Geometric Structure Research Articles

Hydrogen production catalysed by atomically precise metal clusters.

Atomically precise metal clusters that possess the exact atom number, definitive composition, and tunable geometric and electronic structures have emerged as ideal model catalysts for many important chemical processes. Recently, metal clusters have been widely used as excellent catalysts for hydrogen production to explore the relationship between the structure and catalytic properties at the atomic level. In this review, we systematically summarize the significant developments concerning metal clusters as electrocatalysts and photocatalysts for hydrogen generation. This review also puts forward the challenges and perspectives of atomically precise metal clusters in electrocatalysis and photocatalysis in the hope of providing a valuable reference for the rational design of high-performance catalysts for hydrogen production.

Hexa-atom Pt Catalyst Fabricated by a Ligand Engineering Strategy for Efficient Hydrogen Oxidation Reaction.

Atomically precise supported nanocluster catalysts (APSNCs), which feature exact atomic composition, well-defined structures, and unique catalytic properties, offer an exceptional platform for understanding the structure-performance relationship at the atomic level. However, fabricating APSNCs with precisely controlled and uniform metal atom numbers, as well as maintaining a stable structure, remains a significant challenge due to uncontrollable dispersion and easy aggregation during synthetic and catalytic processes. Herein, we developed an effective ligand engineering strategy to construct a Pt6 nanocluster catalyst stabilized on oxidized carbon nanotubes (Pt6/OCNT). The structural analysis revealed that Pt6 nanoclusters in Pt6/OCNT were fully exposed and exhibited a planar structure. Furthermore, the obtained Pt6/OCNT exhibited outstanding acidic HOR performances with a high mass activity of 18.37 A·mgpt-1 along with excellent stability during a 24 h constant operation and good CO tolerance, surpassing those of the commercial Pt/C. Density functional theory (DFT) calculations demonstrated that the unique geometric and electronic structures of Pt6 nanoclusters on OCNT altered the hydrogen adsorption energies on catalytic sites and thus lowered the HOR theoretical overpotential. This work presents a new prospect for designing and synthesizing advanced APSNCs for efficient energy electrocatalysis.

Solid-State Surface-Anchoring Strategy to Prepare Anti-Sintering Supported Metal Cluster Catalysts.

Due to the unique geometric and electronic structures, supported metal clusters with sizes below 3 nm have appealed to great interest in heterogeneous catalysis. However, these supported ultrasmall metal clusters would endure severe particle coalescences under high reaction temperatures. Herein, based on the technology of ball-milling processing, we propose a solid-state "surface-anchoring" strategy to synthesize thermally stabilized Al2O3-supported Ni nanoclusters. Interestingly, when the theoretical Ni loading weight was 1 wt %, highly dispersed Ni species were found where no Ni nanoparticles would be seen after 500 °C calcination. Until the Ni loading weight increased to 5 wt % and the calcination temperature increased to 750 °C, the Ni nanoparticles became significant but still with a size of only about 6.8 nm. With the small Ni nanoparticles, the final 5-Ni-Al2O3-OAm-750 sample worked well as methane dry reforming catalysts with excellent anticoking performance during a 500 h stability test.

Mutually unbiased coherence of Bell Diagonal States* *This work is supported by NSFC under No. 11761073.

This study explores the coherence of Bell-diagonal states under two complete sets of mutually unbiased bases (MUBs), focusing on four measures: the l 1 norm, l p norm, Rényi relative α-entropy, and relative entropy. We initially construct a complete set of MUBs in C4 by incorporating two maximally entangled bases unbiased with respect to the autotensor of mutually unbiased bases (AMUBs), subsequently comparing it with the canonical set documented in existing literature. We establish the expressions for Bell-diagonal states under these two complete sets of MUBs and demonstrate that the aggregate of each coherence measure across both sets is equivalent. Additionally, we present the upper bounds for the sums of the l 1 norm, l p norm, and Rényi relative 2-entropy of coherence. Furthermore, we describe the geometric structure associated with the sum of relative entropy coherence, revealing that an increase in the sum of relative entropy of coherence corresponds to an increase in the parameter of the Bell-diagonal states.

Recent progress in on-surface synthesis of nanoporous graphene materials.

Nanoporous graphene (NPG) materials are generated by removing internal degree-3 vertices from graphene and introducing nanopores with specific topological structures, which have been widely explored and exploited for applications in electronic devices, membranes, and energy storage. The inherent properties of NPGs, such as the band structures, field effect mobilities and topological properties, are crucially determined by the geometric structure of nanopores. On-surface synthesis is an emerging strategy to fabricate low-dimensional carbon nanostructures with atomic precision. In this review, we introduce the progress of on-surface synthesis of atomically precise NPGs, and classify NPGs from the aspects of element types, topological structures, pore shapes, and synthesis strategies. We aim to provide a comprehensive overview of the recent advancements, promoting interdisciplinary collaboration to further advance the synthesis and applications of NPGs.

Analysis of the adhesion mechanism of functionalized carbon nanotubes by molecular dynamics simulation.

Although a lot of research has been carried out on the adhesion mechanism of gecko bristles, the research on materials inspired by gecko bristles is still limited to the design of geometric structure and the optimization of preparation process, and the adhesion mechanism of materials is still unclear. In this paper, the molecular structure of the end of the bristle-like material is focused on, and the interaction between functional group modified carbon nanotubes and the interface is analyzed by molecular dynamics simulation. Thus, the influence of different polar functional groups on the interfacial force between carbon nanotubes and silica is revealed, and the adhesion enhancement mechanism of polar groups on the interface between carbon nanotubes and silica is further verified.

Design and test of a novel converging groove-guided seed tube for precision seeding of maize

In precision seeding operations, the irregular shapes of maize seed particles and the suboptimal geometric structure of the seed tube contribute to the rolling and bouncing of seeds upon falling into the furrow, ultimately compromising seeding uniformity. To address this issue, a convergent groove-guided (CGG) seed tube was proposed based on the principle of brachistochrone curve considering friction (BCCF). The discrete element method (DEM) was employed to conduct a comprehensive phenomenological analysis and numerical investigation of particle guide characteristics. Bench tests and field experiments were designed to verify the simulation results. Through response surface analysis, the optimal seeding performance was achieved at a groove angle of 111.34°, tube incline angle of 1.56°, and ground speed of 7.2 km h−1, resulting in a lateral dispersion landing range of 11.10 mm, angular velocity of 17.38 rad s−1, seed landing speed variation coefficient of 2.29%, and plant spacing variation coefficient of 6.04%. Bench test results unveiled that, under a ground speed of 7.2 km h−1, the variation coefficient of plant spacing for CGG seed tubes was measured at 7.63%, with a deviation of 1.59% from the simulation results. At high ground speeds of 9.0–14.4 km h−1, the seed guiding performance was also better than traditional seed tubes. Consistent results were also verified through field experiments. Therefore, the CGG seed tube manifested superior seed guidance efficacy when juxtaposed with its conventional counterpart, and this design can provide technical support for the realization of seed-to-ground positioning technology.

Cryogenic Photoelectron Spectroscopic and Theoretical Study of the Electronic and Geometric Structures of Undercoordinated Osmium Chloride Anions OsCln- (n = 3-5).

A series of anionic transition metal halides, OsCln- (n = 3-5), have been investigated using a newly developed, home-constructed, cryogenic anion cluster photoelectron spectroscopy. The target anionic species are generated through collision-induced dissociation in a two-stage ion funnel. The measured vertical detachment energies (VDEs) are 3.48, 4.54, and 4.81 eV for n = 3, 4, and 5, respectively. Density functional theory calculations at the B3LYP-D3(BJ)//aug-cc-pVTZ(-pp) level predict the lowest energy structures of the atomic form of OsCln- (n = 3-5) to be a quintet triangle, quartet square, and quintet square-based pyramid, respectively. The CCSD(T)-calculated VDEs and corresponding adiabatic detachment energies agree well with our experimental measurements. Analysis of the corresponding frontier molecular orbitals and charge density differences suggests that the d-orbitals of the transition metal Os play a primary role in the single-photon detachment processes, and the detached electrons originating from different molecular orbitals are distinguishable.

Band engineering in two-dimensional porphyrin- and phthalocyanine-based covalent organic frameworks: insight from molecular design

Two-dimensional covalent organic frameworks (2D COFs) represent an emerging class of crystalline polymeric networks, characterized by their tunable architectures and porosity, synthetic adaptability, and interesting optical, magnetic, and electrical properties. The incorporation of porphyrin (Por) or phthalocyanine (Pc) core units into 2D COFs provides an ideal platform for exploring the relationship between the COF geometric structure and its electronic properties in the case of tetragonal symmetry. In this work, on the basis of tight-binding models and density functional theory calculations, we describe the generic types of electronic band structures that can arise in tetragonal COFs. Three tetragonal lattice symmetries are examined: the basic square lattice, the Lieb lattice, and the checkerboard lattice. The potential topological characteristics of each lattice are explored. The Por-/Pc-based COFs exhibit characteristic band dispersions that are directly linked to their lattice symmetries and the nature of the frontier molecular orbitals of their building units. We show that the band dispersions in these COFs can be tailored by choosing specific symmetries of the molecular building units and/or by modulating the relative energies of the core and linker units. These strategies can be extended to a wide array of COFs, offering an effective approach to engineering their electronic properties.

Large Scale Synthesis of a Stable Prefunctionalized Silver Nanocluster.

Due to the stability issue, It is difficult to prepare a silver nanocluster bearing functional sites, especially at a large scale. We report the synthesis and structure of a stable silver nanocluster bearing multiple surface aldehyde groups [Ag21(Ph2PO2)10(p-CHOPhC≡C)6]SbF6, which allows for postsynthesis modification such as surface functionalization through aldimine condensation to give homochiral clusters. Remarkably, the preparation of this cluster can be done in ~90% high yield at gram scale, which facilitates further studies and potential applications. Through DFT calculations and geometric structure analysis, the high stability of this cluster is attributed to the geometric closure and electronic structure. This is the first time that an effective one-pot method has been developed to synthesize functional silver nanoclusters in high yield. The title cluster will be useful in the development of a variety of cluster-based materials.

Dynamic community detection algorithm based on hyperbolic graph convolution

PurposeCommunity detection is a key factor in analyzing the structural features of complex networks. However, traditional dynamic community detection methods often fail to effectively solve the problems of deep network information loss and computational complexity in hyperbolic space. To address this challenge, a hyperbolic space-based dynamic graph neural network community detection model (HSDCDM) is proposed.Design/methodology/approachHSDCDM first projects the node features into the hyperbolic space and then utilizes the hyperbolic graph convolution module on the Poincaré and Lorentz models to realize feature fusion and information transfer. In addition, the parallel optimized temporal memory module ensures fast and accurate capture of time domain information over extended periods. Finally, the community clustering module divides the community structure by combining the node characteristics of the space domain and the time domain. To evaluate the performance of HSDCDM, experiments are conducted on both artificial and real datasets.FindingsExperimental results on complex networks demonstrate that HSDCDM significantly enhances the quality of community detection in hierarchical networks. It shows an average improvement of 7.29% in NMI and a 9.07% increase in ARI across datasets compared to traditional methods. For complex networks with non-Euclidean geometric structures, the HSDCDM model incorporating hyperbolic geometry can better handle the discontinuity of the metric space, provides a more compact embedding that preserves the data structure, and offers advantages over methods based on Euclidean geometry methods.Originality/valueThis model aggregates the potential information of nodes in space through manifold-preserving distribution mapping and hyperbolic graph topology modules. Moreover, it optimizes the Simple Recurrent Unit (SRU) on the hyperbolic space Lorentz model to effectively extract time series data in hyperbolic space, thereby enhancing computing efficiency by eliminating the reliance on tangent space.

Overcoming Kinetic Limitations of Polyanionic Cathode toward High-Performance Na-Ion Batteries.

Polyanionic cathodes have attracted extensive research interest for Na-ion batteries (NIBs) due to their moderate energy density and desirable cycling stability. However, these compounds suffer from visible capacity fading and significant voltage decay upon the rapid sodium storage process, even if modified through nanoengineering or carbon-coating routes, leading to limited applications in NIBs. Herein, the Na3(VOPO4)2F cathode material with dominantly exposed {001} active facets is demonstrated by a topochemical synthesis route. Owing to the rational geometrical structure design and thereby directly shortening Na diffusion distance, the electrode delivers a reversible capacity of ∼129 mA h g-1 even at a high rate of 10 C, which is very close to the theoretical capacity of 132 mA h g-1, achieving a high energy density of ∼452 W h kg-1 coupled with a high-power density of 4660 W kg-1. When further served as a cathode for nonaqueous, aqueous-based, and solid-state full NIBs, respectively, our designed Na3(VOPO4)2F always enables superior electrochemical performance due to favorable kinetics.

Utilizing a Pathomics Biomarker to Predict the Effectiveness of Bevacizumab in Ovarian Cancer Treatment

The purpose of this investigation is to develop and initially assess a quantitative image analysis scheme that utilizes histopathological images to predict the treatment effectiveness of bevacizumab therapy in ovarian cancer patients. As a widely accessible diagnostic tool, histopathological slides contain copious information regarding underlying tumor progression that is associated with tumor prognosis. However, this information cannot be readily identified by conventional visual examination. This study utilizes novel pathomics technology to quantify this meaningful information for treatment effectiveness prediction. Accordingly, a total of 9828 features were extracted from segmented tumor tissue, cell nuclei, and cell cytoplasm, which were categorized into geometric, intensity, texture, and subcellular structure features. Next, the best performing features were selected as the input for SVM (support vector machine)-based prediction models. These models were evaluated on an open dataset containing a total of 78 patients and 288 whole slides images. The results indicated that the sufficiently optimized, best-performing model yielded an area under the receiver operating characteristic (ROC) curve of 0.8312. When examining the best model’s confusion matrix, 37 and 25 cases were correctly predicted as responders and non-responders, respectively, achieving an overall accuracy of 0.7848. This investigation initially validated the feasibility of utilizing pathomics techniques to predict tumor responses to chemotherapy at an early stage.

Improving deep metric learning via self-distillation and online batch diffusion process

Currently, deep metric learning (DML) methods typically rely on class labels to keep positive samples as closely clustered as possible, while distancing them from negative samples. However, this approach tends to disregard some vital information inherent in the data, such as intra-class information variation, which can hinder the generalization of the trained model. To address this issue, we propose an online batch diffusion-based self-distillation method (OBD-SD), which consists of a progressive self-distillation (PSD) technique and an online batch diffusion process (OBDP). Specifically, PSD is a simple yet effective self-distillation technique that is beneficial for the diversity of embedding representations. OBDP uses the diffusion process to reveal the intrinsic relationships among samples in the mini-batch and produce better soft distance targets. Our approach combines PSD with OBDP, which can extract richer relational information among samples by capturing the local geometric structure of manifolds in each mini-batch. OBD-SD is a highly flexible framework that can be integrated into state-of-the-art DML methods. Our experimental results on CUB200, CARS196, and Stanford Online Products datasets demonstrate that our OBD-SD consistently enhances the performance of existing DML methods, without requiring additional training time, resulting in competitive results.

Experimental Investigation of the Performance of a Novel Ejector–Diffuser System with Different Supersonic Nozzle Arrays

The supersonic–supersonic ejector–diffuser system is employed to suck supersonic low-pressure and low-temperature flow into a high-pressure environment. A new design of a supersonic–supersonic ejector–diffuser was introduced to verify pressure control performance under different operating conditions and vacuum background pressure. A 1D analysis was used to predict the geometrical structure of an ejector–diffuser with a rectangular section based on the given operating conditions. Different numbers and types of nozzle plates were designed and installed on the ejector to study the realizability of avoiding or postponing the aerodynamic choking phenomenon in the mixing section. The effects of different geometrical parameters on the operating performance of the ejector–diffuser system were discussed in detail. Experimental investigation of the effects of different types of nozzle plates and the back pressures on the pressure control performance of the designed ejector–diffuser system were performed in a straight-flow wind tunnel. The results showed that the position, type and number of the nozzle plates have a significant impact on the beginning of the formation of aerodynamic choking. The geometry of the ejector and the operating conditions, especially the backpressure and inlet pressure of the ejecting stream, determined the entrainment ratio of the two supersonic streams. The experimental results showed that long nozzle-plate had a better performance in terms of maintaining pressure stability in the test section, while short a nozzle-plate had a better pressure matching performance and could maintain a higher entrainment ratio under high backpressure conditions.

Novel 3D printing filaments: PLA and zinc carbonate basic composites for laser-assisted thermal decomposition

Additive manufacturing (AM), also known as 3D printing, has revolutionized the production of complex geometric structures across various industries. This study presents an innovative approach by integrating zinc carbonate basic (ZCB) precursor with polylactic acid (PLA) to develop composite filaments for fused deposition modeling (FDM) 3D printers. The resulting filaments undergo surface transformation into zinc oxide (ZnO) through high-power laser irradiation. Thermal analysis (TGA-DSC) and Fourier-transform infrared spectroscopy (FTIR) were used to confirm the decomposition of ZCB ([ZnCO₃]₂·[Zn(OH)₂]₃) into ZnO during the thermal decomposition stages. The study successfully extruded a composite filament containing 10% of ZCB, which worked adequately in 3D printing. The printed parts were analyzed through tensile tests (based on ASTM D638-5 standard), showing a notable difference in mechanical behavior between the commercial filament PLA and the composite filament (PLAC10). Laser irradiation of these samples facilitated a targeted conversion to ZnO, verified through scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDS), X-ray diffraction (XRD), and X-ray photoelectron spectroscopy (XPS). The integration of zinc oxide within the printed structures enhances structural stability and provides surfaces enriched with ZnO, a metal oxide with widely reported applications. Furthermore, an irradiated 3D-printed sample demonstrated chemo-resistive properties upon carbon monoxide (CO) exposure, underlining its potential as a gas sensor and confirming its semiconductor nature. This approach provides a cost-effective and efficient way to develop innovative devices with integrated functional materials.

Low-frequency energy scavenging by a stacked tri-stable piezoelectric energy harvester

We present a portable, stacked and tri-stable energy harvester based on the unique geometrical structure of L-shaped beams and the nonlinearity of magnet force to harness low-frequency and low-level excitations. In this device, multiple L-shaped piezoelectric beams are connected in a head-to-tail manner. Such a special stacked structure reduces the natural frequency of the system while realizing the series connection of multiple piezoelectric sheets in a limited space, thus improving the acquisition efficiency. Additionally, magnetic coupling endows the harvester with tri-stability and consequently enhances the bandwidth responses in low-frequency environments. The mathematical model is developed, and the static behaviors are explored by the bifurcation theory. Furthermore, the complex dynamic frequency method combined with the arc length method is conducted to investigate the dynamic responses with different parameters. Sinusoidal excitation experiments on the prototype verify the rationality of the mathematical model and the low-frequency broadband capability of the harvester. In the experiments, the designed harvester can reach a maximum output power of 1.49 mW at the low excitation amplitude of 0.4 g, and the magnet coupling significantly enhanced the electrical responses. The human motion tests demonstrate that the designed harvester has the potential to harness biomechanical energy into electrical energy for continuous powering of wireless devices.

Lagrangian descriptors with uncertainty

Lagrangian descriptors provide a global dynamical picture of the geometric structures for arbitrarily time-dependent flows with broad applications. This paper develops a mathematical framework for computing Lagrangian descriptors when uncertainty appears. The uncertainty originates from estimating the underlying flow field as a natural consequence of data assimilation or statistical forecast. It also appears in the resulting Lagrangian trajectories. The uncertainty in the flow field directly affects the path integration of the crucial nonlinear positive scalar function in computing the Lagrangian descriptor, making it fundamentally different from many other diagnostic methods. Despite being highly nonlinear and non-Gaussian, closed analytic formulae are developed to efficiently compute the expectation of such a scalar function due to the uncertain velocity field by exploiting suitable approximations. A rapid and accurate sampling algorithm is then built to assist the forecast of the probability density function (PDF) of the Lagrangian trajectories. Such a PDF provides the weight to combine the Lagrangian descriptors along different paths. Simple but illustrative examples are designed to show the distinguished behavior of using Lagrangian descriptors in revealing the flow field when uncertainty appears. Uncertainty can either completely erode the flow3 structure or barely affect the underlying geometry of the flow field. The method is also applied for eddy identification, indicating that uncertainty has distinct impacts on detecting eddies at different time scales. Finally, when uncertainty is incorporated into the Lagrangian descriptor for inferring the source target, the likelihood criterion provides a very different conclusion from the deterministic methods.

Bending shape memory properties and multi-scale viscoelastic behaviors of knitted-fabric reinforced polymer composites

Knitted fabrics with easily deformable loop structure have the potential in the development of shape memory polymeric composites with large recovery deformations. The knitted fabric reinforced shape memory epoxy polymer composites (SMPC) were prepared in this work. The effects of loop densities, orientations and bending radii on shape memory properties of SMPC were investigated. The shape fixity ratio and shape recovery ratio of SMPC subjected to U-shaped bending radius of 5 mm are above 98%. The shape recovery force of SMPC can reach up to 5.9 N. The thermodynamic properties of SMP were also characterized to obtain mechanical parameters and a user-defined material subroutine (UMAT) of shape memory epoxy polymer (SMEP) was written. Based on viscoelastic theory and the multi-scale geometrical structures, the macroscopic homogeneous thermodynamic model and mesoscopic thermodynamic model of knitted fabric reinforced SMPC were established to study the macro-scale stress distribution and meso-scale deformation evolution during shape memory process, respectively. The neutral surface position of SMPC during bending deformation is offset inner. The unique anisotropic loop structure of knitted fabric determines the shape memory behavior of the SMPC. Finally, micro-CT characterizations of knitted fabric reinforced SMPC were conducted to further understand the loop deformation mechanism during shape memory process. This study will provide important theoretical and technical support for large deformation structure design and deformation prediction of smart composites.

Geometric flavours of quantum field theory on a Cauchy hypersurface. Part II: Methods of quantization and evolution

In this series of papers we aim to provide a mathematically comprehensive framework to the Hamiltonian pictures of quantum field theory in curved spacetimes. Our final goal is to study the kinematics and the dynamics of the theory from the point of differential geometry in infinite dimensions. In this second part we use the tools of Gaussian analysis in infinite dimensional spaces introduced in the first part to describe rigorously the procedures of geometric quantization in the space of Cauchy data of a scalar theory. This leads us to discuss and establish relations between different pictures of QFT. We also apply these tools to describe the geometrization of the space of pure states of quantum field theory as a Kähler manifold. We use this to derive an evolution equation that preserves the geometric structure and avoid norm losses in the evolution. This leads us to a modification of the Schrödinger equation via a quantum connection that we discuss and exemplify in a simple case.