The geometric kernel (or simply the kernel) of a polyhedron is the set of points from which the whole polyhedron is visible. Whilst the computation of the kernel of a polygon has been largely ...addressed in the literature, fewer methods have been proposed for polyhedra. The most acknowledged solution for kernel estimation is to solve a linear programming problem. We present a geometric approach that extends and optimizes our previous method (Sorgente, 2021). Experimental results show that our method is more efficient than the algebraic approach over polyhedra with a limited number of vertices and faces, making it particularly suitable for the analysis of volumetric tessellations with non-convex elements. The method is also particularly efficient in detecting non-star-shaped polyhedra. Details on the technical implementation, and discussions on the pros and cons of the method, are also provided.
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•Computation of the kernel of a polyhedron using a geometric approach.•Robust kernel estimation using geometric exact predicates.•An efficient kernel estimation algorithm suitable for volumetric tessellations with non-convex polyhedra.
This paper presents a framework for extending the height-function technique for the calculation of interface normals and curvatures to unstructured non-convex polyhedral meshes with application to ...the piecewise-linear interface calculation volume-of-fluid method. The methodology is developed with reference to a collocated node-based finite-volume two-phase flow solver that utilizes the median-dual mesh, requiring a set of data structures and algorithms for non-convex polyhedral operations: truncation of a polyhedron by a plane, intersection of two polyhedra, joining of two convex polyhedra, volume enforcement of a polyhedron by a plane, and volume fraction initialization by a signed-distance function. By leveraging these geometric tools, a geometric interpolation strategy for embedding structured height-function stencils in unstructured meshes is developed. The embedded height-function technique is tested on surfaces with known interface normals and curvatures, namely cylinder, sphere, and ellipsoid. Tests are performed on the median duals of a uniform cartesian mesh, a wedge mesh, and a tetrahedral mesh, and comparisons are made with conventional methods. Across the tests, the embedded height-function technique outperforms contemporary methods and its accuracy approaches the accuracy that the traditional height-function technique exemplifies on uniform cartesian meshes.
Protein tyrosine phosphatase 1B (PTP1B) serves vital functions in insulin/leptin mediated signaling, and its abnormal expression may contribute to type II diabetes and obesity. In this work, a ...photoelectrochemical (PEC)–quartz crystal microbalance (QCM) dual-mode sensing platform was constructed for PTP1B activity assay based on hollow CuO and TiO2 polyhedra. After the immobilization of PTP1B-specific phosphopeptide (P-peptide) onto the hollow CuO polyhedra-decorated indium-tin oxide (ITO) electrode, the hollow TiO2 polyhedra were introduced to the sensing platform by the specific interaction between TiO2 and phosphate groups of P-peptide. Because of the matched energy levels of CuO and TiO2, a large cathodic photocurrent was produced under visible light irradiation. When PTP1B was present, PTP1B could specifically recognize and dephosphorylate the P-peptide. This led to the removal of TiO2 polyhedra from the electrode, resulting in a decrease of photocurrent. On the other hand, the detached hollow TiO2 polyhedra were further quantitatively detected by a QCM electrode. Thus, the PTP1B activity was highly sensitively and selectively assayed by the constructed PEC–QCM dual-mode biosensor. Moreover, this dual-mode biosensor showed great potential in protein phosphatase activity analysis and the protein phosphatase-targeted drug discovery.
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•A PEC–QCM dual-mode sensing platform was developed for PTP1B activity assay.•Hollow CuO and TiO2 octahedra were used as photoactive materials in PEC sensor.•The constructed dual-mode biosensor exhibits excellent analytical performance.
3D hollow hybrid composites with ultrafine cobalt sulfide nanoparticles uniformly embedded within the well‐graphitized porous carbon polyhedra/carbon nanotubes framework are rationally fabricated ...using a green and one‐step method involving the simultaneous pyrolysis and sulfidation of ZIF‐67. Because of the synergistic coupling effects favored by the unique nanohybridization, these composites exhibit high specific capacity, excellent cycle stability, and superior rate capability when evaluated as electrodes in lithium‐ion batteries.
The field of metallosupramolecular chemistry has advanced rapidly in recent years. Much work in this area has focused on the formation of hollow self-assembled metal-organic architectures and ...exploration of the applications of their confined nanospaces. These discrete, soluble structures incorporate metal ions as ‘glue’ to link organic ligands together into polyhedra.Most of the architectures employed thus far have been highly symmetrical, as these have been the easiest to prepare. Such high-symmetry structures contain pseudospherical cavities, and so typically bind roughly spherical guests. Biomolecules and high-value synthetic compounds are rarely isotropic, highly-symmetrical species. To bind, sense, separate, and transform such substrates, new, lower-symmetry, metal-organic cages are needed. Herein we summarize recent approaches, which taken together form the first draft of a handbook for the design of higher-complexity, lower-symmetry, self-assembled metal-organic architectures.
MoS
has attracted a lot of attention for electrochemical energy storage. Herein, we design and fabricate unusual hierarchical composite nanospheres by cultivating a MoS
sheet-like nanostructure on ...nitrogen-doped carbon polyhedra (designated as CP@MoS
nanospheres). The nitrogen-doped carbon polyhedra are able to significantly boost the electrical conductivity of the hybrid architecture and largely mitigate the agglomeration of the MoS
nanostructure. The sheet-like MoS
nanostructure can render a great deal of storage sites toward lithium and sodium. When measured as a negative electrode for Li storage, these CP@MoS
nanospheres manifest a large charge capacity of approximately 549 mAh g
, a superior cycle life of 900 cycles, and excellent rate property. Furthermore, they also demonstrate improved electrochemical activity for Na
ion storage.
The sluggish kinetics of oxygen reduction reaction (ORR) seriously restrains the practical implementation of fuel cells and metal-air batteries (MABs). While, Pt-based catalysts are well proven to be ...effective for the ORR process, they are rather expensive. Therefore, it is critical to developing low-cost and advanced catalysts with a rationally designed structure and abundant reactive sites as alternatives for Pt-based catalysts. Herein, nitrogen-doped hollow carbon polyhedrons (NHCP) have been fabricated by directly pyrolyzing ZIF-8, templated by NaCl. Benefiting from their hollow porous structure, large surface area, high graphitization degree and desired nitrogen bonding type, the as-synthesized NHCP exhibits exceptional ORR electrocatalytic activity with a half-wave potential (E1/2) of 0.86 V, high selectivity and outstanding long-term stability, exceeding most reported nitrogen-doped metal-free carbon electrocatalysts. Furthermore, the assembled Zn-air battery with NHCP cathode delivers a peak power density of 272 mW cm−2, a specific capacity of 740 mAh g−1 and an operation period of 160 h. This contribution provides a new avenue for designing high-performance electrocatalysts for ORR.
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NiCo2S4 single-shelled hollow polyhedrons (SSHPs) and double-shelled hollow polyhedrons (DSHPs) were synthesized by the same metal-organic-framework-engaged strategy that took advantage of the unique ...reactions of zeolitic imidazolate framework-67 and Ni(NO3)2, H2O, thiacetamide. It was found by XRD, SEM, TEM that the synthesized NiCo2S4 materials showed the hollow polyhedron structure assembled with nanocrystalline (the size was around 10–15 nm), and numerous mesopores existed among these nanocrystalline. As anode materials for lithium-ion batteries, NiCo2S4 SSHPs and DSHPs exhibited excellent cycling stability, but DSHPs were remarkably superior to SSHPs in terms of capacity performance and rate capability. At 0.1C, DSHPs could deliver the discharge capacity of 770.3 mAh g−1 at the 100th cycle, and the average discharge capacity over 100 cycles reached 745.5 mAh g−1. When the current came back to 0.1C after rate measurements, NiCo2S4 DSHPs could stably deliver the discharging capacity of 712.0 mAh g−1, reaching 92.1% of that at the initial 0.1C. The superior Li-storage performance should be attributed to the nanocrystalline, mesopore, and multi-shelled hollow polyhedron structure. The unique NiCo2S4 multi-shelled hollow polyhedrons exhibit great potential as anode materials for high-performance lithium-ion batteries.
Glasses are generally prepared by cooling from the liquid phase, and their properties depend on their thermal history. Recent experiments indicate that glasses prepared by vapour deposition onto a ...substrate can exhibit remarkable stability, and might correspond to equilibrium states that could hitherto be reached only by glasses aged for thousands of years. Here we create ultrastable glasses by means of a computer-simulation process that mimics physical vapour deposition. These stable glasses have, far below the conventional glass-transition temperature, the properties expected for the equilibrium supercooled liquid state, and optimal stability is attained when deposition occurs at the Kauzmann temperature. We also show that the glasses' extraordinary stability is associated with distinct structural motifs, in particular the abundance of regular Voronoi polyhedra and the relative lack of irregular polyhedra.
We enumerate the 188 3-orbit skeletal polyhedra in
E
3
with irreducible symmetry group. The analysis is carried out by determining the polyhedra having each irreducible finite group of isometries as ...their symmetry group. Relevant information of every polyhedron is also organized in tables.
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