In this paper, we consider and resolve a geometric problem by using μ（z）-homeomorphic theory, which is the generalization of quasiconformal mappings. A sufficient condition is given such that a Ct-two-real-dimensio...In this paper, we consider and resolve a geometric problem by using μ（z）-homeomorphic theory, which is the generalization of quasiconformal mappings. A sufficient condition is given such that a Ct-two-real-dimensional connected orientable manifold with almost positive definite metric can be made into a Riemann surface by the method of isothermal coordinates. The result obtained here is actually a generalization of Chern＇s work in 1955.展开更多
Hildebrand classified all semi-homogeneous cones in R3 and computed their cor- responding complete hyperbolic affine spheres. We compute isothermal parametrizations for Hildebrand＇s new examples. After giving their a...Hildebrand classified all semi-homogeneous cones in R3 and computed their cor- responding complete hyperbolic affine spheres. We compute isothermal parametrizations for Hildebrand＇s new examples. After giving their affine metrics and affine cubic forms, we construct the whole associated family for each of Hildebrand＇s examples. The generic member of these affine spheres is given by Weierstrass f,ζ and a functions. In general any regular convex cone in R^3 has a natural associated S^1-family of such cones, which deserves further studies.展开更多
This paper is devoted to the inverse design of strained graphene surfaces for the control of electrons in the semi-classical optical-like regime.Assuming that charge carriers are described by the Dirac equation in cur...This paper is devoted to the inverse design of strained graphene surfaces for the control of electrons in the semi-classical optical-like regime.Assuming that charge carriers are described by the Dirac equation in curved-space and exploiting the fact that wave propagation can be described by ray-optics in this regime,a general computational strategy is proposed in order to find strain fields associated with a desired effective refractive index profile.The latter is first determined by solving semi-classical trajectories and by optimizing a chosen objective functional using a genetic algorithm.Then,the graded refractive index corresponding to the strain field is obtained by using its connection to the metric component in isothermal coordinates.These coordinates are evaluated via numerical quasiconformal transformations by solving the Beltrami equation with a finite volume method.The graphene surface deformation is finally optimized,also using a genetic algorithm,to reproduce the desired index of refraction.Some analytical results and numerical experiments are performed to illustrate the methodology.展开更多
基金Project (No. 10101023) supported by the National Natural Science Foundation of China
文摘In this paper, we consider and resolve a geometric problem by using μ（z）-homeomorphic theory, which is the generalization of quasiconformal mappings. A sufficient condition is given such that a Ct-two-real-dimensional connected orientable manifold with almost positive definite metric can be made into a Riemann surface by the method of isothermal coordinates. The result obtained here is actually a generalization of Chern＇s work in 1955.
基金supported by the NSF of China(10941002,11001262)the Starting Fund for Distinguished Young Scholars of Wuhan Institute of Physics and Mathematics(O9S6031001)
文摘Hildebrand classified all semi-homogeneous cones in R3 and computed their cor- responding complete hyperbolic affine spheres. We compute isothermal parametrizations for Hildebrand＇s new examples. After giving their affine metrics and affine cubic forms, we construct the whole associated family for each of Hildebrand＇s examples. The generic member of these affine spheres is given by Weierstrass f,ζ and a functions. In general any regular convex cone in R^3 has a natural associated S^1-family of such cones, which deserves further studies.
文摘This paper is devoted to the inverse design of strained graphene surfaces for the control of electrons in the semi-classical optical-like regime.Assuming that charge carriers are described by the Dirac equation in curved-space and exploiting the fact that wave propagation can be described by ray-optics in this regime,a general computational strategy is proposed in order to find strain fields associated with a desired effective refractive index profile.The latter is first determined by solving semi-classical trajectories and by optimizing a chosen objective functional using a genetic algorithm.Then,the graded refractive index corresponding to the strain field is obtained by using its connection to the metric component in isothermal coordinates.These coordinates are evaluated via numerical quasiconformal transformations by solving the Beltrami equation with a finite volume method.The graphene surface deformation is finally optimized,also using a genetic algorithm,to reproduce the desired index of refraction.Some analytical results and numerical experiments are performed to illustrate the methodology.
