In this paper, we present a theoretical analysis for linear finite element superconvergent gradient recovery on Par6 mesh, the dual of which is centroidal Voronoi tessellations with the lowest energy per unit volume a...In this paper, we present a theoretical analysis for linear finite element superconvergent gradient recovery on Par6 mesh, the dual of which is centroidal Voronoi tessellations with the lowest energy per unit volume and is the congruent cell predicted by the three-dimensional Gersho＇s conjecture. We show that the linear finite element solution uh and the linear interpolation uI have superclose gradient on Par6 meshes. Consequently, the gradient recovered from the finite element solution by using the superconvergence patch recovery method is superconvergent to Vu. A numerical example is presented to verify the theoretical result.展开更多
Four sets of ternary Ni-Nb-Ta multilayered samples with overall compositions of Ni69Nb8Ta23,Ni55Nb13Ta32,Ni42Nb16Ta42 and Ni29Nb18Ta53,respectively were prepared and subjected to 185 keV xenon ion beam mixing.The expe...Four sets of ternary Ni-Nb-Ta multilayered samples with overall compositions of Ni69Nb8Ta23,Ni55Nb13Ta32,Ni42Nb16Ta42 and Ni29Nb18Ta53,respectively were prepared and subjected to 185 keV xenon ion beam mixing.The experimental results showed that in the four Ni-Nb-Ta multilayered samples,metallic glasses could all be obtained at appropriate doses,supporting the prediction directly from a proven realistic Ni-Nb-Ta interatomic potential through molecular dynamics simulations,and that two different atomic structures were observed,as in the corresponding selected area diffraction patterns,the locations of the diffused bands reflected from the metallic glass phases were observed at different angles for the Ni69Nb8Ta23 and Ni29Nb18Ta53 metallic glasses.Interestingly,Voronoi tellessation analysis indicated that the observed difference in atomic structures could be attributed to the distinct coordinate number spectra,i.e.,the spectrum of the Ni69Nb8Ta23 metallic glass has its coordinate number(CN) equal to 13 as dominating atomic configuration(with a weight of about 27%),whereas for the Ni29Nb18Ta53 metallic glass,CN=14 is the dominating atomic configuration(also about 27%).Moreover,the distinct atomic configurations of the obtained Ni-Nb-Ta metallic glasses could be correlated to the structures of the constituent metals of the ternary Ni-Nb-Ta system,as the first neighbor of fcc is 12 and the sum of the first and second neighbors of bcc is 14,implying the structural heredity did play a role in metallic glass formation.展开更多
基金supported by Singapore AcRF RG59/08 (M52110092)Singapore NRF 2007 IDM-IDM002-010.
文摘In this paper, we present a theoretical analysis for linear finite element superconvergent gradient recovery on Par6 mesh, the dual of which is centroidal Voronoi tessellations with the lowest energy per unit volume and is the congruent cell predicted by the three-dimensional Gersho＇s conjecture. We show that the linear finite element solution uh and the linear interpolation uI have superclose gradient on Par6 meshes. Consequently, the gradient recovered from the finite element solution by using the superconvergence patch recovery method is superconvergent to Vu. A numerical example is presented to verify the theoretical result.
基金supported from the National Natural Science Foundation of China (Grant Nos. 50971072,51131003)the Ministry of Science and Technology of China (973 Program) (Grant Nos. 2011CB606301,2012CB825700)the Administration of Tsinghua University
文摘Four sets of ternary Ni-Nb-Ta multilayered samples with overall compositions of Ni69Nb8Ta23,Ni55Nb13Ta32,Ni42Nb16Ta42 and Ni29Nb18Ta53,respectively were prepared and subjected to 185 keV xenon ion beam mixing.The experimental results showed that in the four Ni-Nb-Ta multilayered samples,metallic glasses could all be obtained at appropriate doses,supporting the prediction directly from a proven realistic Ni-Nb-Ta interatomic potential through molecular dynamics simulations,and that two different atomic structures were observed,as in the corresponding selected area diffraction patterns,the locations of the diffused bands reflected from the metallic glass phases were observed at different angles for the Ni69Nb8Ta23 and Ni29Nb18Ta53 metallic glasses.Interestingly,Voronoi tellessation analysis indicated that the observed difference in atomic structures could be attributed to the distinct coordinate number spectra,i.e.,the spectrum of the Ni69Nb8Ta23 metallic glass has its coordinate number(CN) equal to 13 as dominating atomic configuration(with a weight of about 27%),whereas for the Ni29Nb18Ta53 metallic glass,CN=14 is the dominating atomic configuration(also about 27%).Moreover,the distinct atomic configurations of the obtained Ni-Nb-Ta metallic glasses could be correlated to the structures of the constituent metals of the ternary Ni-Nb-Ta system,as the first neighbor of fcc is 12 and the sum of the first and second neighbors of bcc is 14,implying the structural heredity did play a role in metallic glass formation.
