By using the derivative method, we obtained the same result with that of the previous work of Chen et al. in 2006. Different from the integral form, the derivative form of the surface expression published in this pape...By using the derivative method, we obtained the same result with that of the previous work of Chen et al. in 2006. Different from the integral form, the derivative form of the surface expression published in this paper is derived from differential equation and based on the theory of non-imaging focusing heliostat proposed by Chen et al. in 2001. The comparison of the derivative form of fixed aberration correction surface has been made with that of integral form surface as well as that of spherical surface in concentrating the solar ray.展开更多
A method to reparametrize G retional curve to obtain a C^1 curve is given. A practical G^1 continual connective between adjacent NURUS patches along common guadratic boundary curve is presented in this paper, and a s...A method to reparametrize G retional curve to obtain a C^1 curve is given. A practical G^1 continual connective between adjacent NURUS patches along common guadratic boundary curve is presented in this paper, and a specific algorithm for control points and weights of NURBS patches is discussed.展开更多
We present a theoretical analysis for fully developed convective beat transfer in a circular tube for power law fluids by assuming that the thermal diffusivity is a function of temperature gradient. The analytical eol...We present a theoretical analysis for fully developed convective beat transfer in a circular tube for power law fluids by assuming that the thermal diffusivity is a function of temperature gradient. The analytical eolution is obtained and the heat transfer behaviour is investigated under a constant heat flux boundary condition. It is shown that the Nusselt number strongly depends on the value of power law index n. The Nusselt number sharply decreases in the range of 0 〈 n 〈 0.1. However, for n 〉 0.5, the Nusselt number decreases monotonically with the increasing n, and for n 〉 20, the values of Nusselt number approach a constant.展开更多
Let X be a compact set which is laminated by parabolic Riemiann surfaces. For the CR positive line bundle L, there exists an integer N ∈ N such that for any s 〉 N and any continuous v ∈∧^（0,1）X×L^×s, t...Let X be a compact set which is laminated by parabolic Riemiann surfaces. For the CR positive line bundle L, there exists an integer N ∈ N such that for any s 〉 N and any continuous v ∈∧^（0,1）X×L^×s, there exists a continuous u ∈ L^×s solving δb^-u = v.展开更多
We propose a method that automatically generates discrete bicubic G^1 continuous B-spline surfaces that interpolate the curve network of a ship huliform.First,the curves in the network are classified into two types;bo...We propose a method that automatically generates discrete bicubic G^1 continuous B-spline surfaces that interpolate the curve network of a ship huliform.First,the curves in the network are classified into two types;boundary curves and ＂reference curves＂,The boundary curves correspond to a set of rectangular（or triangular）topological type that can be representes with tensot-product （or degenerate）B-spline surface patches.Next,in the interior of the patches,surface fitting points and cross boundary derivatives are estimated from the reference curves by constructing ＂virtual＂isoparametric curves.Finally,a discrete G^1 continuous B-spline surface is gencrated by a surface fitting algorithm.Several smooth ship hullform surfaces generated from curve networks corresponding to actual ship hullforms demonstrate the quality of the method.展开更多
The problems of geometric continuity for rational Bezter surfaces are discussed. Concise conditions of first order and second order geometric continuity for rational triangular Bézier surfaces are given. Meanwhil...The problems of geometric continuity for rational Bezter surfaces are discussed. Concise conditions of first order and second order geometric continuity for rational triangular Bézier surfaces are given. Meanwhile,a geometric condition for smoothness between adjacent rational Bézier surfaces and the transformation formulae between rational triangular patches and rational rectangular patches are obtained.展开更多
文摘By using the derivative method, we obtained the same result with that of the previous work of Chen et al. in 2006. Different from the integral form, the derivative form of the surface expression published in this paper is derived from differential equation and based on the theory of non-imaging focusing heliostat proposed by Chen et al. in 2001. The comparison of the derivative form of fixed aberration correction surface has been made with that of integral form surface as well as that of spherical surface in concentrating the solar ray.
文摘A method to reparametrize G retional curve to obtain a C^1 curve is given. A practical G^1 continual connective between adjacent NURUS patches along common guadratic boundary curve is presented in this paper, and a specific algorithm for control points and weights of NURBS patches is discussed.
基金Supported by the National Natural Science Foundations of China under Grant No 50476083.
文摘We present a theoretical analysis for fully developed convective beat transfer in a circular tube for power law fluids by assuming that the thermal diffusivity is a function of temperature gradient. The analytical eolution is obtained and the heat transfer behaviour is investigated under a constant heat flux boundary condition. It is shown that the Nusselt number strongly depends on the value of power law index n. The Nusselt number sharply decreases in the range of 0 〈 n 〈 0.1. However, for n 〉 0.5, the Nusselt number decreases monotonically with the increasing n, and for n 〉 20, the values of Nusselt number approach a constant.
基金Supported by the National Natural Science Foundation of China(11271359)
文摘Let X be a compact set which is laminated by parabolic Riemiann surfaces. For the CR positive line bundle L, there exists an integer N ∈ N such that for any s 〉 N and any continuous v ∈∧^（0,1）X×L^×s, there exists a continuous u ∈ L^×s solving δb^-u = v.
文摘We propose a method that automatically generates discrete bicubic G^1 continuous B-spline surfaces that interpolate the curve network of a ship huliform.First,the curves in the network are classified into two types;boundary curves and ＂reference curves＂,The boundary curves correspond to a set of rectangular（or triangular）topological type that can be representes with tensot-product （or degenerate）B-spline surface patches.Next,in the interior of the patches,surface fitting points and cross boundary derivatives are estimated from the reference curves by constructing ＂virtual＂isoparametric curves.Finally,a discrete G^1 continuous B-spline surface is gencrated by a surface fitting algorithm.Several smooth ship hullform surfaces generated from curve networks corresponding to actual ship hullforms demonstrate the quality of the method.
文摘The problems of geometric continuity for rational Bezter surfaces are discussed. Concise conditions of first order and second order geometric continuity for rational triangular Bézier surfaces are given. Meanwhile,a geometric condition for smoothness between adjacent rational Bézier surfaces and the transformation formulae between rational triangular patches and rational rectangular patches are obtained.
