Abstract：A space-filling polyhedron is a polyhedron which ＇tile＇ space, analogous to the way of certain polygons tiled the plane. The cube is the unique space-filling platonic solid. If we make line connections the...Abstract：A space-filling polyhedron is a polyhedron which ＇tile＇ space, analogous to the way of certain polygons tiled the plane. The cube is the unique space-filling platonic solid. If we make line connections the center with the vertices in the certain cube, the cube is divided into six pyramids. And if we glued six pyramids to the faces of the cube, we obtain a ＇rhombic dodecahedron＇. Since cubes are packing a space, rhombic dodecahedra are also space-filling polyhedra and a rhombic dodecahedron is divided into two regular tetrahcdra and one regular octahedron. In this study, we present how rhombic dodecahedron can be split into tetrahedra and octahedron. In this process, we can research a variety of divisions of regular polyhedron.展开更多
In this work,a three-dimensional nonlinear transient thermo-mechanically coupled finite element model(FEM)is established to investigate the variation in temperature and stress fields during electron beam melting(EBM)o...In this work,a three-dimensional nonlinear transient thermo-mechanically coupled finite element model(FEM)is established to investigate the variation in temperature and stress fields during electron beam melting(EBM)of rhombic dodecahedron Ti-6Al-4V alloy.The influence of the processing parameters on the temperature and residual stress evolutions was predicted and verified against existing literature data.The calculated results indicate that the interlayer cooling time has very little effect on both the temperature and stress evolutions,indicating that the interlayer cooling time can be set up as short as possible to reduce manufacturing time.It is presented that the residual stress of the intersection is higher than that of non-intersection.With increasing preheating temperature,the residual stress decreases continuously,which is about 20%–30%for every 50℃rise in temperature.The temperature and stress fields repeated every four layers with the complex periodic scanning strategy.Both x and y-component residual stresses are tensile stresses,while z-component stress is weak compressive or tensile stress in typical paths.It is proposed that the interlayer cooling is necessary to obtain a rhombic dodecahedron with low residual stress.These results can bring insights into the understanding of the residual stress during EBM.展开更多
Multimetallic Pt-based alloys with excavated structures have attracted great interest owing to their compositional and morphological tunability, high specific surface areas, and impressive electro-catalytic activities...Multimetallic Pt-based alloys with excavated structures have attracted great interest owing to their compositional and morphological tunability, high specific surface areas, and impressive electro-catalytic activities. Herein, we report the first facile one-pot synthesis of trimetallic Pt-Ni-Cu highly excavated rhombic dodecahedrons （ERDs） with a yield approaching 100%. More importantly, these highly uniform nanocrystals have three-dimensionally accessible excavated surfaces, where abundant stepped atoms are observed. Benefiting from the highly excavated rhombic dodecahedral structures, electronic and synergistic effects within the trimetallic allo3~ and abundant stepped atoms, the as-prepared trimetallic Pt-Ni-Cu ERDs exhibit an enhanced electro-catalytic performance for the electro-oxidation of methanol compared to commercial Pt/C and bimetallic Pt-Cu ERDs and Pt-Ni-Cu solid rhombic dodecahedrons solid rhombic dodecahedrons （SRDs）.展开更多
以六次甲基四胺(HMTA)和聚乙烯吡咯烷酮(PVP)为混合辅助剂,采用沉淀法合成了立方晶相棱形十二面体Ag3PO4微晶,对其进行了表征,并通过降解罗丹明B考察了其可见光催化活性。实验结果表明:以0.10g(25 g/mol(以Ag NO3计))HMTA和0.10 g PVP...以六次甲基四胺(HMTA)和聚乙烯吡咯烷酮(PVP)为混合辅助剂,采用沉淀法合成了立方晶相棱形十二面体Ag3PO4微晶,对其进行了表征,并通过降解罗丹明B考察了其可见光催化活性。实验结果表明:以0.10g(25 g/mol(以Ag NO3计))HMTA和0.10 g PVP为混合辅助剂合成的棱形十二面体Ag3PO4微晶,其禁带宽度为2.17e V,对罗丹明B有较好的可见光催化活性;在8 mg/L罗丹明B溶液中加入0.4 g/L Ag3PO4,可见光照射12 min时,未添加辅助剂以及分别添加0.10 g PVP、0.10 g HMTA、0.10 g HMTA和0.10 g PVP混合辅助剂制备的Ag3PO4对罗丹明B的降解率分别为67.59%,76.25%,91.88%,99.64%;棱形十二面体Ag3PO4微晶重复使用4次后,罗丹明B的降解率仍达91.59%,说明该光催化剂具有较好的重复使用性能。展开更多
在均质无线自组织网络中,虚拟骨干(Virtual Backbone,VB)的大小是衡量无线自组织网络质量的一个重要因素,虚拟骨干越小,网络路由开销越少。最小虚拟骨干的求取问题能够抽象为最小连通控制集问题。针对二维无线自组织网络上的单位圆盘图(...在均质无线自组织网络中,虚拟骨干(Virtual Backbone,VB)的大小是衡量无线自组织网络质量的一个重要因素,虚拟骨干越小,网络路由开销越少。最小虚拟骨干的求取问题能够抽象为最小连通控制集问题。针对二维无线自组织网络上的单位圆盘图(Unit Disk Graph,UDG)中最小连通控制集问题,目前已有很多研究成果,但是在现实中的某些情况下,单位圆盘图并不能准确地抽象网络。因此,文中提出了在单位球图(Unit Ball Graph,UBG)中构建高质量的连通控制集(Connected Dominating Set,CDS)的算法ST-CDS,给出了单位球图中独立节点个数的一个优化上界,并进一步利用该优化上界得到连通控制集的性能比。所提算法主要运用构造最小斯坦纳节点的斯坦纳树(Steiner Tree with Minimum Number of Steiner Nodes)方法来优化节点之间的连通部分。理论分析表明,ST-CDS算法的性能比为11.8080+ln11,是目前已知该方向研究中最好的结果。仿真结果也验证了ST-CDS算法的可行性。展开更多
For investigation of equilibrium conditions of electrons in an atom, and Ionization Energies of Elements, a simplified deterministic static model is proposed. The electrons are initially uniformly and sparsely arrange...For investigation of equilibrium conditions of electrons in an atom, and Ionization Energies of Elements, a simplified deterministic static model is proposed. The electrons are initially uniformly and sparsely arranged on the outer surface of nucleus. Then, by taking into account the nucleus-electron interaction (attractive and repulsive) and the mutual electron-electron repulsions, and by a simple step-by-step nonlinear static analysis program, all the electrons are found to equilibrate on the outer surface of the same sphere, which is concentric and larger than nucleus. In a second stage, starting from an equilibrium sphere of electrons, one of the electrons is subjected to gradual forced removal, radially and outwards with respect to nucleus. Within each removal step, the produced work increment is determined and the increments are summed. When no more significant attraction is exerted by nucleus to removed electron, the total work gives the Ionization Energy. After removing of single electron, the remaining electrons fall on a lower shell, that is, they equilibrate on the outer surface of a smaller concentric sphere. For nucleus-electron interaction, an L-J (Lennard-Jones) type curve, attractive and repulsive, is adopted. When the parameter of this curve is n > 1.0, the Ionization Energy exhibits an upper bound. As parameter n increases from 1.0 up to 2.0, the attractive potential of L-J curve is gradually weakened. The proposed model is applied on Argon. It is observed that, as the number of electrons increases, the radius of equilibrium sphere increases, too, whereas the attractive nucleus-electron potential is reduced;thus the Ionization Energy is reduced, too. Particularly, as the number of electrons and the radius of equilibrium sphere exceed some critical values, the above two last quantities exhibit abrupt falls. A regular polyhedron is revealed, which can accommodate Elements up to atomic number Z = 146, that is 28 more than Z = 118 of existing last Element, as guide for initial locations of electrons in the above first program.展开更多
Rigid origami has great potential in aerospace applications,especially deployable polyhedrons with one degree of freedom(DOF)and flat-foldability,whose types are few to date.In this paper,we create a novel foldable cu...Rigid origami has great potential in aerospace applications,especially deployable polyhedrons with one degree of freedom(DOF)and flat-foldability,whose types are few to date.In this paper,we create a novel foldable cube and a rhombic dodecahedron by introducing slits and diagonal creases to the surfaces,whose one-DOF rigid and flat-foldable properties are verified by kinematic analysis.Then,based on the isohedral quadrilateral transform,we project the creases and slits of the rhombic dodecahedron onto a tetrahedron to obtain a novel foldable tetrahedron that has two flat-foldable motion paths due to the existence of collinear creases.Following the second path,unnecessary creases are removed,and an origami tetrahedron with simplified creases is constructed.Both origami tetrahedrons possess a small folded area.Kinematic analysis reveals that these newly discovered origami polyhedrons are flat-foldable with one DOF,demonstrating favorable application prospects for space architectures and extraterrestrial habitats.展开更多
文摘Abstract：A space-filling polyhedron is a polyhedron which ＇tile＇ space, analogous to the way of certain polygons tiled the plane. The cube is the unique space-filling platonic solid. If we make line connections the center with the vertices in the certain cube, the cube is divided into six pyramids. And if we glued six pyramids to the faces of the cube, we obtain a ＇rhombic dodecahedron＇. Since cubes are packing a space, rhombic dodecahedra are also space-filling polyhedra and a rhombic dodecahedron is divided into two regular tetrahcdra and one regular octahedron. In this study, we present how rhombic dodecahedron can be split into tetrahedra and octahedron. In this process, we can research a variety of divisions of regular polyhedron.
基金supported by the Natural Science Foundation of Shandong Province,China(No.ZR2019MEM012).
文摘In this work,a three-dimensional nonlinear transient thermo-mechanically coupled finite element model(FEM)is established to investigate the variation in temperature and stress fields during electron beam melting(EBM)of rhombic dodecahedron Ti-6Al-4V alloy.The influence of the processing parameters on the temperature and residual stress evolutions was predicted and verified against existing literature data.The calculated results indicate that the interlayer cooling time has very little effect on both the temperature and stress evolutions,indicating that the interlayer cooling time can be set up as short as possible to reduce manufacturing time.It is presented that the residual stress of the intersection is higher than that of non-intersection.With increasing preheating temperature,the residual stress decreases continuously,which is about 20%–30%for every 50℃rise in temperature.The temperature and stress fields repeated every four layers with the complex periodic scanning strategy.Both x and y-component residual stresses are tensile stresses,while z-component stress is weak compressive or tensile stress in typical paths.It is proposed that the interlayer cooling is necessary to obtain a rhombic dodecahedron with low residual stress.These results can bring insights into the understanding of the residual stress during EBM.
文摘Multimetallic Pt-based alloys with excavated structures have attracted great interest owing to their compositional and morphological tunability, high specific surface areas, and impressive electro-catalytic activities. Herein, we report the first facile one-pot synthesis of trimetallic Pt-Ni-Cu highly excavated rhombic dodecahedrons （ERDs） with a yield approaching 100%. More importantly, these highly uniform nanocrystals have three-dimensionally accessible excavated surfaces, where abundant stepped atoms are observed. Benefiting from the highly excavated rhombic dodecahedral structures, electronic and synergistic effects within the trimetallic allo3~ and abundant stepped atoms, the as-prepared trimetallic Pt-Ni-Cu ERDs exhibit an enhanced electro-catalytic performance for the electro-oxidation of methanol compared to commercial Pt/C and bimetallic Pt-Cu ERDs and Pt-Ni-Cu solid rhombic dodecahedrons solid rhombic dodecahedrons （SRDs）.
文摘以六次甲基四胺(HMTA)和聚乙烯吡咯烷酮(PVP)为混合辅助剂,采用沉淀法合成了立方晶相棱形十二面体Ag3PO4微晶,对其进行了表征,并通过降解罗丹明B考察了其可见光催化活性。实验结果表明:以0.10g(25 g/mol(以Ag NO3计))HMTA和0.10 g PVP为混合辅助剂合成的棱形十二面体Ag3PO4微晶,其禁带宽度为2.17e V,对罗丹明B有较好的可见光催化活性;在8 mg/L罗丹明B溶液中加入0.4 g/L Ag3PO4,可见光照射12 min时,未添加辅助剂以及分别添加0.10 g PVP、0.10 g HMTA、0.10 g HMTA和0.10 g PVP混合辅助剂制备的Ag3PO4对罗丹明B的降解率分别为67.59%,76.25%,91.88%,99.64%;棱形十二面体Ag3PO4微晶重复使用4次后,罗丹明B的降解率仍达91.59%,说明该光催化剂具有较好的重复使用性能。
文摘在均质无线自组织网络中,虚拟骨干(Virtual Backbone,VB)的大小是衡量无线自组织网络质量的一个重要因素,虚拟骨干越小,网络路由开销越少。最小虚拟骨干的求取问题能够抽象为最小连通控制集问题。针对二维无线自组织网络上的单位圆盘图(Unit Disk Graph,UDG)中最小连通控制集问题,目前已有很多研究成果,但是在现实中的某些情况下,单位圆盘图并不能准确地抽象网络。因此,文中提出了在单位球图(Unit Ball Graph,UBG)中构建高质量的连通控制集(Connected Dominating Set,CDS)的算法ST-CDS,给出了单位球图中独立节点个数的一个优化上界,并进一步利用该优化上界得到连通控制集的性能比。所提算法主要运用构造最小斯坦纳节点的斯坦纳树(Steiner Tree with Minimum Number of Steiner Nodes)方法来优化节点之间的连通部分。理论分析表明,ST-CDS算法的性能比为11.8080+ln11,是目前已知该方向研究中最好的结果。仿真结果也验证了ST-CDS算法的可行性。
文摘For investigation of equilibrium conditions of electrons in an atom, and Ionization Energies of Elements, a simplified deterministic static model is proposed. The electrons are initially uniformly and sparsely arranged on the outer surface of nucleus. Then, by taking into account the nucleus-electron interaction (attractive and repulsive) and the mutual electron-electron repulsions, and by a simple step-by-step nonlinear static analysis program, all the electrons are found to equilibrate on the outer surface of the same sphere, which is concentric and larger than nucleus. In a second stage, starting from an equilibrium sphere of electrons, one of the electrons is subjected to gradual forced removal, radially and outwards with respect to nucleus. Within each removal step, the produced work increment is determined and the increments are summed. When no more significant attraction is exerted by nucleus to removed electron, the total work gives the Ionization Energy. After removing of single electron, the remaining electrons fall on a lower shell, that is, they equilibrate on the outer surface of a smaller concentric sphere. For nucleus-electron interaction, an L-J (Lennard-Jones) type curve, attractive and repulsive, is adopted. When the parameter of this curve is n > 1.0, the Ionization Energy exhibits an upper bound. As parameter n increases from 1.0 up to 2.0, the attractive potential of L-J curve is gradually weakened. The proposed model is applied on Argon. It is observed that, as the number of electrons increases, the radius of equilibrium sphere increases, too, whereas the attractive nucleus-electron potential is reduced;thus the Ionization Energy is reduced, too. Particularly, as the number of electrons and the radius of equilibrium sphere exceed some critical values, the above two last quantities exhibit abrupt falls. A regular polyhedron is revealed, which can accommodate Elements up to atomic number Z = 146, that is 28 more than Z = 118 of existing last Element, as guide for initial locations of electrons in the above first program.
基金XZ acknowledges financial support from the Natural Science Foundation ofChina(Project No.52105032)YC grate-fully acknowledges financial support from the Natural Science Founda-tion ofChina(Project No.51825503)+1 种基金the Tencent Foundation(Grant XPLORER-2020-1035)ML acknowledges financial support from the Natural Science Foundation of Shanghai(23ZR 1462600).
文摘Rigid origami has great potential in aerospace applications,especially deployable polyhedrons with one degree of freedom(DOF)and flat-foldability,whose types are few to date.In this paper,we create a novel foldable cube and a rhombic dodecahedron by introducing slits and diagonal creases to the surfaces,whose one-DOF rigid and flat-foldable properties are verified by kinematic analysis.Then,based on the isohedral quadrilateral transform,we project the creases and slits of the rhombic dodecahedron onto a tetrahedron to obtain a novel foldable tetrahedron that has two flat-foldable motion paths due to the existence of collinear creases.Following the second path,unnecessary creases are removed,and an origami tetrahedron with simplified creases is constructed.Both origami tetrahedrons possess a small folded area.Kinematic analysis reveals that these newly discovered origami polyhedrons are flat-foldable with one DOF,demonstrating favorable application prospects for space architectures and extraterrestrial habitats.
