By understanding the structural relationship among three shape-controlled Rh nanostructures, namely, {111} nanotetrahedrons, {111} tetrahedral nanoframes, and <111> skeletal nanotetrapods, we could prepare novel hierarchical dendritic Rh nanostructures with <111> Rh arms as linkers between tetrahedral shaped nanocrystals.

For most algorithms dealing with sets of points in the plane, the only relevant information carried by the input is the combinatorial configuration of the points: the orientation of each triple of points in the set (clockwise, counterclockwise, or collinear). This information is called the order type of the point set. In the dual, realizable order types and abstract order types are combinatoria...

We consider the inverse boundary value problem in the case of discrete electrical networks containing nonlinear (non-ohmic) conductors. For a fixed nonlinear electrical network, we show that under reasonable assumptions, there are well-defined Dirichletto-Neumann and Neumann-to-Dirichlet maps relating boundary voltages and boundary currents. We also generalize work of Curtis, Morrow, and others...

The associahedron is a polytope whose graph is the graph of flips on triangulations of a convex polygon. Pseudotriangulations and multitriangulations generalize triangulations in two different ways, which have been unified by Pilaud and Pocchiola in their study of pseudoline arrangements with contacts supported by a given network. In this paper, we construct the “brick polytope” of a network, o...

Superior infrared nonlinear optical (NLO) crystals are in urgent demand the development of lasers and technologies for communications computing. The critical challenge is to find a crystal with large non-resonant phase-matchable NLO coefficients high laser damage threshold (LDTs) simultaneously, which however scale inversely. This work reports such material, MgSiP2, that exhibits second harmoni...

We present an adaptive subdivision scheme for unstructured tetrahedral meshes inspired by the √ 3-subdivision scheme for triangular meshes. Existing tetrahedral subdivision schemes do not support adaptive refinement and have traditionally been driven by the need to generate smooth three-dimensional deformations of solids. These schemes use edge bisections to subdivide tetrahedra, which generate...

We present an adaptive subdivision scheme for unstructured tetrahedral meshes inspired by the √ 3-subdivision scheme for triangular meshes. Existing tetrahedral subdivision schemes do not support adaptive refinement and have traditionally been driven by the need to generate smooth three-dimensional deformations of solids. These schemes use edge bisections to subdivide tetrahedra, which generate...