The phase transition of tungsten(W)under high pressures was investigated with molecular dynamics simulation.The structure was characterized in terms of the pair distribution function and the largest standard cluster a...The phase transition of tungsten(W)under high pressures was investigated with molecular dynamics simulation.The structure was characterized in terms of the pair distribution function and the largest standard cluster analysis(LSCA).It is found that under 40−100 GPa at a cooling rate of 0.1 K/ps a pure W melt first crystallizes into the body-centred cubic(BCC)crystal,and then transfers into the hexagonal close-packed(HCP)crystal through a series of BCC−HCP coexisting states.The dynamic factors may induce intermediate stages during the liquid−solid transition and the criss-cross grain boundaries cause lots of indistinguishable intermediate states,making the first-order BCC−HCP transition appear to be continuous.Furthermore,LSCA is shown to be a parameter-free method that can effectively analyze both ordered and disordered structures.Therefore,LSCA can detect more details about the evolution of the structure in such structure transition processes with rich intermediate structures.展开更多
Let ω1 and ω 2 be two homogeneous words and suppose that they respectively define the varieties Vω 1 and Vω2 of groups. Denote by θωi the standard exponent of ωi for i =1, 2, which was introduced in Ref. [1]. W...Let ω1 and ω 2 be two homogeneous words and suppose that they respectively define the varieties Vω 1 and Vω2 of groups. Denote by θωi the standard exponent of ωi for i =1, 2, which was introduced in Ref. [1]. We obtain that if Vω1 lohtian Vω2, then ω1θ｜θ ω2.展开更多
This paper investigates the relative 1-canonical images of non-hyperelliptic fibrations of genus 4. It is proved that if a fibre of the relative 1-canonical image ∑ is not a complete intersection in 3 , then the var...This paper investigates the relative 1-canonical images of non-hyperelliptic fibrations of genus 4. It is proved that if a fibre of the relative 1-canonical image ∑ is not a complete intersection in 3 , then the variety ∑ cannot be smooth on this fibre. Moreover, two examples are given to show the occurrence of such cases.展开更多
基金Projects(51661005,U1612442)supported by the National Natural Science Foundation of ChinaProject(QKHJC[2017]1025)supported by the Natural Science Foundation of Guizhou Province,ChinaProject(2018JJ3560)supported by the Natural Science Foundation of Hunan Province,China。
文摘The phase transition of tungsten(W)under high pressures was investigated with molecular dynamics simulation.The structure was characterized in terms of the pair distribution function and the largest standard cluster analysis(LSCA).It is found that under 40−100 GPa at a cooling rate of 0.1 K/ps a pure W melt first crystallizes into the body-centred cubic(BCC)crystal,and then transfers into the hexagonal close-packed(HCP)crystal through a series of BCC−HCP coexisting states.The dynamic factors may induce intermediate stages during the liquid−solid transition and the criss-cross grain boundaries cause lots of indistinguishable intermediate states,making the first-order BCC−HCP transition appear to be continuous.Furthermore,LSCA is shown to be a parameter-free method that can effectively analyze both ordered and disordered structures.Therefore,LSCA can detect more details about the evolution of the structure in such structure transition processes with rich intermediate structures.
基金the Scientific Research Foundation for the Returned Oversears Chinese Scholars,Shanxi Province
文摘Let ω1 and ω 2 be two homogeneous words and suppose that they respectively define the varieties Vω 1 and Vω2 of groups. Denote by θωi the standard exponent of ωi for i =1, 2, which was introduced in Ref. [1]. We obtain that if Vω1 lohtian Vω2, then ω1θ｜θ ω2.
文摘This paper investigates the relative 1-canonical images of non-hyperelliptic fibrations of genus 4. It is proved that if a fibre of the relative 1-canonical image ∑ is not a complete intersection in 3 , then the variety ∑ cannot be smooth on this fibre. Moreover, two examples are given to show the occurrence of such cases.
