Triangle Clusters Research Articles

Delocalization-ratio analysis of 3-center bonding in position-space for closo-boranes and related systems: Approaching the styx picture and beyond.

Closo-boron hydrides BnHn 2- (n = 5-12) are a conceptually well understood class of compounds. For these and a few related prototype compounds, both the local and the global picture of 3-center bonding are extracted from position-space quantities based on the electron density and the pair density. For this purpose, three-center delocalization indices between quantum theory of atoms in molecules (QTAIM) atoms in position space are used to develop a consistent set of local bond and triangle, and global cluster delocalization ratios (DRs), which are quantitatively compared with conceptual Γ values derived from the styx code for each cluster. Combination of the cluster DRs with associated effective numbers of skeletal electron sharing (SES) for selected cluster surface edges, triangles, or the whole cluster yields effective styx type values describing the trend and even the size of the conceptual styx codes for closo-boranes BnHn 2- and related systems with increasing cluster size n reasonably well. For nonuniform cluster topologies, the different vertex degrees are shown to cause systematic 3-center wise bond delocalization effects for the associated edges and triangles of different average vertex degrees. Extension of DR analysis beyond the styx type triangular cluster-surface bonding corresponds to a triangulation of multicentric bonding. The cluster-wise results keep indicating consistency with the mixed 2- and 3-center bonding approach. The successfully established chemical meaning of the local edge, triangle, and global cluster DRs and their associated SES values constitutes the basis for systematic investigations of mixed 2- and 3-center bonding scenarios in particular in intermetallic and related (endohedral) cluster compounds in the future.

Spin–Orbit Coupling Free Nonlinear Spin Hall Effect in a Triangle-Unit Collinear Antiferromagnet with Magnetic Toroidal Dipole

We investigate emergent conductive phenomena triggered by collinear antiferromagnetic orderings. We show that an up-down-zero spin configuration in a triangle cluster leads to linear and nonlinear spin conductivities even without the relativistic spin–orbit coupling; the linear spin conductivity is Drude-type, while the nonlinear spin conductivity has Hall-type characterization. We demonstrate the emergence of both spin conductivities in a breathing kagome system consisting of a triangle cluster. The nonlinear spin conductivity becomes larger than the linear one when the Fermi level lies near the region where a small partial band gap opens. Our results indicate that collinear antiferromagnets with triangular geometry give rise to rich spin conductive phenomena.

An Evolutionary Analysis of Higher-Order Interaction Collaborative Innovation Networks in China’s New Energy Vehicle Industry

As a manifestation of technological innovation achievements, patents reflect the frontier of technological development in the field. The aim of this research is to investigate the spatial evolution of patent collaboration networks and cooperation activities in the Chinese new energy vehicle (NEV) industry. We hypothesize that the higher-order collaboration networks will exhibit the formation of triangle groups centered around core nodes and the emergence of key edges indicating their importance. Key organizations and partners will play a significant role in shaping the future direction of cooperative innovation. The research utilizes data on collaboration patents in the NEV industry in China and constructs higher-order interaction collaboration innovation networks. The spatial evolution of networks and patent cooperation activities are examined using simplex methods. The results indicate that the generalized degree distribution of nodes and edges follows a power-law distribution. Two-dimensional simplex networks gradually form triangle clusters centered on core nodes and key edges. Large companies and research institutes prefer high-depth collaboration, while universities prefer high-breadth collaboration. Furthermore, the development of the new energy vehicle industry has gradually shifted from the eastern region to the central region. In the two-dimensional simplex network, Beijing and Jiangsu play a crucial role as key bridges in fostering stable and deep collaborations. The findings of this study shed light on the spatial evolution of patent collaboration networks and cooperation activities in the Chinese NEV industry. The identification of key organizations and partners, as well as the central positions of certain regions, provides valuable insights for innovation organizations in navigating innovation development and selecting collaboration partners.

Self-similarities in optical flows: Voxel lumens flux fractality in moving shapes in triangulated video frames

This paper introduces self-similarity inherent in the minuscule positive and negative lumens flux (lx) of voxels in dominant moving objects in the foreground of triangulated video frames. A voxel is a volume picture element in a video frame with coordinates that include an elapsed time component as well as the usual horizontal and vertical components. Persistent voxel self-similarities can be seen in the divergence of triangulated video frame voxel (lx) (spread of luminous brightness levels). The main results introduced in this paper include (1) inherent self-similarity in triangle clusters covering moving objects in the foreground of video frames, (2) self-similarities in voxel lumens flux in maximal nucleus triangle clusters (MNC), and (3) every triangulated video frame MNC is a fractal.

Morphological simplification of asphaltic mixture components for micromechanical simulation using finite element method

AbstractIn micromechanical simulations of asphalt mixtures, complex shapes of asphalt mortar and coarse aggregates require numerous elements in the finite element (FE) representation. This makes simulation time‐consuming with a high risk of failure. To conduct simulations with acceptable accuracy and low computational cost, an approach is proposed to simplify the geometry of mixture microstructures with error assessment due to simplification. The methodology comprises four main steps, as follows: (1) coarse aggregates in a specimen are three‐dimensionally reconstructed to conduct surface triangulation; (2) surface triangles are then clustered with a predefined fitting accuracy using the least square method; (3) coarse aggregates are simplified as polyhedrons based on triangle clusters, and the asphalt mortar is then reconstructed using Boolean operations; and (4) the simulation error caused by simplification is assessed based on FE interpolation theory to ensure the reliability of the simulation. Two samples were prepared and then reconstructed for the simulation of a cyclic indirect tensile test. The volume difference for more than 95% aggregates was less than 5% for the two specimens. The difference of stress and strain curves of original and simplified models of the two specimens ranged from 2% to 4%, which indicates that the simulation solutions of the simplified and original microstructures were very close. Furthermore, computational time was significantly reduced due to the simplification of the aggregates. This method facilitates the reliable and highly efficient simulation of asphalt mixtures using the FE method.

The Mesh Tools Package – Introducing Annotated 3D Triangle Maps in ROS

Triangle mesh maps for robotic applications are becoming increasingly popular, but are not yet effectively supported in the Robot Operating System (ROS). We introduce the Mesh Tools package consisting of message definitions, RViz plugins and tools, as well as a persistence layer. These tools make annotated triangle maps available in ROS and allow to publish, edit and inspect such maps within the existing ROS software stack. The persistence layer efficiently loads and stores large mesh maps. The proposed plugins and tools enable the visualization and validation of the complete layered map and associated properties to allow fluid interaction. We demonstrate the seamless integration of our tools in two application areas as a proof-of-concept: Labeling of triangle clusters for semantic mapping and robot navigation on triangle meshes in rough terrain outdoor environments by integrating our tools into an existing navigation stack.

Rotating polygonal depression soliton clusters on the inner surface of a liquid ring.

We report an experimental observation of rotating depression soliton sets on the inner surface of a viscous liquid ring, carrying background waves. These occur within a rotating shallow layer of oil inside a stationary cylindrical container. The solitons are organized either in single, two, or regular polygonal (triangle and hexagon) clusters; they travel in unison at a higher speed than the background traveling waves. The spectral power density reveals a possible energy exchange between the soliton clusters and the background mixed radial-azimuthal modulations through wave radiation.

"Bright" plasmons of triangle or square cluster of nanowires made of noble metals

Plasmon resonances of the "bright" plasmons of triangle or square cluster of coupled nanowires made of noble metal are theoretically investigated. The effect of the spatial configuration of silver and gold nanowires on the sensitivity of hybrid plasmons to changes in the properties of the external medium and on the possibility of near-field concentration is studied.

Efficient energy cumulants for the Baxter–Wu model

In this paper, using both analytic methods and Monte Carlo simulations with our triangle cluster algorithm, we illustrate the scaling behavior of two possible 4th-order connected energy cumulants across the well-known second and first-order phase transitions of the Baxter–Wu model under zero external magnetic field. It is found that 4th-order connected energy cumulant introduced by Janke provides a very good theoretical tool for finding and distinguishing phase transitions, especially in case the order parameter of a particular model is hardly known. Also, the physical importance of the cumulants’ local minima and maxima is investigated, showing that they are finite-size scaling effects.

Behavior of Ag3 Clusters Inside a Nanometer-Sized Space of ZSM-5 Zeolite

We found from DFT calculations that Ag-Ag orbital interactions as well as Ag-O electrostatic interactions determine the structures of three silver cations inside a nanometer-sized cavity of ZSM-5 (Ag(3)-ZSM-5) in lower and higher spin states. Both interactions strongly depend on the number of Al atoms substituted for Si atoms on the ZSM-5 framework (ZSM-5(Al(n))), where n ranges from 1 to 3. In smaller n, stronger Ag-Ag orbital interactions and weaker Ag-O electrostatic interactions operate. Accordingly, there are significant dependencies of the structures of three silver cations on the number of Al atoms. In lower spin states of Ag(3)-ZSM-5(Al(1)) and Ag(3)-ZSM-5(Al(2)), D(3h)-like triangle clusters are contained inside ZSM-5 whereas their higher spin states have triangle clusters distorted significantly from the D(3h) structure. In lower spin states, the totally symmetric orbital consisting of 5s(Ag) orbitals is responsible for cluster formation, whereas in higher spin states occupation of a 5s(Ag)-based orbital with one node results in significant distortion of the triangle clusters. The distortion can be partially understood by analogies to Jahn-Teller distortion of the bare D(3h) Ag(3)(+) cluster in the triplet spin state. When n is 3, we found that three silver cations are isolated in a lower spin state and that a linear cluster consisting of two silver cations is formed in a higher spin state. Thus, we demonstrate from DFT calculations that the number of Al atoms can control the properties of three silver cations inside a ZSM-5 cavity. Since the structural and electronic features of the enclosed silver clusters can link to their catalytic properties, the DFT findings can help us to understand the catalytic activity of Ag-ZSM-5.

Aggregation of frictional particles due to capillary attraction

Capillary attraction between identical millimeter-sized spheres floating at a liquid-air interface and the resulting aggregation are investigated at low Reynolds number. We show that the measured capillary forces between two spheres as a function of distance can be described by expressions obtained using the Nicolson approximation at low Bond numbers for far greater particle sizes than previously assumed. We find that viscous hydrodynamic interactions between the spheres needs to be included to describe the dynamics close to contact. We then consider the aggregates formed when a third sphere is added after the initial two spheres are already in contact. In this case, we find that linear superposition of capillary forces describes the observed approach qualitatively but not quantitatively. Further, we observe an angular dependence of the structure due to a rapid decrease of capillary force with distance of separation, which has a tendency to align the particles before contact. When the three particles come into contact, they may preserve their shape or rearrange to form an equilateral triangle cluster-the lowest-energy state-depending on the competition between attraction between particles and friction. Using these observations, we demonstrate that a linear particle chain can be built from frictional particles with capillary attraction.

Structural analyses and luminescent properties of a series of lead(ii) metal–organic frameworks based on 2-sulfoterephthalate

Hydrothermal reaction of lead(II) salt with monosodium 2-sulfoterephthalate (2-NaH2stp) and three N-donor auxiliary ligands gives rise to a series of 1D–3D Pb(II) coordination polymers:[Pb(2-Hstp)(o-phen)] (1), [Pb(2-Hstp)(2,2′-bipy)(H2O)]·H2O (2), [Pb(2-Hstp) (4,4′-bipy)(H2O)] (3), [Pb(2-Hstp)(H2O)] (4), [Pb3(2-Hstp)(2-stp)(OH)(4,4′-bipy)] (5) and [Pb2(2-stp) (OH)] (6) (o-phen = 1,10-phenanthroline, 2,2′-bipy = 2,2′-bipyridine and 4,4′-bipy = 4,4′-bipyridine). X-ray diffraction structural analyses of these complexes reveal 1, 3, 4 and 6 crystallize in the monoclinic crystal system of the P21/c Space group, while 2 and 5 crystallize in the triclinic Pī space group. Complex 1 possesses 1D left- and right-handed helical double-stranded chains sharing a common axis and Pb nodes, and a great deal of H-bonds and π⋯π interactions between o-phen molecules. For 2, the square H-bond clusters link two left- and right-handed helical single-stranded chains to form 1D dual-chain supramolecular structures. Complex 3 features a 1D bimetallic chain structure containing four left-handed helical chains sharing one common axis: one main helix and three auxiliary helixes in ⋯ABC⋯ order twisting up the main helix. Structural analysis shows that complex 4 presents a 3D 5-connected architecture with the topology symbol as (44, 66). In 5, a 2D double-layer structure arises from the μ3-OH bridged [Pb3(OH)] triangle clusters with 2-stp3− anions. The 3D framework of 6 is constructed from a unique tetra-nuclear lead(II) [Pb4(OH)2] chair-like motif based on two μ3-OH groups and 2-stp3− anions, resulting in the (42, 66) topology. Solid-state fluorescence properties for these crystalline materials are also presented.

Pseudopolymorphism of an adamantane-based bisphenol containing water molecules: a role of clathrate hydrates in hydrogen-bonded networks

An adamantane-based bisphenol (1) assembled into three types of 2D layers with or without channels or a doubly interpenetrated 3D network bearing clathrate hydratesviahydrogen bonds. The different stoichiometries of 1 and water facilitated the formation of the diverse molecular packing structures. Infinite chains and finite triangle clusters of water were formed within the channels and cavities.

How are Centrosymmetric and Noncentrosymmetric Structures Achieved in Uranyl Borates?

Four uranyl borates, UO(2)B(2)O(4) (UBO-1), alpha-(UO(2))(2)[B(9)O(14)(OH)(4)] (UBO-2), beta-(UO(2))(2)[B(9)O(14)(OH)(4)] (UBO-3), and (UO(2))(2)[B(13)O(20)(OH)(3)].1.25H(2)O (UBO-4), have been prepared from boric acid fluxes at 190 degrees C. UBO-3 and UBO-4 are centrosymmetric, whereas UBO-1 and UBO-2 are noncentrosymmetric (chiral and polar). These uranyl borates possess layered structures constructed from UO(8) hexagonal bipyramids, BO(3) triangles, and BO(4) tetrahedra. In the case of UBO-4, clusters of BO(3) triangles link the layers together to form open slabs with a thickness of almost 2 nm. The ability of uranyl borates to use very similar layers to yield both centrosymmetric and noncentrosymmetric layers is detailed in this work.

The Use of Precomputed Triangle Clusters for Accelerated Ray Tracing in Dynamic Scenes

AbstractIn this paper we present a hybrid algorithm for building the bounding volume hierarchy (BVH) that is used in accelerating ray tracing of animated models. This algorithm precomputes densely packed clusters of triangles on surfaces. Folowing that, a set of clusters is used to rebuild the BVH in every frame. Our approach utilizes the assumption that groups of connected triangles remain connected throughout the course of the animation. We introduce a novel heuristic to create triangle clusters that are designed for high performance ray tracing. This heuristic combines the density of connectivity, geometric size and the shape of the cluster.Our approach accelerates the BVH builder by an order of magnitude rebuilding only the set of clusters that is much smaller than the original set of triangles. The speed‐up is achieved against a ‘brute‐force’ BVH builder that repartitions all triangles in every frame of animation without using any pre‐clustering. The rendering performance is not affected when a cluster contains a few dozen triangles. We demonstrate the real‐time/interactive ray tracing performance for highly‐dynamic complex models.

Spontaneous formation of Mn nanocluster arrays on aSi(111)−7×7surface observed with STM

An extreme low-deposition rate has been used to fabricate highly ordered Mn nanocluster arrays on A Si(111)-7x7 surface. Scanning tunneling microscopy (STM) studies reveal that the Mn nanoclusters prefer to occupy the faulted half-unit cells of the Si(1110)-7x7 with preference fraction similar to 95%. High-resolution STM images demonstrate that two types of three-dimensional Mn nanoclusters coexist in the arrays; one is an identical triangle cluster and the other is an off-center pear cluster. A planar identical Mn cluster has been obtained at the initial deposition stages, indicating the coverage-dependent Mn clustering. Careful analysis of the initial adsorption stage of Mn reveals that individual Mn atoms prefer to occupy the bridging B(2) sites around Si rest atoms and the substitution site of Si center adatoms. The formation mechanism of Mn nanocluster arrays is attributed to the delicate balance between thermodynamic tendency and kinetic limitation.

A mechanism for the downturn in inverse susceptibility in triangle-based frustrated spinsystems

A mechanism for the downturn of inverse magnetic susceptibility below an intermediatetemperature, recently observed in many experiments, is proposed as an intrinsic featureof lattices with triangle-based frustrated geometries. The temperature at thebending of the inverse susceptibility curve may be related to the features of otherthermodynamic properties; the hump of the specific heat and the emergence of a1/3 plateau in magnetization under a magnetic field. This fact is derived through a MonteCarlo simulation study of the Ising model on triangular and kagome lattices,and the exact calculation for the single and small-sized triangle clusters, on boththe Ising and Heisenberg models. These results may indicate the dominance ofS(Sz) = 1/2 quantum (classical) trimer formation in the intermediate-energy regime in two-dimensionaltriangle-based lattices.

Partial phonon densities of states ofFe57in Fe-Cr: Analysis by a local-order cluster expansion

Nuclear resonant inelastic x-ray scattering spectra were measured for $^{57}\mathrm{Fe}$ in disordered body-centered-cubic alloys of Fe-Cr. Partial phonon density of states (DOS) curves were obtained from these data. These results, in conjunction with the results of Ruckert et al. [Hyperfine Interact. 126, 363 (2000)] on Fe-Cr thin-film multilayers and alloys, were analyzed with a local-order cluster expansion method. Interaction partial phonon DOS functions for the different short-range correlation functions were obtained from the disordered alloys. These interaction DOS functions were used in reconstructing the $^{57}\mathrm{Fe}$ partial DOS curves measured by Ruckert et al. on a set of thin-film multilayer samples of $^{57}\mathrm{Fe}∕^{56}\mathrm{Fe}∕\mathrm{Cr}$. The method worked well using terms up to a combined first- and second-nearest-neighbor triangle cluster, which were obtained reliably from the disordered alloys. The limitations of a basis set of correlation functions from disordered alloys are discussed but shown to be acceptable for the chemical trends of phonons in the Fe-Cr system.

Exchange distortion and spin Jahn–Teller effect for triangular and tetrahedral spin clusters of spin- [formula omitted

We study the effects of magneto-elastic coupling on the degenerate ground state of the antiferromagnetic Heisenberg model on regular triangle and tetrahedron clusters of spin- 1 2 . Both give very similar results because of the characteristics of their symmetry. Quantum-mechanical distortion appears through fluctuation of normal modes and the degeneracy of the ground state is not lifted. The tetragonal distortion at the non-magnetic phase transition of vanadium spinels is discussed.

Magneto-optical effect induced by spin chirality of the itinerant ferromagnetNd2Mo2O7

It is demonstrated both theoretically and experimentally that the spin chirality associated with a noncoplanar spin configuration produces a magneto-optical effect. Numerical study of the two-band Hubbard model on a triangle cluster shows that the optical Hall conductivity $\sigma_{xy}(\omega)$ is proportional to the spin chirality. The detailed comparative experiments on pyrochlore-type molybdates $R_2$Mo$_2$O$_7$ with $R=$Nd (Ising-like moments) and $R=$Gd (Heisenberg-like ones) clearly distinguishes the two mechanisms, i.e., spin chirality and spin-orbit interactions. It is concluded that for $R$=Nd, $\sigma_{xy}(\omega)$ is dominated by the spin chirality for the dc ($\omega=0$) and the $d \to d$ incoherent intraband optical transitions between Mo atoms.