In this paper, we define dual curvature motion on the dual hyperbolic unit sphere H2<sub style="margin-left:-8px;">0 in the dual Lorentzian space D31 with dual signature (+,+-) . We carry the obtained ...In this paper, we define dual curvature motion on the dual hyperbolic unit sphere H2<sub style="margin-left:-8px;">0 in the dual Lorentzian space D31 with dual signature (+,+-) . We carry the obtained results to the Lorentzian line space R3<sub style="margin-left:-8px;">1 by means of Study mapping. Then we make an analysis of the orbits during the dual hyperbolic spherical curvature motion. Finally, we find some line congruences, the family of ruled surfaces and ruled surfaces in R3<sub style="margin-left:-8px;">1.展开更多
In this paper,we present a finite difference method to track a network of curves whose motion is determined by mean curvature.To study the effect of inhomogeneous surface tension on the evolution of the network of cu...In this paper,we present a finite difference method to track a network of curves whose motion is determined by mean curvature.To study the effect of inhomogeneous surface tension on the evolution of the network of curves,we include surfactant which can diffuse along the curves.The governing equations consist of one parabolic equation for the curve motion coupled with a convection-diffusion equation for the surfactant concentration along each curve.Our numerical method is based on a direct discretization of the governing equations which conserves the total surfactant mass in the curve network.Numerical experiments are carried out to examine the effects of inhomogeneous surface tension on the motion of the network,including the von Neumann law for cell growth in two space dimensions.展开更多
文摘In this paper, we define dual curvature motion on the dual hyperbolic unit sphere H2<sub style="margin-left:-8px;">0 in the dual Lorentzian space D31 with dual signature (+,+-) . We carry the obtained results to the Lorentzian line space R3<sub style="margin-left:-8px;">1 by means of Study mapping. Then we make an analysis of the orbits during the dual hyperbolic spherical curvature motion. Finally, we find some line congruences, the family of ruled surfaces and ruled surfaces in R3<sub style="margin-left:-8px;">1.
基金supported in part by National Science Council of Taiwan under research grant NSC-97-2628-M-009-007-MY3 and MoE-ATU projectH.Huang is supported by grants from the Natural Science and Engineering Research Council(NSERC)of Canada and the Mathematics of Information Technology and Complex Systems(MI-TACS)of Canada。
文摘In this paper,we present a finite difference method to track a network of curves whose motion is determined by mean curvature.To study the effect of inhomogeneous surface tension on the evolution of the network of curves,we include surfactant which can diffuse along the curves.The governing equations consist of one parabolic equation for the curve motion coupled with a convection-diffusion equation for the surfactant concentration along each curve.Our numerical method is based on a direct discretization of the governing equations which conserves the total surfactant mass in the curve network.Numerical experiments are carried out to examine the effects of inhomogeneous surface tension on the motion of the network,including the von Neumann law for cell growth in two space dimensions.
