Following Jacobi＇s geometrization of Lagrange＇s least action principle, trajectories of classical mechanics can be characterized as geodesics on the configuration space M with respect to a suitable metric which is t...Following Jacobi＇s geometrization of Lagrange＇s least action principle, trajectories of classical mechanics can be characterized as geodesics on the configuration space M with respect to a suitable metric which is the conformal modification of the kinematic metric by the factor （U ＋ h）, where U and h are the potential function and the total energy, respectively. In the special case of 3-body motions with zero angular momentum, the global geometry of such trajectories can be reduced to that of their moduli curves, which record the change of size and shape, in the moduli space of oriented m-triangles, whose kinematic metric is, in fact, a Riemannian cone over the shape space M^＊≌S^2 （1/2）. In this paper, it is shown that the moduli curve of such a motion is uniquely determined by its shape curve （which only records the change of shape） in the case of h≠0, while in the special case of h = 0 it is uniquely determined up to scaling. Thus, the study of the global geometry of such motions can be further reduced to that of the shape curves, which are time-parametrized curves on the 2-sphere characterized by a third order ODE. Moreover, these curves have two remarkable properties, namely the uniqueness of parametrization and the monotonieity, that constitute a solid foundation for a systematic study of their global geometry and naturally lead to the formulation of some pertinent problems.展开更多
In this study, the electrochemical behavior of monocrystalline bare Si and Ag-coated Si in hydrofluoric acid （HF） solutions with and without hydrogen peroxide （H202） was systematically tested with an electrochemic...In this study, the electrochemical behavior of monocrystalline bare Si and Ag-coated Si in hydrofluoric acid （HF） solutions with and without hydrogen peroxide （H202） was systematically tested with an electrochemical technique. By analyzing the po- larization curves, the corrosion processes were quantified and the etchants which govern the formation of silicon nanowires （SiNWs） were determined. It was discovered that both H202 and Ag enhanced the reduction reactions, irrespective of the con- ductivity type and doping concentration of Si. It is believed that the formation of SiNWs via Metal-Catalyzed Electroless Etching is a process controlled by cathodic reduction reactions.展开更多
文摘Following Jacobi＇s geometrization of Lagrange＇s least action principle, trajectories of classical mechanics can be characterized as geodesics on the configuration space M with respect to a suitable metric which is the conformal modification of the kinematic metric by the factor （U ＋ h）, where U and h are the potential function and the total energy, respectively. In the special case of 3-body motions with zero angular momentum, the global geometry of such trajectories can be reduced to that of their moduli curves, which record the change of size and shape, in the moduli space of oriented m-triangles, whose kinematic metric is, in fact, a Riemannian cone over the shape space M^＊≌S^2 （1/2）. In this paper, it is shown that the moduli curve of such a motion is uniquely determined by its shape curve （which only records the change of shape） in the case of h≠0, while in the special case of h = 0 it is uniquely determined up to scaling. Thus, the study of the global geometry of such motions can be further reduced to that of the shape curves, which are time-parametrized curves on the 2-sphere characterized by a third order ODE. Moreover, these curves have two remarkable properties, namely the uniqueness of parametrization and the monotonieity, that constitute a solid foundation for a systematic study of their global geometry and naturally lead to the formulation of some pertinent problems.
基金supported by the National Basic Research Program of China("973"Project)(Grant No.2012CB932400)China Postdoctoral Science Foundation(Grant No.2014M560934)
文摘In this study, the electrochemical behavior of monocrystalline bare Si and Ag-coated Si in hydrofluoric acid （HF） solutions with and without hydrogen peroxide （H202） was systematically tested with an electrochemical technique. By analyzing the po- larization curves, the corrosion processes were quantified and the etchants which govern the formation of silicon nanowires （SiNWs） were determined. It was discovered that both H202 and Ag enhanced the reduction reactions, irrespective of the con- ductivity type and doping concentration of Si. It is believed that the formation of SiNWs via Metal-Catalyzed Electroless Etching is a process controlled by cathodic reduction reactions.
