In general, triangular and quadrilateral elements are commonly applied in two-dimensional finite element methods. If they are used to compute polycrystalline materials, the cost of computation can be quite significant...In general, triangular and quadrilateral elements are commonly applied in two-dimensional finite element methods. If they are used to compute polycrystalline materials, the cost of computation can be quite significant. Polygonal elements can do well in simulation of the materials behavior and provide greater flexibility for the meshing of complex geometries. Hence, the study on the polygonal element is a very useful and necessary part in the finite element method. In this paper, an n-sided polygonal element based on quadratic spline interpolant, denoted by PS2 element, is presented using the triangular area coordinates and the B-net method. The PS2 element is conforming and can exactly model the quadratic field. It is valid for both convex and non-convex polygonal element, and insensitive to mesh distortions. In addition, no mapping or coordinate transformation is required and thus no Jacobian matrix and its inverse are evaluated. Some appropriate examples are employed to evaluate the performance of the proposed element.展开更多
A stabilized and convergent finite element formulation for the generalized Stokes problem is proposed and a posteriori analysis is performed to produce an error indicator. On this basis adaptive numerical method for s...A stabilized and convergent finite element formulation for the generalized Stokes problem is proposed and a posteriori analysis is performed to produce an error indicator. On this basis adaptive numerical method for solying the problem is developed . Numerical calculations are performed to confirm the reliability and effectiveness of the method.展开更多
We used density functional theory(DFT)calculations to study the influence of alkali earth metal element(AE)doping on the crystal structure and electronic band structure ofα-Si3N4.The diversity of atomic radii of alka...We used density functional theory(DFT)calculations to study the influence of alkali earth metal element(AE)doping on the crystal structure and electronic band structure ofα-Si3N4.The diversity of atomic radii of alkaline earth metal elements results in structural expansion when they were doped into theα-Si3N4 lattice.Formation energies of the doped structures indicate that dopants prefer to occupy the interstitial site under the nitrogen-deficient environment,while substitute Si under the nitrogen-rich environment,which provides a guide to synthesizingα-Si3N4 with different doping types by controlling nitrogen conditions.For electronic structures,energy levels of the dopants appear in the bottom of the conduction band or the top of the valence band or the forbidden band,which reduces the bandgap ofα-Si3N4.展开更多
Our previous research has indicated that granular elemental S (ES) fertilizers are not effective in the year of application and also are not consistently as effective as sulphate-S in increasing seed yield of canola i...Our previous research has indicated that granular elemental S (ES) fertilizers are not effective in the year of application and also are not consistently as effective as sulphate-S in increasing seed yield of canola in subsequent years, especially when applied at seeding in spring, because of slow dispersion of elemental S particles from granules for subsequent oxidation of ES to sulphate-S. A field experiment was established in autumn 2010 to determine the relative effectiveness of a new rapid release elemental S (RRES, now called Vitasul) fertilizer, in comparison to sulphate-S fertilizer, with various combinations of application times and placement methods (applied at 20 kg·S·ha-1) on seed yield, straw yield, oil and protein concentration in seed, N and S uptake, partial factor productivity (PFP—kg·seed·kg-1 applied N·ha-1—blanket application of 120 kg·N·ha-1), S use efficiency (SUE—increase in kg·seed·kg-1 applied S·ha-1) and percent recovery of applied S in seed + straw (%) of canola in 2011, 2012 and 2013 growing seasons on a S-deficient Gray Luvisol loam soil at Star City, Saskatchewan. The 11 treatments included two granular S sources (RRES and potassium sulphate) and five application time/placement method combinations (broadcast in autumn and incorporated in spring, broadcast in spring pre-tillage [broadcast and incorporated], broadcast in spring pre-emergence, sideband in spring and seedrow-placed in spring), plus a zero-S control. There was a significant response of seed yield of canola to applied S in all 3 years, but the responses varied with S source and with application time-placement combinations in different years. Seed yield increased considerably with all sulphate-S treatments compared to the zero-S control, although seed yield tended to be slightly lower in some spring and/or autumn broadcast treatments than the other sulphate-S treatments. Compared to the zero-S control, seed yield also increased significantly with all RRES treatments, but the increase was greater with autumn applied RRES than the spring applied RRES in many cases. Autumn applied RRES produced only slightly lower seed yield but spring applied RRES produced much lower seed yield than the highest yielding spring applied sulphate-S treatments. In 2011, straw yields increased significantly with applied S in some S treatments, but there was no significant effect of S fertilization on straw yield in 2012 and 2013. Oil concentration in canola seed increased only with sulphate-S fertilizer treatments in 2011, and it increased with both sulphate-S and ES sources in 2012 and 2013. There was no effect of any S treatment on the protein concentration in canola seed. The response trends of total N uptake and PFP were usually similar to seed yield for both S sources, but total S uptake, SUE and % recovery of applied S were lower with RRES than sulphate-S in many/most cases. In conclusion, the findings suggested the potential of spring broadcast pre-emergence RRES or autumn broadcast RRES in preventing S deficiency in hybrid canola, although seed yields were still slightly lower than the ideal highest yielding spring broadcast/incorporated sulphate-S treatment.展开更多
In this paper, the general calculation formulas of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0 are obtained, and the recurrence relation of different power order radial matrix eleme...In this paper, the general calculation formulas of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0 are obtained, and the recurrence relation of different power order radial matrix elements are also derived.展开更多
基金supported by the National Natural Science Foundation of China (60533060, 10672032, 10726067)Science Foundation of Dalian University of Technology (SFDUT07001)
文摘In general, triangular and quadrilateral elements are commonly applied in two-dimensional finite element methods. If they are used to compute polycrystalline materials, the cost of computation can be quite significant. Polygonal elements can do well in simulation of the materials behavior and provide greater flexibility for the meshing of complex geometries. Hence, the study on the polygonal element is a very useful and necessary part in the finite element method. In this paper, an n-sided polygonal element based on quadratic spline interpolant, denoted by PS2 element, is presented using the triangular area coordinates and the B-net method. The PS2 element is conforming and can exactly model the quadratic field. It is valid for both convex and non-convex polygonal element, and insensitive to mesh distortions. In addition, no mapping or coordinate transformation is required and thus no Jacobian matrix and its inverse are evaluated. Some appropriate examples are employed to evaluate the performance of the proposed element.
文摘A stabilized and convergent finite element formulation for the generalized Stokes problem is proposed and a posteriori analysis is performed to produce an error indicator. On this basis adaptive numerical method for solying the problem is developed . Numerical calculations are performed to confirm the reliability and effectiveness of the method.
基金Funded by National Key Research and Development Program of China(No.2017YFB0310400)the National Natural Science Foundation of China(Nos.51872217,51932006,51972246 and 51521001)+3 种基金Fundamental Research Funds for the Central Universities in ChinaState Key Laboratory of Advanced Electromagnetic Engineering and Technology(Huazhong University of Science and Technology),the Joint Fund(No.6141A02022255)the Major Program of the Specialized Technological Innovation of HuBei Province,China(No.2019AFA176)the“111”Project(No.B13035)。
文摘We used density functional theory(DFT)calculations to study the influence of alkali earth metal element(AE)doping on the crystal structure and electronic band structure ofα-Si3N4.The diversity of atomic radii of alkaline earth metal elements results in structural expansion when they were doped into theα-Si3N4 lattice.Formation energies of the doped structures indicate that dopants prefer to occupy the interstitial site under the nitrogen-deficient environment,while substitute Si under the nitrogen-rich environment,which provides a guide to synthesizingα-Si3N4 with different doping types by controlling nitrogen conditions.For electronic structures,energy levels of the dopants appear in the bottom of the conduction band or the top of the valence band or the forbidden band,which reduces the bandgap ofα-Si3N4.
文摘Our previous research has indicated that granular elemental S (ES) fertilizers are not effective in the year of application and also are not consistently as effective as sulphate-S in increasing seed yield of canola in subsequent years, especially when applied at seeding in spring, because of slow dispersion of elemental S particles from granules for subsequent oxidation of ES to sulphate-S. A field experiment was established in autumn 2010 to determine the relative effectiveness of a new rapid release elemental S (RRES, now called Vitasul) fertilizer, in comparison to sulphate-S fertilizer, with various combinations of application times and placement methods (applied at 20 kg·S·ha-1) on seed yield, straw yield, oil and protein concentration in seed, N and S uptake, partial factor productivity (PFP—kg·seed·kg-1 applied N·ha-1—blanket application of 120 kg·N·ha-1), S use efficiency (SUE—increase in kg·seed·kg-1 applied S·ha-1) and percent recovery of applied S in seed + straw (%) of canola in 2011, 2012 and 2013 growing seasons on a S-deficient Gray Luvisol loam soil at Star City, Saskatchewan. The 11 treatments included two granular S sources (RRES and potassium sulphate) and five application time/placement method combinations (broadcast in autumn and incorporated in spring, broadcast in spring pre-tillage [broadcast and incorporated], broadcast in spring pre-emergence, sideband in spring and seedrow-placed in spring), plus a zero-S control. There was a significant response of seed yield of canola to applied S in all 3 years, but the responses varied with S source and with application time-placement combinations in different years. Seed yield increased considerably with all sulphate-S treatments compared to the zero-S control, although seed yield tended to be slightly lower in some spring and/or autumn broadcast treatments than the other sulphate-S treatments. Compared to the zero-S control, seed yield also increased significantly with all RRES treatments, but the increase was greater with autumn applied RRES than the spring applied RRES in many cases. Autumn applied RRES produced only slightly lower seed yield but spring applied RRES produced much lower seed yield than the highest yielding spring applied sulphate-S treatments. In 2011, straw yields increased significantly with applied S in some S treatments, but there was no significant effect of S fertilization on straw yield in 2012 and 2013. Oil concentration in canola seed increased only with sulphate-S fertilizer treatments in 2011, and it increased with both sulphate-S and ES sources in 2012 and 2013. There was no effect of any S treatment on the protein concentration in canola seed. The response trends of total N uptake and PFP were usually similar to seed yield for both S sources, but total S uptake, SUE and % recovery of applied S were lower with RRES than sulphate-S in many/most cases. In conclusion, the findings suggested the potential of spring broadcast pre-emergence RRES or autumn broadcast RRES in preventing S deficiency in hybrid canola, although seed yields were still slightly lower than the ideal highest yielding spring broadcast/incorporated sulphate-S treatment.
文摘In this paper, the general calculation formulas of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0 are obtained, and the recurrence relation of different power order radial matrix elements are also derived.
