The question of how to choose a copula model that best fits a given dataset is a predominant limitation of the copula approach, and the present study aims to investigate the techniques of goodness-of-fit tests for mul...The question of how to choose a copula model that best fits a given dataset is a predominant limitation of the copula approach, and the present study aims to investigate the techniques of goodness-of-fit tests for multi-dimensional copulas. A goodness-of-fit test based on Rosenblatt＇s transformation was mathematically expanded from two dimensions to three dimensions and procedures of a bootstrap version of the test were provided. Through stochastic copula simulation, an empirical application of historical drought data at the Lintong Gauge Station shows that the goodness-of-fit tests perform well, revealing that both trivariate Gaussian and Student t copulas are acceptable for modeling the dependence structures of the observed drought duration, severity, and peak. The goodness-of-fit tests for multi-dimensional copulas can provide further support and help a lot in the potential applications of a wider range of copulas to describe the associations of correlated hydrological variables. However, for the application of copulas with the number of dimensions larger than three, more complicated computational efforts as well as exploration and parameterization of corresponding copulas are required.展开更多
Large eddy simulation （LES） using the Smagorinsky eddy viscosity model is added to the two-dimensional nine velocity components （D2Q9） lattice Boltzmann equation （LBE） with multi-relaxation-time （MRT） to simul...Large eddy simulation （LES） using the Smagorinsky eddy viscosity model is added to the two-dimensional nine velocity components （D2Q9） lattice Boltzmann equation （LBE） with multi-relaxation-time （MRT） to simulate incompressible turbulent cavity flows with the Reynolds numbers up to 1 × 10^7. To improve the computation efficiency of LBM on the numerical simulations of turbulent flows, the massively parallel computing power from a graphic processing unit （GPU） with a computing unified device architecture （CUDA） is introduced into the MRT-LBE-LES model. The model performs well, compared with the results from others, with an increase of 76 times in computation efficiency. It appears that the higher the Reynolds numbers is, the smaller the Smagorinsky constant should be, if the lattice number is fixed. Also, for a selected high Reynolds number and a selected proper Smagorinsky constant, there is a minimum requirement for the lattice number so that the Smagorinsky eddy viscosity will not be excessively large.展开更多
This paper analyzes the dynamic characteristics of the variations of the beach volumes for three level zonesof the Yanjing Beach in the Shuidong Bay of the western Guangdong Province by using the methods of dynamic sy...This paper analyzes the dynamic characteristics of the variations of the beach volumes for three level zonesof the Yanjing Beach in the Shuidong Bay of the western Guangdong Province by using the methods of dynamic systemanalysis and the multi-dimensional spectral estimation. The results show that the variations of the beach volume arecharaCterized by the multiband oscillations with a dominant semimonth period. Upwards the low tide level, the beachtends to be stable. The estimates of the partial coherences and the partial phases indicate that the variations of thebeach volumes are mainly the results of the direct actions of the waves which are influenced by the tidal level changesand driven by the wind stress. The simulation results of the beach volume series for different beach heart zones bythreshold mixed regressive models indicate that the influence of the tide on the variations of the beach volumes is weakened and the direct actions of the wave energy and the wind stress are apparently enhanced with the increase of thebeach height.(This project was supported by the National Natural Science Foundation of China.)展开更多
VMIB (virtual multi-dimensional internal bonds) is a multiscale mechanical model developed from the VIB (virtual internal bond) theory. In VIB theory,the solid mate-rial is considered to consist of random-distributed ...VMIB (virtual multi-dimensional internal bonds) is a multiscale mechanical model developed from the VIB (virtual internal bond) theory. In VIB theory,the solid mate-rial is considered to consist of random-distributed material particles in microscale. These particles are connected with normal bonds. The macro constitutive relation is derived from the cohesive law between particles. However,in VMIB,the micro particles are connected with both normal and shear bonds. The macro constitutive relation is derived in terms of bond stiffness coefficients. It has been theoretically certified that there exists a corresponding relationship between the two bond stiffness coefficients and the two macro material constants,i.e. the Young’s modulus and Poisson ratio. This corresponding relationship suggests that it should be necessary and sufficient to simultaneously account for the normal and shear interactions between particles. Due to the fact that the fracture criterion is directly incorporated into the constitutive relation,both VIB and VMIB present many advantages in simulating fractures of materials. In the damage model of rock mass,a damage tensor is usually defined to describe the distribution of cracks. The damage value in one direction determines the relative stiffness of rock mass in this direction. In VMIB solid,the relative distribution density of micro bonds in one direction determines the relative macro stiffness of the material in this direction. The effects of the damage value and the relative distribution density of bonds are consistent. To simulate the failure behavior of rock mass with VMIB,the presented paper sets up a quantitative relationship between the damage tensor and the rela-tive distribution density of bonds. Comparison of the theoretical and the experi-mental results shows that VMIB model can represent the effect of distributed cracks on rock mass with this relationship. The presented work provides a founda-tion for further simulating fracture behavior of rock mass with VMIB model,and an alternative approach for modeling other multi-cracked body.展开更多
基金supported by the Program of Introducing Talents of Disciplines to Universities of the Ministry of Education and State Administration of the Foreign Experts Affairs of China (the 111 Project, Grant No.B08048)the Special Basic Research Fund for Methodology in Hydrology of the Ministry of Sciences and Technology of China (Grant No. 2011IM011000)
文摘The question of how to choose a copula model that best fits a given dataset is a predominant limitation of the copula approach, and the present study aims to investigate the techniques of goodness-of-fit tests for multi-dimensional copulas. A goodness-of-fit test based on Rosenblatt＇s transformation was mathematically expanded from two dimensions to three dimensions and procedures of a bootstrap version of the test were provided. Through stochastic copula simulation, an empirical application of historical drought data at the Lintong Gauge Station shows that the goodness-of-fit tests perform well, revealing that both trivariate Gaussian and Student t copulas are acceptable for modeling the dependence structures of the observed drought duration, severity, and peak. The goodness-of-fit tests for multi-dimensional copulas can provide further support and help a lot in the potential applications of a wider range of copulas to describe the associations of correlated hydrological variables. However, for the application of copulas with the number of dimensions larger than three, more complicated computational efforts as well as exploration and parameterization of corresponding copulas are required.
基金supported by College of William and Mary,Virginia Institute of Marine Science for the study environment
文摘Large eddy simulation （LES） using the Smagorinsky eddy viscosity model is added to the two-dimensional nine velocity components （D2Q9） lattice Boltzmann equation （LBE） with multi-relaxation-time （MRT） to simulate incompressible turbulent cavity flows with the Reynolds numbers up to 1 × 10^7. To improve the computation efficiency of LBM on the numerical simulations of turbulent flows, the massively parallel computing power from a graphic processing unit （GPU） with a computing unified device architecture （CUDA） is introduced into the MRT-LBE-LES model. The model performs well, compared with the results from others, with an increase of 76 times in computation efficiency. It appears that the higher the Reynolds numbers is, the smaller the Smagorinsky constant should be, if the lattice number is fixed. Also, for a selected high Reynolds number and a selected proper Smagorinsky constant, there is a minimum requirement for the lattice number so that the Smagorinsky eddy viscosity will not be excessively large.
文摘This paper analyzes the dynamic characteristics of the variations of the beach volumes for three level zonesof the Yanjing Beach in the Shuidong Bay of the western Guangdong Province by using the methods of dynamic systemanalysis and the multi-dimensional spectral estimation. The results show that the variations of the beach volume arecharaCterized by the multiband oscillations with a dominant semimonth period. Upwards the low tide level, the beachtends to be stable. The estimates of the partial coherences and the partial phases indicate that the variations of thebeach volumes are mainly the results of the direct actions of the waves which are influenced by the tidal level changesand driven by the wind stress. The simulation results of the beach volume series for different beach heart zones bythreshold mixed regressive models indicate that the influence of the tide on the variations of the beach volumes is weakened and the direct actions of the wave energy and the wind stress are apparently enhanced with the increase of thebeach height.(This project was supported by the National Natural Science Foundation of China.)
基金the National Natural Science Foundation of China (Grant No. 50609013)
文摘VMIB (virtual multi-dimensional internal bonds) is a multiscale mechanical model developed from the VIB (virtual internal bond) theory. In VIB theory,the solid mate-rial is considered to consist of random-distributed material particles in microscale. These particles are connected with normal bonds. The macro constitutive relation is derived from the cohesive law between particles. However,in VMIB,the micro particles are connected with both normal and shear bonds. The macro constitutive relation is derived in terms of bond stiffness coefficients. It has been theoretically certified that there exists a corresponding relationship between the two bond stiffness coefficients and the two macro material constants,i.e. the Young’s modulus and Poisson ratio. This corresponding relationship suggests that it should be necessary and sufficient to simultaneously account for the normal and shear interactions between particles. Due to the fact that the fracture criterion is directly incorporated into the constitutive relation,both VIB and VMIB present many advantages in simulating fractures of materials. In the damage model of rock mass,a damage tensor is usually defined to describe the distribution of cracks. The damage value in one direction determines the relative stiffness of rock mass in this direction. In VMIB solid,the relative distribution density of micro bonds in one direction determines the relative macro stiffness of the material in this direction. The effects of the damage value and the relative distribution density of bonds are consistent. To simulate the failure behavior of rock mass with VMIB,the presented paper sets up a quantitative relationship between the damage tensor and the rela-tive distribution density of bonds. Comparison of the theoretical and the experi-mental results shows that VMIB model can represent the effect of distributed cracks on rock mass with this relationship. The presented work provides a founda-tion for further simulating fracture behavior of rock mass with VMIB model,and an alternative approach for modeling other multi-cracked body.
