We derive for crystal optics in coordinate-invariant way the cone approximation of refraction vectors in the neighborhood of optic axes and determine its invariants and eigenvectors. It proved to describe an elliptic ...We derive for crystal optics in coordinate-invariant way the cone approximation of refraction vectors in the neighborhood of optic axes and determine its invariants and eigenvectors. It proved to describe an elliptic cone. The second invariant of the operator of the wave equation with respect to similarity transformations determines the special cases of degeneration including the optic axes where the polarization of the waves due to self-intersection of the dispersion surface is not uniquely determined. This second invariant is included in all investigations and it is taken into account in the illustrations. It is biquadratic in the refraction vectors and the corresponding forth-order surface in three-dimensional space splits in two separate shells and a non-rational product decomposition describing this is found. We give also a more general classification of all possible solutions of an equation with an arbitrary three-dimensional operator.展开更多
The work presented previously by the authors(Cai and Liou,1982)has been extended in this paper. By making use of our improved model the calculations on scattering phase matrices of hexagonal prism ice crystals(HPIC)ha...The work presented previously by the authors(Cai and Liou,1982)has been extended in this paper. By making use of our improved model the calculations on scattering phase matrices of hexagonal prism ice crystals(HPIC)have been conducted for monodisperse and polydisperse systems.Compared with the model of Cai and Liou,the required computational quantity is decreased by about two orders of magni- tude and the errors of results are less for the new model.Meanwhile,the scattering phase matrices of triangular pyramid ice crystals(TPIC)are also computed in the paper,and the comparison between the scatterings of the two forms of ice crystals is performed.展开更多
文摘We derive for crystal optics in coordinate-invariant way the cone approximation of refraction vectors in the neighborhood of optic axes and determine its invariants and eigenvectors. It proved to describe an elliptic cone. The second invariant of the operator of the wave equation with respect to similarity transformations determines the special cases of degeneration including the optic axes where the polarization of the waves due to self-intersection of the dispersion surface is not uniquely determined. This second invariant is included in all investigations and it is taken into account in the illustrations. It is biquadratic in the refraction vectors and the corresponding forth-order surface in three-dimensional space splits in two separate shells and a non-rational product decomposition describing this is found. We give also a more general classification of all possible solutions of an equation with an arbitrary three-dimensional operator.
文摘The work presented previously by the authors(Cai and Liou,1982)has been extended in this paper. By making use of our improved model the calculations on scattering phase matrices of hexagonal prism ice crystals(HPIC)have been conducted for monodisperse and polydisperse systems.Compared with the model of Cai and Liou,the required computational quantity is decreased by about two orders of magni- tude and the errors of results are less for the new model.Meanwhile,the scattering phase matrices of triangular pyramid ice crystals(TPIC)are also computed in the paper,and the comparison between the scatterings of the two forms of ice crystals is performed.
