In this paper, the mathematical and physical model was developed based on thermodynamics and solidification theory before the eutectoid transformation of nodular graphite iron occurred. The Local Element Substitute an...In this paper, the mathematical and physical model was developed based on thermodynamics and solidification theory before the eutectoid transformation of nodular graphite iron occurred. The Local Element Substitute and Magnification Method was brought forward and 3-dimensional numerical simulation program based on the model and the new assistant algorithm was developed and used to calculate the samples. Results of calculation have good agreement with experimental data. To display the microstructure formation during solidification of nodular graphite iron, a 2-dimensional numerical simulation program combined with the result of the 3-dimensional numerical simulation of experimental samples was compiled.展开更多
Bimetallic alloys could form three typical structures including solid solution,heterostructure,and intermetallic compound,depending on the interactions between identical and different atoms.Although the trend can be p...Bimetallic alloys could form three typical structures including solid solution,heterostructure,and intermetallic compound,depending on the interactions between identical and different atoms.Although the trend can be predicted by the types of binary phase diagram,different synthetic protocols will trap the system in various kinetic intermediates among the three typical structures.Herein,we studied the phase evolution and elemental segregation in the alloy nanoparticles of immiscible Pd-Ru before and after thermal annealing.By developing an analysis method of local element segregation(LES)based on the energy dispersive spectroscopy(EDS)mapping signals,we were able to quantify the mixing of Pd and Ru atoms during the gradual phase transition from face-centered cubic(fcc)to hexagonal close packed(hcp).Density functional theory was also applied to calculate the energies of all possible PdRu4 structures(93 fcc models and 267 hcp models),which helps to rationalize the phase transition and element segregation.The annealing process also leads to the change of the electronic structure,which further influences the performance in the electrocatalytic hydrogen evolution reaction.The highest activity of PdRu4-400 was largely attributed to the proper interface between the Pd-rich fcc phase and Ru-rich hcp phase,as revolved by the above methods.展开更多
We examine a simple averaging formula for the gradieni of linear finite elemelitsin Rd whose interpolation order in the Lq-norm is O(h2) for d < 2q and nonuniformtriangulations. For elliptic problems in R2 we deriv...We examine a simple averaging formula for the gradieni of linear finite elemelitsin Rd whose interpolation order in the Lq-norm is O(h2) for d < 2q and nonuniformtriangulations. For elliptic problems in R2 we derive an interior superconvergencefor the averaged gradient over quasiuniform triangulations. Local error estimatesup to a regular part of the boundary and the effect of numerical integration arealso investigated.展开更多
Based on the low-order conforming finite element subspace （Vh, Mh） such as the P1-P0 triangle element or the Q1-P0 quadrilateral element, the locally stabilized finite element method for the Stokes problem with nonl...Based on the low-order conforming finite element subspace （Vh, Mh） such as the P1-P0 triangle element or the Q1-P0 quadrilateral element, the locally stabilized finite element method for the Stokes problem with nonlinear slip boundary conditions is investigated in this paper. For this class of nonlinear slip boundary conditions including the subdifferential property, the weak variational formulation associated with the Stokes problem is an variational inequality. Since （Vh, Mh） does not satisfy the discrete inf-sup conditions, a macroelement condition is introduced for constructing the locally stabilized formulation such that the stability of （Vh, Mh） is established. Under these conditions, we obtain the H1 and L2 error estimates for the numerical solutions.展开更多
The aim of this paper is to provide a local superconvergence analysis for ined finite element methods of Poission equation. We shall prove that if p is smmoth enough in a local regionΩ0Ω1Ω and rectangular mesh is ...The aim of this paper is to provide a local superconvergence analysis for ined finite element methods of Poission equation. We shall prove that if p is smmoth enough in a local regionΩ0Ω1Ω and rectangular mesh is imposed onΩ1, then local superconvergence for are expected. Thus, by post-processing operators P and we have obtained the follwing local superconvergence error estimate:展开更多
文摘In this paper, the mathematical and physical model was developed based on thermodynamics and solidification theory before the eutectoid transformation of nodular graphite iron occurred. The Local Element Substitute and Magnification Method was brought forward and 3-dimensional numerical simulation program based on the model and the new assistant algorithm was developed and used to calculate the samples. Results of calculation have good agreement with experimental data. To display the microstructure formation during solidification of nodular graphite iron, a 2-dimensional numerical simulation program combined with the result of the 3-dimensional numerical simulation of experimental samples was compiled.
基金This work was financially supported by the National Natural Science Foundation of Tianjin,China(No.22175127)Institute of Energy,Hefei Comprehensive National Science Center(No.19KZS207).
文摘Bimetallic alloys could form three typical structures including solid solution,heterostructure,and intermetallic compound,depending on the interactions between identical and different atoms.Although the trend can be predicted by the types of binary phase diagram,different synthetic protocols will trap the system in various kinetic intermediates among the three typical structures.Herein,we studied the phase evolution and elemental segregation in the alloy nanoparticles of immiscible Pd-Ru before and after thermal annealing.By developing an analysis method of local element segregation(LES)based on the energy dispersive spectroscopy(EDS)mapping signals,we were able to quantify the mixing of Pd and Ru atoms during the gradual phase transition from face-centered cubic(fcc)to hexagonal close packed(hcp).Density functional theory was also applied to calculate the energies of all possible PdRu4 structures(93 fcc models and 267 hcp models),which helps to rationalize the phase transition and element segregation.The annealing process also leads to the change of the electronic structure,which further influences the performance in the electrocatalytic hydrogen evolution reaction.The highest activity of PdRu4-400 was largely attributed to the proper interface between the Pd-rich fcc phase and Ru-rich hcp phase,as revolved by the above methods.
文摘We examine a simple averaging formula for the gradieni of linear finite elemelitsin Rd whose interpolation order in the Lq-norm is O(h2) for d < 2q and nonuniformtriangulations. For elliptic problems in R2 we derive an interior superconvergencefor the averaged gradient over quasiuniform triangulations. Local error estimatesup to a regular part of the boundary and the effect of numerical integration arealso investigated.
基金supported by the National Natural Science Foundation of China(10901122)Zhejiang Provincial Natural Science Foundation (Y6090108)supported by the National Natural Science Foundation of China(10971165)
文摘Based on the low-order conforming finite element subspace （Vh, Mh） such as the P1-P0 triangle element or the Q1-P0 quadrilateral element, the locally stabilized finite element method for the Stokes problem with nonlinear slip boundary conditions is investigated in this paper. For this class of nonlinear slip boundary conditions including the subdifferential property, the weak variational formulation associated with the Stokes problem is an variational inequality. Since （Vh, Mh） does not satisfy the discrete inf-sup conditions, a macroelement condition is introduced for constructing the locally stabilized formulation such that the stability of （Vh, Mh） is established. Under these conditions, we obtain the H1 and L2 error estimates for the numerical solutions.
文摘The aim of this paper is to provide a local superconvergence analysis for ined finite element methods of Poission equation. We shall prove that if p is smmoth enough in a local regionΩ0Ω1Ω and rectangular mesh is imposed onΩ1, then local superconvergence for are expected. Thus, by post-processing operators P and we have obtained the follwing local superconvergence error estimate:
