A new case configuration in R^3, the conjugate-nest consisted of one regular tetrahedron and one regular octahedron is discussed. If the configuration is a central configuration, then all masses of outside layer are e...A new case configuration in R^3, the conjugate-nest consisted of one regular tetrahedron and one regular octahedron is discussed. If the configuration is a central configuration, then all masses of outside layer are equivalent, the masses of inside layer are also equivalent. At the same time the following relation between ρ(r =√3/3ρ is the radius ratio of the sizes) and mass ratio τ=~↑m/m must be satisfied τ=~↑m/m=ρ(ρ+3)(3+2ρ+ρ^2)^-3/2+ρ(-ρ+3)(3-2ρ+ρ^2)^-3/2-4.2^-3/2ρ^-2-^-1ρ^-2/2(1+ρ)(3+2ρ+ρ^2)^-3/2+2(ρ-1)(3-2ρ+ρ^2)^-3/2-4(2√2)^-3ρ, and for any mass ratio τ, when mass ratio r is in the open interval (0, 0.03871633950 ... ), there exist three central configuration solutions(the initial configuration conditions who imply hamagraphic solutions) corresponding radius ratios are r1, r2, and r3, two of them in the interval (2.639300779… , +∞) and one is in the interval (0.7379549890…, 1.490942703… ). when mass ratio τ is in the open interval (130.8164950… , +∞), in the same way there have three corresponding radius ratios, two of them in the interval (0, 0.4211584789... ) and one is in the interval (0.7379549890…, 1.490942703…). When mass ratio τ is in the open interval (0.03871633950…, 130.8164950…), there has only one solution r in the interval (0.7379549890…, 1.490942703… ).展开更多
He defect properties in Sc, Y, Gd, Tb, Dy, Ho, Er and Lu were studied using first-principles calculations based on density functional theory. The results indicate that the formation energy of an interstitial He atom i...He defect properties in Sc, Y, Gd, Tb, Dy, Ho, Er and Lu were studied using first-principles calculations based on density functional theory. The results indicate that the formation energy of an interstitial He atom is smaller than that of a substitutional He atom in all hcp rare-earth metals considered. Furthermore, the tetrahedral interstitial position is more favorable than an octahedral position for He defects. The results are compared with those from bcc and fcc metals.展开更多
基金NSF of China(10231010)NSF of Chongqing EducationCommittee(071105)NSF of SXXYYB(070X)
文摘A new case configuration in R^3, the conjugate-nest consisted of one regular tetrahedron and one regular octahedron is discussed. If the configuration is a central configuration, then all masses of outside layer are equivalent, the masses of inside layer are also equivalent. At the same time the following relation between ρ(r =√3/3ρ is the radius ratio of the sizes) and mass ratio τ=~↑m/m must be satisfied τ=~↑m/m=ρ(ρ+3)(3+2ρ+ρ^2)^-3/2+ρ(-ρ+3)(3-2ρ+ρ^2)^-3/2-4.2^-3/2ρ^-2-^-1ρ^-2/2(1+ρ)(3+2ρ+ρ^2)^-3/2+2(ρ-1)(3-2ρ+ρ^2)^-3/2-4(2√2)^-3ρ, and for any mass ratio τ, when mass ratio r is in the open interval (0, 0.03871633950 ... ), there exist three central configuration solutions(the initial configuration conditions who imply hamagraphic solutions) corresponding radius ratios are r1, r2, and r3, two of them in the interval (2.639300779… , +∞) and one is in the interval (0.7379549890…, 1.490942703… ). when mass ratio τ is in the open interval (130.8164950… , +∞), in the same way there have three corresponding radius ratios, two of them in the interval (0, 0.4211584789... ) and one is in the interval (0.7379549890…, 1.490942703…). When mass ratio τ is in the open interval (0.03871633950…, 130.8164950…), there has only one solution r in the interval (0.7379549890…, 1.490942703… ).
基金supported by the National Natural Science Foundation of China (Grant No. 10976007)the Fundamental Research Funds for the Central Universities (Grant No. ZYGX2009J040)+1 种基金the Science and Tech-nology Foundation of China Academy of Engineering Physics (Grant No. 2009A0301015)the US Department of Energy, Office of Fusion En-ergy Science (Grant No. DE-AC06-76RLO 1830)
文摘He defect properties in Sc, Y, Gd, Tb, Dy, Ho, Er and Lu were studied using first-principles calculations based on density functional theory. The results indicate that the formation energy of an interstitial He atom is smaller than that of a substitutional He atom in all hcp rare-earth metals considered. Furthermore, the tetrahedral interstitial position is more favorable than an octahedral position for He defects. The results are compared with those from bcc and fcc metals.