Earth’s internal core and crustal magnetic fields,as measured by geomagnetic satellites like MSS-1(Macao Science Satellite-1)and Swarm,are vital for understanding core dynamics and tectonic evolution.To model these i...Earth’s internal core and crustal magnetic fields,as measured by geomagnetic satellites like MSS-1(Macao Science Satellite-1)and Swarm,are vital for understanding core dynamics and tectonic evolution.To model these internal magnetic fields accurately,data selection based on specific criteria is often employed to minimize the influence of rapidly changing current systems in the ionosphere and magnetosphere.However,the quantitative impact of various data selection criteria on internal geomagnetic field modeling is not well understood.This study aims to address this issue and provide a reference for constructing and applying geomagnetic field models.First,we collect the latest MSS-1 and Swarm satellite magnetic data and summarize widely used data selection criteria in geomagnetic field modeling.Second,we briefly describe the method to co-estimate the core,crustal,and large-scale magnetospheric fields using satellite magnetic data.Finally,we conduct a series of field modeling experiments with different data selection criteria to quantitatively estimate their influence.Our numerical experiments confirm that without selecting data from dark regions and geomagnetically quiet times,the resulting internal field differences at the Earth’s surface can range from tens to hundreds of nanotesla(nT).Additionally,we find that the uncertainties introduced into field models by different data selection criteria are significantly larger than the measurement accuracy of modern geomagnetic satellites.These uncertainties should be considered when utilizing constructed magnetic field models for scientific research and applications.展开更多
The movement of global ocean circulation in the Earth’s main magnetic field generates a measurable induced magnetic field(about 2 nT at geomagnetic satellite altitudes).However,this ocean circulation-induced magnetic...The movement of global ocean circulation in the Earth’s main magnetic field generates a measurable induced magnetic field(about 2 nT at geomagnetic satellite altitudes).However,this ocean circulation-induced magnetic field has not been previously estimated or incorporated into geomagnetic field models,potentially causing leakage into the core field model.Here,we present a method to account for the circulation-induced magnetic field during geomagnetic field modeling.First,a forward model of the circulation-induced magnetic field is constructed by numerically solving electromagnetic induction equations based on a realistic ocean circulation model.Then,this forward model is subtracted from the observed data.Finally,the core and lithospheric fields,magnetospheric and Earth’s mantle-induced fields,and the ocean tide-induced magnetic field are co-estimated.Applying our method to over 20 years of MSS-1,Swarm,CryoSat-2,and CHAMP satellite magnetic data,we derive a new multisource geomagnetic field model(MGFM).We find that incorporating a forward model of the circulation-induced magnetic field marginally improves the fit to the data.Furthermore,we demonstrate that neglecting the circulation-induced magnetic field in geomagnetic field modeling results in leakage into the core field model.The highlights of the MGFM model include:(i)a good agreement with the widely used CHAOS model series;(ii)the incorporation of magnetic fields induced by both ocean tides and circulation;and(iii)the suppression of leakage of the circulation-induced magnetic field into the core field model.展开更多
It is well known that coarse-grained super-elastic NiTi shape memory alloys(SMAs)exhibit localized rather than homogeneous martensite transformation(MT),which,however,can be strongly influenced by either internal size...It is well known that coarse-grained super-elastic NiTi shape memory alloys(SMAs)exhibit localized rather than homogeneous martensite transformation(MT),which,however,can be strongly influenced by either internal size(grain size,GS)or the external size(geometric size).The coupled effect of GS and geometric size on the functional properties has not been clearly understood yet.In this work,the super-elasticity,one-way,and stress-assisted two-way shape memory effects of the polycrystalline NiTi SMAs with different aspect ratios(length/width for the gauge section)and different GSs are investigated based on the phase field method.The coupled effect of the aspect ratio and GS on the functional properties is adequately revealed.The simulated results indicate that when the aspect ratio is lower than about 4:1,the stress biaxiality and stress heterogeneity in the gauge section of the sample become more and more obvious with decreasing the aspect ratio,which can significantly influence the microstructure evolution in the process involving external stress.Therefore,the corresponding functional property is strongly dependent on the aspect ratio.With decreasing the GS and the aspect ratio(to be lower than 4:1),both the aspect ratio and GS can affect the MT or martensite reorientation in each grain and the interaction among grains.Thus,due to the strong internal constraint(i.e.,the constraint of grain boundary)and the external constraint(i.e.,the constraint of geometric boundary),the capabilities of the functional properties of NiTi SMAs are gradually weakened and highly dependent on these two factors.展开更多
By combining data from the Challenging Minisatellite Payload(CHAMP),Swarm-A,and newest Macao Science Satellite-1(MSS-1) missions,we constructed a lithospheric magnetic field model up to spherical harmonic degree N = 1...By combining data from the Challenging Minisatellite Payload(CHAMP),Swarm-A,and newest Macao Science Satellite-1(MSS-1) missions,we constructed a lithospheric magnetic field model up to spherical harmonic degree N = 100.To isolate the lithospheric magnetic field signals,we utilized the latest CHAOS-8(CHAMP,Φrsted,and SAC-C 8) model and MGFM(Multisource Geomagnetic Field Model) to remove nonlithospheric sources,including the core field,magnetospheric field,ocean tidal field,and ocean circulation field.Subsequently,orbit-by-orbit processing was applied to both scalar and vector data,such as spherical harmonic high-pass filtering,singular spectrum analysis,and line leveling,to suppress noise and residual signals along the satellite tracks.With an orbital inclination of only 41°,MSS-1 effectively captures fine-scale lithospheric magnetic field signals in mid-to low-latitude regions.Its data exhibit a root mean square error of only 0.77 nT relative to the final model,confirming the high quality and utility of lithospheric field modeling.The resulting model exhibits excellent consistency with the MF7(Magnetic Field Model 7),maintaining a high correlation up to N = 90 and still exceeding 0.65 at N = 100.These results demonstrate the reliability and value of MSS-1 data in global lithospheric magnetic field modeling.展开更多
As the demand for advanced material design and performance prediction continues to grow,traditional phase-field models are increasingly challenged by limitations in computational efficiency and predictive accuracy,par...As the demand for advanced material design and performance prediction continues to grow,traditional phase-field models are increasingly challenged by limitations in computational efficiency and predictive accuracy,particularly when addressing high-dimensional and complex data in multicomponent systems.To overcome these challenges,this study proposes an innovative model,LSGWO-BP,which integrates an improved Grey Wolf Optimizer(GWO)with a backpropagation neural network(BP)to enhance the accuracy and efficiency of quasi-phase equilibrium predictions within the KKS phase-field framework.Three mapping enhancement strategies were investigated–Circle-Root,Tent-Cosine,and Logistic-Sine mappings-with the Logistic mapping further improved via Sine perturbation to boost global search capability and convergence speed in large-scale,complex data scenarios.Evaluation results demonstrate that the LSGWO-BP model significantly outperforms conventional machine learning approaches in predicting quasi-phase equilibrium,achieving a 14%–28%reduction in mean absolute error(MAE).Substantial improvements were also observed in mean squared error,root mean squared error,and mean absolute percentage error,alongside a 7%–33%increase in the coefficient of determination(R2).Furthermore,the model exhibits strong potential for microstructural simulation applications.Overall,the study confirms the effectiveness of the LSGWO-BP model in materials science,especially in enhancing phase-field modeling efficiency and enabling accurate,intelligent prediction for multicomponent alloy systems,thereby offering robust support for microstructure prediction and control.展开更多
The China Seismo-Electromagnetic Satellite(CSES) was successfully launched in February 2018. The high precision magnetometer(HPM) on board the CSES has captured high-quality magnetic data that have been used to derive...The China Seismo-Electromagnetic Satellite(CSES) was successfully launched in February 2018. The high precision magnetometer(HPM) on board the CSES has captured high-quality magnetic data that have been used to derive a global lithospheric magnetic field model. While preparing the datasets for this lithospheric magnetic field model, researchers found that they still contained prominent residual trends within the magnetic anomaly even once signals from other sources had been eliminated. However, no processing was undertaken to deal with the residual trends during modeling to avoid subjective processing and represent the realistic nature of the data. In this work, we analyze the influence of these residual trends on the lithospheric magnetic field modeling.Polynomials of orders 0–3 were used to fit the trend of each track and remove it for detrending. We then derived four models through detrending-based processing, and compared their power spectra and grid maps with those of the CSES original model and CHAOS-7model. The misfit between the model and the dataset decreased after detrending the data, and the convergence of the inverted spherical harmonic coefficients improved. However, detrending reduced the signal strength and the power spectrum, while detrending based on high-order polynomials introduced prominent distortions in details of the magnetic anomaly. Based on this analysis, we recommend along-track detrending by using a zero-order polynomial(removing a constant value) on the CSES magnetic anomaly data to drag its mean value to zero. This would lead to only a slight reduction in the signal strength while significantly improving the stability of the inverted coefficients and details of the anomaly.展开更多
Typhoon Chaba was the most intense typhoon to strike western Guangdong since Typhoon Mujigae in 2015.According to the National Disaster Reduction Center of China,in the morning of July 7,2022,over 1.5 million people i...Typhoon Chaba was the most intense typhoon to strike western Guangdong since Typhoon Mujigae in 2015.According to the National Disaster Reduction Center of China,in the morning of July 7,2022,over 1.5 million people in Guangdong,Guangxi,and Hainan were affected by Typhoon Chaba.The typhoon also caused the“Fukui 001”ship to be in distress in the waters near Yangjiang,Guangdong,on July 2,resulting in big casualties.Studies have indicated that wind field forecast for Typhoon Chaba was not accurate.To better simulate typhoon events and assess their impacts,we proposed the use of a model wind field(Fujita-Takahashi)integrated with the Copernicus Marine and Environmental Monitoring Service(CMEMS)data to reconstruct effectively the overall wind field of Typhoon Chaba.The simulation result aligns well with the observations,particularly at the Dashu Island Station,showing consistent trends in wind speed changes.However,certain limitations were noted.The model shows that the attenuation of wind speed is slower when typhoon neared land than that observed,indicating that the model has a high simulation accuracy for the ocean wind field,but may have deviations near coastal areas.The result is accurate for open sea but deviated for near land due to the land friction effect.Therefore,we recommend to adjust the model to improve the accuracy for near coasts.展开更多
A thermodynamic consistent phase field model is developed to describe the sintering process with multiphase powders. In this model, the interface region is assumed to be a mixture of different phases with the same che...A thermodynamic consistent phase field model is developed to describe the sintering process with multiphase powders. In this model, the interface region is assumed to be a mixture of different phases with the same chemical potential, but with different compositions. The interface diffusion and boundary diffusion are also considered in the model. As an example, the model is applied to the sintering process with Fe-Cu powders. The free energy of each phase is described by the well-developed thermodynamic models, together with the published optimized parameters. The microstructure and solute distribution during the sintering process can both be obtained quantitively.展开更多
This paper focuses on estimating a new high-resolution Earth’s gravity field model named SGG-UGM-2 from satellite gravimetry,satellite altimetry,and Earth Gravitational Model 2008(EGM2008)-derived gravity data based ...This paper focuses on estimating a new high-resolution Earth’s gravity field model named SGG-UGM-2 from satellite gravimetry,satellite altimetry,and Earth Gravitational Model 2008(EGM2008)-derived gravity data based on the theory of the ellipsoidal harmonic analysis and coefficient transformation(EHA-CT).We first derive the related formulas of the EHA-CT method,which is used for computing the spherical harmonic coefficients from grid area-mean and point gravity anomalies on the ellipsoid.The derived formulas are successfully evaluated based on numerical experiments.Then,based on the derived least-squares formulas of the EHA-CT method,we develop the new model SGG-UGM-2 up to degree 2190 and order 2159 by combining the observations of the Gravity Field and Steady-State Ocean Circulation Explorer(GOCE),the normal equation of the Gravity Recovery and Climate Experiment(GRACE),marine gravity data derived from satellite altimetry data,and EGM2008-derived continental gravity data.The coefficients of degrees 251–2159 are estimated by solving the block-diagonal form normal equations of surface gravity anomalies(including the marine gravity data).The coefficients of degrees 2–250 are determined by combining the normal equations of satellite observations and surface gravity anomalies.The variance component estimation technique is used to estimate the relative weights of different observations.Finally,global positioning system(GPS)/leveling data in the mainland of China and the United States are used to validate SGG-UGM-2 together with other models,such as European improved gravity model of the earth by new techniques(EIGEN)-6C4,GECO,EGM2008,and SGG-UGM-1(the predecessor of SGG-UGM-2).Compared to other models,the model SGG-UGM-2 shows a promising performance in the GPS/leveling validation.All GOCE-related models have similar performances both in the mainland of China and the United States,and better performances than that of EGM2008 in the mainland of China.Due to the contribution of GRACE data and the new marine gravity anomalies,SGG-UGM-2 is slightly better than SGG-UGM-1 both in the mainland of China and the United States.展开更多
Tectonically, the northwestern South China Sea （SCS） is located at the junction between three micro-plates, i.e., the Indochina, South China and Zhongsha-Xisha micro-plates, and involves three basins, i.e., the Ying...Tectonically, the northwestern South China Sea （SCS） is located at the junction between three micro-plates, i.e., the Indochina, South China and Zhongsha-Xisha micro-plates, and involves three basins, i.e., the Yinggehai Basin, the Qiongdongnan Basin and Xisha Trough in the east, and the Zhongjiannan Basin in the south. Since the Pliocene （5.3 Ma）, the Yinggehai Basin has experienced repeated accelerating subsidence, high thermal fluid, and widely developing mud-rich overpressure chambers, abundant mud diapers and crust-mantle mixed CO2. While a large central canyon was developed in the Qiongdongnan Basin, new rift occurred in the Xisha ~rough. These characteristics demonstrate a single tectonic unit for the northwestern SCS, for which we have undertaken stress field modeling to understand its plate deformations and sedimen- tary responses. Our results demonstrate that an extension tectonic event occurred after 5.3 Ma in theYingge- hal-Qiongdongnan-Xisha trough area, which is characterized by thinner crust C〈16000 m）, half-graben or graben structural style and thicker sedimentary sequences （〉3 500 m）. A new rift system subsequently was developed in this area; this event was mainly driven by the combined effects of different movement veloc- ity and direction of the three micro-plates, and the far-field effect of the continental collision between the Indian Plate and the Tibetan Plateau, and subduction of the Pacific Plate underneath the Eurasian Plate.展开更多
Target detection is always an important application in hyperspectral image processing field. In this paper, a spectral-spatial target detection algorithm for hyperspectral data is proposed.The spatial feature and spec...Target detection is always an important application in hyperspectral image processing field. In this paper, a spectral-spatial target detection algorithm for hyperspectral data is proposed.The spatial feature and spectral feature were unified based on the data filed theory and extracted by weighted manifold embedding. The novelties of the proposed method lie in two aspects. One is the way in which the spatial features and spectral features were fused as a new feature based on the data field theory, and the other is that local information was introduced to describe the decision boundary and explore the discriminative features for target detection. The extracted features based on data field modeling and manifold embedding techniques were considered for a target detection task.Three standard hyperspectral datasets were considered in the analysis. The effectiveness of the proposed target detection algorithm based on data field theory was proved by the higher detection rates with lower False Alarm Rates（FARs） with respect to those achieved by conventional hyperspectral target detectors.展开更多
Single dendrite and multi-dendrite growth for Al-2 mol pct Si alloy during isothermal solidification are simulated by phase field method. In the case of single equiaxed dendrite growth, the secondary and the necking p...Single dendrite and multi-dendrite growth for Al-2 mol pct Si alloy during isothermal solidification are simulated by phase field method. In the case of single equiaxed dendrite growth, the secondary and the necking phenomenon can be observed. For multi-dendrite growth, there exists the competitive growth among the dendrites during solidification. As solidification proceeds, growing and coarsening of the primary arms occurs, together with the branching and coarsening of the secondary arms. When the diffusion fields of dendrite tips come into contact with those of the branches growing from the neighboring dendrites, the dendrites stop growing and being to ripen and thicken.展开更多
Phase field method offers the prospect of being able to perform realistic numerical experiments on dendrite growth in metallic systems. In this study, the growth process of multiple dendrites in AI-2-mole-%-Si binary ...Phase field method offers the prospect of being able to perform realistic numerical experiments on dendrite growth in metallic systems. In this study, the growth process of multiple dendrites in AI-2-mole-%-Si binary alloy under isothermal solidification was simulated using phase field model. The simulation results showed the impingement of arbitrarily oriented crystals and the competitive growth among the grains during solidification. With the increase of growing time, the grains begin to coalesce and impinge the adjacent grains. When the dendrites start to impinge, the dendrite growth is obviously inhibited.展开更多
Due to unique advantages in clearly understanding the interrelationship between city and its hinterland, as well as city and city, the study of urban spheres of influence is becoming highlight in regional research. Th...Due to unique advantages in clearly understanding the interrelationship between city and its hinterland, as well as city and city, the study of urban spheres of influence is becoming highlight in regional research. This paper improves traditional field model from two aspects： the composite indicator and regional accessibility, in order to delineate urban spheres of influence more reasonably. Taking three years of central China as a case study, this paper investigates dynamic evolution of urban spheres of influence. Focusing on the evolution of spatial pattern, we abstract five types and its corresponding three stages theoretically. Finally, recommendation of development has been made for each stage. This study undertakes certain exploration in the study of urban spheres of influence from the perspective of theory and practice, hoping to provide some references for the study in this field and other regional research.展开更多
Fracture is a very common failure mode of the composite materials,which seriously affects the reliability and service-life of composite materials.Therefore,the study of the fracture behavior of the composite materials...Fracture is a very common failure mode of the composite materials,which seriously affects the reliability and service-life of composite materials.Therefore,the study of the fracture behavior of the composite materials is of great significance and necessity,which demands an accurate and efficient numerical tool in general cases because of the complexity of the arising boundary-value or initial-boundary value problems.In this paper,a phase field model is adopted and applied for the numerical simulation of the crack nucleation and propagation in brittle linear elastic two-phase perforated/particulate composites under a quasi-static tensile loading.The phase field model can well describe the initiation,propagation and coalescence of the cracks without assuming the existence and the geometry of the initial cracks in advance.Its numerical implementation is realized within the framework of the finite element method(FEM).The accuracy and the efficiency of the present phase field model are verified by the available reference results in literature.In the numerical examples,we first study and discuss the influences of the hole/particle size on the crack propagation trajectory and the force-displacement curve.Then,the effects of the hole/particle shape on the crack initiation and propagation are investigated.Furthermore,numerical examples are presented and discussed to show the influences of the hole/particle location on the crack initiation and propagation characteristics.It will be demonstrated that the present phase field model is an efficient tool for the numerical simulation of the crack initiation and propagation problems in brittle two-phase composite materials,and the corresponding results may play an important role in predicting and preventing possible hazardous crack initiation and propagation in engineering applications.展开更多
A model has been established to simulate the realistic spatio-temporal microstructure evolution in recrystallization of a magnesium alloy using the phase field approach. A set of rules have been proposed to decide the...A model has been established to simulate the realistic spatio-temporal microstructure evolution in recrystallization of a magnesium alloy using the phase field approach. A set of rules have been proposed to decide the real physical value of all parameters in the model. The thermodynamic software THERMOCALC is applied to determine the local chemical free energy and strain energy, which is added to the free energy density of grains before recrystallization. The Arrhenius formula is used to describe boundary mobility and the activity energy is suggested with a value of zinc segregation energy at the boundary. However, the mobility constant in the formula was found out by fitting to a group of grain size measurements during recrystallization of the alloy. The boundary range is suggested to decide the gradient parameters in addition of fitting to the experimental boundary energy value. These parameter values can be regarded as a database for other similar simulations and the fitting rules can also be applied to build up databases for any other alloy systems. The simulated results show a good agreement with reported experimental measurement of the alloy at the temperatures from 300 to 400℃ for up to 100 min but not at 250℃. This implies a mechanism variation in activity energy of the boundary mobility in the alloy at low temperature.展开更多
The application of Tikhonov regularization method dealing with the ill-conditioned problems in the regional gravity field modeling by Poisson wavelets is studied. In particular, the choices of the regularization matri...The application of Tikhonov regularization method dealing with the ill-conditioned problems in the regional gravity field modeling by Poisson wavelets is studied. In particular, the choices of the regularization matrices as well as the approaches for estimating the regularization parameters are investigated in details. The numerical results show that the regularized solutions derived from the first-order regularization are better than the ones obtained from zero-order regularization. For cross validation, the optimal regularization parameters are estimated from L-curve, variance component estimation（VCE） and minimum standard deviation（MSTD） approach, respectively, and the results show that the derived regularization parameters from different methods are consistent with each other. Together with the firstorder Tikhonov regularization and VCE method, the optimal network of Poisson wavelets is derived, based on which the local gravimetric geoid is computed. The accuracy of the corresponding gravimetric geoid reaches 1.1 cm in Netherlands, which validates the reliability of using Tikhonov regularization method in tackling the ill-conditioned problem for regional gravity field modeling.展开更多
Unlike Earth,Mars lacks a global dipolar magnetic field but is dominated by patches of a remnant crustal magnetic field.In 2021,the Chinese Mars Rover will land on the surface of Mars and measure the surface magnetic ...Unlike Earth,Mars lacks a global dipolar magnetic field but is dominated by patches of a remnant crustal magnetic field.In 2021,the Chinese Mars Rover will land on the surface of Mars and measure the surface magnetic field along a moving path within the possible landing region of 20°W-50°W,20°N-30°N.One scientific target of the Rover is to monitor the variation in surface remnant magnetic fields and reveal the source of the ionospheric current.An accurate local crustal field model is thus considered necessary as a field reference.Here we establish a local crust field model for the candidate landing site based on the joint magnetic field data set from Mars Global Explorer(MGS)and Mars Atmosphere and Volatile Evolution(MAVEN)data combined.The model is composed of 1,296 dipoles,which are set on three layers but at different buried depths.The application of the dipole model to the joint data set allowed us to calculate the optimal parameters of their dipoles.The calculated results demonstrate that our model has less fitting error than two other state-of-the art global crustal field models,which would indicate a more reasonable assessment of the surface crustal field from our model.展开更多
A cellular automaton （CA）-finite element （FE） model and a phase field （PF）-FE model were used to simulate equiaxed dendritic growth during the solidification of hexagonal metals. In the CA-FE model, the conserva...A cellular automaton （CA）-finite element （FE） model and a phase field （PF）-FE model were used to simulate equiaxed dendritic growth during the solidification of hexagonal metals. In the CA-FE model, the conservation equations of mass and energy were solved in order to calculate the temperature field, solute concentration, and the dendritic growth morphology. CA-FE simulation results showed reasonable agreement with the previously reported experimental data on secondary dendrite arm spacing （SDAS） vs cooling rate. In the PF model, a PF variable was used to distinguish solid and liquid phases similar to the conventional PF models for solidification of pure materials. Another PF variable was considered to determine the evolution of solute concentration. Validation of both models was performed by comparing the simulation results with the analytical model developed by Lipton-Glicksman-Kurz （LGK）, showing quantitatively good agreement in the tip growth velocity at a given melt undercooling. Application to magnesium alloy AZ91 （approximated with the binary Mg-8.9 wt% AI） illustrates the difficulty of modeling dendrite growth in hexagonal systems using CA-FE regarding mesh-induced anisotropy and a better performance of PF-FE in modeling multiple arbitrarily-oriented dendrites growth.展开更多
Microscopic stress distribution in a metallic material which has complex microstructure is simulated using a phase field model.The fundamental equations which take into account the coupling effects among phase transfo...Microscopic stress distribution in a metallic material which has complex microstructure is simulated using a phase field model.The fundamental equations which take into account the coupling effects among phase transformation,temperature and stress/strain are used,while thermal effects are neglected to focus on the volumetric change due to phase transformation in this paper.A two-dimensional square region is considered,and the evolution of microscopic stress and the resultant residual stress distribution are calculated using the finite element method.As the phase transformation progresses and grains grow larger,stress is generated around the growing interface.When a grain collides with another one,specifically large stress is observed.Residual stress is finally distributed in the microstructure formed,and apparently large stresses are retained along the grain boundaries. Subsequently,dependency of the stress distribution on microstructure pattern is investigated.First,variously sized square grains are tested,and it reveals that the maximum stress tends to decrease as the grain size becomes smaller.Next,the shapes of the grains are varied.As a result,the stress distribution is remarkably affected,while the maximum stress value does not change so much.More complicated grain arrangement is finally tested with eight or nine grain models.Then,it is revealed as a common feature that large stress is generated along the grain boundaries and that the stress distribution is dependent on the grain arrangement.展开更多
基金supported by the National Natural Science Foundation of China(42250101)the Macao Foundation。
文摘Earth’s internal core and crustal magnetic fields,as measured by geomagnetic satellites like MSS-1(Macao Science Satellite-1)and Swarm,are vital for understanding core dynamics and tectonic evolution.To model these internal magnetic fields accurately,data selection based on specific criteria is often employed to minimize the influence of rapidly changing current systems in the ionosphere and magnetosphere.However,the quantitative impact of various data selection criteria on internal geomagnetic field modeling is not well understood.This study aims to address this issue and provide a reference for constructing and applying geomagnetic field models.First,we collect the latest MSS-1 and Swarm satellite magnetic data and summarize widely used data selection criteria in geomagnetic field modeling.Second,we briefly describe the method to co-estimate the core,crustal,and large-scale magnetospheric fields using satellite magnetic data.Finally,we conduct a series of field modeling experiments with different data selection criteria to quantitatively estimate their influence.Our numerical experiments confirm that without selecting data from dark regions and geomagnetically quiet times,the resulting internal field differences at the Earth’s surface can range from tens to hundreds of nanotesla(nT).Additionally,we find that the uncertainties introduced into field models by different data selection criteria are significantly larger than the measurement accuracy of modern geomagnetic satellites.These uncertainties should be considered when utilizing constructed magnetic field models for scientific research and applications.
基金supported by the National Natural Science Foundation of China(42250101,42250102)the Macao Foundation.
文摘The movement of global ocean circulation in the Earth’s main magnetic field generates a measurable induced magnetic field(about 2 nT at geomagnetic satellite altitudes).However,this ocean circulation-induced magnetic field has not been previously estimated or incorporated into geomagnetic field models,potentially causing leakage into the core field model.Here,we present a method to account for the circulation-induced magnetic field during geomagnetic field modeling.First,a forward model of the circulation-induced magnetic field is constructed by numerically solving electromagnetic induction equations based on a realistic ocean circulation model.Then,this forward model is subtracted from the observed data.Finally,the core and lithospheric fields,magnetospheric and Earth’s mantle-induced fields,and the ocean tide-induced magnetic field are co-estimated.Applying our method to over 20 years of MSS-1,Swarm,CryoSat-2,and CHAMP satellite magnetic data,we derive a new multisource geomagnetic field model(MGFM).We find that incorporating a forward model of the circulation-induced magnetic field marginally improves the fit to the data.Furthermore,we demonstrate that neglecting the circulation-induced magnetic field in geomagnetic field modeling results in leakage into the core field model.The highlights of the MGFM model include:(i)a good agreement with the widely used CHAOS model series;(ii)the incorporation of magnetic fields induced by both ocean tides and circulation;and(iii)the suppression of leakage of the circulation-induced magnetic field into the core field model.
基金supported by the National Natural Science Foundation of China (Grant Nos.12202294 and 12022208)the Project funded by China Postdoctoral Science Foundation (Grant No.2022M712243)the Fundamental Research Funds for the Central Universities (Grant No.2023SCU12098).
文摘It is well known that coarse-grained super-elastic NiTi shape memory alloys(SMAs)exhibit localized rather than homogeneous martensite transformation(MT),which,however,can be strongly influenced by either internal size(grain size,GS)or the external size(geometric size).The coupled effect of GS and geometric size on the functional properties has not been clearly understood yet.In this work,the super-elasticity,one-way,and stress-assisted two-way shape memory effects of the polycrystalline NiTi SMAs with different aspect ratios(length/width for the gauge section)and different GSs are investigated based on the phase field method.The coupled effect of the aspect ratio and GS on the functional properties is adequately revealed.The simulated results indicate that when the aspect ratio is lower than about 4:1,the stress biaxiality and stress heterogeneity in the gauge section of the sample become more and more obvious with decreasing the aspect ratio,which can significantly influence the microstructure evolution in the process involving external stress.Therefore,the corresponding functional property is strongly dependent on the aspect ratio.With decreasing the GS and the aspect ratio(to be lower than 4:1),both the aspect ratio and GS can affect the MT or martensite reorientation in each grain and the interaction among grains.Thus,due to the strong internal constraint(i.e.,the constraint of grain boundary)and the external constraint(i.e.,the constraint of geometric boundary),the capabilities of the functional properties of NiTi SMAs are gradually weakened and highly dependent on these two factors.
基金the support of the National Natural Science Foundation of China (Nos. 42250103, 41974073, and 41404053)the Macao Foundation and the preresearch project of Civil Aerospace Technologies (Nos. D020308 and D020303)funded by China’s National Space Administration, and the Specialized Research Fund for State Key Laboratories。
文摘By combining data from the Challenging Minisatellite Payload(CHAMP),Swarm-A,and newest Macao Science Satellite-1(MSS-1) missions,we constructed a lithospheric magnetic field model up to spherical harmonic degree N = 100.To isolate the lithospheric magnetic field signals,we utilized the latest CHAOS-8(CHAMP,Φrsted,and SAC-C 8) model and MGFM(Multisource Geomagnetic Field Model) to remove nonlithospheric sources,including the core field,magnetospheric field,ocean tidal field,and ocean circulation field.Subsequently,orbit-by-orbit processing was applied to both scalar and vector data,such as spherical harmonic high-pass filtering,singular spectrum analysis,and line leveling,to suppress noise and residual signals along the satellite tracks.With an orbital inclination of only 41°,MSS-1 effectively captures fine-scale lithospheric magnetic field signals in mid-to low-latitude regions.Its data exhibit a root mean square error of only 0.77 nT relative to the final model,confirming the high quality and utility of lithospheric field modeling.The resulting model exhibits excellent consistency with the MF7(Magnetic Field Model 7),maintaining a high correlation up to N = 90 and still exceeding 0.65 at N = 100.These results demonstrate the reliability and value of MSS-1 data in global lithospheric magnetic field modeling.
基金supported by the National Natural Science Foundation of China(Grant Nos.52161002,51661020 and 11364024)。
文摘As the demand for advanced material design and performance prediction continues to grow,traditional phase-field models are increasingly challenged by limitations in computational efficiency and predictive accuracy,particularly when addressing high-dimensional and complex data in multicomponent systems.To overcome these challenges,this study proposes an innovative model,LSGWO-BP,which integrates an improved Grey Wolf Optimizer(GWO)with a backpropagation neural network(BP)to enhance the accuracy and efficiency of quasi-phase equilibrium predictions within the KKS phase-field framework.Three mapping enhancement strategies were investigated–Circle-Root,Tent-Cosine,and Logistic-Sine mappings-with the Logistic mapping further improved via Sine perturbation to boost global search capability and convergence speed in large-scale,complex data scenarios.Evaluation results demonstrate that the LSGWO-BP model significantly outperforms conventional machine learning approaches in predicting quasi-phase equilibrium,achieving a 14%–28%reduction in mean absolute error(MAE).Substantial improvements were also observed in mean squared error,root mean squared error,and mean absolute percentage error,alongside a 7%–33%increase in the coefficient of determination(R2).Furthermore,the model exhibits strong potential for microstructural simulation applications.Overall,the study confirms the effectiveness of the LSGWO-BP model in materials science,especially in enhancing phase-field modeling efficiency and enabling accurate,intelligent prediction for multicomponent alloy systems,thereby offering robust support for microstructure prediction and control.
基金a project funded by the China National Space Administration (CNSA) and the Ministry of Emergency Management of Chinasupported by the Civil Aerospace Technology Pilot Research Project (D040203)+1 种基金the National Natural Science Foundation of China (42004051, 42274214)the APSCO Earthquake Research Project Phase Ⅱ and Dragon 6 cooperation 2025-2029 (95437)。
文摘The China Seismo-Electromagnetic Satellite(CSES) was successfully launched in February 2018. The high precision magnetometer(HPM) on board the CSES has captured high-quality magnetic data that have been used to derive a global lithospheric magnetic field model. While preparing the datasets for this lithospheric magnetic field model, researchers found that they still contained prominent residual trends within the magnetic anomaly even once signals from other sources had been eliminated. However, no processing was undertaken to deal with the residual trends during modeling to avoid subjective processing and represent the realistic nature of the data. In this work, we analyze the influence of these residual trends on the lithospheric magnetic field modeling.Polynomials of orders 0–3 were used to fit the trend of each track and remove it for detrending. We then derived four models through detrending-based processing, and compared their power spectra and grid maps with those of the CSES original model and CHAOS-7model. The misfit between the model and the dataset decreased after detrending the data, and the convergence of the inverted spherical harmonic coefficients improved. However, detrending reduced the signal strength and the power spectrum, while detrending based on high-order polynomials introduced prominent distortions in details of the magnetic anomaly. Based on this analysis, we recommend along-track detrending by using a zero-order polynomial(removing a constant value) on the CSES magnetic anomaly data to drag its mean value to zero. This would lead to only a slight reduction in the signal strength while significantly improving the stability of the inverted coefficients and details of the anomaly.
基金Supported by the National Key Research and Development Program of China(Nos.2021YFC3101801,2023YFC3008200)the National Natural Science Foundation of China(Nos.42476219,41976200)+6 种基金the National Foreign Experts Program(No.S20240134)the Innovative Team Plan of the Department of Education of Guangdong Province(No.2023KCXTD015)the Tropical Ocean Environment in Western Coastal Waters Observation and Research Station of Guangdong Province(No.2024B1212040008)the Independent Research Project of the Southern Ocean Laboratory(No.SML2022SP301)the Shandong Innovation and Development Research Institute Think Tank Projectthe Guangdong Ocean University Scientific Research Program(No.060302032106)the Start-up Fund for Ph D Researchers(No.060302032104)。
文摘Typhoon Chaba was the most intense typhoon to strike western Guangdong since Typhoon Mujigae in 2015.According to the National Disaster Reduction Center of China,in the morning of July 7,2022,over 1.5 million people in Guangdong,Guangxi,and Hainan were affected by Typhoon Chaba.The typhoon also caused the“Fukui 001”ship to be in distress in the waters near Yangjiang,Guangdong,on July 2,resulting in big casualties.Studies have indicated that wind field forecast for Typhoon Chaba was not accurate.To better simulate typhoon events and assess their impacts,we proposed the use of a model wind field(Fujita-Takahashi)integrated with the Copernicus Marine and Environmental Monitoring Service(CMEMS)data to reconstruct effectively the overall wind field of Typhoon Chaba.The simulation result aligns well with the observations,particularly at the Dashu Island Station,showing consistent trends in wind speed changes.However,certain limitations were noted.The model shows that the attenuation of wind speed is slower when typhoon neared land than that observed,indicating that the model has a high simulation accuracy for the ocean wind field,but may have deviations near coastal areas.The result is accurate for open sea but deviated for near land due to the land friction effect.Therefore,we recommend to adjust the model to improve the accuracy for near coasts.
基金Project(2011CB606306)supported by the National Basic Research Program of ChinaProject(51101014)supported by the National Natural Science Foundation of ChinaProject(SKLSP201214)supported by the State Key Laboratory of Solidification Processing in Northwestern Polytechnical University,China
文摘A thermodynamic consistent phase field model is developed to describe the sintering process with multiphase powders. In this model, the interface region is assumed to be a mixture of different phases with the same chemical potential, but with different compositions. The interface diffusion and boundary diffusion are also considered in the model. As an example, the model is applied to the sintering process with Fe-Cu powders. The free energy of each phase is described by the well-developed thermodynamic models, together with the published optimized parameters. The microstructure and solute distribution during the sintering process can both be obtained quantitively.
基金We appreciate the help from Torsten Mayer-Gürr and Andreas Kvas for providing us the NEQ system of the ITSG-Grace2018 model.This research was financially supported by the National Natural Science Foundation of China(41574019 and 41774020)the German Academic Exchange Service(DAAD)Thematic Network Project(57421148)+2 种基金the Major Project of High-Resolution Earth Observation System,and Science Fund for Creative Research Groups of the National Natural Science Foundation of China(41721003)the Fundamental Research Funds for the Central Universities(N170103009)We also thank the editor and the anonymous reviewers for their constructive remarks that helped us to improve the quality of the manuscript.
文摘This paper focuses on estimating a new high-resolution Earth’s gravity field model named SGG-UGM-2 from satellite gravimetry,satellite altimetry,and Earth Gravitational Model 2008(EGM2008)-derived gravity data based on the theory of the ellipsoidal harmonic analysis and coefficient transformation(EHA-CT).We first derive the related formulas of the EHA-CT method,which is used for computing the spherical harmonic coefficients from grid area-mean and point gravity anomalies on the ellipsoid.The derived formulas are successfully evaluated based on numerical experiments.Then,based on the derived least-squares formulas of the EHA-CT method,we develop the new model SGG-UGM-2 up to degree 2190 and order 2159 by combining the observations of the Gravity Field and Steady-State Ocean Circulation Explorer(GOCE),the normal equation of the Gravity Recovery and Climate Experiment(GRACE),marine gravity data derived from satellite altimetry data,and EGM2008-derived continental gravity data.The coefficients of degrees 251–2159 are estimated by solving the block-diagonal form normal equations of surface gravity anomalies(including the marine gravity data).The coefficients of degrees 2–250 are determined by combining the normal equations of satellite observations and surface gravity anomalies.The variance component estimation technique is used to estimate the relative weights of different observations.Finally,global positioning system(GPS)/leveling data in the mainland of China and the United States are used to validate SGG-UGM-2 together with other models,such as European improved gravity model of the earth by new techniques(EIGEN)-6C4,GECO,EGM2008,and SGG-UGM-1(the predecessor of SGG-UGM-2).Compared to other models,the model SGG-UGM-2 shows a promising performance in the GPS/leveling validation.All GOCE-related models have similar performances both in the mainland of China and the United States,and better performances than that of EGM2008 in the mainland of China.Due to the contribution of GRACE data and the new marine gravity anomalies,SGG-UGM-2 is slightly better than SGG-UGM-1 both in the mainland of China and the United States.
基金The major project of the China National Science and Technology "Large Oil and Gas Fields and Coal bed Gas Development" under contract No.2011ZX05023-003-003the Fundamental Research Funds for the Central Universities under contract No.1350219123
文摘Tectonically, the northwestern South China Sea （SCS） is located at the junction between three micro-plates, i.e., the Indochina, South China and Zhongsha-Xisha micro-plates, and involves three basins, i.e., the Yinggehai Basin, the Qiongdongnan Basin and Xisha Trough in the east, and the Zhongjiannan Basin in the south. Since the Pliocene （5.3 Ma）, the Yinggehai Basin has experienced repeated accelerating subsidence, high thermal fluid, and widely developing mud-rich overpressure chambers, abundant mud diapers and crust-mantle mixed CO2. While a large central canyon was developed in the Qiongdongnan Basin, new rift occurred in the Xisha ~rough. These characteristics demonstrate a single tectonic unit for the northwestern SCS, for which we have undertaken stress field modeling to understand its plate deformations and sedimen- tary responses. Our results demonstrate that an extension tectonic event occurred after 5.3 Ma in theYingge- hal-Qiongdongnan-Xisha trough area, which is characterized by thinner crust C〈16000 m）, half-graben or graben structural style and thicker sedimentary sequences （〉3 500 m）. A new rift system subsequently was developed in this area; this event was mainly driven by the combined effects of different movement veloc- ity and direction of the three micro-plates, and the far-field effect of the continental collision between the Indian Plate and the Tibetan Plateau, and subduction of the Pacific Plate underneath the Eurasian Plate.
文摘Target detection is always an important application in hyperspectral image processing field. In this paper, a spectral-spatial target detection algorithm for hyperspectral data is proposed.The spatial feature and spectral feature were unified based on the data filed theory and extracted by weighted manifold embedding. The novelties of the proposed method lie in two aspects. One is the way in which the spatial features and spectral features were fused as a new feature based on the data field theory, and the other is that local information was introduced to describe the decision boundary and explore the discriminative features for target detection. The extracted features based on data field modeling and manifold embedding techniques were considered for a target detection task.Three standard hyperspectral datasets were considered in the analysis. The effectiveness of the proposed target detection algorithm based on data field theory was proved by the higher detection rates with lower False Alarm Rates（FARs） with respect to those achieved by conventional hyperspectral target detectors.
基金financially supported by the Educational Department of Liaoning Province (No.20060744)the Shenyang Nurturing Young Scientific Technological Talents Items (No.1081230-1-00)
文摘Single dendrite and multi-dendrite growth for Al-2 mol pct Si alloy during isothermal solidification are simulated by phase field method. In the case of single equiaxed dendrite growth, the secondary and the necking phenomenon can be observed. For multi-dendrite growth, there exists the competitive growth among the dendrites during solidification. As solidification proceeds, growing and coarsening of the primary arms occurs, together with the branching and coarsening of the secondary arms. When the diffusion fields of dendrite tips come into contact with those of the branches growing from the neighboring dendrites, the dendrites stop growing and being to ripen and thicken.
基金supported by the Doctor Foundational Research Project in Shenyang Ligong University(Serial Number:0010).
文摘Phase field method offers the prospect of being able to perform realistic numerical experiments on dendrite growth in metallic systems. In this study, the growth process of multiple dendrites in AI-2-mole-%-Si binary alloy under isothermal solidification was simulated using phase field model. The simulation results showed the impingement of arbitrarily oriented crystals and the competitive growth among the grains during solidification. With the increase of growing time, the grains begin to coalesce and impinge the adjacent grains. When the dendrites start to impinge, the dendrite growth is obviously inhibited.
基金Key Project of National Natural Science Foundation of China, No.40830741 Key Project of the National Eleventh-Five Year Research Program of China, No.2008BAH31B01 The Main Direction Program of Knowledge Innovation of the Chinese Academy of Sciences, No.KZCX2-YW-321
文摘Due to unique advantages in clearly understanding the interrelationship between city and its hinterland, as well as city and city, the study of urban spheres of influence is becoming highlight in regional research. This paper improves traditional field model from two aspects： the composite indicator and regional accessibility, in order to delineate urban spheres of influence more reasonably. Taking three years of central China as a case study, this paper investigates dynamic evolution of urban spheres of influence. Focusing on the evolution of spatial pattern, we abstract five types and its corresponding three stages theoretically. Finally, recommendation of development has been made for each stage. This study undertakes certain exploration in the study of urban spheres of influence from the perspective of theory and practice, hoping to provide some references for the study in this field and other regional research.
基金the National Natural Science Foundation of China(Grants U1333201 and U1833116)。
文摘Fracture is a very common failure mode of the composite materials,which seriously affects the reliability and service-life of composite materials.Therefore,the study of the fracture behavior of the composite materials is of great significance and necessity,which demands an accurate and efficient numerical tool in general cases because of the complexity of the arising boundary-value or initial-boundary value problems.In this paper,a phase field model is adopted and applied for the numerical simulation of the crack nucleation and propagation in brittle linear elastic two-phase perforated/particulate composites under a quasi-static tensile loading.The phase field model can well describe the initiation,propagation and coalescence of the cracks without assuming the existence and the geometry of the initial cracks in advance.Its numerical implementation is realized within the framework of the finite element method(FEM).The accuracy and the efficiency of the present phase field model are verified by the available reference results in literature.In the numerical examples,we first study and discuss the influences of the hole/particle size on the crack propagation trajectory and the force-displacement curve.Then,the effects of the hole/particle shape on the crack initiation and propagation are investigated.Furthermore,numerical examples are presented and discussed to show the influences of the hole/particle location on the crack initiation and propagation characteristics.It will be demonstrated that the present phase field model is an efficient tool for the numerical simulation of the crack initiation and propagation problems in brittle two-phase composite materials,and the corresponding results may play an important role in predicting and preventing possible hazardous crack initiation and propagation in engineering applications.
基金the National Natural Science Foundation of China for the financial support under the grant Nos.50771028 and 50471024Education Ministry of China for an outstanding teacher research fund to this study.
文摘A model has been established to simulate the realistic spatio-temporal microstructure evolution in recrystallization of a magnesium alloy using the phase field approach. A set of rules have been proposed to decide the real physical value of all parameters in the model. The thermodynamic software THERMOCALC is applied to determine the local chemical free energy and strain energy, which is added to the free energy density of grains before recrystallization. The Arrhenius formula is used to describe boundary mobility and the activity energy is suggested with a value of zinc segregation energy at the boundary. However, the mobility constant in the formula was found out by fitting to a group of grain size measurements during recrystallization of the alloy. The boundary range is suggested to decide the gradient parameters in addition of fitting to the experimental boundary energy value. These parameter values can be regarded as a database for other similar simulations and the fitting rules can also be applied to build up databases for any other alloy systems. The simulated results show a good agreement with reported experimental measurement of the alloy at the temperatures from 300 to 400℃ for up to 100 min but not at 250℃. This implies a mechanism variation in activity energy of the boundary mobility in the alloy at low temperature.
基金supported by the National Natural Science Foundation of China (Nos.41374023,41131067,41474019)the National 973 Project of China (No.2013CB733302)+2 种基金the China Postdoctoral Science Foundation (No.2016M602301)the Key Laboratory of Geospace Envi-ronment and Geodesy,Ministry of Education,Wuhan University (No.15-02-08)the State Scholarship Fund from Chinese Scholarship Council (No.201306270014)
文摘The application of Tikhonov regularization method dealing with the ill-conditioned problems in the regional gravity field modeling by Poisson wavelets is studied. In particular, the choices of the regularization matrices as well as the approaches for estimating the regularization parameters are investigated in details. The numerical results show that the regularized solutions derived from the first-order regularization are better than the ones obtained from zero-order regularization. For cross validation, the optimal regularization parameters are estimated from L-curve, variance component estimation（VCE） and minimum standard deviation（MSTD） approach, respectively, and the results show that the derived regularization parameters from different methods are consistent with each other. Together with the firstorder Tikhonov regularization and VCE method, the optimal network of Poisson wavelets is derived, based on which the local gravimetric geoid is computed. The accuracy of the corresponding gravimetric geoid reaches 1.1 cm in Netherlands, which validates the reliability of using Tikhonov regularization method in tackling the ill-conditioned problem for regional gravity field modeling.
基金supported by the Strategic Priority Research Program of the Chinese Academy of Sciences(grant no.XDA17010201)the National Natural Science Foundation of China(grants nos.41922031,41774188,41525016,and 41621063).
文摘Unlike Earth,Mars lacks a global dipolar magnetic field but is dominated by patches of a remnant crustal magnetic field.In 2021,the Chinese Mars Rover will land on the surface of Mars and measure the surface magnetic field along a moving path within the possible landing region of 20°W-50°W,20°N-30°N.One scientific target of the Rover is to monitor the variation in surface remnant magnetic fields and reveal the source of the ionospheric current.An accurate local crustal field model is thus considered necessary as a field reference.Here we establish a local crust field model for the candidate landing site based on the joint magnetic field data set from Mars Global Explorer(MGS)and Mars Atmosphere and Volatile Evolution(MAVEN)data combined.The model is composed of 1,296 dipoles,which are set on three layers but at different buried depths.The application of the dipole model to the joint data set allowed us to calculate the optimal parameters of their dipoles.The calculated results demonstrate that our model has less fitting error than two other state-of-the art global crustal field models,which would indicate a more reasonable assessment of the surface crustal field from our model.
基金supported by the National Science Foundation(USA) through Grant No.CBET-0931801the Department of Energy(USA)through cooperative agreement No.DE-FC-26-06NT42755
文摘A cellular automaton （CA）-finite element （FE） model and a phase field （PF）-FE model were used to simulate equiaxed dendritic growth during the solidification of hexagonal metals. In the CA-FE model, the conservation equations of mass and energy were solved in order to calculate the temperature field, solute concentration, and the dendritic growth morphology. CA-FE simulation results showed reasonable agreement with the previously reported experimental data on secondary dendrite arm spacing （SDAS） vs cooling rate. In the PF model, a PF variable was used to distinguish solid and liquid phases similar to the conventional PF models for solidification of pure materials. Another PF variable was considered to determine the evolution of solute concentration. Validation of both models was performed by comparing the simulation results with the analytical model developed by Lipton-Glicksman-Kurz （LGK）, showing quantitatively good agreement in the tip growth velocity at a given melt undercooling. Application to magnesium alloy AZ91 （approximated with the binary Mg-8.9 wt% AI） illustrates the difficulty of modeling dendrite growth in hexagonal systems using CA-FE regarding mesh-induced anisotropy and a better performance of PF-FE in modeling multiple arbitrarily-oriented dendrites growth.
文摘Microscopic stress distribution in a metallic material which has complex microstructure is simulated using a phase field model.The fundamental equations which take into account the coupling effects among phase transformation,temperature and stress/strain are used,while thermal effects are neglected to focus on the volumetric change due to phase transformation in this paper.A two-dimensional square region is considered,and the evolution of microscopic stress and the resultant residual stress distribution are calculated using the finite element method.As the phase transformation progresses and grains grow larger,stress is generated around the growing interface.When a grain collides with another one,specifically large stress is observed.Residual stress is finally distributed in the microstructure formed,and apparently large stresses are retained along the grain boundaries. Subsequently,dependency of the stress distribution on microstructure pattern is investigated.First,variously sized square grains are tested,and it reveals that the maximum stress tends to decrease as the grain size becomes smaller.Next,the shapes of the grains are varied.As a result,the stress distribution is remarkably affected,while the maximum stress value does not change so much.More complicated grain arrangement is finally tested with eight or nine grain models.Then,it is revealed as a common feature that large stress is generated along the grain boundaries and that the stress distribution is dependent on the grain arrangement.
