Concave Polyhedron Research Articles

Morphology engineering of heterogeneous carbon particles toward boosted dielectric polarization for ultrathin and strong loss absorber

Micron-carbon particles with polymorphous concave polyhedron have been easily prepared via high-efficiency spray drying-carbonization process, which is aimed at boosting dielectric polarization toward the feature of high the real part of the complex permittivity accompanied with low level dielectric loss for achieving ultrathin absorber. In addition, the effect of geometry on the microstructure and microwave absorption (MA) performances was systematically studied for the first time. A minimum reflection loss (RLmin) of −55.07 dB under ultrathin thickness of 1.23 mm and a broad effective absorption bandwidth (<-10 dB) of 4.0 GHz at 1.3 mm were obtained for composites filled with polymorphous concave polyhedral carbon particles, meanwhile the loading contents have been reduced from 30 wt% spherical filler to 22.5 wt% polymorphous concave polyhedral filler. Optimized MA performance with strong loss and ultrathin thickness has been identified as attenuation mechanism dominated by interference cancellation and assisted by dielectric loss for the first time. This work not only provides an insight to realize engineering applications of carbonaceous absorbents but also reveals the intrinsic attenuation mechanism of microwave absorbing materials.

Crystallographic-Morphological Connections in Star Shaped Metal-Organic Frameworks.

The symmetry of a crystal's morphology usually reflects the symmetry of the crystallographic packing. For single crystals, the space and point groups allow only a limited number of mathematical descriptions of the morphology (forms), all of which are convex polyhedrons. In contrast, concave polyhedrons are a hallmark of twinning and polycrystallinity and are typically inconsistent with single crystallinity. Here we report a new type of structure: a concave polyhedron shape single crystal having a multidomain appearance and a rare space group (P622). Despite these unusual structural features, the hexagonal symmetry is revealed at the morphological levels.

Highly Efficient PTCA/Co3O4/CuO/S2O82- Ternary Electrochemiluminescence System Combined with a Portable Chip for Bioanalysis.

Herein, we reported an efficient electrochemiluminescence (ECL) biosensor chip for sensitive detection of neuron-specific enolase (NSE). First, 3,4,9,10-perylenetetracarboxylic acid with good luminescence characteristics was used as a luminophore to obtain a stable ECL signal. Subsequently, hollow porous Co3O4/CuO concave polyhedron nanocages (CPNCs) were designed as co-reaction promoters to amplify the luminescence signals for highly sensitive trace detection of NSE. In brief, the rapid cyclic conversion of Co3+/Co2+ and Cu2+/Cu+ redox pairs could continuously catalyze the reduction of persulfate (S2O82-), thus providing a large number of essential active intermediates (SO4•-) for ECL emission. Meanwhile, the unique structure of Co3O4/CuO CPNCs possessed a large specific surface area, which greatly improved its catalytic efficiency. Third, NKFRGKYKC was developed as an affinity ligand for specific antibody fixation, which improved incubation efficiency and protected bioactivity of antibodies. Finally, we independently designed a microchip and applied it for ECL detection to improve the practical application ability of the sensor. The developed biosensor exhibited good sensitivity with a wide linear range (10 fg/mL to 100 ng/mL) and a low detection limit (3.42 fg/mL), which played an active role in the clinical application of sensing analysis.

Torsion–Shear Behaviour at Interlocking Joints: Calibration of Discrete Element-Deformable Models Using Experimental and Numerical Analyses

ABSTRACT An interlocking block is a concave polyhedron with non-planar joints connecting the blocks together. The possibility of the fracture within a masonry interlocking block is a major challenge that has remained rather unexplored yet. Different fracture scenarios can be taken into account through considering the crack planes at which the block can be set apart. The plastic failure inside the block can also be represented through the continuum plastic deformation of the block composed of continuum finite elements. For an interlocking block with a cuboid projection above (lock), this paper intends to analyse the torsion–shear behaviour of the lock experimentally and numerically based on the discrete element method. Two strategies are developed to model a concave block: the lock and main body of an interlocking block are set to be rigid and connected with a cohesive contact in between; the concave interlocking polyhedron is set to be deformable with elasto-plastic behaviour. Given the same material properties, the torsion–shear capacities of the lock obtained by the two numerical models and the experimental test are compared to each other. A parametric analysis is then provided to calibrate the deformable model.

The synthesis and structure of the [PdAu13(PPh3)3(SR)7]+ nanocluster.

Metal alloy nanoclusters have attracted increasing attention due to the synergistic effect of the foreign atoms. For the first time the synthesis and crystal structure of the [PdAu13(PPh3)3(SR)7]+ nanocluster is reported. The crystal structure of the nanocluster was determined by single crystal X-ray diffraction. The [PdAu13(PPh3)3(SR)7]+ nanocluster has a concave polyhedron Au9Pd kernel, which looks like a girl dancing ballet. The structure shows that [PdAu13(PPh3)3(SR)7]+ has an open shell. Meanwhile, we also carried out ultraviolet-visible (Uv-vis) absorption spectroscopy and fluorescence spectroscopy to study the optical properties of the [PdAu13(PPh3)3(SR)7]+ nanocluster.

Specific Self‐Repairing by Morphology Prejudging

AbstractThe thin surface layer growth during the regeneration of incomplete potassium dihydrogen phosphate crystal is more perplexing than the ordinary layer‐by‐layer growth. In a previous paper, the driving force of the thin surface layer growth was discussed; the present paper focuses on the regeneration process and final regeneration morphology. Based on the analysis of thin surface layer area per unit repaired volume, it is found that convex polyhedron is more advantageous than concave polyhedron. It is also found that the general morphology of repaired incomplete crystal is convex polyhedron of minimum volume covered by singular surfaces. The most important thing is, numbers of regeneration details suggest that the incomplete crystal achieves the self‐repairing by morphology prejudging.

In Russian

The paper deals with a relatively new type of three-dimensional sorbents that are called metal-organic frameworks. The chemical compounds of this kind can be regarded as crystal sponges since they are microporous solid phases with exclusively large area of accessible internal surface. The most expressive manifestation of the peculiarity of the metal-organic frameworks is the topological equivalence of the metal-organic frameworks with principally different chemical nature. This phenomenon is sometimes called an isoreticular paradox. Such sorbents possess an exclusive identity of pores which is provided by the crystalline order in their structures. In its turn the crystalline order of the structure imposes severe restrictions on the geometry and topology of cavities in the structure frame and on the spatial symmetry of the structure itself. Revealing the characteristic features of structure forming in metal-organic coordination polymers enabled to estimate the relative frequencies of possible spatial structures of metal-organic frameworks. The isoreticular paradox originates from the finite number of formally possible Fedorov groups being aggravated by the sharply uneven distribution of the probabilities of these groups in real crystal structures. An atomic configuration of a frame cavity is isomorphic to a concave polyhedron. The symmetry of such polyhedra is to comply with the crystal lattice. We have found eleven Hessel groups that correspond to possible cavity polyhedral and estimated the relative probabilities of cavity configurations in the frame structures. The structural design of framework sorbents should provide the topologic combinations of atomic complexes and molecular linkers providing the cavity configurations of the above mentioned eleven types and forming the centrosymmetric spatial structure.

Particle Shape Control via Etching of Core@Shell Nanocrystals

The application of nanocrystals as heterogeneous catalysts and plasmonic nanoparticles requires fine control of their shape and chemical composition. A promising idea to achieve synergistic effects is to combine two distinct chemical and/or physical functionalities in bimetallic core@shell nanocrystals. Although techniques for the synthesis of single-component nanocrystals with spherical or anisotropic shape are well-established, new methods are sought to tailor multicomponent nanocrystals. Here, we probe etching in a controlled redox environment as a synthesis technique for multicomponent nanocrystals. Our Monte Carlo computer simulations demonstrate the appearance of characteristic non-equilibrium intermediate microstructures that are further thermodynamically tested and analyzed with molecular dynamics. Convex platelet, concave polyhedron, pod, cage, and strutted-cage shapes are obtained at room temperature with fully coherent structure exposing crystallographic facets and chemical elements along distinct particle crystallographic directions. We observe that structural and dynamic properties are markedly modified compared to the untreated compact nanocrystal.

Porous CoP concave polyhedron electrocatalysts synthesized from metal–organic frameworks with enhanced electrochemical properties for hydrogen evolution

Porous CoP concave polyhedrons were prepared by a topological conversion from Co-MOFs with enhanced electrochemical HER activities.

折畳める筒と、アクチュエータ、ベローズへの応用可能性

This paper presents a new concept of actuators and bellows based on the rigid foldable cylinder discovered recently. Connelly et al proved that when a concave polyhedron is deformed, its volume remains constant in 1997. In spite of this rigorous mathematical theory, we have observed a real model of rigid polyhedral cylinder which changed volume substantially at some particular situation. Inspired with this phenomenon, we have identified that particular situation where the model, made of practical engineering material, can change its volume. This phenomenon is now applied to propose the new concept for actuators and bellows.

Hydrazine-Linked Convergent Self-Assembly of Sophisticated Concave Polyhedrons of β-Ni(OH)2 and NiO from Nanoplate Building Blocks

Intelligent self-assembly of nanobuilding blocks during the formation of Ni(OH)(2) single crystals with concave polyhedron structure was studied. The nickel hydroxide nanoplates pile up together with the aid of hydrazine molecules and grow along the [001] direction to form the brand-new geometry of concave polyhedrons. The novel nanostructure looks like a regularly twisted triangular prism wringed smoothly in the middle and could be attributed to the inherent spatial asymmetry of the nickel hydroxide crystal structure and the hydrogen bonds linked with the added hydrazine molecules. On the basis of the putative mechanism, polyhedrons with different longitudinal sizes (0.3-1 mum) were synthesized by adjusting the quantities of hydrazine. We also obtained NiO polyhedron crystals with similarly piled plates by calcinations of the Ni(OH)(2) polyhedrons. Our preliminary electrochemical experiments show that the Ni(OH)(2) polyhedrons have potential applications in electrochemical storage.

多面体の類似度の定量化に関する研究 （第１報） 凸分解を利用した新しいデータ構造の提案とその生成アルゴリズムについて

As a basis for treating geometrical similarities of 3-D objects, an idea of a new data structure called layer structure with convex for representing polyhedra is presented. The two layer structure, which can be constructed uniquely for a polyhedron, consists of convex components separated into two layers, i.e., the first layer includes only positive convex components to be added and the second layer represents negative convex components to be subtracted from positive ones. The procedure for constructing the two layer structure consists of the following two processes. (1) Forward process: A concave polyhedron is decomposed and represented as a hierarchical tree structure with convex components. (2) Backward process: Components belonging to leaf nodes of the tree structure are put into the two layer structure according to the level of the node. The components are removed from the original polyhedron after processing each leaf node of the tree structure. These procedures are repeated to the modified object until the processes reach to the root node. The two layer structure can be applied for extracting features of polyhedra such as protrusions, holes and pockets, and comparing 3-D objects.

3 Dimentional Image. Unique Shape Recovery of a Polyhedron Based on Interreflections.

We discuss the uniqueness of 3-D shape recovery of a polyhedron from a single shading image, and propose an approach to uniquely determine the concave shape solution by using interreflections as a constraint. In this paper, we show that if interreflection distribution is not considered, multiple convex (or concave) shape solutions usually exist for a pyramid with three or more visible facets. However, if interreflection distribution is used as a constraint to limit the number of shape solutions (for a concave polyhedron), polyhedral shape can be uniquely determined. Interreflections, which considered to be deleterious in conventional approaches, are an important constraint for shape-from-shading.

Representation and reconstruction of polygons and polyhedra using Hierarchical Extended Gaussian Images

In this paper, two new representation schemes called the Branched Gaussian Image (BGI) and the Hierarchical Extended Gaussian Image (HEGI) are proposed. They can be used for uniquely representing both concave and convex, two-dimensional figures and three-dimensional objects. The representation by the Branched Gaussian Image involves several Gaussian spheres connected by branches where the traversing directions might be different. Examples showing how the use of the BGI enables us to achieve the mapping and inverse mapping of concave polygons and polyhedra uniquely are presented. The Gaussian spheres in the BGI can be organized into a tree-like hierarchical structure known as the Hierarchical Extended Gaussian Image. A general procedure for mapping a polygon or polyhedron to its HEGI representation is described. An approach for reconstructing concave polygons from Branched Gaussian Images is presented. The reconstruction of a concave polyhedron from its Hierarchical Extended Gaussian Images by using an iterative method or a closed-form method for each convex component is also described.

An Accurate Conversion Method from Boundary Representations to Octree Data

In general, B?Reps model is used for three dimensional model creation. In recent years, the octree data structure gets into the spotlight as the computer technology makes rapid progress. Although several conversion algorithms of B?Reps into the octree data structure were proposed, former methods could not apply to B?Reps models with a concave shape. This paper describes a new conversion approach of a concave polyhedron into the octree data structure model. The proposed method consists of four processes, dividing a concave polygon into several convex polygons, determining whether octants intersect polygons, searching inner octants and calculating the volume occupied by a B?Reps object. Several experimental results show that the method is effective for the concave polyhedron and high conversion accuracy is obtained.

An algorithm for the general solution of hidden line removal for intersecting solids

A general solution for the removal of hidden lines from a three-dimensional scene is presented. The presented algorithm can accurately construct the Junction lines ( J-lines) formed when objects penetrate each other. It allows the user to define an object as a line, a plane, a convex, or a concave polyhedron, which can include inner edges on any facet of an object ( i.e., holes inside an object). The Roberts algorithm is also discussed to provide a comparison between the CPU time and restrictions with the new algorithm.

Determining Algorithm of Three-Dimensional Convex Hull Used for Set Operations of Solids and Its Application to Interference Problems

This paper discusses a determining algorithm for the three-dimensional convex hull which is well-fitted to deal with interference problems of solids requiring a three-dimensional convex hull of a given shape for their solution and is available for set operations. The paper also deals with the application of this algorithm to specific interference problems. The proposed algorithm is devised to determine the smallest convex polyhedron containing a concave polyhedron given by a solid model beforehand, as a solid model having the same data structure as that of the concave polyhedron. It features the use of Euler operators, a general method for determining a solid model. This means that the proposed algorithm does not depend on the data structure of a solid model and that all convex polyhedrons obtained during the process of determining a three-dimensional convex hull are also in the form of solid model. Because of such a feature, the three-dimensional convex hull determined by the algorithm can be used for set operations with the given concave polyhedrons, and therefore, the algorithm provides a convenient approach to interference problems of solids requiring a three-dimensional convex hull of a given shape for their solution. As an example of the application of the proposed algorithm to practical purposes, this paper also discusses a study on the extraction of undercuts in mold design using this algorithm. The findings indicate that the proposed algorithm is useful in solving such practical problems.

Determining Algorithms Of Surface VisibilityOn A Solid Model And Its Application

This paper discusses an algorithm, called three-dimensional convex hull, which is devised to determine the smallest convex polyhedron containing a concave polyhedron given by a solid model beforehand, as a solid model having the same data structure as that of the concave polyhedron, and describes its application to detect potential undercut problem in injection moulds design. Because of some disadvantages of the algorithm on detecting potential undercut, the author proposes a different method to generate the minimal contour solid and extensional solids from a computer solid model. Real undercuts are obtained through a Boolean difference operation on the minimal contour solid by subtracting the extensional solids and the original solid model. This method completely based on solid modelling techniques.