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
The growth of nanocrystal superlattices of 5 nm single domain Au nanocrystals at an air-toluene interface induces formation of well-defined thin films （300--400 nm） with large coherence lengths. High-resolution elec...The growth of nanocrystal superlattices of 5 nm single domain Au nanocrystals at an air-toluene interface induces formation of well-defined thin films （300--400 nm） with large coherence lengths. High-resolution electron microscopy showed that polyhedral holes （negative supracrystal） were formed on the nanocrystal superlattice surface. Formation of negative supracrystals is attributed to inclusion in the superlattice of organic molecules （dodecanethiol）, which are present in concentrated zones at the air-toluene interface. The coexistence of two supracrystalline structures （bcc/fcc） is attributed to diffusion of dodecanethiol molecules resulting in a Bain deformation of the nanocrystal array.展开更多
We constructed and developed an in-situ cryogenic nanomechanical system to study small-scale mechanical behavior of materials at low temperatures. Uniaxial compression of two body-centered-cubic （bcc） metals, Nb and...We constructed and developed an in-situ cryogenic nanomechanical system to study small-scale mechanical behavior of materials at low temperatures. Uniaxial compression of two body-centered-cubic （bcc） metals, Nb and W, with diameters between 400 and 1300 rim, was studied at room temperature and at 165 K. Experiments were conducted inside of a Scanning Electron Microscope （SEM） equipped with a nanomechanical module, with simultaneous cooling of sample and diamond tip. Stress-strain data at 165 K exhibited higher yield strengths and more extensive strain bursts on average, as compared to those at 298 K. We discuss these differences in the framework of nano-sized plasticity and intrinsic lattice resistance. Dislocation dynamics simulations with surface-controlled dislocation multiplication were used to gain insight into size and temperature effects on deformation of nano-sized bcc metals.展开更多
In this paper, the Hausdorff dimension of the intersection of self-similar fractals in Euclidean space R^n generated from an initial cube pattern with an(n-m)-dimensional hyperplane V in a fixed direction is discussed...In this paper, the Hausdorff dimension of the intersection of self-similar fractals in Euclidean space R^n generated from an initial cube pattern with an(n-m)-dimensional hyperplane V in a fixed direction is discussed. The authors give a sufficient condition which ensures that the Hausdorff dimensions of the slices of the fractal sets generated by "multirules" take the value in Marstrand's theorem, i.e., the dimension of the self-similar sets minus one. For the self-similar fractals generated with initial cube pattern, this sufficient condition also ensures that the projection measure μVis absolutely continuous with respect to the Lebesgue measure L^m. When μV《 L^m, the connection of the local dimension ofμVand the box dimension of slices is given.展开更多
We develop a new geometric approach to deal with qubit information systems using colored graph theory. More precisely, we present a one to one correspondence between graph theory, and qubit systems, which may be explo...We develop a new geometric approach to deal with qubit information systems using colored graph theory. More precisely, we present a one to one correspondence between graph theory, and qubit systems, which may be explored to attack qubit information problems using torie geometry considered as a powerful tool to understand modern physics including string theory. Concretely, we examine in some details the cases of one, two, and three qubits, and we find that they are associated with CP1, CP1×CP1 and CP1×CP1× CP1 toric varieties respectively. Using a geometric procedure referred to as a colored toric geometry, we show that the qubit physics can be converted into a scenario handling toric data of such manifolds by help of hypercube graph theory. Operations on toric information can produce universal quantum gates.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.
文摘The growth of nanocrystal superlattices of 5 nm single domain Au nanocrystals at an air-toluene interface induces formation of well-defined thin films （300--400 nm） with large coherence lengths. High-resolution electron microscopy showed that polyhedral holes （negative supracrystal） were formed on the nanocrystal superlattice surface. Formation of negative supracrystals is attributed to inclusion in the superlattice of organic molecules （dodecanethiol）, which are present in concentrated zones at the air-toluene interface. The coexistence of two supracrystalline structures （bcc/fcc） is attributed to diffusion of dodecanethiol molecules resulting in a Bain deformation of the nanocrystal array.
基金the financial support of the Kavli Nanoscience Institute (KNI) through LEE Seok-Woo’s prized post-doctoral fellowship, of the Keck Institute for Space Studies at Caltech, and of JRG’s NASA Early Career grantCHENG YinTong acknowledges the financial support of the Caltech SURF program
文摘We constructed and developed an in-situ cryogenic nanomechanical system to study small-scale mechanical behavior of materials at low temperatures. Uniaxial compression of two body-centered-cubic （bcc） metals, Nb and W, with diameters between 400 and 1300 rim, was studied at room temperature and at 165 K. Experiments were conducted inside of a Scanning Electron Microscope （SEM） equipped with a nanomechanical module, with simultaneous cooling of sample and diamond tip. Stress-strain data at 165 K exhibited higher yield strengths and more extensive strain bursts on average, as compared to those at 298 K. We discuss these differences in the framework of nano-sized plasticity and intrinsic lattice resistance. Dislocation dynamics simulations with surface-controlled dislocation multiplication were used to gain insight into size and temperature effects on deformation of nano-sized bcc metals.
基金supported by the National Natural Science Foundation of China(Nos.11371329,11471124,11071090,11071224,11101159,11401188)K.C.Wong Magna Fund in Ningbo University,the Natural Science Foundation of Zhejiang Province(Nos.LR13A010001,LY12F02011)the Natural Science Foundation of Guangdong Province(No.S2011040005741)
文摘In this paper, the Hausdorff dimension of the intersection of self-similar fractals in Euclidean space R^n generated from an initial cube pattern with an(n-m)-dimensional hyperplane V in a fixed direction is discussed. The authors give a sufficient condition which ensures that the Hausdorff dimensions of the slices of the fractal sets generated by "multirules" take the value in Marstrand's theorem, i.e., the dimension of the self-similar sets minus one. For the self-similar fractals generated with initial cube pattern, this sufficient condition also ensures that the projection measure μVis absolutely continuous with respect to the Lebesgue measure L^m. When μV《 L^m, the connection of the local dimension ofμVand the box dimension of slices is given.
文摘We develop a new geometric approach to deal with qubit information systems using colored graph theory. More precisely, we present a one to one correspondence between graph theory, and qubit systems, which may be explored to attack qubit information problems using torie geometry considered as a powerful tool to understand modern physics including string theory. Concretely, we examine in some details the cases of one, two, and three qubits, and we find that they are associated with CP1, CP1×CP1 and CP1×CP1× CP1 toric varieties respectively. Using a geometric procedure referred to as a colored toric geometry, we show that the qubit physics can be converted into a scenario handling toric data of such manifolds by help of hypercube graph theory. Operations on toric information can produce universal quantum gates.
