Edge Length Research Articles

Rigidity of Nonconvex Polyhedra with Respect to Edge Lengths and Dihedral Angles

Rigidity of Nonconvex Polyhedra with Respect to Edge Lengths and Dihedral Angles

Fabrication and tribological properties of bionic surface texture self-lubricating 60NiTi alloy via selective laser melting and infiltration

Due to its low elastic modulus, low density, non-magnetic and good lubricity, 60NiTi alloy is considered a novel fourth-generation aerospace bearing material. In this paper, 60NiTi biomimetic surface textured self-lubricating composites were fabricated by selective laser melting (SLM) and high-temperature fusion infiltration (HTFI). The effects of different slit widths (NTD), edge lengths (NTA), and soft metal Sn-Pb-Ag (SPA) infiltration on its tribological properties were studied. The results show that the NTA-SPA structural samples with medium texture density (ρ=16%) promoted the diffusion of the lubricant phase to the friction surface, resulting in a complete lubricant film. The COF stabilized at 0.2, and the wear rate decreased to 0.56×10-3 mm3/Nm, providing a more stable self-lubrication effect compared to the NTD-SPA sample.

Spatial Distributions and Edge Relationships of Plant Communities in Coastal Barrens in Nova Scotia, Canada

Coastal barrens support varied vegetation that includes wetlands, dwarf shrublands, and small patches of forest. Forest expansion, sea-level rise and recreational trails affect plant communities but spatial vegetation patterns within barrens are unknown. Using high-resolution multispectral aerial imagery, we classified plant communities and other land cover types using 500m x 500m landcover maps at three coastal barrens sites on the Atlantic coast of Nova Scotia, Canada. Community patches were compared using size and shape metrics; shared edge length identified adjacent communities. Community distributions were modelled using environmental variables such as elevation and distance to coast. Forty distinct plant communities were detected, with shrublands (37.5% total area), dwarf shrublands (23.3%) and bog wetlands (13.9%) the most abundant. Average patch size was 9.2 m2; average patch density was 951 patches/ha, indicating fine scale community variability. Recreational vehicle trails occurred primarily in bog wetlands. Dwarf shrublands and some wetland types were closest to the coastline; taller shrublands and tree islands occurred further from the coast. Edge relationships revealed a vegetation height gradient across the forest-barren ecotone: tree islands were mostly adjacent to tall shrub communities, followed by progressively shorter vegetation. Topographic variability and distance to coast were important predictors of community distribution. Edge relationships among communities allowed identification of those most at risk from trail disturbance, forest expansion and coastal squeeze.

Spectroscopic Differentiation of Structural Transitions from Carbon Nanobelts to Carbon Nanotubes.

In this study, simulated X-ray photoelectron spectroscopy (XPS) and Raman spectroscopy were utilized to differentiate the early stage structures as carbon nanobelts (CNBs) evolved into carbon nanotubes (CNTs). The effects of edge type, length, and diameter on the spectroscopic characteristics of armchair and zigzag CNTs were examined. Variations in XPS spectra were found to correspond to changes in the bandgap, while Raman spectra provided distinct bands associated with specific structural features. Notably, in armchair CNTs, the C 1s XPS peak positions exhibited clear differences depending on the structure. Additionally, the Kekulé vibration band and other characteristic bands in Raman spectra varied with length and diameter, enabling differentiation of armchair CNT structures. Although the structural analysis of zigzag CNTs was challenging using XPS, Raman spectroscopy proved to be effective in distinguishing structural differences. This study lays the groundwork for future spectroscopic analyses, contributing to the broader understanding of nanocarbon materials such as CNBs and CNTs and their potential applications in advanced electronic materials.

Computing Hive Plots: A Combinatorial Framework

Hive plots are a graph visualization style placing vertices on a set of radial axes emanating from a common center and drawing edges as smooth curves connecting their respective endpoints. In previous work on hive plots, assignment to an axis and vertex positions on each axis were determined based on selected vertex attributes and the order of axes was prespecified. Here, we present a new framework focusing on combinatorial aspects of these drawings to extend the original hive plot idea and optimize visual properties such as the total edge length and the number of edge crossings in the resulting hive plots. Our framework comprises three steps: (1) partition the vertices into multiple groups, each corresponding to an axis of the hive plot; (2) optimize the cyclic axis order to bring more strongly connected groups near each other; (3) optimize the vertex ordering on each axis to minimize edge crossings. Each of the three steps is related to a well-studied, but NP-complete computational problem. We combine and adapt suitable exact and heuristic algorithmic approaches, implement them as an instantiation of our framework, and show in a case study how it can be applied in a practical setting. Furthermore, we conduct computational experiments to gain further insights regarding the algorithmic choices of our framework. The code of the implementation and a prototype web application can be found on OSF.

Spikes and spines in 4D Lorentzian simplicial quantum gravity

Simplicial approaches to quantum gravity such as quantum Regge calculus and spin foams include configurations where bulk edges can become arbitrarily large while the boundary edges are kept small. Spikes and spines are prime examples for such configurations. They pose a significant challenge for a desired continuum limit, for which the average lengths of edges ought to become very small. Here we investigate spike and spine configurations in four-dimensional Lorentzian quantum Regge calculus. We find that the expectation values of arbitrary powers of the bulk length are finite. To that end, we explore new types of asymptotic regimes for the Regge amplitudes, in which some of the edges are much larger than the remaining ones. The amplitudes simplify considerably in such asymptotic regimes and the geometric interpretation of the resulting expressions involves a dimensional reduction, which might have applications to holography.

FIB/SEM serial sectioning as a versatile tool for microstructural analysis

Abstract FIB/SEM tomography is a serial sectioning method in which the cross-sectional area of the sample is stepwise removed with a focused ion beam (FIB) and the exposed cross-sectional area is imaged with a scanning electron microscope (SEM). All imaging techniques of the SEM can be used, which allows the application to a wide range of materials science questions. On the one hand, resolutions of a few nm can be achieved, and on the other hand, volumes with edge lengths of 100 μm and more can be examined. This article gives an overview of the current state of the art and the practical implementation of FIB/ SEM serial sectioning. The special aspects of the integration of energy dispersive X-ray spectroscopy (EDS) and electron backscatter diffraction (EBSD) are also discussed.

Interpreting the edge angle efficiency of middle palaeolithic lithic assemblage with Artifact-3D – A case study Barwaniya W1, North Karanpura Valley, Eastern India

The lithic technology is directly linked with knapping skills, cognition, and economic production of a particular culture. The central objective of lithic production was to obtain desirable edge angles and sharpness for cutting/ butchering work in an efficient manner to achieve the highest utility/ efficiency and low production ratio. The angle of an edge, whether unaltered or retouched and as part of the overall tool design, is undoubtedly a parameter that influences the behavioural dimension of a lithic artefact. Thus, lithics artefacts' work efficiency or knapping efficiency depends on their working (cutting) edge angle, length of the parallel edge, centre of gravity, length of lithic, and lesser rate of edge angle damage. The present research has analysed the working edge angle of the Middle Palaeolithic Levallois assemblage from the newly discovered site of Barwaniya W1 from the North Karanpura Valley (North of Upper Damodar Basin), Jharkhand, India with the help of semi-automated 3D edge angle analysis technique. the current study scrutinises the entirety of an artefact's edge angle through automated positioning based on surface tension and a higher number of reference measurement points on the 3D scan surface of the artefact. This research has digitally measured the Middle Palaeolithic quartzite flake-based assemblage from Barwaniya W1 and their working edge angle, parallel edge (thick blunt side used for hafting), and centre of gravity with Artefact-3D software which has provided us with precise measurement without human errors and ambiguity. Further, this research has replicated the quartzite lithic assemblage of Barwaniya W1 with the Levallois reduction technique to interpret the edge angle efficiency.

Algorithms for the thief orienteering problem on directed acyclic graphs

We consider the scenario of routing an agent called a thief through a weighted graph G=(V,E) from a start vertex s to an end vertex t. A set I of items each with weight wi and profit pi is distributed among V∖{s,t}. The thief, who has a knapsack of capacity W, must follow a simple path from s to t within a given time T while packing in the knapsack a set of items taken from the vertices along the path of total weight at most W and maximum profit. The travel time across an edge depends on the edge length and current knapsack load.The thief orienteering problem (ThOP) is a generalization of the orienteering problem, the longest path problem, and the 0-1 knapsack problem. We prove that there exists no approximation algorithm for ThOP with constant approximation ratio unless P=NP, and we present a polynomial-time approximation scheme (PTAS) for a relaxed version of ThOP when G is directed and acyclic that produces solutions that use time at most T(1+ϵ) for any constant ϵ>0. We also present a fully polynomial-time approximation scheme (FPTAS) for ThOP on arbitrary undirected graphs where the travel time depends only on the lengths of the edges and T is the length of a shortest path from s to t plus a constant K. Finally, we present a FPTAS for a restricted version of the problem where the input graph is a clique.

High Temperature, Isothermal Growth Promotes Close Packing and Thermal Stability in DNA-Engineered Colloidal Crystals.

We report a strategy to accelerate the synthesis and increase the crystallinity of colloidal crystals (CCs) engineered with DNA. Specifically, by holding the DNA-modified Au particle building blocks above the Tm of the DNA bonding elements (i.e., free from the particles), but slightly below the Tm of the anticipated CC during the assembly process, crystallinity is increased, and enthalpically favored phases with high degrees of facet registration are observed. We studied the utility of this approach with systems for which the commonly adopted slow-cooling approach yielded primarily amorphous aggregates. In particular, we used it to synthesize high-volume fraction CCs from large (80 nm) anisotropic nanoparticles (cubes and rhombic dodecahedra) with short (<14 nm) DNA designed to restrict the degrees of freedom for the DNA bonds and maintain the anisotropy of the particle building block. Small-angle X-ray scattering and electron microscopy studies show that the crystalline phases synthesized via this method are more thermally stable than their corresponding aggregate phases, likely due to an increased number of DNA-DNA bonds between particles. Crystal size tunability (between 0.5 and 15 μm edge lengths) and epitaxial growth were demonstrated using this strategy by modulating the NaCl concentration in tandem with previously synthesized CC nuclei. Taken together, this isothermal strategy demonstrates how to deliberately crystallize a wide variety of anisotropic colloidal materials and expands the phase space accessible to nanoparticles modified with DNA.

Discretization of Continuous Spaces using Barycentric Subdivision Method with Metric Space Constraints on the Nearest Neighbour Edges

The Rao-Wilton-Glisson (RWG) is a commonly used basis function in the numerical solution of the electric field integral equation (EFIE) using the Method of Moments (MoM) and Galerkin approach. This method relies on triangular patches to approximate the surface current. Traditionally, barycentric subdivision of a primary triangle into n-sub-triangles has been used with RWG basis function to solve the EFIE using MoM. This paper presents a method of approximating a surface using triangular patches by sub-dividing a primary triangle into (2n-1) subtriangles. which creates a denser mesh than the widely used nine (9) points quadrature method. The structure is approximated by small square patches, which are further sub-divided into two primary triangles. By applying barycentric sub-division, the primary triangles are decomposed into sub-triangles to create a mesh over the surface of the structure. Using graph theory, the triangular meshes are defined by the function, G (V, E), where V and E are the vertices and edges of the triangles in the mesh space, respectively. The connectivity matrix of shared edges is found by imposing a constraint on the edge length using metric spaces. This method approximates a square patch with 32 scalene triangles and shows that it can be used to reconstruct equilateral patches and doubly split double ring into mesh structures.

The extent and impact of exotic vine invasions in fragmented mesic forests in Eastern Australia

AbstractExotic vines threaten biodiversity causing damage to forest structure. We investigated the distribution of exotic vines across different patchily distributed plant communities. We surveyed patches of 12 threatened, mesic forest communities along the coastal plain in New South Wales, Australia to determine how exotic and native vine distribution and density were influenced by characteristics of forest patches and neighbouring land use. Vine density and stem widths were measured in quadrats in the edge and interior of patches. Canopy cover, number of dead trees, area to perimeter ratio and surrounding land use were recorded for each patch. Our results show that exotic vine assemblages were influenced by anthropogenic land use surrounding patches but not influenced by community type. Most exotic vine species were present across the whole region where surveys were undertaken. Exotic vines species were sometimes at high densities but had smaller stem widths than native species and there was no change in density from the edges into the interior. Araujia sericifera and Ipomoea cairica were the most prevalent exotic species and together with the fast edge growing Anredera cordifolia are of key concern. In contrast, native vine assemblages were species rich, with some individuals having large stem widths suggesting greater age and we found species composition varied with plant community type. Native vines showed continual recruitment and appeared more specialized to the attributes of each plant community. Surrounding anthropogenic land uses (residential, agricultural and industrial) were the most important factors predicting invasion of exotic vines and were more important than the length of edges. This suggests that the surrounding matrix characteristics were influencing degradation of the interior of these patches, rather than exotic vines invading along an invasion front from the edge. Exotic vines need to be controlled across the entirety of patches, rather than a focus on edge control practices.

Low‐Temperature Single‐Crystal Structure and Phonon Properties of A‐Site Ordered Double Perovskite CaMnTi2O6

AbstractWe have used high‐pressure methods to synthesize CaMnTi2O6 single crystals with edge lengths of up to 70 μm. Compared to previously reported synthetic pathways, we were able to use gold capsules and smaller pressures of 4 GPa. X‐ray diffraction analysis of the single crystals at low temperatures between 100 and 230 K confirmed that no phase transitions occur in this temperature range. We found square planar‐coordinated Mn ions to shift further out of the plane with lower temperatures which could lead to a higher polarization. The measured Raman spectrum of CaMnTi2O6 has been compared with quantum chemically calculated Raman spectrum to assign the vibrational modes. Calculated single‐crystal Raman spectrum has also been also analyzed from the point of view of direction dependency of the Raman intensities.

A novel sandwich ELISA method for quantifying CHI3L1 in blood serum and cerebrospinal fluid multiple sclerosis patients using sustainable photo-irradiated zero-valence gold nanoparticles

The widespread occurrence of chronic demyelinating MS presents a significant challenge for ongoing research aimed at comprehending its progression, diagnosis, and treatment. In our research, we have devised a novel approach to quantify CHI3L1 (Chitinase-3-like protein 1), which has emerged as a valuable biomarker in MS because of its involvement in inflammation, tissue remodeling, and immune response—crucial factors in regulating damaged nerve cells and preventing their accumulation in the brain, utilizing sandwich ELISA technology. This innovative method primarily depends on gold nanoparticles synthesized through a novel process of photo-irradiation with ultraviolet light. The crystal structure and particle size of sustainable zero-valent gold nanoparticles were measured using X-ray diffraction (XRD), which proved the cubic shape, with a cubic unit cell edge length of 4.0095 Å. The transmission electron microscopy (TEM) and field emission scanning electron microscope (FE-SEM) demonstrated that the distribution of Au NPs is uniform, with an average diameter of 22 nm. The UV–Vis spectrum, displaying a pronounced absorbance peak at a wavelength of 548 nm, suggests the presence of Au NPs. The optimal conditions for the formation of the Au-biotinylated antibody-HRP complex were studied. The optimum pH was 7, the dilution ratio of AuNPs with biotinylated antibody-HRP was 1:3, and the concentration of nanogold was (1 × 10−3 mg/ml) to avoid increasing it. Then a standard curve was drawn for this method and compared to the traditional method, and it was found to be twice as sensitive as the traditional method, with a high accuracy of CV% (3–6 %) as well as a rapid color generation for measurement. This method, based on gold nanoparticles that are considered a carrier for biotinylated antibody-HRP, was applied for the first time to measure CHI3L1 in the sera and cerebrospinal fluid of patients with multiple sclerosis, and the results demonstrated the accuracy and sensitivity of the method. The method has the potential to be an excellent tool for evaluating CHI3L1 and may have applications in other diseases for rapid diagnosis and timely treatment.

Effect of ultrasonic vibration on the roll bending deformation behavior of ultra-thin-walled corrugated sheets

The ultra-thin-walled corrugated sheet is a crucial component of metal honeycomb structures. Due to the size effect, the traditional roll bend forming process often leads to significant dimensional deviations in ultra-thin-walled corrugated sheets. To address this issue, an ultrasonic vibration-assisted roll bend forming process was proposed. First, an ultrasonic vibration-assisted roll bend forming device was designed, which had a special drive roller structure that can alter the original axial direction of ultrasonic vibration to produce a radial vibration with an amplitude of 0–2 µm. Under the high-frequency impact and acoustic softening effect of ultrasonic vibration, the ultra-thin-walled corrugated sheets formed numerous plastic penetration zones. As a result, the influence of individual grain heterogeneity was weakened and the stress distribution states underwent an interchange. Therefore, the ultra-thin-walled corrugated sheets demonstrated improved edge length uniformity, increased hardness in the deformed areas, reduced surface roughness, and decreased springback angle. However, excessive ultrasonic amplitude resulted in severe thinning or even rupture. Ultimately, high-quality ultra-thin-walled corrugated sheets were successfully fabricated using pure titanium foil with a t/d of 5.4 and an ultrasonic amplitude of 1.6 μm.

Coherent Phonon Dynamics in Plasmonic Gold Tetrahedral Nanoparticle Ensembles.

Coherent phonon modes supported by plasmonic nanoparticles offer prospective applications in chemical and biological sensing. Whereas the characterization of these phonon modes often requires single-particle measurements, synthetic routes to narrow size distributions of nanoparticles permit ensemble investigations. Recently, the synthesis of highly monodisperse gold tetrahedral nanoparticles with tunable edge lengths and corner sharpnesses has been developed. Herein, we characterize a size series of these nanoparticles in colloidal dispersion via transient absorption spectroscopy to examine their mechanical and plasmonic responses upon photoexcitation. Oscillations of transient absorption signals are observed in the plasmon resonance and correspond to the lowest-order radial breathing modes of the nanoparticles, the frequencies of which are affected by the edge length and truncation of the corners. Homogeneous quality factor values ranging from 24 to 34 are observed for the oscillations that convey potential utility in mass-sensing and plasmon-exciton-coupling photonics schemes. Finite-difference time domain and finite element analysis calculations establish specific optically relevant phonon modes.

Crashworthiness analysis of hierarchically reinforced double-square tubes under axial impact

Two strategies are proposed to design new hierarchically reinforced double-square tubes (HRDST). Strategy A: adding triangles from inside to outside in one direction. Strategy B: adding triangles along both the outer and inner quadrilateral directions at the same time. Their crashworthiness analyses are carried out under the conditions of the same wall thickness and the same mass. The results show that the proposed double square tubes, combined with the gradient hierarchical design, can effectively improve the crashworthiness of the structure under both conditions. The improvement of strategy B is more significant than that of strategy A. The energy absorption (EA), specific energy absorption (SEA), and crushing force efficiency (CFE) and initial peak crush force (IPCF) of HRDSTB-3 are improved by 2343.87%, 493.17%, 573.74% and 262.73%, respectively, under the same wall thickness. The EA, SEA, CFE of HRDSTB-3 also increased by 111.23%, 111.23%, and 226.34%, respectively, for the same mass, while the IPCF decreased by 35.27%. The parametric study shows that the effect of wall thickness on structural crashworthiness is significant, but the rate of increase between two adjacent wall thicknesses decreases as the wall thickness increases. The inner and outer edge length ratios (k) also have a substantial effect on structural crashworthiness, with SEA and CFE being 24.42% and 23.47% higher for k = 5/12 compared to k = 8/12 for HRDSTA-3, and 29.24% and 27.55% higher for k = 4/12 compared to k = 8/12 for HRDSTB-3. Finally, comparing HRDSTA-3 and HRDSTB-3 with other square-layered multicellular designs, the results show that the two designs proposed in this paper, combining double square tubes with gradient hierarchies, exhibit better crashworthiness. Compared with MSTL2-2, the SEA of HRDSTA-3 and HRDSTB-3 are 27.98% and 33.01% higher, respectively, and the CFE is 27.86% and 32.96% higher, respectively.

Targeted imaging of lysosomal zinc ions with a tetrahedral DNA framework fluorescent reporter.

Abnormal levels of zinc ions within endo-lysosomes have been implicated in the progression of Alzheimer's disease (AD), yet the detection of low-concentration zinc ions at the organelle level remains challenging. Here we report the design of an endo-lysosome-targeted fluorescent reporter, Znluorly, for imaging endogenous zinc ions. Znluorly is constructed from an amphiphilic DNA framework (DNF) with programmable size and shape, which can encapsulate zinc-responsive fluorophores within its hydrophobic nanocavity. We find that the tetrahedral DNFs of 20 bp in the edge length are effectively located within endo-lysosomes, which can detect zinc ions with a detection limit of ∼31.9nM (a sensitivity that is ∼2.5 times that of the free fluorophore). Given the organelle-targeting ability and high zinc sensitivity of Znluorly, we employ it to detect endogenous endo-lysosomal zinc ions in neuron cells. We monitor the dynamics of zinc levels in AD model cells and zebrafish, corroborating the positive correlation between zinc levels and AD hallmarks including Aβ aggregates and learning/memory impairments. Our study provides a generalizable strategy for organelle-specific theranostic applications.

Efficiently shape-selective synthesis of single crystal silver nanocube with the combination of HNO3/NaCl and reaction time for developing surface enhanced Raman scattering (SERS) substrate

Shape control of noble nanomaterials has garnered significant attention in the past decade because niche applications rely on the relationship between the nanoparticle morphology and optical properties. Although many chemical methods have been reported, there is still a need for improvement in terms of uniformity, yields, and synthesis scale. This work exploited the novel modification approach based on the polyol method to control synthesis to obtain a high amount of single-crystal silver nanocubes (AgNCs) with relatively homogeneous sizes and edge lengths of approximately 100 nm. Furthermore, we have discovered the high effectiveness of controlling temperature conditions to examine the conversion from silver nanocubes to tetrahedron nanoparticles, which had been rarely studied before. These as-prepared AgNCs colloidal solutions were further used to develop the SERS substrate on the glass slide through the facile drop cast method. Additionally, through synthesis using ethylene glycol and redispersed in the ethanol solvent, the obtained AgNCs have a high probability coverage on the glass slide once natural evaporation technique to achieve a remarkable amplification effect and reproducibility behavior. It was explored that these substrates could significantly enhance the Raman signal of 4-mercaptobenzoic acid (4-MBA), which is utilized as the probe molecule to assess the SERS behaviors. The enhancement factor (EF) of the SERS substrates prepared using AgNCs was approximately 3.6 × 106. The presence of 4-MBA could be detected with AgNCs in concentrations ranging from 0.01 to 10 mM, with a limit of detection (LOD) of 8.40 μM and a limit of quantification (LOQ) of 25.46 μM. Through analyzing over 20 different spots on various AgNC substrates, synthesized with similar methods and conditions, the Raman signals of 4-MBA were almost unchanged, with a relative standard deviation (RSD) value of 5.81%, indicating that the SERS signal produced by AgNC substrates was highly reproducible. Based on the results, the SERS nanosubstrates developed with AgNCs could potentially be used to detect trace amounts of other harmful organic compounds.

Quantification of bone microarchitecture using photon-counting CT at different radiation doses: A comparison with µCT

PurposeAccurate measurements of trabecular bone microarchitecture are required for a proper assessment of bone fragility. Photon-counting detector CT (PCD-CT) has different technical properties than conventional CT, resulting in higher resolution and thereby potentially enabling in-vivo measurement of trabecular microarchitecture. The purpose of this study was to quantify trabecular bone microarchitectural parameters with PCD-CT at varying radiation doses and compare this to µCT as gold standard. MethodBoth distal radii, distal tibiae, femoral heads, and two vertebrae were dissected from one human. All specimens were scanned ex-vivo on a PCD-CT system (slice increment 0.1 mm; pixel size 0.1042–0.127 mm) and a µCT system (isotropic voxel size 49–68.4 µm). The radiation doses of the PCD-CT scans were varied from 2.5 to 120 mGy based on the volume CT dose index (CTDIvol32). For the PCD-CT scans, contrast-to-noise ratio and trabecular sharpness were calculated and compared between radiation doses. µCT and PCD-CT scans were registered. The trabecular bone was then segmented from all PCD-CT and µCT scans and split into cubes with 6-mm edge length. For each cube, bone volume over total volume, trabecular thickness, trabecular number, and trabecular heterogeneity were calculated and compared between corresponding PCD-CT and µCT cubes. ResultsWith increasing dose, contrast-to-noise ratio and trabecular sharpness values increased for the PCD-CT images. Already at the lowest dose, high correlations between the trabecular microarchitectural parameters between µCT and PCD-CT were found (R2 = 0.55–0.95), which improved with increasing radiation dose (R2 = 0.76–0.96 at 20 mGy). ConclusionsPCD-CT can be used to quantify trabecular bone microarchitecture, with accuracy comparable to µCT and at clinically relevant radiation doses.