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Onion-Like Inorganic Fullerenes from a Polyhedral Perspective
Published in Klaus D. Sattler, st Century Nanoscience – A Handbook, 2020
Ch. Chang, A. B. C. Patzer, D. Sülzle, H. Bauer
The polygonal faces are n-gons (n = 3, 4, 5, ...) which intersect at the edges and at the vertices. The vertices can be specified by their vertex configuration, which denotes the kind and number of faces that meet at a vertex. If all faces of a polyhedron are regular and congruent, i.e. they are all of the same kind and all vertex environments are equivalent, we have the well-known family of the five Platonic polyhedra (see also Table 15.2). Allowing for different regular n-gons but keeping the condition of equal vertex configurations, we arrive at the class of Archimedean solids (cf. Table 15.3), which are also called semi-regular. Other families of polyhedra are obtained by further relaxing the conditions and/or imposing special criteria on the nature of the faces and vertices. Another important geometric property of not necessarily convex polyhedra is called duality. Any polyhedron can be associated with a second, its so-called, dual polyhedron, where the vertices of one correspond to the faces of the other and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other. Thus, the number of faces and vertices is interchanged, while the number of edges remains constant.
Crushing behaviors of horse-hoof-wall inspired corrugated tubes under multiple loading conditions
Published in Mechanics of Advanced Materials and Structures, 2021
Wen Ma, Suchao Xie, Zhixiang Li, Zhejun Feng, Kunkun Jing
Based on the collapse configuration of the HCTs, the external energy dissipated of HCTs is equal to the sum of energy dissipation of corrugated plates, vertex tubes, and intersections of different parts. The mean crushing force acting over the whole fold is equal to the external energy. Therefore, where and are, respectively, the mean crushing force, the wavelength of a fold, the energy dissipated by corrugation plates, intersections, and vertex configurations. k lied in the range of 0.7–0.75 is the effective collapse coefficient to explicate the situation where the folds are never completely compacted [32, 33]. And the value of k is taken as 0.75 in this study. One point needs to be emphasized that the vertex configuration can be divided into eight types in this study, which can be regarded as circle and polygon geometry. The energy dissipation calculation of circular tube is different from that of polygonal tube, so it will be solved separately as and
Gain Scheduled Adaptive Control Scheme for Damping SSOs in PMSG-Integrated Power System Under High Wind Speed Variability
Published in Electric Power Components and Systems, 2021
Tong Wang, Mingxin Jin, Babak Jafarpisheh, Anamitra Pal, Zengping Wang
The rest of the paper is organized as follows. In Section 2, the linearized state space model of PMSG-integrated power system is established. The design principle, polytope vertex configuration, and the application procedure of the polytopic LPV controller are also presented in this section. Section 3 takes the four-machine two-area system as an example to describe the controller design process. The simulation results presented in Section 4 demonstrate that the polytopic LPV controller proposed in this paper has good effectiveness and adaptability in suppressing SSO modes of a PMSG-integrated power system during high wind speed variability in comparison to three other LMI-based control techniques. Section 5 concludes this paper.