Abstract Generalized B-splines have been employed as geometric modeling and numerical simu- lation tools for isogeometric analysis （IGA for short）. However, the previous models used in IGA, such as trigonometric gen...Abstract Generalized B-splines have been employed as geometric modeling and numerical simu- lation tools for isogeometric analysis （IGA for short）. However, the previous models used in IGA, such as trigonometric generalized B-splines or hyperbolic generalized B-splines, are not the unified mathematical representation of conics and polynomial parametric curves/surfaces. In this paper, a unified approach to construct the generalized non-uniform B-splines over the space spanned by {α（t）,β（t）,ξ（t）, η（t）, 1, t,……. , tn-4} is proposed, and the corresponding isogeometric analysis framework for PDE solving is also studied. Compared with the NURBS-IGA method, the proposed frameworks have several advantages such as high accuracy, easy-to-compute derivatives and integrals due to the non-rational form. Furthermore, with the proposed spline models, isogeometric analysis can be performed on the computational domain bounded by transcendental curves/surfaces, such as the involute of circle, the helix/helicoid, the catenary/catenoid and the cycloid. Several numerical examples for isogeometrie heat conduction problems are presented to show the effectiveness of the proposed methods.展开更多
In this paper, Yau’s conjecture on harmonic functions in Riemannian manifolds is generalized to Alexandrov spaces. It is proved that the space of harmonic functions with polynomial growth of a fixed rate is finite di...In this paper, Yau’s conjecture on harmonic functions in Riemannian manifolds is generalized to Alexandrov spaces. It is proved that the space of harmonic functions with polynomial growth of a fixed rate is finite dimensional and strong Liouville theorem holds in Alexandrov spaces with nonnegative curvature.展开更多
According to the principle of thermal activation process, the energy state of a material under the action of stress is a function of local stress. A generalized Butler-Volmer relationship for the electrode reaction on...According to the principle of thermal activation process, the energy state of a material under the action of stress is a function of local stress. A generalized Butler-Volmer relationship for the electrode reaction on the surface of a curved electrode is derived,which takes account of the effects of local stress and the radius of mean curvature. From this relationship, the overpotential is found to be proportional to hydrostatic stress and the activation volume under the condition of open circuit. The conditions for the deposition of the material made solely from solute atoms and the formation of surface pits and porous structures are obtained,using the generalized Butler-Volmer relationship.展开更多
基金supported by Zhejiang Provincial Natural Science Foundation of China under Grant No.LR16F020003the National Nature Science Foundation of China under Grant Nos.61472111,61602138+1 种基金the Open Project Program of the State Key Lab of CAD&CG(A1703)Zhejiang University
文摘Abstract Generalized B-splines have been employed as geometric modeling and numerical simu- lation tools for isogeometric analysis （IGA for short）. However, the previous models used in IGA, such as trigonometric generalized B-splines or hyperbolic generalized B-splines, are not the unified mathematical representation of conics and polynomial parametric curves/surfaces. In this paper, a unified approach to construct the generalized non-uniform B-splines over the space spanned by {α（t）,β（t）,ξ（t）, η（t）, 1, t,……. , tn-4} is proposed, and the corresponding isogeometric analysis framework for PDE solving is also studied. Compared with the NURBS-IGA method, the proposed frameworks have several advantages such as high accuracy, easy-to-compute derivatives and integrals due to the non-rational form. Furthermore, with the proposed spline models, isogeometric analysis can be performed on the computational domain bounded by transcendental curves/surfaces, such as the involute of circle, the helix/helicoid, the catenary/catenoid and the cycloid. Several numerical examples for isogeometrie heat conduction problems are presented to show the effectiveness of the proposed methods.
文摘In this paper, Yau’s conjecture on harmonic functions in Riemannian manifolds is generalized to Alexandrov spaces. It is proved that the space of harmonic functions with polynomial growth of a fixed rate is finite dimensional and strong Liouville theorem holds in Alexandrov spaces with nonnegative curvature.
文摘According to the principle of thermal activation process, the energy state of a material under the action of stress is a function of local stress. A generalized Butler-Volmer relationship for the electrode reaction on the surface of a curved electrode is derived,which takes account of the effects of local stress and the radius of mean curvature. From this relationship, the overpotential is found to be proportional to hydrostatic stress and the activation volume under the condition of open circuit. The conditions for the deposition of the material made solely from solute atoms and the formation of surface pits and porous structures are obtained,using the generalized Butler-Volmer relationship.
