The three-dimensional lattice Boltzmann method(LBM)is used to simulate the motion of a spherical squirmer in a square tube,and the steady motion velocity of a squirmer with different Reynolds numbers(Re,ranging from 0...The three-dimensional lattice Boltzmann method(LBM)is used to simulate the motion of a spherical squirmer in a square tube,and the steady motion velocity of a squirmer with different Reynolds numbers(Re,ranging from 0.1 to 2)and swimming types is investigated and analyzed to better understand the swimming characteristics of microorganisms in different environments.First,as the Reynolds number increases,the effect of the inertial forces becomes significant,disrupting the squirmer's ability to maintain its theoretical velocity.Specifically,as the Reynolds number increases,the structure of the flow field around the squirmer changes,affecting its velocity of motion.Notably,the swimming velocity of the squirmer exhibits a quadratic relationship with the type of swimming and the Reynolds number.Second,the narrow tube exerts a significant inhibitory effect on the squirmer motion.In addition,although chirality does not directly affect the swimming velocity of the squirmer,it can indirectly affect the velocity by changing its motion mode.展开更多
This paper presents an integrated study from fracture propagation modeling to gas flow modeling and a correlation analysis to explore the key controlling factors of intensive volume fracturing.The fracture propagation...This paper presents an integrated study from fracture propagation modeling to gas flow modeling and a correlation analysis to explore the key controlling factors of intensive volume fracturing.The fracture propagation model takes into account the interaction between hydraulic fracture and natural fracture by means of the displacement discontinuity method(DDM)and the Picard iterative method.The shale gas flow considers multiple transport mechanisms,and the flow in the fracture network is handled by the embedded discrete fracture model(EDFM).A series of numerical simulations are conducted to analyze the effects of the cluster number,stage spacing,stress difference coefficient,and natural fracture distribution on the stimulated fracture area,fractal dimension,and cumulative gas production,and their correlation coefficients are obtained.The results show that the most influential factors to the stimulated fracture area are the stress difference ratio,stage spacing,and natural fracture density,while those to the cumulative gas production are the stress difference ratio,natural fracture density,and cluster number.This indicates that the stress condition dominates the gas production,and employing intensive volume fracturing(by properly increasing the cluster number)is beneficial for improving the final cumulative gas production.展开更多
随着电子封装微型化、多功能化的发展,三维封装已成为封装技术的主要发展方向,叠层CSP封装具有封装密度高、互连性能好等特性,是实现三维封装的重要技术。针对超薄芯片传统叠层CSP封装过程中容易产生圆片翘曲、金线键合过程中容易出现O...随着电子封装微型化、多功能化的发展,三维封装已成为封装技术的主要发展方向,叠层CSP封装具有封装密度高、互连性能好等特性,是实现三维封装的重要技术。针对超薄芯片传统叠层CSP封装过程中容易产生圆片翘曲、金线键合过程中容易出现OBOP不良、以及线弧(wire loop)的CPK值达不到工艺要求等问题,文中简要介绍了芯片减薄方法对圆片翘曲的影响,利用有限元(FEA)的方法进行芯片减薄后对悬空功能芯片金线键合(Wirebond)的影响进行分析,Film on Wire(FOW)的贴片(Die Attach)方法在解决悬空功能芯片金线键合中的应用,以及FOW贴片方式对叠层CSP封装流程的简化。采用FOW贴片技术可以达到30%的成本节约,具有很好的经济效益。展开更多
It is widely accepted that a robust and efficient method to compute the linear spatial amplified rate ought to be developed in three-dimensional (3D) boundary layers to predict the transition with the e^N method, es...It is widely accepted that a robust and efficient method to compute the linear spatial amplified rate ought to be developed in three-dimensional (3D) boundary layers to predict the transition with the e^N method, especially when the boundary layer varies significantly in the spanwise direction. The 3D-linear parabolized stability equation (3D- LPSE) approach, a 3D extension of the two-dimensional LPSE (2D-LPSE), is developed with a plane-marching procedure for investigating the instability of a 3D boundary layer with a significant spanwise variation. The method is suitable for a full Mach number region, and is validated by computing the unstable modes in 2D and 3D boundary layers, in both global and local instability problems. The predictions are in better agreement with the ones of the direct numerical simulation (DNS) rather than a 2D-eigenvalue problem (EVP) procedure. These results suggest that the plane-marching 3D-LPSE approach is a robust, efficient, and accurate choice for the local and global instability analysis in 2D and 3D boundary layers for all free-stream Mach numbers.展开更多
The squeeze flow of a rigid-plastic medium between parallel disks is considered for small gaps with partial wall slip. The stress distribution and the squeeze force between parallel disks of a rigid-plastic medium wit...The squeeze flow of a rigid-plastic medium between parallel disks is considered for small gaps with partial wall slip. The stress distribution and the squeeze force between parallel disks of a rigid-plastic medium with the following four diferent slip boundary conditions are obtained. (1) The Coulombic friction condition is applied, and the stress distribution on the wall is derived, which is linear or exponential distribution in the no-slip area or slip area. (2) It is assumed that the slip velocity at the disks increases linearly with the radius up to the rim slip velocity, with the stress distribution and the squeeze force gained. (3) The assumption that the slip velocity at the disks is related to the shear stress component is used, with the stress distribution and the squeeze force obtained, which is equivalent to the result given in (2). (4) Rational velocity components are introduced, and the stress distribution is satisfed.展开更多
In this paper,an efcient multigrid-DEIM semi-reduced-order model is developed to accelerate the simulation of unsteady single-phase compressible fow in porous media.The cornerstone of the proposed model is that the fu...In this paper,an efcient multigrid-DEIM semi-reduced-order model is developed to accelerate the simulation of unsteady single-phase compressible fow in porous media.The cornerstone of the proposed model is that the full approximate storage multigrid method is used to accelerate the solution of fow equation in original full-order space,and the discrete empirical interpolation method(DEIM)is applied to speed up the solution of Peng-Robinson equation of state in reduced-order subspace.The multigrid-DEIM semi-reduced-order model combines the computation both in full-order space and in reducedorder subspace,which not only preserves good prediction accuracy of full-order model,but also gains dramatic computational acceleration by multigrid and DEIM.Numerical performances including accuracy and acceleration of the proposed model are carefully evaluated by comparing with that of the standard semi-implicit method.In addition,the selection of interpolation points for constructing the low-dimensional subspace for solving the Peng-Robinson equation of state is demonstrated and carried out in detail.Comparison results indicate that the multigrid-DEIM semi-reduced-order model can speed up the simulation substantially at the same time preserve good computational accuracy with negligible errors.The general acceleration is up to 50-60 times faster than that of standard semi-implicit method in two-dimensional simulations,but the average relative errors of numerical results between these two methods only have the order of magnitude 10^(−4)-10^(−6)%.展开更多
A series of experiments on a solid feed system was performed to investigate the effect of negative pressure gradient on the gas-solid flow pattern and hydrodynamic characteristics.Based on the non-fluidized gas-solid ...A series of experiments on a solid feed system was performed to investigate the effect of negative pressure gradient on the gas-solid flow pattern and hydrodynamic characteristics.Based on the non-fluidized gas-solid two phase flow and particulate mechanics in the standpipe,a method for predicting the pressure of the air passing through the recycle chamber and the pressure drop through the loop seal slit in these systems is also presented.The predicted pressure profile along the negative pressure gradient from the proposed model exhibits a good agreement with the experimental data.The experimental data show that the gas flow in the standpipe is always upward in the negative pressure gradients,while the direction ofthe superficial gas velocity through the recycle chamber of the loop seal does not affect the pressure drop in standpipe.It increases with an increasing negative pressure gradient.展开更多
Searching for the optimal cabin layout plan is an efective way to improve the efciency of the overall design and reduce a ship’s operation costs.The multitasking states of a ship involve several statuses when facing ...Searching for the optimal cabin layout plan is an efective way to improve the efciency of the overall design and reduce a ship’s operation costs.The multitasking states of a ship involve several statuses when facing diferent missions during a voyage,such as the status of the marine supply and emergency escape.The human fow and logistics between cabins will change as the state changes.An ideal cabin layout plan,which is directly impacted by the above-mentioned factors,can meet the diferent requirements of several statuses to a higher degree.Inevitable deviations exist in the quantifcation of human fow and logistics.Moreover,uncontrollability is present in the fow situation during actual operations.The coupling of these deviations and uncontrollability shows typical uncertainties,which must be considered in the design process.Thus,it is important to integrate the demands of the human fow and logistics in multiple states into an uncertainty parameter scheme.This research considers the uncertainties of adjacent and circulating strengths obtained after quantifying the human fow and logistics.Interval numbers are used to integrate them,a two-layer nested system of interval optimization is introduced,and diferent optimization algorithms are substituted for solving calculations.The comparison and analysis of the calculation results with deterministic optimization show that the conclusions obtained can provide feasible guidance for cabin layout scheme.展开更多
In biomedical research fields,the in vio Aow cytometry(IVFC)is a widely used technology which is able to monitor target cells dynamically in living animals.Although the setup of IVFC system has been well established,b...In biomedical research fields,the in vio Aow cytometry(IVFC)is a widely used technology which is able to monitor target cells dynamically in living animals.Although the setup of IVFC system has been well established,baseline drift is still a challenge in the process of quantifying circulating cells.Previous methods,i.e.,the dynamic peak picking method,counted cells by setting a static threshold without considering the baseline drift,leading to an inaccurate cell quantification.Here,we developed a method of cell counting for IVFC data with baseline drift by interpolation fitting,automatic segmentation and wavelet-based denoising.We demonstrated its performance for IVFC signals with three types of representative baseline drift.Compared with non-baseline correction methods,this method showed a higher sensitivity and specificity,as well as a better result in the Pearson's correlation coefficient and the mean-squared error(MSE).展开更多
Aming at the problem of the low accuracy of low dynamic vehicle velocity under the environment of uneven distribution of light intensity,an improved adaptive Kalman filter method for the velocity error estimate by the...Aming at the problem of the low accuracy of low dynamic vehicle velocity under the environment of uneven distribution of light intensity,an improved adaptive Kalman filter method for the velocity error estimate by the fusion of optical flow tracking and scale mvaiant feature transform(SIFT)is proposed.The algorithm introduces anonlinear fuzzy membership function and the filter residual for the noise covariance matrix in the adaptive adjustment process.In the process of calculating the velocity of the vehicle,the tracking and matching of the inter-frame displacement a d the vehicle velocity calculation a e carried out by using the optical fow tracing and the SIF'T methods,respectively.Meanwhile,the velocity difference between theoutputs of thesetwo methods is used as the observation of the improved adaptive Kalman filter.Finally,the velocity calculated by the optical fow method is corrected by using the velocity error estimate of the output of the modified adaptive Kalman filter.The results of semi-physical experiments show that the maximum velocityeror of the fusion algorithm is decreased by29%than that of the optical fow method,and the computation time is reduced by80%compared with the SIFT method.展开更多
In this paper,we introduce and analyze an augmented mixed discontinuous Galerkin(MDG)method for a class of quasi-Newtonian Stokes flows.In the mixed formulation,the unknowns are strain rate,stress and velocity,which a...In this paper,we introduce and analyze an augmented mixed discontinuous Galerkin(MDG)method for a class of quasi-Newtonian Stokes flows.In the mixed formulation,the unknowns are strain rate,stress and velocity,which are approximated by a discontinuous piecewise polynomial triplet ■for k≥0.Here,the discontinuous piecewise polynomial function spaces for the field of strain rate and the stress field are designed to be symmetric.In addition,the pressure is easily recovered through simple postprocessing.For the benefit of the analysis,we enrich the MDG scheme with the constitutive equation relating the stress and the strain rate,so that the well-posedness of the augmented formulation is obtained by a nonlinear functional analysis.For k≥0,we get the optimal convergence order for the stress in broken ■(div)-norm and velocity in L^(2)-norm.Furthermore,the error estimates of the strain rate and the stress in-norm,and the pressure in L^(2)-norm are optimal under certain conditions.Finally,several numerical examples are given to show the performance of the augmented MDG method and verify the theoretical results.Numerical evidence is provided to show that the orders of convergence are sharp.展开更多
A reliable economic risk map is critical for effective debris-flow mitigation.However,the uncertainties surrounding future scenarios in debris-flow frequency and magnitude restrict its application.To estimate the econ...A reliable economic risk map is critical for effective debris-flow mitigation.However,the uncertainties surrounding future scenarios in debris-flow frequency and magnitude restrict its application.To estimate the economic risks caused by future debris flows,a machine learning-based method was proposed to generate an economic risk map by multiplying a debris-flow hazard map and an economic vulnerability map.We selected the Gyirong Zangbo Basin as the study area because frequent severe debris flows impact the area every year.The debris-flow hazard map was developed through the multiplication of the annual probability of spatial impact,temporal probability,and annual susceptibility.We employed a hybrid machine learning model-certainty factor-genetic algorithm-support vector classification-to calculate susceptibilities.Simultaneously,a Poisson model was applied for temporal probabilities,while the determination of annual probability of spatial impact relied on statistical results.Additionally,four major elements at risk were selected for the generation of an economic loss map:roads,vegetation-covered land,residential buildings,and farmland.The economic loss of elements at risk was calculated based on physical vulnerabilities and their economic values.Therefore,we proposed a physical vulnerability matrix for residential buildings,factoring in impact pressure on buildings and their horizontal distance and vertical distance to debrisflow channels.In this context,an ensemble model(XGBoost) was used to predict debris-flow volumes to calculate impact pressures on buildings.The results show that residential buildings occupy 76.7% of the total economic risk,while roadcovered areas contribute approximately 6.85%.Vegetation-covered land and farmland collectively represent 16.45% of the entire risk.These findings can provide a scientific support for the effective mitigation of future debris flows.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.12132015 and 12372251)the Fundamental Research Funds for the Provincial Universities of Zhejiang of China(No.2023YW69)。
文摘The three-dimensional lattice Boltzmann method(LBM)is used to simulate the motion of a spherical squirmer in a square tube,and the steady motion velocity of a squirmer with different Reynolds numbers(Re,ranging from 0.1 to 2)and swimming types is investigated and analyzed to better understand the swimming characteristics of microorganisms in different environments.First,as the Reynolds number increases,the effect of the inertial forces becomes significant,disrupting the squirmer's ability to maintain its theoretical velocity.Specifically,as the Reynolds number increases,the structure of the flow field around the squirmer changes,affecting its velocity of motion.Notably,the swimming velocity of the squirmer exhibits a quadratic relationship with the type of swimming and the Reynolds number.Second,the narrow tube exerts a significant inhibitory effect on the squirmer motion.In addition,although chirality does not directly affect the swimming velocity of the squirmer,it can indirectly affect the velocity by changing its motion mode.
基金supported by the National Natural Science Foundation of China(Nos.52274038,5203401042174143)+1 种基金the Taishan Scholars Project(No.tsqnz20221140)the Open Fund of State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation(Southwest Petroleum University)of China(No.PLN2020-5)。
文摘This paper presents an integrated study from fracture propagation modeling to gas flow modeling and a correlation analysis to explore the key controlling factors of intensive volume fracturing.The fracture propagation model takes into account the interaction between hydraulic fracture and natural fracture by means of the displacement discontinuity method(DDM)and the Picard iterative method.The shale gas flow considers multiple transport mechanisms,and the flow in the fracture network is handled by the embedded discrete fracture model(EDFM).A series of numerical simulations are conducted to analyze the effects of the cluster number,stage spacing,stress difference coefficient,and natural fracture distribution on the stimulated fracture area,fractal dimension,and cumulative gas production,and their correlation coefficients are obtained.The results show that the most influential factors to the stimulated fracture area are the stress difference ratio,stage spacing,and natural fracture density,while those to the cumulative gas production are the stress difference ratio,natural fracture density,and cluster number.This indicates that the stress condition dominates the gas production,and employing intensive volume fracturing(by properly increasing the cluster number)is beneficial for improving the final cumulative gas production.
文摘随着电子封装微型化、多功能化的发展,三维封装已成为封装技术的主要发展方向,叠层CSP封装具有封装密度高、互连性能好等特性,是实现三维封装的重要技术。针对超薄芯片传统叠层CSP封装过程中容易产生圆片翘曲、金线键合过程中容易出现OBOP不良、以及线弧(wire loop)的CPK值达不到工艺要求等问题,文中简要介绍了芯片减薄方法对圆片翘曲的影响,利用有限元(FEA)的方法进行芯片减薄后对悬空功能芯片金线键合(Wirebond)的影响进行分析,Film on Wire(FOW)的贴片(Die Attach)方法在解决悬空功能芯片金线键合中的应用,以及FOW贴片方式对叠层CSP封装流程的简化。采用FOW贴片技术可以达到30%的成本节约,具有很好的经济效益。
基金Project supported by the National Natural Science Foundation of China(Nos.11272183,11572176,11402167,11202147,and 11332007)the National Program on Key Basic Research Project of China(No.2014CB744801)
文摘It is widely accepted that a robust and efficient method to compute the linear spatial amplified rate ought to be developed in three-dimensional (3D) boundary layers to predict the transition with the e^N method, especially when the boundary layer varies significantly in the spanwise direction. The 3D-linear parabolized stability equation (3D- LPSE) approach, a 3D extension of the two-dimensional LPSE (2D-LPSE), is developed with a plane-marching procedure for investigating the instability of a 3D boundary layer with a significant spanwise variation. The method is suitable for a full Mach number region, and is validated by computing the unstable modes in 2D and 3D boundary layers, in both global and local instability problems. The predictions are in better agreement with the ones of the direct numerical simulation (DNS) rather than a 2D-eigenvalue problem (EVP) procedure. These results suggest that the plane-marching 3D-LPSE approach is a robust, efficient, and accurate choice for the local and global instability analysis in 2D and 3D boundary layers for all free-stream Mach numbers.
基金Project supported by the National Natural Science Foundation of China(No.10372113).
文摘The squeeze flow of a rigid-plastic medium between parallel disks is considered for small gaps with partial wall slip. The stress distribution and the squeeze force between parallel disks of a rigid-plastic medium with the following four diferent slip boundary conditions are obtained. (1) The Coulombic friction condition is applied, and the stress distribution on the wall is derived, which is linear or exponential distribution in the no-slip area or slip area. (2) It is assumed that the slip velocity at the disks increases linearly with the radius up to the rim slip velocity, with the stress distribution and the squeeze force gained. (3) The assumption that the slip velocity at the disks is related to the shear stress component is used, with the stress distribution and the squeeze force obtained, which is equivalent to the result given in (2). (4) Rational velocity components are introduced, and the stress distribution is satisfed.
基金This study is supported by the National Natural Science Foundation of China(Nos.51904031,51936001)the Beijing Natural Science Foundation(No.3204038)the Jointly Projects of Beijing Natural Science Foundation and Beijing Municipal Education Commission(No.KZ201810017023).
文摘In this paper,an efcient multigrid-DEIM semi-reduced-order model is developed to accelerate the simulation of unsteady single-phase compressible fow in porous media.The cornerstone of the proposed model is that the full approximate storage multigrid method is used to accelerate the solution of fow equation in original full-order space,and the discrete empirical interpolation method(DEIM)is applied to speed up the solution of Peng-Robinson equation of state in reduced-order subspace.The multigrid-DEIM semi-reduced-order model combines the computation both in full-order space and in reducedorder subspace,which not only preserves good prediction accuracy of full-order model,but also gains dramatic computational acceleration by multigrid and DEIM.Numerical performances including accuracy and acceleration of the proposed model are carefully evaluated by comparing with that of the standard semi-implicit method.In addition,the selection of interpolation points for constructing the low-dimensional subspace for solving the Peng-Robinson equation of state is demonstrated and carried out in detail.Comparison results indicate that the multigrid-DEIM semi-reduced-order model can speed up the simulation substantially at the same time preserve good computational accuracy with negligible errors.The general acceleration is up to 50-60 times faster than that of standard semi-implicit method in two-dimensional simulations,but the average relative errors of numerical results between these two methods only have the order of magnitude 10^(−4)-10^(−6)%.
文摘A series of experiments on a solid feed system was performed to investigate the effect of negative pressure gradient on the gas-solid flow pattern and hydrodynamic characteristics.Based on the non-fluidized gas-solid two phase flow and particulate mechanics in the standpipe,a method for predicting the pressure of the air passing through the recycle chamber and the pressure drop through the loop seal slit in these systems is also presented.The predicted pressure profile along the negative pressure gradient from the proposed model exhibits a good agreement with the experimental data.The experimental data show that the gas flow in the standpipe is always upward in the negative pressure gradients,while the direction ofthe superficial gas velocity through the recycle chamber of the loop seal does not affect the pressure drop in standpipe.It increases with an increasing negative pressure gradient.
基金the National Natural Science Foundation of China under Grant No.51879023.
文摘Searching for the optimal cabin layout plan is an efective way to improve the efciency of the overall design and reduce a ship’s operation costs.The multitasking states of a ship involve several statuses when facing diferent missions during a voyage,such as the status of the marine supply and emergency escape.The human fow and logistics between cabins will change as the state changes.An ideal cabin layout plan,which is directly impacted by the above-mentioned factors,can meet the diferent requirements of several statuses to a higher degree.Inevitable deviations exist in the quantifcation of human fow and logistics.Moreover,uncontrollability is present in the fow situation during actual operations.The coupling of these deviations and uncontrollability shows typical uncertainties,which must be considered in the design process.Thus,it is important to integrate the demands of the human fow and logistics in multiple states into an uncertainty parameter scheme.This research considers the uncertainties of adjacent and circulating strengths obtained after quantifying the human fow and logistics.Interval numbers are used to integrate them,a two-layer nested system of interval optimization is introduced,and diferent optimization algorithms are substituted for solving calculations.The comparison and analysis of the calculation results with deterministic optimization show that the conclusions obtained can provide feasible guidance for cabin layout scheme.
基金the grants of the National Major Scientific Research Program of China(Grant Nos.2011CB910404 and 2012CB966801)the National N ature Science Foundation of China(Grant No.61227017)the National Science Fund for Distinguished Young Scholars(Grant No.61425006).
文摘In biomedical research fields,the in vio Aow cytometry(IVFC)is a widely used technology which is able to monitor target cells dynamically in living animals.Although the setup of IVFC system has been well established,baseline drift is still a challenge in the process of quantifying circulating cells.Previous methods,i.e.,the dynamic peak picking method,counted cells by setting a static threshold without considering the baseline drift,leading to an inaccurate cell quantification.Here,we developed a method of cell counting for IVFC data with baseline drift by interpolation fitting,automatic segmentation and wavelet-based denoising.We demonstrated its performance for IVFC signals with three types of representative baseline drift.Compared with non-baseline correction methods,this method showed a higher sensitivity and specificity,as well as a better result in the Pearson's correlation coefficient and the mean-squared error(MSE).
基金The National Natural Science Foundation of China(No.51375087,51405203)the Transformation Program of Science and Technology Achievements of Jiangsu Province(No.BA2016139)
文摘Aming at the problem of the low accuracy of low dynamic vehicle velocity under the environment of uneven distribution of light intensity,an improved adaptive Kalman filter method for the velocity error estimate by the fusion of optical flow tracking and scale mvaiant feature transform(SIFT)is proposed.The algorithm introduces anonlinear fuzzy membership function and the filter residual for the noise covariance matrix in the adaptive adjustment process.In the process of calculating the velocity of the vehicle,the tracking and matching of the inter-frame displacement a d the vehicle velocity calculation a e carried out by using the optical fow tracing and the SIF'T methods,respectively.Meanwhile,the velocity difference between theoutputs of thesetwo methods is used as the observation of the improved adaptive Kalman filter.Finally,the velocity calculated by the optical fow method is corrected by using the velocity error estimate of the output of the modified adaptive Kalman filter.The results of semi-physical experiments show that the maximum velocityeror of the fusion algorithm is decreased by29%than that of the optical fow method,and the computation time is reduced by80%compared with the SIFT method.
基金supported by the National Natural Science Foundation of China(Grant No.12171383)the National Natural Science Foundation of China(Grant No.11971377).
文摘In this paper,we introduce and analyze an augmented mixed discontinuous Galerkin(MDG)method for a class of quasi-Newtonian Stokes flows.In the mixed formulation,the unknowns are strain rate,stress and velocity,which are approximated by a discontinuous piecewise polynomial triplet ■for k≥0.Here,the discontinuous piecewise polynomial function spaces for the field of strain rate and the stress field are designed to be symmetric.In addition,the pressure is easily recovered through simple postprocessing.For the benefit of the analysis,we enrich the MDG scheme with the constitutive equation relating the stress and the strain rate,so that the well-posedness of the augmented formulation is obtained by a nonlinear functional analysis.For k≥0,we get the optimal convergence order for the stress in broken ■(div)-norm and velocity in L^(2)-norm.Furthermore,the error estimates of the strain rate and the stress in-norm,and the pressure in L^(2)-norm are optimal under certain conditions.Finally,several numerical examples are given to show the performance of the augmented MDG method and verify the theoretical results.Numerical evidence is provided to show that the orders of convergence are sharp.
基金supported by the Key Laboratory of Mountain Hazards and Earth Surface Processes,Chinese Academy of Sciencesthe European Union’s Horizon 2020 research and innovation program Marie Skłodowska-Curie Actions Research and Innovation Staff Exchange (RISE)under grant agreement (Grant No.778360)+1 种基金the National Natural Science Foundation of China (Grant No.51978533)the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No.XDA20030301).
文摘A reliable economic risk map is critical for effective debris-flow mitigation.However,the uncertainties surrounding future scenarios in debris-flow frequency and magnitude restrict its application.To estimate the economic risks caused by future debris flows,a machine learning-based method was proposed to generate an economic risk map by multiplying a debris-flow hazard map and an economic vulnerability map.We selected the Gyirong Zangbo Basin as the study area because frequent severe debris flows impact the area every year.The debris-flow hazard map was developed through the multiplication of the annual probability of spatial impact,temporal probability,and annual susceptibility.We employed a hybrid machine learning model-certainty factor-genetic algorithm-support vector classification-to calculate susceptibilities.Simultaneously,a Poisson model was applied for temporal probabilities,while the determination of annual probability of spatial impact relied on statistical results.Additionally,four major elements at risk were selected for the generation of an economic loss map:roads,vegetation-covered land,residential buildings,and farmland.The economic loss of elements at risk was calculated based on physical vulnerabilities and their economic values.Therefore,we proposed a physical vulnerability matrix for residential buildings,factoring in impact pressure on buildings and their horizontal distance and vertical distance to debrisflow channels.In this context,an ensemble model(XGBoost) was used to predict debris-flow volumes to calculate impact pressures on buildings.The results show that residential buildings occupy 76.7% of the total economic risk,while roadcovered areas contribute approximately 6.85%.Vegetation-covered land and farmland collectively represent 16.45% of the entire risk.These findings can provide a scientific support for the effective mitigation of future debris flows.