Curve and surface blending is an important operation in CAD systems, in which a non-uniform rational B-spline （NURBS） has been used as the de facto standard. In local comer blending, two curves intersecting at that ...Curve and surface blending is an important operation in CAD systems, in which a non-uniform rational B-spline （NURBS） has been used as the de facto standard. In local comer blending, two curves intersecting at that comer are first made disjoint, and then the third blending curve is added-in to smoothly join the two curves with G^1- or G^2-continuity. In this paper we present a study to solve the joint problem based on curve extension. The following nice properties of this extension algorithm are exploited in depth： （1） The parameterization of the original shapes does not change; （2） No additional fragments are created. Various examples are presented to demonstrate that our solution is simple and efficient.展开更多
The rapid transition between spherical and γ-soft shapes in Zn isotopes in the mass A 70 region,is analyzed using excitation spectra and collective wave functions obtained by diagonalization of a five-dimensional Ham...The rapid transition between spherical and γ-soft shapes in Zn isotopes in the mass A 70 region,is analyzed using excitation spectra and collective wave functions obtained by diagonalization of a five-dimensional Hamiltonian for quadrupole vibrational and rotational degrees of freedom,with parameters determined by constrained self-consistent relativistic mean-field calculations for triaxial shapes.The microscopic potential energy surfaces,together with the characteristic collective observables,illustrate a rapid transition from near spherical shape at the N = 40 subshell,to γ-soft deformed shapes for lighter isotopes.The calculated spectra display fingerprints of a second-order shape phase transition that can be approximately described by the E(5) analytic solution.展开更多
The phase-field crystal(PFC) model is employed to study the shape transition of strained islands in heteroepitaxy on vicinal substrates.The influences of both substrate vicinal angles β and the lattice mismatch ξ ar...The phase-field crystal(PFC) model is employed to study the shape transition of strained islands in heteroepitaxy on vicinal substrates.The influences of both substrate vicinal angles β and the lattice mismatch ξ are discussed.The increase of substrate vicinal angles is found to be capable of significantly changing the surface nanostructures of epitaxial films.The surface morphology of films undergoes a series of transitions that include Stranski-Krastonov(SK) islands,the couple growth of islands and the step flow as well as the formation of step bunching.In addition,the larger ξ indicates an increased strained island density after coarsening,and results in the incoherent growth of strained islands with the creation of misfit dislocations.Coarsening,coalescence and faceting of strained islands are also observed.Some facets in the shape transition of strained islands are found to be stable and can be determined by β and crystal symmetry of the film.展开更多
基金supported by the National Natural Science Foundation of China (Nos. 60603085 and 60736019)the Hi-Tech Research and Development (863) Program of China (No. 2007AA01Z336)Tsinghua Basic Research Foundation, China # Expanded based on "Note on industrial applications of Hu’s surface
文摘Curve and surface blending is an important operation in CAD systems, in which a non-uniform rational B-spline （NURBS） has been used as the de facto standard. In local comer blending, two curves intersecting at that comer are first made disjoint, and then the third blending curve is added-in to smoothly join the two curves with G^1- or G^2-continuity. In this paper we present a study to solve the joint problem based on curve extension. The following nice properties of this extension algorithm are exploited in depth： （1） The parameterization of the original shapes does not change; （2） No additional fragments are created. Various examples are presented to demonstrate that our solution is simple and efficient.
基金supported in part by the Major State Basic Research Developing Program (Grant No 2007CB815000)the National Natural Science Foundation of China (Grant Nos 11005004, 10775004 and 10975008)+1 种基金the Southwest University Initial Research Foundation Grant to Doctor (Grant No.SWU110039)MZOS (Grant No 1191005-1010)
文摘The rapid transition between spherical and γ-soft shapes in Zn isotopes in the mass A 70 region,is analyzed using excitation spectra and collective wave functions obtained by diagonalization of a five-dimensional Hamiltonian for quadrupole vibrational and rotational degrees of freedom,with parameters determined by constrained self-consistent relativistic mean-field calculations for triaxial shapes.The microscopic potential energy surfaces,together with the characteristic collective observables,illustrate a rapid transition from near spherical shape at the N = 40 subshell,to γ-soft deformed shapes for lighter isotopes.The calculated spectra display fingerprints of a second-order shape phase transition that can be approximately described by the E(5) analytic solution.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51075335,51174168,10902086 and 50875217)the Northwestern Polytechnical University Foundation for Fundamental Research (Grant Nos. 201109 and NPU-FFR-JC201005)
文摘The phase-field crystal(PFC) model is employed to study the shape transition of strained islands in heteroepitaxy on vicinal substrates.The influences of both substrate vicinal angles β and the lattice mismatch ξ are discussed.The increase of substrate vicinal angles is found to be capable of significantly changing the surface nanostructures of epitaxial films.The surface morphology of films undergoes a series of transitions that include Stranski-Krastonov(SK) islands,the couple growth of islands and the step flow as well as the formation of step bunching.In addition,the larger ξ indicates an increased strained island density after coarsening,and results in the incoherent growth of strained islands with the creation of misfit dislocations.Coarsening,coalescence and faceting of strained islands are also observed.Some facets in the shape transition of strained islands are found to be stable and can be determined by β and crystal symmetry of the film.
基金The US Department of Energy Grants(DE-FG05-88ER40407,DE-FG02-95ER40934,DE-FG02-95ER40939,DE-FG05-87ER40311)and Contract(W-7405-ENG48,DE-AC03-76SF00098,DE-AC07-99ID13727,DE-AC07-761DO1570)The Work at Tsinghua University was supported by National Natural Science Foundation of China(19775028,10375032,10775078)by Major State Basic Research Development Program of China(2007CB815005,G2000077400)~~
