This paper mainly deals with the point groups and single forms of octagonal quasicrystals and the description of one-dimensional quasilattice. The authors present a new sequence for describing the arrangement of quasi...This paper mainly deals with the point groups and single forms of octagonal quasicrystals and the description of one-dimensional quasilattice. The authors present a new sequence for describing the arrangement of quasiperiods in one-dimensional quasilattice. The first ten numbers of quasiperiods of this sequence are 1, 1, 2, 5, 12, 29, 70, 169, 408 and 985. The arrangement of quasiperiods in the first five steps are a, b, ab. babab and babababbabab. Seven p(?)nt groups and nine single forms for the octagonal system have been deduced, They are as follows: Point groups: 8.8m, 82, 8/m, 8/mmm, 8 and 82m; single forms: octagonal prism, dioctagonal prism. octagonal pyramid. dioctagonal pyramid. octagonal dipyramid, dioctagonal dipyramid, octagonal scalenohedron, dioctagonal scalenohedron and octagonal trapezohedron. Besides seven point groups and nine single forms for the dodecahegonal system have also been deduced.展开更多
The four different schemes of Group Explicit Method (GEM): GER, GEL, SAGE andDAGE have been claimed to be unstable when employed for electrochemical digital simulations withlarge model diffusion coefficient D_M. Howev...The four different schemes of Group Explicit Method (GEM): GER, GEL, SAGE andDAGE have been claimed to be unstable when employed for electrochemical digital simulations withlarge model diffusion coefficient D_M. However, in this investigation, in spite of the conditionalstability of GER and GEL, the SAGE scheme, which is a combination of GEL and GER, was found to beunconditionally stable when used for simulations of electrochemical reaction-diffusions and had aperformance comparable with or even better than the Fast Quasi Explicit Finite Difference Method(FQEFD) in some aspects. Corresponding differential equations of SAGE scheme for digital simulationsof various electrochemical mechanisms with both uniform and exponentially expanded space units wereestablished. The effectiveness of the SAGE method was further demonstrated by the simulations of anEC and a catalytic mechanism with very large homogeneous rate constants.展开更多
文摘This paper mainly deals with the point groups and single forms of octagonal quasicrystals and the description of one-dimensional quasilattice. The authors present a new sequence for describing the arrangement of quasiperiods in one-dimensional quasilattice. The first ten numbers of quasiperiods of this sequence are 1, 1, 2, 5, 12, 29, 70, 169, 408 and 985. The arrangement of quasiperiods in the first five steps are a, b, ab. babab and babababbabab. Seven p(?)nt groups and nine single forms for the octagonal system have been deduced, They are as follows: Point groups: 8.8m, 82, 8/m, 8/mmm, 8 and 82m; single forms: octagonal prism, dioctagonal prism. octagonal pyramid. dioctagonal pyramid. octagonal dipyramid, dioctagonal dipyramid, octagonal scalenohedron, dioctagonal scalenohedron and octagonal trapezohedron. Besides seven point groups and nine single forms for the dodecahegonal system have also been deduced.
文摘The four different schemes of Group Explicit Method (GEM): GER, GEL, SAGE andDAGE have been claimed to be unstable when employed for electrochemical digital simulations withlarge model diffusion coefficient D_M. However, in this investigation, in spite of the conditionalstability of GER and GEL, the SAGE scheme, which is a combination of GEL and GER, was found to beunconditionally stable when used for simulations of electrochemical reaction-diffusions and had aperformance comparable with or even better than the Fast Quasi Explicit Finite Difference Method(FQEFD) in some aspects. Corresponding differential equations of SAGE scheme for digital simulationsof various electrochemical mechanisms with both uniform and exponentially expanded space units wereestablished. The effectiveness of the SAGE method was further demonstrated by the simulations of anEC and a catalytic mechanism with very large homogeneous rate constants.
