT) data. We determined the location and volume of necrosis to investigate its clinical efficacy. Metho...Objective: We constructed 3D-model of ONFH in computer according to three-dimensional computerized tomography (3D-CT) data. We determined the location and volume of necrosis to investigate its clinical efficacy. Method: Totally 92 hips (59 cases) with ONFH (44 males, 15 females) were included, with mean age of 37.5 years (range from 26 to 58). Totally 20 cases (35 hips) were induced by corticosteroid (CTSs), 31 (49 hips) induced by alcohol, 4 (4 hips) induced by trauma and 4 (4 hips) idiopathic. All the hips were categorized into stage ARCO II. Finally diagnosed by MRI, all hips were scanned by CT to acquire data in DICOM format. The images were imported into software to extract 3D-shape of femoral heads, necrotic foci, their volumes and distribution in each quadrant. Deviation of volumes between digital image and biopsy specimen was analyzed by SAS9.1 package. Correlativity between collapse and volume of necrosis under specific pathogeneses was also analyzed. Among the cases necessitating total hip arthroplasty (THA) due to advancing to ARCO III, we randomly selected 8 of them to perform 3D-CT scanning thrice prior to surgical operation. Total femoral heads harvested were torn asunder. Cubic capacity of femoral heads and necrotic foci were hereby measured and compared with those acquired from digital models. Result: Through the digital model, necrotic foci were found mainly locating within the super lateral portion of femoral head, coinciding with those observed in biopsy specimen. Average volumetric ratio of digitally acquired necrosis focus/femoral head in 58 collapsed hips was 36.8%. The ratio of the 34 hips without collapse was 17.3%. In collapsed femoral heads, the distribution of necrosis focus was 23.4% in quadrant 1 (q1), 23.6% in q2, 12.1% in q3, 14.4% in q4, 9.0% in q5, 11.8% in q6, 1.6% in q7 and 3.9% in q8. In femoral heads without collapse, the distribution was 34.2% in q1, 29.6% in q2, 11.8% in q3, 11.3% in q4, 6.0% in q5, 6.0% in q6, 0.5% in q7 and 0.4% in q8. As for the average cubic capacities of femoral heads and necrotic foci, those acquired from the digital model and biopsy specimen had no significant difference in matched-pairs test (t = -1.49, P = 0.179 for femoral heads and t = -1.52, P = 0.172 for necrotic foci). There was significant difference (F = 2.720, P = 0.035 P was respectively 0.0001 and 0.0005). Decision tree model showed that 94.6% (53/56) hips would progress into collapse if the volumetric ratio of necrotic tissue was over 23.48%. Otherwise, if distribution in q2 was over 45.13%, 83.3% (5/6) hips would progress into collapse. No collapse (0/30) would occur if the distribution of necrotic tissue in q2 was under 45.13%. Conclusion: Digital 3D-model reconstructed from CT scanning can precisely incarnate spatial orientation of necrotic foci in femoral head. Multinomial logistic regression and decision-making tree shows that volumetric ratio of necrotic tissues plays an important role in anticipating collapse of femoral head.展开更多
This paper presents a finite element calculation for the electronic structure and strain distribution of self-organized InAs/GaAs quantum rings. The strain distribution calculations are based on the continuum elastic ...This paper presents a finite element calculation for the electronic structure and strain distribution of self-organized InAs/GaAs quantum rings. The strain distribution calculations are based on the continuum elastic theory. An ideal three-dimensional circular quantum ring model is adopted in this work. The electron and heavy-hole energy levels of the InAs/GaAs quantum rings are calculated by solving the three-dimensional effective mass SchrSdinger equation including the deformation potential and piezoelectric potential up to the second order induced by the strain. The calculated results show the importance of strain and piezoelectric effects, and these effects should be taken into consideration in analysis of the optoelectronic characteristics of strain quantum rings.展开更多
A theoretical analysis of three-dimensional Couette flow with radiation effect on temperature distribution has been analysed, when the injection of the fluid at the lower stationary plate is a transverse sinusoidat on...A theoretical analysis of three-dimensional Couette flow with radiation effect on temperature distribution has been analysed, when the injection of the fluid at the lower stationary plate is a transverse sinusoidat one and its corresponding removal by constant suction through the upper porous plate is in uniform motion. Due to this type of injection velocity, the flow becomes three-dimensional. The effect of Prandtl number, radiation parameter and injection parameter on rate of heat transfer has been examined by the help of graphs. The Prandtl number has a much greater effect on the.temperature distribution than the injection or radiation parameter.展开更多
This paper utilizes the mathematical concept of approximation within an ellipsoid from a single viewpoint to present the spatial mass distribution function of the Earth's interior and its internal potential.The pr...This paper utilizes the mathematical concept of approximation within an ellipsoid from a single viewpoint to present the spatial mass distribution function of the Earth's interior and its internal potential.The primary focus lies in constructing the volume distribution of masses in the planet's interior, with the expansion coefficients being linear combinations of the Stokes constants. Several possible approaches are suggested for determining accurately these coefficients employing three-dimensional(biorthogonal)polynomials. By expressing the mass distribution function of the Earth's interior and its internal potential as a series, an algorithm is introduced for the calculation of gravitational energy. It allows us to estimate fluctuations in gravitational energy. The implementation of this algorithm offers the means of establishing the extent to which the Earth deviates from a state of hydrostatic equilibrium as a celestial body.Due to the aforementioned method, calculations have been conducted to validate its effectiveness and reliability. This example is given as an illustration of a given method for studying the internal structure of planets.展开更多
This study describes an ultrasonic velocity profiler that uses a <span style="white-space:normal;"><span style="font-family:;" "="">new ultrasonic array transducer with u...This study describes an ultrasonic velocity profiler that uses a <span style="white-space:normal;"><span style="font-family:;" "="">new ultrasonic array transducer with unique 5-element configuration</span></span><span style="white-space:normal;"><span style="font-family:;" "="">, with all five elements acting as transmitters and four elements as receivers. The receivers are designed to reduce the amount of uncertainty. As the fluid moves through this setup, four Doppler frequencies are obtained. The multi-dimensional velocity information along the measurement line can be reconstructed. The transducer has a compact geometry suitable for a wide range of applications, including narrow flow areas. The transducer’s basic frequency and sound pressure are selected and evaluated to be compatible with the application. First, to confirm the measurement ability, the measurement of the developed system in two-dimensional flow is validated by comparing it to the theoretical data. The uncertainty of measurement was within 15%. Second, the three-dimensional measurement in turbulent and swirling flow is proved experimentally to check the applicability of the proposed technique.</span></span>展开更多
In this paper, we analyze lithospheric density distribution of China and surrounding regions on the basis of 30＇ × 30＇ gravity data and 1°×1 °P-wave velodty data, Firstly, we used the empirical e...In this paper, we analyze lithospheric density distribution of China and surrounding regions on the basis of 30＇ × 30＇ gravity data and 1°×1 °P-wave velodty data, Firstly, we used the empirical equation be- tween the density and the P-wave velocity difference as the base of the initial model of the Asian lithospheric density. Secondly, we calculated the gravity anomaly, caused by the Moho discontinuity and the sedimentary layer discontinuity, by the Parker formula. Thirdly, the gravity anomaly of the spherical harmonics with 2 40 order for the anomalous body below the lithosphere is calculated based on the model of EGM96. Finally, by using Algebra Reconstruction Techniques （ART）, the inversion of 30＇ ~ 30＇ residual lithospheric Bouguer gravity anomaly caused by the lithosphere yields a rather detailed struc- tural model. The results show that the lithospheric density distribution of China and surrounding regions has a certain connection with the tectonic structure. The density is relatively high in the Philippine Sea plate, Japan Sea, the Indian plate, the Kazakhstan shield and the Western Siberia plain, whereas the Tibetan Plateau has low-density characteristics. The minimum value of density lies in the north of Philippines, in the Taiwan province and in the Ryukyu island arc.展开更多
Coordinated contraction of skeletal muscles relies on selective connections between the muscles and multiple classes of the spinal motoneuro ns.Howeve r,current research on the spatial location of the spinal motoneuro...Coordinated contraction of skeletal muscles relies on selective connections between the muscles and multiple classes of the spinal motoneuro ns.Howeve r,current research on the spatial location of the spinal motoneurons innervating differe nt muscles is limited.In this study,we investigated the spatial distribution and relative position of different motoneurons that control the deep muscles of the mouse hindlimbs,which were innervated by the obturator nerve,femoral nerve,inferior gluteal nerve,deep pe roneal nerve,and tibial nerve.Locations were visualized by combining a multiplex retrograde tracking technique compatible with three-dimensional imaging of solvent-cleared o rgans(3DISCO)and 3-D imaging technology based on lightsheet fluorescence microscopy(LSFM).Additionally,we propose the hypothesis that"messenger zones"exist as interlaced areas between the motoneuron pools that dominate the synergistic or antagonist muscle groups.We hypothesize that these interlaced neurons may participate in muscle coordination as messenger neurons.Analysis revealed the precise mutual positional relationships among the many motoneurons that innervate different deep muscles of the mouse.Not only do these findings update and supplement our knowledge regarding the overall spatial layout of spinal motoneurons that control mouse limb muscles,but they also provide insights into the mechanisms through which muscle activity is coordinated and the architecture of motor circuits.展开更多
The three-dimensional stress distributions in the area surrounding indentation pattern for three different materials, Al2O3, Si3N4 and SiC were analyzed by finite element method(FEM). Those theoretical results were al...The three-dimensional stress distributions in the area surrounding indentation pattern for three different materials, Al2O3, Si3N4 and SiC were analyzed by finite element method(FEM). Those theoretical results were also compared with the experimental ones by Rockwell hardness test. The effect of loading stress on the plastic deformation in specimens, surface was investigated on the assumption of shear strain energy theory by Huber-Mises when the materials were indented. The distributions of nomal stress, shear stress, and Mises stress were analysed with variations of loading conditions. It is clear that the analytical results for the stress distributions, the crack length and its density of probability are in good agreement with the experimental results.展开更多
文摘In terms of asymmetrical three-dimensional distribution(ID) of luminous intensity(LI) of light-emitting-diode(LED),a testing system was conducted in this study. Design and principle of the testing system were introduced. 31 photometers were placed on a concentric circle,and all of them were used to gather LI data of LED at the same time. The data acquisition card(DAC) was used to gather multichannel data and controlled motor. Experimental results indicated that the testing system had achieved the goal of testing three-dimensional distribution of LI. And each parameter could meet the requirements of industrial production and measurement.
基金supported by the National Natural Science Foundation of China (Grant Nos.52306213, 52376115)the Natural Science Foundation of Jiangsu Province (BK20220955)the Fundamental Research Funds for the Central Universities (Grant No.30924010921)。
文摘Asymmetric flames exhibit distinct dynamic characteristics and combustion patterns during combustion,which are crucial for optimizing combustion efficiency and performance.Accurate derivation of three-dimensional temperature and absorption coefficient distributions in asymmetric flames is essential for real-world flame measurement applications.However,retrieving these data presents a significant challenge,as the process requires solving an ill-posed inverse problem.To tackle this issue,we propose a multi-spectral light field imaging model that utilizes the Monte Carlo ray tracing method to capture these distributions.This model enables the reconstruction of both temperature and absorption coefficients using Tikhonov regularization combined with Bayesian optimization method.Our analysis investigates the uncertainties associated with temperature reconstruction,taking into account factors such as uniform and non-uniform absorption coefficient distributions,the reconstruction technique employed,and the signal-to-noise ratio.Notably,our findings suggest that the absorption properties within the flame have a minimal impact due to the flame medium's optical thickness.Moreover,a comparative assessment between the Tikhonov regularization method and the least-square QR decomposition method reveals that,for comparable accuracy in reconstruction,the Tikhonov method requires a shorter computational time.Ultimately,the uncertainty related to the signal-to-noise ratio emerges as the most influential factor affecting the relative error in the reconstruction of the flame's absorption coefficient.
文摘Gas diffusion layers(GDLs)are an important component of polymer electrolyte membrane(PEM)fuel cells.They are around 100–400μm thick in typical fuel cell design,which contribute a considerable volume in fuel cell and influence the stack’s volumetric power density.Thus,thin GDLs are considered a viable strategy to increase fuel cell power per volume,which is crucial to fuel cell automobile application.The impacts of the GDL physical processes on cell performance are investigated,with a focus on thin GDLs,through advanced three-dimensional(3-D)non-isothermal two-phase modeling.The 3-D model is based on the conservation equations for mass,momentum,heat,species(oxygen,hydrogen,water,etc.),electron,and proton,coupled with the electrochemical kinetics.It is found that thin GDLs can deteriorate oxygen starvation under the land,reducing local and overall cell performances.In addition,the temperature spatial variation in fuel cell increases when reducing GDL thickness,which can lead to dryout of local GDL and hence electrode in the cathode.For the 25μm thick GDL,the temperature variation can be as high as 17°C at 1.3 A/cm2,raising a major concern of local hot spot formation.Analysis is presented to explain a few important physical processes in GDLs,including the in-plane heat removal by GDL,vapor diffusion driven by temperature gradient,and gas flow in GDLs.The 3-D distributions of reactant and product species and temperature are disclosed,showing that advanced modeling is important to assist thin GDL design for fuel cells.
基金supported by the National Natural Science Foundation of China(No.52274026)the National Key Research and Development Program(No.2022YFC2806504)the CNOOC Research Project(No.KJGG-2022-17-04 and NO.KJGG-2022-17-05).
文摘Effective isolation between the cement sheath and the sandstone is crucial for the development and production of oil and gas wells in sandstone formations.In this study,a cement-sandstone composite(CSC)was prepared,and based onμ-CT three-dimensional reconstruction imaging and finite element analysis(FEA)techniques,the stress distribution and potential failure mechanism at the cement-sandstone bonding interface under axial loading were analyzed.The key findings are as follows:(1)stress concentrations are highly likely to form at the gap between the cement and sandstone interface and around interfacial voids,with Von Mises stress reaching critical levels of 18.0-20.0 MPa at these locations,significantly exceeding the stress magnitudes in well-bonded regions;(2)the phenomenon of local stress concentration driven by interfacial defects can be identified as the main basis for predicting damage location in interfacial debonding and continuous shear under axial load;(3)ensuring tight cementation at the cement-sandstone interface and minimizing interfacial voids are paramount for preventing stress-induced failure;(4)the critical Von Mises stress value of 20 MPa at the interface defect can be used as a benchmark for material selection and designed to ensure long-term integrity in oil and gas well applications subjected to similar axial loads.These findings contribute to a more accurate understanding of the failure mechanism of the cement-sandstone interface and to the precise design of material properties,thereby ensuring the long-term integrity of oil and gas well applications subjected to similar axial loads.
基金Supported by the Gansu Provincial Special Fund for Scientific and Technological Innovation and Development(2019ZX-06)Fundamental Research Funds for the Central Universities(lzujbky-2020-kb31)Meteorological Science and Technology Research Project of Shandong Meteorological Bureau(2019sdqxm14)。
文摘Northwest China is recognized as a main source and a major transport channel of dust aerosols in East Asia.With a fragile ecological environment,this region is quite sensitive to global climate change.Based on the satellite-derived aerosol three-dimensional distribution,the direct radiative effects of dust aerosols over Northwest China are evaluated.Aerosols over Northwest China are mainly distributed in the Tarim Basin,Junggar Basin,Gobi Desert,and Loess Plateau.The aerosol extinction coefficients are greater than 0.36 km-1 over the Tarim Basin and 0.16 km^(-1) over the Gobi Desert and Loess Plateau,decreasing with height.Aerosols over Northwest China are mainly composed of pure dust and polluted dust.These dust aerosols can modify the horizontal temperature gradient,vertical thermodynamic structure,and diurnal temperature range by absorbing and scattering shortwave radiation and emitting longwave radiation.For the column atmosphere,the radiative effect of dust aerosols shows heating effect of approximately 0.3 K day^(-1) during the daytime and cooling effect of approximately-0.4 K day^(-1) at night.In the vertical direction,dust aerosols can heat up the lower atmosphere(0.5–1.5 K day^(-1))and cool down the upper atmosphere(about-1.0 K day^(-1))during the daytime,while they cool down the lower atmosphere(-3 to-1.5 K day^(-1))and heat up the upper atmosphere(1–1.5 K day^(-1))at night.There are also significant lateral and vertical variations in the dust radiative effects corresponding to their spatial distributions.This study provides some scientific basis for reducing uncertainty in the investigation of aerosol radiative effects and provides observation evidence for simulation studies.
基金supported by the Open Research Fund of Key Laboratory for Lake Pollution Control of the Ministry of Ecology and Environment(No.2024HPYKFZD04)the Fundamental Research Funds for the Central Publicinterest Scientific Institution(No.2025YSKY-04)the National Natural Science Foundation of China(Nos.U1902207 and 42207265).
文摘Wind-induced circulation is the main form of lake flow for shallow lakes and plays an important role in algae population distribution.This study constructed a three-dimensional hydrodynamic model(EFDC)of the plateau lake Erhai,China using accuracy wind field observation,runoff data and monthly algae data during 2022–2023.The model successfully reproduced the circulation characteristics of Erhai under prevailing wind directions.The results showed that the lake flow velocity in Lake Erhai is higher in winter than in summer,with lower velocities near shore particularly in the northern and central parts of the lake.There is a negative correlation between algal biomass and flow velocity(FV)in different zones,with lower FV favoring the accumulation of algal biomass,particularly for Microcystis,Dolichospermum,and Peridinium.Additionally,due to buoyancy,cyanobacteria are highly affected by wind direction and tend to accumulate in downwind regions of the prevailing wind direction.This study demonstrates that wind-induced circulation is a crucial factor affecting the spatial distribution of dominant algae populations in shallow plateau lakes with weak hydrodynamic force.Further,the risk of bloom occurrence in Lake Erhai will be higher due to the background of global climate change and the lake’s wind speed decline.In conclusion,we suggest implementing targeted zoning measures to control algal blooms and establishing stricter regulations for nitrogen and phosphorus control to counterbalance the promotion of algal bloom accumulation in low-velocity zones caused by reduced wind speed.
基金the Chinese Academy of Sciences Research Center for Ecology and Environment of Central Asia(RCEECA),the construction and joint research for the China-Tajikistan“Belt and Road”Joint Laboratory on Biodiversity Conservation and Sustainable Use(2024YFE0214200)the Shanghai Cooperation Organization Partnership and International Technology Cooperation Plan of Science and Technology Projects(2023E01018,2025E01056)the Chinese Academy of Sciences President’s International Fellowship Initiative(PIFI)(2024VBC0006).
文摘Tajikistan represents a core region of the biodiversity hotspot in Central Asian mountains and has exceptional vascular plant diversity.However,the species diversity of the country faces urgent conservation challenges.There has been a lack of a comprehensive and multidimensional assessment to inform strategic conservation planning.Therefore,this study integrated 4 key biodiversity indices including species richness(SR),phylogenetic diversity(PD),threatened species richness(TSR),and endemic species richness(ESR)to map species diversity distribution patterns,identify conservation gaps,and elucidate their effects of climatic factors.This study revealed that species diversity shows a clear trend of decreasing from the western region to the eastern region of Tajikistan.The central–western mountains(specifically the Gissar-Darvasian and Zeravshanian regions)emerge as irreplaceable biodiversity hotspots.However,we found a severe spatial mismatch between these priority areas and the existing protected areas(PAs).Protection coverage for all hotspots was alarmingly low,ranging from 31.00%to 38.00%.Consequently,a critical 64.80%of integrated priority areas fall outside of the current PAs,representing a major conservation gap.This study identified precipitation seasonality and isothermality as the principal drivers,collectively explaining over 50.00%of the diversity variation and suggesting high vulnerability to hydrological shifts.Furthermore,we detected significant geographic sampling bias in the public biodiversity databases,with the most critical hotspot being systematically under-sampled.This study provides a robust scientific basis for conservation action,highlighting the urgent need to strategically expand PAs in the under-protected southwestern region and to mitigate critical sampling gaps through targeted data digitization and field surveys.These measures are indispensable for securing Tajikistan’s unique biodiversity and achieving the Kunming-Montreal Global Biodiversity Framework Target 3(“30×30 Protection”).
基金supported by the Second Tibetan Plateau Scientific Expedition and Research Program(STEP)(No.2019QZKK0208)the National Natural Science Foundation of China(Nos.42171148 and 42330512)the Key R&D Project from the Science and Technology Department of Tibet(No.XZ202501ZY0030).
文摘Nitrogen(N)and phosphorus(P)are essential nutrients and can significantly impact primary productivity of the ecosystem causing water environmental problems.However,their cycling mechanisms are not well understood in alpine mountains with climate change.Hence,94 samples of river water were collected from 2018 to 2020 in the headwaters of the Shule River Basin to assess the nutrients spatiotemporal distribution and combined ap-proach of water quality index to assess water quality and potential sources.The findings depict that high nutrient concentrations were found to coincide with snowmelt and glacial meltwater and rainfall recharge periods,while total flux peaked from June to September due to increased runoff.Notably,total nitrogen(TN)concentrations were significantly higher near the town,primarily attributed to the replenishment of nitrate(NO_(3)^(‒)-N)from live-stock manure.The high total P(TP)was near the glacier,which was attributed to the transportation of glacial sediments into the river,and pH was another critical factor.N was the primary nutrient limiting factor for the growth of phytoplankton in river water.Although the migration and transport of nutrients have altered with climate change,river water quality is good in alpine mountains based on an overall evaluation.These findings contribute to enriching nutrient datasets and highlight the importance of water resource management and water quality assessment in sensitive and fragile alpine mountains.
基金supported by the Science and Technology Project of Sichuan Electric Power Company“Power Supply Guarantee Strategy for Urban Distribution Networks Considering Coordination with Virtual Power Plant during Extreme Weather Event”(No.521920230003).
文摘Ensuring reliable power supply in urban distribution networks is a complex and critical task.To address the increased demand during extreme scenarios,this paper proposes an optimal dispatch strategy that considers the coordination with virtual power plants(VPPs).The proposed strategy improves systemflexibility and responsiveness by optimizing the power adjustment of flexible resources.In the proposed strategy,theGaussian Process Regression(GPR)is firstly employed to determine the adjustable range of aggregated power within the VPP,facilitating an assessment of its potential contribution to power supply support.Then,an optimal dispatch model based on a leader-follower game is developed to maximize the benefits of the VPP and flexible resources while guaranteeing the power balance at the same time.To solve the proposed optimal dispatch model efficiently,the constraints of the problem are reformulated and resolved using the Karush-Kuhn-Tucker(KKT)optimality conditions and linear programming duality theorem.The effectiveness of the strategy is illustrated through a detailed case study.
基金Project supported by the State Key Program of National Natural Science Foundation of China (Grant No 60534030)Program for Changjiang Scholars and Innovative Research Team in University (Grant No IRT0434)
文摘This paper presents a reconstruction model of three-dimensional temperature distribution in furnace based on radiative energy images captured by charge-coupled device （CCD） cameras within the visible wavelength range. Numerical simulation case was used in this study and a zigzag eccentric temperature distribution was assumed to verify the model. Least square QR-factorization （LSQR） method was introduced to deal with reconstruction equation. It is found that the reconstructed temperature distributions in low-temperature areas had some fluctuations and high-temperature areas were reconstructed well. The whole reconstruction relative error was mainly due to errors in low-temperature areas and the relative error for highest-temperature reconstruction was quite small.
基金financially supported by the National Natural Science Foundation of China(No.90814009)
文摘A three-dimensional crustal density model beneath North China is determined using P-wave traveltimes and gravity datum by sequential inversion method in this paper. To improve the uniqueness of the solution, we used a linear relationship between velocity and density to achieve mutual conversions and constraints between velocity difference and density difference. Algebraic reconstruction technique （ART） was used in density inversion, which highly improved the calculation speed comparing with common least squares method. The inversion results indicate that the crustal density beneath North China is extremely inhomogeneous with its distribution coherent with regional tectonics. The lower crust of Taihang mountain tectonic zone shows an obvious low density characteristic. We proposed that it may be an indicator of upwelling of mantle materials or partial melting of lowermost crust.
文摘To study the three-dimensional spatial and temporal distributions of dust in tunneling roadways,and to solve the problems of inadequate time and limited number of monitoring points,this paper designs a device for the real-time monitoring and storage of data on the concentrations of dust at multiple measuring points in the same section of a tunnel.The proposed device can measure the total concentration of dust and that of respirable dust in real time at different instances and locations,and using different working procedures.These measurements are used to study the temporal and spatial migration of dust.The results show that there was a sharp fluctuation zone 0–25 m from the heading face,about 25–40 m was high speed subsidence,beyond 40 m was gentle subsidence,The change of respiratory dust is much smoother.At different distances from the heading face,the total dust concentration exhibited a process of“violent oscillation–rapid descent–stable descent,”while the respirable dust exhibited a process of“fluctuating ascent–gradual subsidence.”Changes in the concentrations of total dust and respirable dust dust were consistent at different positions in the same section of the tunnel.The concentration of dust near the wall was low,and those along the sidewalk and air duct of the roadway were slightly higher than in the middle.The concentration of dust farther down the air duct decreased more slowly than that in the remaining lines of measurement.Small amounts of dust featuring large particles settled quickly.High concentrations of dust were observed to be intermittent,and the background value of dust concentration within 100 m of heading face was between 0.5 and 3 mg/m3.
文摘Objective: We constructed 3D-model of ONFH in computer according to three-dimensional computerized tomography (3D-CT) data. We determined the location and volume of necrosis to investigate its clinical efficacy. Method: Totally 92 hips (59 cases) with ONFH (44 males, 15 females) were included, with mean age of 37.5 years (range from 26 to 58). Totally 20 cases (35 hips) were induced by corticosteroid (CTSs), 31 (49 hips) induced by alcohol, 4 (4 hips) induced by trauma and 4 (4 hips) idiopathic. All the hips were categorized into stage ARCO II. Finally diagnosed by MRI, all hips were scanned by CT to acquire data in DICOM format. The images were imported into software to extract 3D-shape of femoral heads, necrotic foci, their volumes and distribution in each quadrant. Deviation of volumes between digital image and biopsy specimen was analyzed by SAS9.1 package. Correlativity between collapse and volume of necrosis under specific pathogeneses was also analyzed. Among the cases necessitating total hip arthroplasty (THA) due to advancing to ARCO III, we randomly selected 8 of them to perform 3D-CT scanning thrice prior to surgical operation. Total femoral heads harvested were torn asunder. Cubic capacity of femoral heads and necrotic foci were hereby measured and compared with those acquired from digital models. Result: Through the digital model, necrotic foci were found mainly locating within the super lateral portion of femoral head, coinciding with those observed in biopsy specimen. Average volumetric ratio of digitally acquired necrosis focus/femoral head in 58 collapsed hips was 36.8%. The ratio of the 34 hips without collapse was 17.3%. In collapsed femoral heads, the distribution of necrosis focus was 23.4% in quadrant 1 (q1), 23.6% in q2, 12.1% in q3, 14.4% in q4, 9.0% in q5, 11.8% in q6, 1.6% in q7 and 3.9% in q8. In femoral heads without collapse, the distribution was 34.2% in q1, 29.6% in q2, 11.8% in q3, 11.3% in q4, 6.0% in q5, 6.0% in q6, 0.5% in q7 and 0.4% in q8. As for the average cubic capacities of femoral heads and necrotic foci, those acquired from the digital model and biopsy specimen had no significant difference in matched-pairs test (t = -1.49, P = 0.179 for femoral heads and t = -1.52, P = 0.172 for necrotic foci). There was significant difference (F = 2.720, P = 0.035 P was respectively 0.0001 and 0.0005). Decision tree model showed that 94.6% (53/56) hips would progress into collapse if the volumetric ratio of necrotic tissue was over 23.48%. Otherwise, if distribution in q2 was over 45.13%, 83.3% (5/6) hips would progress into collapse. No collapse (0/30) would occur if the distribution of necrotic tissue in q2 was under 45.13%. Conclusion: Digital 3D-model reconstructed from CT scanning can precisely incarnate spatial orientation of necrotic foci in femoral head. Multinomial logistic regression and decision-making tree shows that volumetric ratio of necrotic tissues plays an important role in anticipating collapse of femoral head.
基金Project supported by the National High Technology Research and Development Program of China (Grant No 2009AA03Z405)the National Natural Science Foundation of China (Grant Nos 60908028 and 60971068)the High School Innovation and Introducing Talent Project of China (Grant No B07005)
文摘This paper presents a finite element calculation for the electronic structure and strain distribution of self-organized InAs/GaAs quantum rings. The strain distribution calculations are based on the continuum elastic theory. An ideal three-dimensional circular quantum ring model is adopted in this work. The electron and heavy-hole energy levels of the InAs/GaAs quantum rings are calculated by solving the three-dimensional effective mass SchrSdinger equation including the deformation potential and piezoelectric potential up to the second order induced by the strain. The calculated results show the importance of strain and piezoelectric effects, and these effects should be taken into consideration in analysis of the optoelectronic characteristics of strain quantum rings.
文摘A theoretical analysis of three-dimensional Couette flow with radiation effect on temperature distribution has been analysed, when the injection of the fluid at the lower stationary plate is a transverse sinusoidat one and its corresponding removal by constant suction through the upper porous plate is in uniform motion. Due to this type of injection velocity, the flow becomes three-dimensional. The effect of Prandtl number, radiation parameter and injection parameter on rate of heat transfer has been examined by the help of graphs. The Prandtl number has a much greater effect on the.temperature distribution than the injection or radiation parameter.
文摘This paper utilizes the mathematical concept of approximation within an ellipsoid from a single viewpoint to present the spatial mass distribution function of the Earth's interior and its internal potential.The primary focus lies in constructing the volume distribution of masses in the planet's interior, with the expansion coefficients being linear combinations of the Stokes constants. Several possible approaches are suggested for determining accurately these coefficients employing three-dimensional(biorthogonal)polynomials. By expressing the mass distribution function of the Earth's interior and its internal potential as a series, an algorithm is introduced for the calculation of gravitational energy. It allows us to estimate fluctuations in gravitational energy. The implementation of this algorithm offers the means of establishing the extent to which the Earth deviates from a state of hydrostatic equilibrium as a celestial body.Due to the aforementioned method, calculations have been conducted to validate its effectiveness and reliability. This example is given as an illustration of a given method for studying the internal structure of planets.
文摘This study describes an ultrasonic velocity profiler that uses a <span style="white-space:normal;"><span style="font-family:;" "="">new ultrasonic array transducer with unique 5-element configuration</span></span><span style="white-space:normal;"><span style="font-family:;" "="">, with all five elements acting as transmitters and four elements as receivers. The receivers are designed to reduce the amount of uncertainty. As the fluid moves through this setup, four Doppler frequencies are obtained. The multi-dimensional velocity information along the measurement line can be reconstructed. The transducer has a compact geometry suitable for a wide range of applications, including narrow flow areas. The transducer’s basic frequency and sound pressure are selected and evaluated to be compatible with the application. First, to confirm the measurement ability, the measurement of the developed system in two-dimensional flow is validated by comparing it to the theoretical data. The uncertainty of measurement was within 15%. Second, the three-dimensional measurement in turbulent and swirling flow is proved experimentally to check the applicability of the proposed technique.</span></span>
基金supported by Project SinoProbe-02: Experiment and Integration of Deep Probe Techniques in ChinaNational Natural Science Foundation of China (NSFC, Grant No. 40874067)the Research Fund for the Doctoral Program of Higher Education (Grant No. 20070491520)
文摘In this paper, we analyze lithospheric density distribution of China and surrounding regions on the basis of 30＇ × 30＇ gravity data and 1°×1 °P-wave velodty data, Firstly, we used the empirical equation be- tween the density and the P-wave velocity difference as the base of the initial model of the Asian lithospheric density. Secondly, we calculated the gravity anomaly, caused by the Moho discontinuity and the sedimentary layer discontinuity, by the Parker formula. Thirdly, the gravity anomaly of the spherical harmonics with 2 40 order for the anomalous body below the lithosphere is calculated based on the model of EGM96. Finally, by using Algebra Reconstruction Techniques （ART）, the inversion of 30＇ ~ 30＇ residual lithospheric Bouguer gravity anomaly caused by the lithosphere yields a rather detailed struc- tural model. The results show that the lithospheric density distribution of China and surrounding regions has a certain connection with the tectonic structure. The density is relatively high in the Philippine Sea plate, Japan Sea, the Indian plate, the Kazakhstan shield and the Western Siberia plain, whereas the Tibetan Plateau has low-density characteristics. The minimum value of density lies in the north of Philippines, in the Taiwan province and in the Ryukyu island arc.
基金supported by the Chinese National General Program of the National Natural Science Foundation of China,No.82072162(to XY)。
文摘Coordinated contraction of skeletal muscles relies on selective connections between the muscles and multiple classes of the spinal motoneuro ns.Howeve r,current research on the spatial location of the spinal motoneurons innervating differe nt muscles is limited.In this study,we investigated the spatial distribution and relative position of different motoneurons that control the deep muscles of the mouse hindlimbs,which were innervated by the obturator nerve,femoral nerve,inferior gluteal nerve,deep pe roneal nerve,and tibial nerve.Locations were visualized by combining a multiplex retrograde tracking technique compatible with three-dimensional imaging of solvent-cleared o rgans(3DISCO)and 3-D imaging technology based on lightsheet fluorescence microscopy(LSFM).Additionally,we propose the hypothesis that"messenger zones"exist as interlaced areas between the motoneuron pools that dominate the synergistic or antagonist muscle groups.We hypothesize that these interlaced neurons may participate in muscle coordination as messenger neurons.Analysis revealed the precise mutual positional relationships among the many motoneurons that innervate different deep muscles of the mouse.Not only do these findings update and supplement our knowledge regarding the overall spatial layout of spinal motoneurons that control mouse limb muscles,but they also provide insights into the mechanisms through which muscle activity is coordinated and the architecture of motor circuits.
文摘The three-dimensional stress distributions in the area surrounding indentation pattern for three different materials, Al2O3, Si3N4 and SiC were analyzed by finite element method(FEM). Those theoretical results were also compared with the experimental ones by Rockwell hardness test. The effect of loading stress on the plastic deformation in specimens, surface was investigated on the assumption of shear strain energy theory by Huber-Mises when the materials were indented. The distributions of nomal stress, shear stress, and Mises stress were analysed with variations of loading conditions. It is clear that the analytical results for the stress distributions, the crack length and its density of probability are in good agreement with the experimental results.
