9-intersection model is the most popular framework used for formalizing the spatial relations between two spatial objectsA andB. It transforms the topological relationships between two simple spatial objectsA andB int...9-intersection model is the most popular framework used for formalizing the spatial relations between two spatial objectsA andB. It transforms the topological relationships between two simple spatial objectsA andB into point-set topology problem in terms of the intersections ofA’s boundary (?A), interior (A 0) and (A ?) withB’s boundary (?B), interior (B 0) and exterior (B ?). It is shown in this paper that there exist some limitations of the original 9-intersection model due to its definition of an object’s exterior as its complement, and it is difficult to distinguish different disjoint relations and relations between complex objects with holes, difficult or even impossible to compute the intersections with the two object’s complements (?A∩B ?,A 0∩?B ?,A ?∩?B,A ?∩B 0 andA ?∩B ?)since the complements are infinitive. The authors suggest to re-define the exterior of spatial object by replacing the complement with its Voronoi region. A new Voronoi-based 9-intersection (VNI) is proposed and used for formalizing topological relations between spatial bojects. By improving the 9-intersection model, it is now possible to distinguish disjoint relations and to deal with objects with holes. Also it is possible to compute the exterior-based intersections and manipulate spatial relations with the VNI.展开更多
In order to quantitatively evaluate the spurious dianeutral mixing in a global ocean model MPAS-Ocean （Model for Prediction Across Scales） using a spherical centroidal voronoi tessellations developed jointly by the ...In order to quantitatively evaluate the spurious dianeutral mixing in a global ocean model MPAS-Ocean （Model for Prediction Across Scales） using a spherical centroidal voronoi tessellations developed jointly by the National Center for Atmospheric Research and the Los Alamos National Laboratory in the United States, we choose z＊ vertical coordinate system in MPAS-Ocean, in which all physical mixing processes, such as convection adjustment and explicit diffusion parameter schemes, are omitted, using a linear equation of state. By calculating the Reference Potential Energy （RPE）, front revolution position, time rate of RPE change, probability density function distribution and dimensionless parameter 2＂, from the perspectives of resolution, viscosity, Horizontal Grid Reynolds Number （HGRN）, Rea, and momentum transmission scheme, using two ideal cases, overflow and baroclinic eddy channel, we qualitatively analyze the simulation results by comparison with the three non-isopycnal models in Ilicak et al. （2012）, i.e., MITocM, MOM, and ROMS. The results show that the spurious dianeutral mixing in the MPAS-Ocean increases over time. The spurious dianeutral transport is proportional to the HGRN directly and is reduced by increasing the lateral viscosity or using a finer resolution to control HGRN. When the HGRN is less than 10, spurious transport is reduced significantly. When using the proper viscosity closure, MPAS-Ocean performs better than MIT6c and MOM, closely to ROMS, in the 2D case without rotation, and much better than the above-mentioned three ocean models under the condition of 3D space with rotation due to the cell area difference between the hexa- gon cell and the quadrilateral cell with the same resolution. Both the Zalesak （1979） flux corrected transport scheme and Leith closure in MPAS-Ocean play an excellent role in reducing spurious dianeutral mixing. The performance of Leith scheme is preferable to the condition of three-dimensional baroclinic eddy.展开更多
From the geological structure of the columnar jointed rock mass, a visual model was established in software AUTOCAD by programming based on the algorithm of the Voronoi diagram. Furthermore, a program to convert the A...From the geological structure of the columnar jointed rock mass, a visual model was established in software AUTOCAD by programming based on the algorithm of the Voronoi diagram. Furthermore, a program to convert the AUTOCAD model into 3DEC (3-dimensional distinct element code) model was developed, and a numerical model was established in 3DEC. Moreover, the results of triaxial compression tests of columnar jointed rock masses were simulated numerically. The REV (representative element volume) scale was studied, and the result shows that the REV size is 3 m × 3 m. The proposed approach, the established model and the numerical simulation were applied to study the macro-mechanical properties and the equivalent strength parameters of the columnar jointed rock mass. The numerical simulation results are in good accordance with the in-situ test results.展开更多
Motivated by an animal territoriality model,we consider a centroidal Voronoi tessellation algorithm from a dynamical systems perspective.In doing so,we discuss the stability of an aligned equilibrium configuration for...Motivated by an animal territoriality model,we consider a centroidal Voronoi tessellation algorithm from a dynamical systems perspective.In doing so,we discuss the stability of an aligned equilibrium configuration for a rectangular domain that exhibits interesting symmetry properties.We also demonstrate the procedure for performing a center manifold reduction on the system to extract a set of coordinates which capture the long term dynamics when the system is close to a bifurcation.Bifurcations of the system restricted to the center manifold are then classified and compared to numerical results.Although we analyze a specific set-up,these methods can in principle be applied to any bifurcation point of any equilibrium for any domain.展开更多
基金Project supported by the National Natural Science Foundation of China(No.49471059)
文摘9-intersection model is the most popular framework used for formalizing the spatial relations between two spatial objectsA andB. It transforms the topological relationships between two simple spatial objectsA andB into point-set topology problem in terms of the intersections ofA’s boundary (?A), interior (A 0) and (A ?) withB’s boundary (?B), interior (B 0) and exterior (B ?). It is shown in this paper that there exist some limitations of the original 9-intersection model due to its definition of an object’s exterior as its complement, and it is difficult to distinguish different disjoint relations and relations between complex objects with holes, difficult or even impossible to compute the intersections with the two object’s complements (?A∩B ?,A 0∩?B ?,A ?∩?B,A ?∩B 0 andA ?∩B ?)since the complements are infinitive. The authors suggest to re-define the exterior of spatial object by replacing the complement with its Voronoi region. A new Voronoi-based 9-intersection (VNI) is proposed and used for formalizing topological relations between spatial bojects. By improving the 9-intersection model, it is now possible to distinguish disjoint relations and to deal with objects with holes. Also it is possible to compute the exterior-based intersections and manipulate spatial relations with the VNI.
基金supported by the National Natural Science Foundation of China (Grant No.41175089)
文摘In order to quantitatively evaluate the spurious dianeutral mixing in a global ocean model MPAS-Ocean （Model for Prediction Across Scales） using a spherical centroidal voronoi tessellations developed jointly by the National Center for Atmospheric Research and the Los Alamos National Laboratory in the United States, we choose z＊ vertical coordinate system in MPAS-Ocean, in which all physical mixing processes, such as convection adjustment and explicit diffusion parameter schemes, are omitted, using a linear equation of state. By calculating the Reference Potential Energy （RPE）, front revolution position, time rate of RPE change, probability density function distribution and dimensionless parameter 2＂, from the perspectives of resolution, viscosity, Horizontal Grid Reynolds Number （HGRN）, Rea, and momentum transmission scheme, using two ideal cases, overflow and baroclinic eddy channel, we qualitatively analyze the simulation results by comparison with the three non-isopycnal models in Ilicak et al. （2012）, i.e., MITocM, MOM, and ROMS. The results show that the spurious dianeutral mixing in the MPAS-Ocean increases over time. The spurious dianeutral transport is proportional to the HGRN directly and is reduced by increasing the lateral viscosity or using a finer resolution to control HGRN. When the HGRN is less than 10, spurious transport is reduced significantly. When using the proper viscosity closure, MPAS-Ocean performs better than MIT6c and MOM, closely to ROMS, in the 2D case without rotation, and much better than the above-mentioned three ocean models under the condition of 3D space with rotation due to the cell area difference between the hexa- gon cell and the quadrilateral cell with the same resolution. Both the Zalesak （1979） flux corrected transport scheme and Leith closure in MPAS-Ocean play an excellent role in reducing spurious dianeutral mixing. The performance of Leith scheme is preferable to the condition of three-dimensional baroclinic eddy.
基金Projects(50911130366, 50979030) supported by the National Natural Science Foundation of China
文摘From the geological structure of the columnar jointed rock mass, a visual model was established in software AUTOCAD by programming based on the algorithm of the Voronoi diagram. Furthermore, a program to convert the AUTOCAD model into 3DEC (3-dimensional distinct element code) model was developed, and a numerical model was established in 3DEC. Moreover, the results of triaxial compression tests of columnar jointed rock masses were simulated numerically. The REV (representative element volume) scale was studied, and the result shows that the REV size is 3 m × 3 m. The proposed approach, the established model and the numerical simulation were applied to study the macro-mechanical properties and the equivalent strength parameters of the columnar jointed rock mass. The numerical simulation results are in good accordance with the in-situ test results.
文摘Motivated by an animal territoriality model,we consider a centroidal Voronoi tessellation algorithm from a dynamical systems perspective.In doing so,we discuss the stability of an aligned equilibrium configuration for a rectangular domain that exhibits interesting symmetry properties.We also demonstrate the procedure for performing a center manifold reduction on the system to extract a set of coordinates which capture the long term dynamics when the system is close to a bifurcation.Bifurcations of the system restricted to the center manifold are then classified and compared to numerical results.Although we analyze a specific set-up,these methods can in principle be applied to any bifurcation point of any equilibrium for any domain.
