Based on the generalized gauge function, a numerical criterion which specifies the topological rela-tionship between convex polyhedra is presented. It can be applied to detecting the overlap, just contact or separatio...Based on the generalized gauge function, a numerical criterion which specifies the topological rela-tionship between convex polyhedra is presented. It can be applied to detecting the overlap, just contact or separation between two sets of convex polyhedra. As the solution of a linear programming problem, the value of this criterion can be calculated easily. The presented criterion is available to provide heuristic information for generating intermediate configuration point as well as checking the hypothesized path for admissibility in flexible-trajectory path planning ap-proach.展开更多
Based on the concept of gauge function, the pseudo minimum translational distance (PMTD) between two convex objects is defined in this paper. PMTD not only provides a measure of the clearance between two separating ob...Based on the concept of gauge function, the pseudo minimum translational distance (PMTD) between two convex objects is defined in this paper. PMTD not only provides a measure of the clearance between two separating objects, but also quantifies the penetration of two objects intersecting each other. It is proved that the PMTD is differentiate almost everywhere w. r.t. the configuration variable of the objects. Algorithms for calculating PMTD and its derivative are also presented.展开更多
Convex polyhedral cuprate clusters are being formed through lateral frustration when the a and c lattice parameters of the tetragonal ACuO2 infinite layer structure will become identical by substitution of a large cat...Convex polyhedral cuprate clusters are being formed through lateral frustration when the a and c lattice parameters of the tetragonal ACuO2 infinite layer structure will become identical by substitution of a large cation (A = Ba2+). However, the corner-shared CuO2 plaquettes of the infinite network suffer a topotactic rearrangement forming edge-connected units, for instance Cu18O24 cages (polyhedron notation [4641238]) with 2 compound (space group P4/ nmm) will be discussed. The possibility to construct a cuprate super-cage with m3m symmetry (polyhedron notation [4641242438]) is being reported. This super-cage still consists of edge-connected CuO2 plaquettes when fully decorated with copper ions, but with different curvatures, arranged in circles of 9.39 ? of diameter with 139.2° Cu-O-Cu antiferromagnetic super-exchange interaction. On the one hand, the realization of such a quite stable cuprate super-cage as a candidate for high-Tc superconductivity depends on whether a template of suitable size such as the cation or C(CH3)4 enables its formation, and on the other hand the cage can further be stabilized by highly charged cations located along the [111] direction. Synthesis options will be proposed based on suggested cage formation pathways. An X-ray powder pattern was calculated for a less dense cluster structure of Im3m space group with a lattice parameter of a = 14.938 ? and two formula units of Cu46O51 to facilitate future identification. Characteristic X-ray scattering features as identification tool were obtained when the electron distribution of the hollow polyhedron was approximated with electron density in a spherical shell.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘Based on the generalized gauge function, a numerical criterion which specifies the topological rela-tionship between convex polyhedra is presented. It can be applied to detecting the overlap, just contact or separation between two sets of convex polyhedra. As the solution of a linear programming problem, the value of this criterion can be calculated easily. The presented criterion is available to provide heuristic information for generating intermediate configuration point as well as checking the hypothesized path for admissibility in flexible-trajectory path planning ap-proach.
基金the National Natural Science Foundation of China (Grant Nos. 59805004, 59990470) the National Distinguished Youth Foundation (Grant No. 59725514).
文摘Based on the concept of gauge function, the pseudo minimum translational distance (PMTD) between two convex objects is defined in this paper. PMTD not only provides a measure of the clearance between two separating objects, but also quantifies the penetration of two objects intersecting each other. It is proved that the PMTD is differentiate almost everywhere w. r.t. the configuration variable of the objects. Algorithms for calculating PMTD and its derivative are also presented.
文摘Convex polyhedral cuprate clusters are being formed through lateral frustration when the a and c lattice parameters of the tetragonal ACuO2 infinite layer structure will become identical by substitution of a large cation (A = Ba2+). However, the corner-shared CuO2 plaquettes of the infinite network suffer a topotactic rearrangement forming edge-connected units, for instance Cu18O24 cages (polyhedron notation [4641238]) with 2 compound (space group P4/ nmm) will be discussed. The possibility to construct a cuprate super-cage with m3m symmetry (polyhedron notation [4641242438]) is being reported. This super-cage still consists of edge-connected CuO2 plaquettes when fully decorated with copper ions, but with different curvatures, arranged in circles of 9.39 ? of diameter with 139.2° Cu-O-Cu antiferromagnetic super-exchange interaction. On the one hand, the realization of such a quite stable cuprate super-cage as a candidate for high-Tc superconductivity depends on whether a template of suitable size such as the cation or C(CH3)4 enables its formation, and on the other hand the cage can further be stabilized by highly charged cations located along the [111] direction. Synthesis options will be proposed based on suggested cage formation pathways. An X-ray powder pattern was calculated for a less dense cluster structure of Im3m space group with a lattice parameter of a = 14.938 ? and two formula units of Cu46O51 to facilitate future identification. Characteristic X-ray scattering features as identification tool were obtained when the electron distribution of the hollow polyhedron was approximated with electron density in a spherical shell.
