A semi-analytical model for determining the equilibrium configuration and the radial breathing mode (RBM) frequency of single-wall carbon nanotubes (CNTs) is presented. By taking advantage of the symmetry characterist...A semi-analytical model for determining the equilibrium configuration and the radial breathing mode (RBM) frequency of single-wall carbon nanotubes (CNTs) is presented. By taking advantage of the symmetry characteristics, a CNT structure is represented by five independent variables. A line search optimization procedure is employed to determine the equilibrium values of these variables by minimizing the potential energy. With the equilibrium configuration obtained, the semi-analytical model enables an efficient calculation of the RBM frequency of the CNTs. The radius and radial breathing mode frequency results obtained from the semi-analytical approach are compared with those from molecular dynamics (MD) and ab initio calculations. The results demonstrate that the semi-analytical approach offers an efficient and accurate way to determine the equilibrium structure and radial breathing mode frequency of CNTs.展开更多
Background:The basic exercise involved in TCC is a series of individual movements that are linked together in a continuous manner and that flow smoothly from one movement to another.Deep breathing and mental concentra...Background:The basic exercise involved in TCC is a series of individual movements that are linked together in a continuous manner and that flow smoothly from one movement to another.Deep breathing and mental concentration are also required to achieve harmony展开更多
基金supported by the National Science Foundation (Grant CBET-0955096)
文摘A semi-analytical model for determining the equilibrium configuration and the radial breathing mode (RBM) frequency of single-wall carbon nanotubes (CNTs) is presented. By taking advantage of the symmetry characteristics, a CNT structure is represented by five independent variables. A line search optimization procedure is employed to determine the equilibrium values of these variables by minimizing the potential energy. With the equilibrium configuration obtained, the semi-analytical model enables an efficient calculation of the RBM frequency of the CNTs. The radius and radial breathing mode frequency results obtained from the semi-analytical approach are compared with those from molecular dynamics (MD) and ab initio calculations. The results demonstrate that the semi-analytical approach offers an efficient and accurate way to determine the equilibrium structure and radial breathing mode frequency of CNTs.
文摘Background:The basic exercise involved in TCC is a series of individual movements that are linked together in a continuous manner and that flow smoothly from one movement to another.Deep breathing and mental concentration are also required to achieve harmony
