Edge Length Research Articles

Numerical Investigation on Dynamic Response of Carbon Fiber Honeycomb Sandwich Panels Subject to Underwater Impact Load

This study investigates the dynamic response and failure mechanisms of carbon fiber honeycomb sandwich structures under underwater impact loads using finite element numerical simulation. The geometric modeling was performed using HyperMesh, and the dynamic response simulations were carried out in ABAQUS, focusing on honeycomb core configurations with varying edge lengths, heights, and gradient forms. The Hashin damage model was employed to describe the damage evolution of the composite materials. The simulation results revealed that the dynamic response was significantly influenced by the initial shock wave pressure and the geometrical parameters of the honeycomb cells. Larger cell-edge lengths and heights generally resulted in improved energy absorption and reduced rear panel displacement. Among the different configurations, interlayer gradient honeycomb structures demonstrated superior impact resistance compared to homogeneous and in-plane gradient structures, particularly under higher initial shock wave pressures. These findings contribute to optimizing the design of carbon fiber honeycomb sandwich structures for enhanced impact resistance in relevant applications.

Enhancement of n-butanol sensing performance of porous ZnO flakes by decorating Ag nanoparticles

This study designs to investigate a high-performance n-butanol gas sensor with a porous morphology. Porous ZnO flakes modified with Ag particles are prepared in two steps using hydrothermal and precipitation methods. Morphological analysis of the samples shows that the ZnO flakes were covered with mesopores with high porosity, and their edge lengths ranged from 3 μm to 6 μm, with a minimum thickness of 11.3 nm. Through rigorous gas sensing testing, we find that the optimal mass percentage Ag-ZnO sensor provided significantly better sensing behavior, with a 100.8 response for 100 ppm n-butanol, compared to 14.5 for the pure ZnO sensor, a 5.95-fold improvement. In addition, the sensor's optimal operating temperature is reduced from 290 °C to 190 °C, increasing its adaptability and versatility in practical applications. In subsequent tests, it is found that this Ag-ZnO sensor not only shows excellent selectivity to n-butanol but also favorable stability, with no significant degradation during 30 days of continuous testing. The experimental analysis shows that the formation of porous flake structure and the modification of Ag particles are effective approaches to improve the ZnO gas sensor.

Solving the area-length systems in discrete gravity using homotopy continuation

Abstract Area variables are intrinsic to connection formulations of general relativity, in contrast to the fundamental length variables prevalent in metric formulations. Within 4D discrete gravity, particularly based on triangulations, the area-length system establishes a relationship between area variables associated with triangles and the edge length variables. This system is comprised of polynomial equations derived from Heron’s formula, which relates the area of a triangle to its edge lengths. Using tools from numerical algebraic geometry, we study the area-length systems. In particular, we show that given the ten triangular areas of a single 4-simplex, there could be up to 64 compatible sets of edge lengths. Moreover, we show that these 64 solutions do not, in general, admit formulae in terms of the areas by analyzing the Galois group, or monodromy group, of the problem. We show that by introducing additional symmetry constraints, it is possible to obtain such formulae for the edge lengths. We take the first steps toward applying our results within discrete quantum gravity, specifically for effective spin foam models.

Synthesis and characterization of octahedron and cube shape Mn0.5Zn0.5Fe2O4 particle dispersion for magnetic fluid hyperthermia

The present work reports a synthesis of octahedron (A55NO) and cube-shaped (A55NC) Mn0.5Zn0.5Fe2O4 ferrite nanoparticle dispersion in distilled water. The crystal structure analyzed using powder X-ray diffraction (XRD) shows the crystallite sizes of 17.7 ± 0.4 nm and 11.9 ± 1.0 nm, respectively, for the A55NO and A55NC particles. The morphology as seen from transmission electron microscopy (TEM) confirms 17.8 ± 0.3 nm (σ = 0.27) and 8.7 ± 0.3 nm (σ = 0.33) edge lengths, respectively, for octahedron and cube-shaped particles. The thermogravimetric analyzer (TGA) and Fourier transform infrared (FTIR) spectroscopy are used to confirm the chemical binding of the surfactant with a sharp transition at 208.67 °C and 218.32 °C, respectively, for octahedron and cube-shaped particles, indicating the removal of the surfactant due to its decomposition from the particle surface. Both the particles are highly magnetic and have 75.32 Am2/kg and 72.93 Am2/kg saturation magnetization, as revealed by their M − H loops using a vibrating sample magnetometer (VSM). The stability of the sample is confirmed using the particle size analyzer (DLS) and the Zeta potential analyzer. The induction heating capacity of the fluid was investigated using the Embrell Easy Heat model LA6310 at 330 kHz. The heating response shows that even a minimum concentration of 1 mg/mL is sufficient to achieve the hyperthermic window temperature of 42 °C for both samples, which, unlike the same composition prepared by other routes, makes it impossible to go beyond 38 °C. Moreover, octahedron particle dispersion can reach this window temperature within 10 min, whereas cube particle dispersion requires only 15 min. The findings of this study hold significant practical value since it confirms that Mn0.5Zn0.5Fe2O4 composition with tuneable shape has the potential to work as a temperature-controlled magnetic switch for magnetic fluid hyperthermia under the defined safety limit with the minimum concentration.

Efficient Path Planning Algorithm Based on Laser SLAM and an Optimized Visibility Graph for Robots

Mobile robots’ efficient path planning has long been a challenging task due to the complexity and dynamism of environments. If an occupancy grid map is used in path planning, the number of grids is determined by grid resolution and the size of the actual environment. Excessively high resolution increases the number of traversed grid nodes and thus prolongs path planning time. To address this challenge, this paper proposes an efficient path planning algorithm based on laser SLAM and an optimized visibility graph for mobile robots, which achieves faster computation of the shortest path using the optimized visibility graph. Firstly, the laser SLAM algorithm is used to acquire the undistorted LiDAR point cloud data, which are converted into a visibility graph. Secondly, a bidirectional A* path search algorithm is combined with the Minimal Construct algorithm, enabling the robot to only compute heuristic paths to the target node during path planning in order to reduce search time. Thirdly, a filtering method based on edge length and the number of vertices of obstacles is proposed to reduce redundant vertices and edges in the visibility graph. Additionally, the bidirectional A* search method is implemented for pathfinding in the efficient path planning algorithm proposed in this paper to reduce unnecessary space searches. Finally, simulation and field tests are conducted to validate the algorithm and compare its performance with classic algorithms. The test results indicate that the method proposed in this paper exhibits superior performance in terms of path search time, navigation time, and distance compared to D* Lite, FAR, and FPS algorithms.

Molecular Structural Characteristics and 3D Model Reconstruction of Organic Matter in Longmaxi Formation Shale.

The establishment of molecular structure modeling is an important means to study the pore characteristics of shale organic matter and is significant for molecular-level simulations of gas storage and diffusion. Using 13C NMR, FTIR, and XPS combined with the split-peak fitting technique, the structural characteristics of the aromatic structure, aliphatic structure, and oxygen functional groups of kerogen from the shale of the Longmaxi Formation, Wuxi County, Chongqing Municipality, were quantitatively characterized. A macromolecular structure model of the kerogen was also constructed by using the 2D macromolecular structure model construction method in combination with elemental analysis experiments. The results showed that the 2D single-molecule structural model of the sample consisted of 2 benzenes, 2 naphthalenes, 1 anthracene, 5 pyrenes, 1 pyridine, and 1 pyrrole. The C skeleton types were 93 protonated arylons, 39 bridged arylons, 6 carboxylons, 5 alkyl-substituted carbons, 2 oxygen-substituted carbons, 4 methylene carbons, and 3 methylons. The established 2D molecular structure formula was C152H82O12N2. The final 3D macromolecular structure model consisted of 14 2D molecular structures (structural formula C2128H1148O168N28), with the density set to 1.77 cm3/g, compressed in a cubic cell with an edge length of 3.05 nm. Finally, the adsorption results showed that the experimental adsorption of CO2 adsorption was less than the simulated adsorption, completing the validation of the model. The above study provides a method for determining the molecular structure of kerogen in the Longmaxi Formation shale, which can guide the study of the pore structure characteristics of the Longmaxi Formation shale.

Influence of Remote Laser Cutting on Magnetic Loss and Mechanical Properties in 0.2 mm Silicon Steel

Energy loss due to eddy current generation is a significant factor in reduced efficiency of electrical machines, therefore motor cores with thinner sheets are required due to their effect in reducing eddy currents. However, reducing the thickness of laminations is challenging due to the high tooling costs in blanking due to the small tolerances required, whilst other methods such as conventional laser cutting are too slow to be commercially viable. In this paper the influence of remote laser cutting on thin electrical steel sheets (Cogent/Tata Steel NO20 3.2% Si) has been investigated on the tensile strain to fracture, fatigue life, edge hardness, and energy loss in an AC magnetisation cycle for two laser power levels. The laser power has found to have no statistically significant influence on the bulk mechanical properties of the material, but significantly affects the measured specific loss. The latter was associated with the increased edge hardness at higher laser powers. Based on the parameters selected it is highly questionable whether RLC offers a viable method for lamination cutting, significant refinement of the laser parameters and/or the use an alternative laser such as an ultra-fast pulsed laser is required to be competitive with existing methods. Additionally, it is shown that energy loss increases linearly with respect to length of the cut edge - to the minimum cut spacing tested of 6 mm. These results can be used to optimise laser parameters to reduce the degradation of magnetic properties by decreasing laser power where possible.

Development of a Simple Analytical Model to Facilitate Preoperative Surgical Planning in Valve-Sparing Aortic Root Replacement.

Valve-sparing root replacement (VSRR) is attractive for aortic root dilation as it preserves the native aortic valve (AoV). Low effective height (eH) after reconstruction is a risk factor for repair failure and reoperation. We developed and validated a quantitative AoV repair strategy to reliably restore normal valve proportions to promote long-term function. Normal AoV proportions were used to derive geometric relationships for sinotubular junction diameter (DSTJ), free edge length (FEL), free edge angle, and commissure height. These relationships informed two models for predicting eH following VSRR: (1) assuming valve symmetry and (2) accounting for valve asymmetry. Porcine heart (n = 6) ex vivo validation was performed under 4 VSRR scenarios: "Ideal" (tube graft size targeting FEL/DSTJ = 1.28), "Oversized" (one graft size larger than Ideal), "Undersized" (two sizes smaller), and "Undersized + Plicated" (FEL/DSTJ = 1.28 restored with leaflet plication). Our analytical models predicted eH using preoperative measurements and estimated reconstructed dimensions. The Oversized graft exhibited similar eH to Ideal but higher regurgitation in the ex vivo model, whereas the Undersized graft demonstrated lower eH and regurgitation. Plication in the Undersized graft restored valve function (regurgitation & eH) similar to Ideal in the ex vivo model and above Ideal in the analytical models. Both analytical models predicted ex vivo eH well except in the Oversized and Undersized + Plicated conditions. Utilizing measurements from preoperative imaging and simple mathematical models, patient-specific operative plans for VSRR can be created by estimating valve dimensions necessary to achieve favorable valve features post-repair. Clinical application of this approach promises to improve consistency in achieving optimal long-term dimensions and durability.

Optimally Ordered Orthogonal Neighbor Joining Trees for Hierarchical Cluster Analysis.

We propose to use optimally ordered orthogonal neighbor-joining (O 3 NJ) trees as a new way to visually explore cluster structures and outliers in multi-dimensional data. Neighbor-joining (NJ) trees are widely used in biology, and their visual representation is similar to that of dendrograms. The core difference to dendrograms, however, is that NJ trees correctly encode distances between data points, resulting in trees with varying edge lengths. We optimize NJ trees for their use in visual analysis in two ways. First, we propose to use a novel leaf sorting algorithm that helps users to better interpret adjacencies and proximities within such a tree. Second, we provide a new method to visually distill the cluster tree from an ordered NJ tree. Numerical evaluation and three case studies illustrate the benefits of this approach for exploring multi-dimensional data in areas such as biology or image analysis.

Novel additively manufactured dihedral tiling architected metamaterial conformed with pentagon and rhombus: design and mechanical properties

The design of novel mechanical metamaterials has drawn inspiration from several sources to develop new structures. Additionally, additive manufacturing has widened the possibilities for producing intricate geometries. With this in mind, a novel architected metamaterial based on dihedral tiling is presented here, and its mechanical response is characterized experimentally. The architecture comprises two shapes: a pentagon and rhombuses, arranged in a manner dependent on each other. Three parameters were defined as variables to generate several design variations and analyze the impact of geometry on their effective mechanical properties: pentagon edge length (l), pattern rotation angle (θ), and strut thickness (t). For this purpose, the selected designs were additively manufactured using Thermoplastic Polyurethane (TPU) and tested under compression. It was found that t is directly proportional to relative density, and consequently, to apparent stiffness, while l is inversely proportional to both properties. On the other hand, θ has a minor influence on apparent stiffness and is more related to the deformed shape obtained. Overall, it was observed that the response depends on the combination of all geometrical parameters, meaning the apparent properties cannot be related to the response of only one of the shapes. This behavior differs from lattices based on a singular shape, in which the properties of the whole metamaterial are usually related to those of the unit cell.

Heat Kernel Asymptotics for Scaling Limits of Isoradial Graphs

AbstractWe consider the asymptotics of the discrete heat kernel on isoradial graphs for the case where the time and the edge lengths tend to zero simultaneously. Depending on the asymptotic ratio between time and edge lengths, we show that two different regimes arise: (i) a Gaussian regime and (ii) a Poissonian regime, which resemble the short-time asymptotics of the heat kernel on (i) Euclidean spaces and (ii) graphs, respectively.

Deep masseteric triangular area to define masseter neurovascular bundle: A cadaveric study

IntroductionFacial reanimation procedures are used in the treatment of the disorder that impairs mimetic function and jeopardizes physical and psychological health, and one of the most important instruments of these techniques is the masseteric neurovascular bundle (NVB) and proper identification at the mandibular notch level. In the current study, a triangular area (deep masseteric triangle, DMT) on the lateral surface of the masseter muscle that was identified to help reliable determination of the masseteric NVB at the mandibular notch level. Material and methods40 parotideomasseteric region dissections were performed in 10 female and 10 male donated cadavers. Structures lateral to the masseter muscle were removed. The edge length of the masseter muscle on the zygomatic arch side was measured. After the edges of the DMT were measured, the masseteric NVB was found by dissection and its distance (depth) from the skin line was measured. ResultsThe mean lengths of the superior, posterior, and anterior margins were 17.3 (±4.5) mm, 25.9 (±6.2) mm, and 26.3 (±6.5) mm, respectively. The total length of the upper edge of the masseteric muscle attached to the zygomatic arch averaged 52.7 (±5.2) mm. The masseteric neurovascular bundle was detected at a depth of approximately 17 mm from the skin of the parotideamasseteric region. DiscussionThe visualization of the DMT can be used as an important landmark for access to branch-free part of the masseteric nerve. Moreover, an specific approach for masseteric NVB localization can be established by drawing a line between the mandibular angle and the midpoint of the upper edge of the DMT. This technique can greatly improve the accuracy of both masseteric nerve harvesting and masseteric nerve block procedures.

Crashworthiness study of double square gradient hierarchical tubes

A new type of bi-double square gradient hierarchical tube (DSGHT) is proposed, and its crashworthiness under consistent wall thickness is analyzed. The results show that the energy absorption (EA), specific energy absorption (SEA), and crush force efficiency (CFE) of DSGHT3 are increased by 1305.14%, 430.14%, and 469.50%, respectively, compared to DSGHT0. The combination of double square tubes and gradient laminar design effectively enhances the crashworthiness of the structure. A parametric study indicates that increasing wall thickness significantly improves crashworthiness, with EA, SEA, and CFE improvements of 805.75%, 125.83%, and 126.83%, respectively, at a wall thickness of 0.8 mm compared to 0.2 mm. However, the effect of wall thickness gradient distribution on structural crashworthiness is minimal. Conversely, the ratio of the inner to outer square tube edge length (δ) significantly impacts crashworthiness; SEA and CFE increase by 37.77% and 37.35%, respectively, when δ is 6/12 compared to 8/12. Finally, DSGHT3 was compared to other hierarchical, tree-shaped fractal structures, and it demonstrated superior crashworthiness. Specifically, DSGHT3 has 35.32% and 34.29% higher SEA and CFE, respectively, compared with MSTL2-2.

Uniquely Realisable Graphs in Analytic Normed Planes

Abstract A framework $(G,p)$ in Euclidean space $\mathbb{E}^{d}$ is globally rigid if it is the unique realisation, up to rigid congruences, of $G$ with the edge lengths of $(G,p)$. Building on key results of Hendrickson [28] and Connelly [14], Jackson and Jordán [29] gave a complete combinatorial characterisation of when a generic framework is global rigidity in $\mathbb{E}^{2}$. We prove an analogous result when the Euclidean norm is replaced by any norm that is analytic on $\mathbb{R}^{2} \setminus \{0\}$. Specifically, we show that a graph $G=(V,E)$ has an open set of globally rigid realisations in a non-Euclidean analytic normed plane if and only if $G$ is 2-connected and $G-e$ contains 2 edge-disjoint spanning trees for all $e\in E$. We also prove that the analogous necessary conditions hold in $d$-dimensional normed spaces.

A nonparametric measure of contrast in x-ray images

Objective. We propose a nonparametric figure of merit, the contrast equivalent distance CED, to measure contrast directly from clinical images. Approach. A relative brightness distance δ is calculated by making use of the order statistic of the pixel values. By multiplying δ with the grey value range R, the mean brightness distance MBD is obtained. From the MBD, the CED and the distance-to-noise ratio DNR can be derived. The latter is the ratio of the MBD and a previously suggested nonparametric measure τ for the noise.Since the order statistic is independent of the spatial arrangement of the pixel values, the measures can be obtained directly from clinical images. We apply the new measures to mammography images of an anthropomorphic phantom and of a phantom with a step wedge as well as to CT images of a head phantom. Main results. For low-noise images of a step wedge, the MBD is equivalent to the conventional grey value distance. While this measure permits the evaluation of clinical images, it is sensitive to noise. Therefore, noise has to be quantified at the same time. When the ratio σ/τ of the noise standard deviation σ to τ is available, validity limits for the CED as a measure of contrast can be established. The new figures of merit can be calculated for entire images as well as on regions of interest (ROI) with an edge length not smaller than 32 px.Significance. The new figures of merit are suited to quantify the quality of clinical images without relying on the assumption of a linear, shift-invariant system. They can be used for any kind of greyscale image, provided the ratio σ/τ can be estimated. This will hopefully help to achieve the optimisation of image quality vs dose required by radioprotection laws.

Experimental study on compression properties of composite aluminum honeycomb sandwich structures

AbstractThe mechanical properties of the carbon fiber and glass fiber composite honeycomb sandwich structure were studied through compression experiments. The influence of different aluminum honeycomb edge lengths, upper and lower panel thickness, aluminum honeycomb thickness, and loading speed on the compression failure load of carbon fiber composite laminates sandwich structure is analyzed. The influence of different aluminum honeycomb edge lengths and thicknesses on the compression failure load of glass fiber composite laminates sandwich structure was studied. The results show that the thickness of the panel has a significant effect on the failure load of the carbon fiber composite laminate sandwich structure, and the loading speed has a significant effect on the failure load of the carbon fiber composite laminate sandwich structure. The greater the loading speed, the greater the value of the failure load. The edge length and thickness of the aluminum honeycomb have a certain effect on the damage load of the carbon fiber composite laminates sandwich structure, but the influence on the mechanical properties of the glass fiber composite laminates sandwich structure is much greater.Highlights The compression performance of composite sandwich structures was experimentally studied. The influence of composite panel thickness was studied. The influence of aluminum honeycomb edge length and thickness was studied. The influence of loading speed was studied.

An experimental feasibility study of a 4π gamma-ray imager using detector response patterns

We constructed a gamma-ray imager that estimates the distribution of gamma-ray sources based on the response patterns of multiple gamma-ray detectors randomly positioned in three-dimensional space. The Coded Cube Camera for Gamma-ray (C3G), comprising eight Gd3Al2Ga3O12 (Ce) scintillator and eighteen lead cubes is housed in a cubical casing with an 86 mm edge length and weighs approximately 600 g. The results of the 4π imaging experiment confirmed the feasibility of imaging a 10 MBq 137Cs source 3 m away for a 10 min measurement. C3G operates with only eight channels, instead of the hundreds needed by a typical imager. This setup allows for a simplified circuit and reconstruction algorithm, resulting in a cost-effective and reliable system. With its compact and lightweight design and 4π field of view, this technology is expected to find extensive applications in astronomy, medicine, nuclear security, and decommissioning projects.

Morphometric features of larvae of the mussel Mytilus galloprovincialis (Lamarck, 1819) (Bivalvia: Mytilidae) in ontogenesis

Sequentially appearing in ontogenesis, the morphometric features of mussel Mytilus galloprovincialis larvae can serve as a basis for their species identification among the pool of larvae of other bivalve mollusc species found in the Black Sea plankton. The study presents the photographs of live mussel larvae and scanning electron microscope (SEM) images of the larvae hinge at different developmental stages: D-veliger, veliger, veliconcha and pediveliger. There was shown the sequence of morphological changes in provinculum, as well as the shell’s size and shape changes, from the earliest straight-hinge stage of veliger up to metamorphosis. The correlation between shell width (C, µm) and shell length (L, µm) [ ; R2 = 0.9879], as well as the correlation between hinge edge length (l, µm) and shell length (L, µm) [ ; R2 = 0.9872] were determined for mussel larvae ranging in size from 98 to 350 µm. By employing energy dispersive X-ray spectroscopy EDS(x), the elemental composition of the larvae shell’s hinge edge at the stages of veliger, veliconcha and pediveliger was determined; and it showed the presence of calcium, carbon, oxygen, sodium and chlorine. Magnesium was detected in pediveligers’ hinge edge only.

Optical properties of CeF3 crystal at high temperature or pressure by first principles and its application in isolators

In this work, CeF3 single crystal was successfully grown by Bridgman method. The XRD diffraction was tested and the data matched well with the standard card. Further trying its optical performance, CeF3 single crystal has very high transmittance of 90 %, the cut-off absorption edge length of the crystal is better than 300 nm. Testing the magneto-optical Verdet constant of CeF3 single crystal and trial-produced optical isolator shows that the Verdet constants of CeF3 single crystals in the magneto-optical field are similar to those of TGG crystals. The band structure, state density, optical properties and elastic constants of CeF3 crystal under different temperature and pressure are calculated by first principles. The results show that CeF3 crystal has excellent thermal stability and mechanical stability. Under high temperature conditions, light absorption and loss are small, and the optical properties are stable. Under high pressure, the crystal exhibits certain stability and impact resistance, and the optical properties are relatively stable. The results show that CeF3 crystal has significant advantages in replacing TGG crystal in laser field, and has a certain application prospect in window materials.

In plane mechanical properties of hexagonal V-chiral and Tri-chiral metamaterials

The reasonable design of man-made multifunctional metamaterials with advanced mechanical and physical properties that are not found in nature is both challenging and important. In this paper, novel chiral structures are designed by adding V- and Tri- chiral elements to the typical hexagonal honeycomb substrate, so as to realize the modulation of in plane mechanical properties. Finite element simulations show that the Poisson's ratio of the hexagonal V-chiral structure is negative when the strain is greater than 0.4, and that of the hexagonal Tri-chiral structure is always negative. Quasi-static compression tests show that the introduction of chiral properties results in a stronger load-bearing capacity, and the hexagonal Tri-chiral structure has a stronger energy absorption (EA) and specific energy absorption (SEA) capability. A parametric study is carried out by means of FEM, by adjusting the geometrical parameters of the proposed structures, the performance in terms of energy absorption and compressive stiffness can be improved. Subsequently, Bloch-Floquet theorem is employed for the dispersion relations of the chiral metamaterials and the results show that compared to conventional hexagonal honeycomb, chiral metamaterials are able to generate band gaps in a lower frequency range. Numerical simulation results show that the bandwidth of the proposed novel chiral metamaterials can be tuned through a reasonable selection of hexagonal edge length, wall thickness and radius. Experimental investigations are conducted to test the vibration transmission rate of Structure Ⅲ, and the results prove that the structure is capable of vibration suppression in the target frequency band range. Finally, by filling Structure Ⅲ with steel columns, the structure generates band gaps in the lower frequency range, hence the application of this chiral metamaterial is broadened.