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During the process of five-axis free-form milling, tool orientation and surface curvature of the workpiece have significant effects on tool wear. Five-axis milling experiments are carried out on 17-4PH stainless steel using a carbide ball end mill. The influence of tool orientation on the amount of wear, cutting force, and chip morphology of the ball end cutter was investigated. The results show that tool wear is slighter at a tool inclination angle of approximately 15°, reducing tool wear by up to 29.55% compared with other angles. The inclination angle also has great effects on the milling force and torque signals, a suitable tool inclination angle makes the milling force and torque signals smooth, and the standard deviation is only 0.94 N and 0.017 N·m, respectively. In addition, the chips can reflect the stability of the machining process to some extent. On this basis, different workpiece surfaces were selected to investigate the effect of workpiece surface characteristics on tool wear. The results show that more severe tool wear and higher milling force signals on curved surfaces occurred with smaller radii of curvature. An appropriate tool orientation in relation to the curvature of the workpiece surface can significantly reduce tool wear; concave surfaces are suitable for machining with small angle of inclination, e.g., 5° ~ 10°, whereas convex surfaces are suitable for machining with larger angle of inclination, e.g., 20° ~ 25°. [ABSTRACT FROM AUTHOR]

Multi-view stereo (MVS) can fulfill dense three-dimensional reconstruction from a collection of multi-view images. Although deep learning-based MVS has significantly enhanced the reconstruction performance, the reconstruction accuracy and completeness still require improvements to meet the need of real applications of three-dimensional content generation. So, a new MVS method, the curvature-guided multi-view stereo with transformers, is presented. By exploring inter-view relationships and measuring the size of the receptive field and feature information on the image surface using the surface curvature, the proposed method adapts to various candidate scales of curvatures to extract more detailed features adaptively for precise cost computation. Furthermore, a transformer-based feature-matching network is proposed to identify inter-view similarity better and enhance feature-matching accuracy. Additionally, a similarity measurement module based on feature matching integrates curvature and inter-view similarity measurement tightly to further improve reconstruction accuracy. Experiments on the DTU dataset and Tanks and Temples dataset validate the proposed method. [ABSTRACT FROM AUTHOR]

Currently, hybrid noble metal nanostructures have garnered significant interest due to their exceptional properties and diverse applications in fields such as catalysis, energy conversion, plasmonic sensing, and surface-enhanced Raman scattering (SERS). In this work, we report the highly site-specific growth of a single Ag island on both the concave face and the sharp tip of concave Au nanocube (c-AuNC) seeds, resulting in different c-AuNC-Ag Janus heterostructures. This site specificity was achieved by combining the surface curvature effect of the c-AuNCs with strong ligand-mediated interfacial energy control. Further integration of interfacial energy and growth kinetic control led to the formation of c-AuNC-(Ag)n core–satellite structures with varying numbers of Ag satellites. Benefiting from the continuous tunability of the interfacial energy and growth kinetics, the structural evolution of the c-AuNC-Ag hybrid structures continuously occurred, enabling precise control of the Au–Ag bimetallic structures. Notably, the resulting c-AuNC-Ag structures showed tunable intense localized surface plasmon resonance (LSPR) absorptions within the 400–1000 nm wavelength along with strong SERS signals. The broad spectral absorption and strong SERS made the c-AuNC-Ag structures promising candidates for SERS and LSPR-based applications, including sensing, imaging, light energy harvesting, and conversion. Moreover, the effective synthetic control demonstrated in this work could facilitate the development of advanced hybrid metal nanomaterials with valuable properties, further broadening their application potential across various fields. [ABSTRACT FROM AUTHOR]

Columns in traditional timber structures are commonly seen resting on stone bases and are very important in resisting lateral loads. This paper numerically modeled the lateral resistance of the columns combined with experimental investigation. Different numerical models were developed, based on which sensitivity analyses were performed. A practical numerical modelling strategy was further proposed and verified. The analysis results indicated that instead of material properties and contact area, the columns' lateral performance was much more sensitive to the variation of surface curvature at bottom surface. Without consideration of the surface curvature, the modeling error in the initial stiffness and peak load of a column was more than 607% and 8%, respectively. By best matching the load–displacement curves of tested column specimens, the optimal surface curvature was identified as 1/20306.5 mm−1. Then, a practical finite numerical model, characterized by the optimal curvature at the bottom surface, was proposed. This modelling method was validated by use of existing test results of traditional timber columns with different diameters and vertical compression loads. The modelling load–displacement curves agreed well with experimental curves both in terms of the initial lateral stiffness and peak load. Detailed simulation results based on the practical modelling strategy were presented and discussed. [ABSTRACT FROM AUTHOR]

A model is proposed for the formation of the workpiece–tool contact zone in belt grinding of blades for gas turbine engines on CNC machine tools. The model takes account of fluctuation of the forces applied to the contact element; and the complex shape of the contact element and the workpiece. The Femlab modeling software employed permits assessment of the contact area and conclusions regarding the distribution of the belt pressure over the workpiece surface. [ABSTRACT FROM AUTHOR]

ABSTRACTWire and Arc Additive Manufacturing (WAAM) with high efficiency and low-cost is an economical choice for the rapid fabrication of medium-to-large-sized metallic components and has attracted great attention from scholars and entrepreneurs in recent years. However, defects such as porosity, and humps, could occur occasionally after each layer of deposition on weld bead surfaces due to disturbances and process abnormities. Detection and quantitative evaluation of weld bead defects is crucial to ensure successful deposition and the quality of the entire component. In this paper, a novel defect detection and evaluation system was developed for WAAM utilizing machine vision technology. The system incorporated new defect detection algorithms based on analysing the 2D curvature of the weld bead height curve and the 3D curvature of the weld bead point cloud. Furthermore, a defect evaluation algorithm was developed based on reconstructing the normal weld bead contour using geometric features extracted from the accumulated point cloud. This system enables the automatic detection of weld bead morphology during the WAAM process, offering important information about the location, type, and volume of defects for effective interlayer repairs and enhanced part quality.

Understanding bone surface curvatures is crucial for the advancement of bone material design, as these curvatures play a significant role in the mechanical behavior and functionality of bone structures. Previous studies have demonstrated that bone surface curvature distributions could be used to characterize bone geometry and have been proposed as key parameters for biomimetic microstructure design and optimization. However, understanding of how bone surface curvature distributions correlate with bone microstructure and mechanical properties remains limited. This study hypothesized that bone surface curvature distributions could be used to predict the microstructure as well as mechanical properties of trabecular bone. To test the hypothesis, a convolutional neural network (CNN) model was trained and validated to predict the histomorphometric parameters (e.g., BV/TV, BS, Tb.Th, DA, Conn.D, and SMI), geometric parameters (e.g., plate area PA, plate thickness PT, rod length RL, rod diameter RD, plate-to-plate nearest neighbor distance NNDPP, rod-to-rod nearest neighbor distance NNDRR, plate number PN, and rod number RN), as well as the apparent stiffness tensor of trabecular bone using various bone surface curvature distributions, including maximum principal curvature distribution, minimum principal curvature distribution, Gaussian curvature distribution, and mean curvature distribution. The results showed that the surface curvature distribution-based deep learning model achieved high fidelity in predicting the major histomorphometric parameters and geometric parameters as well as the stiffness tenor of trabecular bone, thus supporting the hypothesis of this study. The findings of this study underscore the importance of incorporating bone surface curvature analysis in the design of synthetic bone materials and implants. [ABSTRACT FROM AUTHOR]

This paper explores the superior performance of quaternion multi-layer perceptron (QMLP) neural networks over real-valued multi-layer perceptron (MLP) neural networks, a phenomenon that has been empirically observed but not thoroughly investigated. The study utilizes loss surface visualization and projection techniques to examine quaternion-based optimization loss surfaces for the first time. The primary contribution of this research is the statistical evidence that QMLP models yield smoother loss surfaces than real-valued neural networks, which are measured and compared using a robust quantitative measure of loss surface "goodness" based on estimates of surface curvature. Extensive computational testing validates the effectiveness of these surface curvature estimates. The paper presents a comprehensive comparison of the average surface curvature of a tuned QMLP model and a tuned real-valued MLP model on both a regression task and a classification task. The results provide strong support for the improved optimization performance observed in QMLPs across various problem domains. [ABSTRACT FROM AUTHOR]

A method of forming a curved orthogonal coordinate system on a plane and a technique of constructing new surface shapes with curved trapezoidal plans are presented. Multiple examples of curved trapezoidal plans based on different directrix curves and surfaces with the given plans, including combinations of surfaces with different conjugate directrix curves, are illustrated. The proposed technique of surface forming may be used in architecture and construction for development of thin-walled space structures in both urban and industrial buildings. But for the analysis of thin shells, geometric characteristics of the middle surface of the shell are usually used. Vector equation of surfaces with curved trapezoidal plan was used to obtain the formulas for the fundamental form coefficients and surface curvatures. Examples of calculation of the fundamental form coefficients and curvatures of surfaces with particular directrix curves and vertical coordinate functions are presented.

The curvature variation regularity of the blade surface is complex and requires a high level of machining accuracy. In order to research the influence of interpolation tolerance on the machining accuracy of blade surface at different positions, the non-uniform rational b-spline was used to build the blade surface and analyze the curvature variation regularity at different positions, and the distribution regularity of interpolation tolerance at different curvature positions on interpolation moving points was explored based on the NC (Numerical Control) program. In addition, the NC interpolation principle is used to analyze the effect of different interpolation tolerance parameters on the machining accuracy of blade surfaces, and the appropriate interpolation moving point coordinates were obtained through the five-axis coordinate system transformation theory, and the five-axis cutting simulation and experiment were carried out. The results show that there are many interpolation moving points at the position with large curvature. With interpolation tolerances of 0.1 mm, 0.03 mm and 0.003 mm, the interpolation errors obtained in the regions with large curvature are 0.005 mm, 0.0034 mm and 0.0025 mm, respectively. The smaller the interpolation tolerance, the smaller the interpolation error. What is more, the smaller the interpolation tolerance is, the more obvious the improvement of interpolation accuracy will be when the interpolation tolerance is reduced. Besides, when sampling length of 250 μm, the surface roughness (Ra) detected at the small curvature position and the large curvature position are 0.434 and 1.070μm respectively. The surface roughness is better in position with smaller curvature, however, it is worse in position with larger curvature. The analytical regularity is in good agreement with both simulation and experiment values. It provides a reference for improving NC machining accuracy for similar blade surfaces.

Polishing path optimization plays a crucial role in achieving high-quality and uniform surface polishing of free-form surfaces. To address the issue of uncontrollable ripple errors caused by uneven material removal in traditional contact polishing, this paper proposes an adaptive polishing path optimization method for uniform polishing of free-form surfaces based on footprint evolution. The presented approach considers the influence of curvature on footprint evolution and seeks to dynamically optimize the spacing between adjacent paths. This optimization ensures suitable overlap between neighboring footprints, ultimately leading to the achievement of uniform depth removal. Through modeling simulations and experimental comparisons involving different contact curvatures, it has been conclusively established that surface curvature plays a pivotal role in footprint evolution. Additionally, surface polishing experiments yielded results indicating a reduction in surface waviness within the central polishing area, decreasing from a root-mean-square value of 5.1766 to 4.1448 nm. These outcomes preliminary demonstrate the effectiveness of the proposed method. This study presents an efficient curvature adaptive path planning approach based on footprint evolution, offering new insights into achieving uniform polishing and suppressing waviness errors on free-form surfaces. [ABSTRACT FROM AUTHOR]

Understanding bone surface curvatures is crucial for the advancement of bone material design, as these curvatures play a significant role in the mechanical behavior and functionality of bone structures. Previous studies have demonstrated that bone surface curvature distributions could be used to characterize bone geometry and have been proposed as key parameters for biomimetic microstructure design and optimization. However, understanding of how bone surface curvature distributions correlate with bone microstructure and mechanical properties remains limited. This study hypothesized that bone surface curvature distributions could be used to predict the microstructure as well as mechanical properties of trabecular bone. To test the hypothesis, a convolutional neural network (CNN) model was trained and validated to predict the histomorphometric parameters (e.g., BV/TV, BS, Tb.Th, DA, Conn.D, and SMI), geometric parameters (e.g., plate area PA, plate thickness PT, rod length RL, rod diameter RD, plate-to-plate nearest neighbor distance NNDPP, rod-to-rod nearest neighbor distance NNDRR, plate number PN, and rod number RN), as well as the apparent stiffness tensor of trabecular bone using various bone surface curvature distributions, including maximum principal curvature distribution, minimum principal curvature distribution, Gaussian curvature distribution, and mean curvature distribution. The results showed that the surface curvature distribution-based deep learning model achieved high fidelity in predicting the major histomorphometric parameters and geometric parameters as well as the stiffness tenor of trabecular bone, thus supporting the hypothesis of this study. The findings of this study underscore the importance of incorporating bone surface curvature analysis in the design of synthetic bone materials and implants.

This paper aims to explore the influence of surface curvature distribution on the mechanical properties of lattice structures. In this study, a series of typical structure types were designed to obtain lattice structures with different surface Gaussian curvatures, including BCC (body center cubic) configuration, cross-cube configuration, and diamond lattice structure. Then, the above-mentioned porous structural sample was formed by SLM (selective laser melting), and the relevant mechanical properties were obtained by simulation and experiment. In addition, a characteristic method to describe the surface curvature of discrete triangular plaques is proposed and used to calculate the curvature distribution of the designed lattice structure. The results show that the lattice structure with concentrated Gaussian curvature distribution on the surface has good mechanical properties. Especially, for the cross-cube structure, the elastic modulus of the traditional configuration lattice structure increases by 79%, and the elastic modulus of the stretched structure increases by 70% when the volume fraction increased from 10 to 15%. Meanwhile, the elastic modulus for the traditional structure and the stretched structure increases by 41% and 14%, respectively, when the volume fraction of the structure increases from 15 to 20%. It is noted that the influence of surface curvature distribution on mechanical properties is slightly inferior to the volume fraction, which provides a new idea for the quantitative evaluation and design of porous structural properties. In addition, the BCC structure with concentrated curvature distribution provides a new scheme for the protection device after the stress climb stage after the elastic stage. Furthermore, the influence of surface curvature on the mechanical properties of lattice structures described in this paper will provide new inspiration for lattice structures in the fields of biocompatibility and heat exchange. [ABSTRACT FROM AUTHOR]

The problem of the size dependence of physical properties is one of the most intriguing when we transit to the nano-level. Experiments have shown that this effect is characteristic of the elastic modulus of many polymeric nanofibers obtained by electrospinning. Existing explanations of this effect did not offer a general understanding of the physical nature of this phenomenon. In this study, we propose a universal model of this phenomenon. We consider the structure of fibers within the framework of the core-shell model, in which the shell is approximated by a thin elastic surface. The analysis of deformation is based on the fundamental laws of the mechanics of deformation of twisted thin shells and, unlike the theories proposed earlier, does not require any additional artificial arguments. This approach made it possible to obtain a simple analytical expression for the size dependence of the elastic modulus, which represents it as the sum of the bulk modulus of the core and two additional moduli proportional to D–1 and D–3, respectively. The resulting model corresponds to all available (from published sources) experimental data, related to polymer of very different chemical structure, and therefore can be considered as universal.

We use the wave theory of light to study the brightness and the geometrical characteristics of bright stripes appearing on the bottom of a pool. The brightness of those stripes is linked to the distribution of refracted-light intensity in the vicinity of a caustics where the ray-optics approximation is inapplicable. The caustics arises whenever light is refracted on a wavy water surface. The relationships among the parameters of the surface waves and the width of the bright stripes (i.e., the caustic zone) are obtained. The correctness of our relationships is verified by the experiment carried out in a water pool. Our formulae can be used to develop the optical systems for determining the wave parameters (in particular, the sea-surface curvature on large scales) by recording the bright-stripes characteristics. [ABSTRACT FROM AUTHOR]

This paper reports a study to determine the tension of complex chemical threads made of Kevlar, carbon, polyethylene, and meta-aramid when interacting with the working bodies of knitting machines in the process of forming technical knitwear. An increase in tension after the guide surface of the working body due to a change in the value of the friction forces in the contact zone was established. It has been proven that the tension of the selected complex chemical threads after the guide surface of the working body is affected by the tension of the thread in front of the guide surface of the working body of the knitting machine. Also, the amount of tension is affected by the radius of curvature of the cylindrical guide surface of the working body and the angle of thread coverage of the guide surface of the working body of the knitting machine. This has made it possible to determine thread tension even at the initial stage of designing the technological process of thread processing on knitting machines, during the production of technical knitwear. On the basis of experimental studies for Kevlar, carbon, polyethylene, and meta-aramid complex threads, regression dependences of the stress after the cylindrical guide surface of the working body of the knitting machine were constructed. The analysis of regression dependences made it possible to establish the value of the radius of curvature of the guides when the tension of complex chemical threads before the knitting zone on knitting machines would take a minimum value. This will minimize the stress on complex threads during their processing. So, there are reasons to assert the possibility of directed regulation of the process of changing the tension of Kevlar, carbon, polyethylene, and meta-aramid complex threads during the formation of technical knitwear on knitting machines by selecting the value of the geometric parameters of the guides. [ABSTRACT FROM AUTHOR]

The problem of the size dependence of physical properties is one of the most intriguing when we transit to the nano-level. Experiments have shown that this effect is characteristic of the elastic modulus of many polymeric nanofibers obtained by electrospinning. Existing explanations of this effect did not offer a general understanding of the physical nature of this phenomenon. In this study, we propose a universal model of this phenomenon. We consider the structure of fibers within the framework of the core-shell model, in which the shell is approximated by a thin elastic surface. The analysis of deformation is based on the fundamental laws of the mechanics of deformation of twisted thin shells and, unlike the theories proposed earlier, does not require any additional artificial arguments. This approach made it possible to obtain a simple analytical expression for the size dependence of the elastic modulus, which represents it as the sum of the bulk modulus of the core and two additional moduli proportional to D-1 and D-3, respectively. The resulting model corresponds to all available (from published sources) experimental data, related to polymer of very different chemical structure, and therefore can be considered as universal. [ABSTRACT FROM AUTHOR]

Understanding the guest‐induced dynamic deformation process of covalent organic frameworks (COFs) is vitally important to further increase their stimulus‐response performances. Here we report on the dark‐field microscopic (DFM) imaging approach to in situ monitor the guest‐induced deformation evolution of individual COF‐300 crystals in real time. We observe not only transient and nonequilibrium intermediate deformation states but also local surface curvature‐driven diverse adsorption behaviours of single COF‐300 particles for dichloromethane (DCM), undergoing one, two, and multiple expansion‐contraction deformations as well as contraction‐to‐expansion transition. The surface curvature‐dominated deformations are ascribed to the significant differences in the adsorption capacity for DCM at the curved tip and flat side regions, in which DCM can be adsorbed preferentially by curved tip regions of COF‐300. [ABSTRACT FROM AUTHOR]

The individual influence of target dynamics, curvature, bio-inspired (Pangolin's scale) surface pattern, and presence of external ('V'-shaped) and spaced internal grooves ('M'-shaped) on ballistic performance of lightweight aluminum (6061-T6) target has been investigated. Target thickness of 10 mm and an armor piercing projectile of 9 mm diameter, 7.85 g weight were considered for the numerical simulation. The initial impact velocity of the projectile was varied in the range of 400 to 800 m/s. Compared to the static target, the exit velocity of the projectile was observed to be less (2.3%) for the dynamic target. When the target is moving, it significantly alters the penetration direction and increases the travel length of the projectile. When the 'α' of the target was increased (5 mm to 8 mm), significant improvement (3.63%) in ballistic performance was noted. Among the several conditions simulated, when the curved target received the projectile's impact at an offset distance (35 mm) from the center of the target showed a better performance (up to 10.7%). In addition an angular deflection (–5.1°) of the projectile from the center of the target was noted. Compared to curved targets, increased angular deflection (35°) of the projectile was observed for target having bio-inspired (pangolin's scale) pattern. This is due to cantilever action offered by the scaled pattern. Even though the presence of V-notch pattern could able to resist the projectile's impact, the ballistic resistance was observed to be marginal due to higher stress concentration at the notch root region. Compared to all other cases, the spaced internal grooves ('M' shape) inside the target, enhanced the ballistic resistance (72%) for groove dimensions of pitch and width of 3.5 mm and 0.5 mm. [ABSTRACT FROM AUTHOR]

To address the problem of low overall machining efficiency of free-form surfaces and difficulty in ensuring machining quality, this paper proposes a MATLAB-based free-form surface division method. The surface division is divided into two stages: Partition area identification and area boundary determination. In the first stage, the free-form surface is roughly divided into convex, concave, and saddle regions according to the curvature of the surface, and then the regions are subdivided based on the fuzzy c-means clustering algorithm. In the second stage, according to the clustering results, the Voronoi diagram algorithm is used to finally determine the boundary of the surface patch. We used NURBS to describe free-form surfaces and edit a set of MATLAB programs to realize the division of surfaces. The proposed method can easily and quickly divide the surface area, and the simulation results show that the proposed method can shorten machining time by 36% compared with the traditional machining method. It is proved that the method is practical and can effectively improve the machining efficiency and quality of complex surfaces. [ABSTRACT FROM AUTHOR]

Natural gas hydrate nucleation is a complex physical and chemical process that is not well understood presently. In this article, an improved thermodynamic model is proposed to analyze the effects of surface curvature and wettability on methane hydrate nucleation for the first time. The results indicate that methane hydrate nucleation is more difficult on hydrophilic curvature surfaces under the same conditions, with a larger critical nucleation radius and required energy barrier than on hydrophobic surfaces. Furthermore, a convex surface is more favorable for forming methane hydrate under the same conditions than a concave surface. The model's results are critical in elucidating the microscopic mechanism of methane hydrate nucleation and providing a theoretical foundation for developing technologies for strengthening and inhibiting hydrate formation. [ABSTRACT FROM AUTHOR]

In this paper, the grand canonical Monte Carlo (GCMC) method was used to explore the effects of four pore structures (disordered pore, wedge pore, carbon nanotube, and slit pore structures) and surface curvature of activated carbon on the adsorption and separation of CO2/N2. On the whole, carbon nanotubes have the greatest selectivity for CO2, followed by disordered pores, wedge pores, and slit pores. The effect of pore structure on the interaction energy of gas molecules is similar to that of selectivity, in which the fluid–solid potential energy between adsorbates and adsorbents plays an important role. Due to the different affinity between adsorbate molecules and activated carbon, CO2 with high affinity is more sensitive to the change of pore size. Therefore, under high pressure, the density of CO2 in the slit pore is greater than that in the wedge pore. However, N2 with poor affinity is limited by the surface area, resulting in the density of it in the wedge pore is always higher than that in the slit pore. Although the existence of non-six membered corannulene rings in activated carbon can't always cause the increase of specific surface area, the surface curvature of activated carbon caused by it can increase strong energetically adsorption sites. Hence, the surface curvature plays a positive role in the adsorption density, interaction energy, and CO2 selectivity. The discovery of CO2/N2 adsorption and separation at the molecular level is expected to provide valuable insights. [ABSTRACT FROM AUTHOR]

The structure of a protein plays a pivotal role in determining its function. Often, the protein surface's shape and curvature dictate its nature of interaction with other proteins and biomolecules. However, marked by corrugations and roughness, a protein's surface representation poses significant challenges for its curvature‐based characterization. In the present study, we employ unsupervised machine learning to segment the protein surface into patches. To measure the surface curvature of a patch, we present an algebraic sphere fitting method that is fast, accurate, and robust. Moreover, we use local curvatures to show the existence of "shape complementarity" in protein–protein, antigen–antibody, and protein‐ligand interfaces. We believe that the current approach could help understand the relationship between protein structure and its biological function and can be used to find binding partners of a given protein. [ABSTRACT FROM AUTHOR]

In this paper, the grand canonical Monte Carlo (GCMC) method was used to explore the effects of four pore structures (disordered pore, wedge pore, carbon nanotube, and slit pore structures) and surface curvature of activated carbon on the adsorption and separation of CO2/N2. On the whole, carbon nanotubes have the greatest selectivity for CO2, followed by disordered pores, wedge pores, and slit pores. The effect of pore structure on the interaction energy of gas molecules is similar to that of selectivity, in which the fluid–solid potential energy between adsorbates and adsorbents plays an important role. Due to the different affinity between adsorbate molecules and activated carbon, CO2 with high affinity is more sensitive to the change of pore size. Therefore, under high pressure, the density of CO2 in the slit pore is greater than that in the wedge pore. However, N2 with poor affinity is limited by the surface area, resulting in the density of it in the wedge pore is always higher than that in the slit pore. Although the existence of non-six membered corannulene rings in activated carbon can't always cause the increase of specific surface area, the surface curvature of activated carbon caused by it can increase strong energetically adsorption sites. Hence, the surface curvature plays a positive role in the adsorption density, interaction energy, and CO2 selectivity. The discovery of CO2/N2 adsorption and separation at the molecular level is expected to provide valuable insights. [ABSTRACT FROM AUTHOR]

The main goal of this study is determining the influence of surface curvature on 3D scanning accuracy of dental castings. The hypothesis is that 3D scanning errors occur on the geometry (surfaces) of a higher curvature on the dental anatomy. Ten dental castings (five mandibular and five maxillar) were 3D scanned with four different dental 3D scanners. As a reference device Atos Core industrial 3D scanner was used. Using a qualitative-quantitative approach of dividing every tooth in three areas (OS - occlusal surface, CSB - crown surface buccal side, CSP - crown surface palatal side) and observing the frequency of maximal deviation for each area a deviation map was obtained, which shows on what area, are the biggest deviations and in which frequency they emerge. In total 160 teeth were analysed. To conclude, 3D scanning errors occur more frequently on the geometry (surfaces) of a higher curvature on the dental anatomy. Future work suggests conducting a full numerical analysis to find a correlation between the accuracy of 3D scanned teeth surface and a surface curvature. Comparing the 3D scanning deviation to the calculated curvature of the surface could unveil which curvature is hard to 3D scan and generates errors.

An incoming canonical spatially developing turbulent boundary layer (SDTBL) over a 2-D curved hill is numerically investigated via the Reynolds-averaged Navier–Stokes (RANS) equations plus two eddy-viscosity models: the K − ω SST (henceforth SST) and the Spalart–Allmaras (henceforth SA) turbulence models. A spatially evolving thermal boundary layer has also been included, assuming temperature as a passive scalar ( P r = 0.71) and a turbulent Prandtl number, P r t , of 0.90 for wall-normal turbulent heat flux modeling. The complex flow with a combined strong adverse/favorable streamline curvature-driven pressure gradient caused by concave/convex surface curvatures has been replicated from wind-tunnel experiments from the literature, and the measured velocity and pressure fields have been used for validation purposes (the thermal field was not experimentally measured). Furthermore, direct numerical simulation (DNS) databases from the literature were also employed for the incoming turbulent flow assessment. Concerning first-order statistics, the SA model demonstrated a better agreement with experiments where the turbulent boundary layer remained attached, for instance, in C p , C f , and U s predictions. Conversely, the SST model has shown a slightly better match with experiments over the flow separation zone (in terms of C p and C f ) and in U s profiles just upstream of the bubble. The Reynolds analogy, based on the S t / (C f / 2) ratio, holds in zero-pressure gradient (ZPG) zones; however, it is significantly deteriorated by the presence of streamline curvature-driven pressure gradient, particularly due to concave wall curvature or adverse-pressure gradient (APG). In terms of second-order statistics, the SST model has better captured the positively correlated characteristics of u ′ and v ′ or positive Reynolds shear stresses ( < u ′ v ′ > > 0) inside the recirculating zone. Very strong APG induced outer secondary peaks in < u ′ v ′ > and turbulence production as well as an evident negative slope on the constant shear layer. [ABSTRACT FROM AUTHOR]

We have investigated the effects of rib surface curvature of a superhydrophobic wall in both laminar and turbulent channel flows. Direct numerical simulation is performed for laminar flows and large eddy simulation is performed for turbulent flows. The parametric study shows that a convex rib surface leads to a lower flow ratethan a flat rib for all Reynolds numbers. A concave rib surface firstly increases and then decreases the flow rate as the curvature angle becomes larger, where an optimal curvature angle exists to maximise flow rate. The value of the optimal curvature angle varies with the Reynolds number. A curved rib surface can modify the distribution of the mean velocity and turbulent statistics near the SH wall. Analysis shows that the overall effect of a curved rib surface on the flow rate is the combination of the wetted area augmentation and the change to the spanwise flow interaction, which depends on the curvature angle and the Reynolds number. The SH wall does not change the fundamental structures of near-wall vortices in turbulent flows. The ridge-groove pattern formed by the curved rib surface can provide additional drag reduction similar to that arising from the surface riblets. [ABSTRACT FROM AUTHOR]

Scaffold surface curvature is crucial to guide cell growth and form tissues, and the Young’s modulus of an implant should match the tissue in the implant site. Usually, the curvature and modulus are coupled with volume fraction. Inspired by the lattice slip phenomenon, we propose two structural design methods, linear slip transformation (LST) and rotational slip transformation (RST), to distort an original structure for largely tuning its curvature distribution and Young’s modulus within the restrictions of fixed structural type, volume fraction, and fabricated material. Here samples were additively manufactured using Ti6Al4V. Compared to original triply periodic minimal surfaces (TPMS) based lattices, the curvature distribution spectrum was largely broadened, and negative curvatures were introduced by both LST (generating symmetrical curvature distribution) and RST (generating asymmetrical curvature distribution). Additionally, LST and RST can continuously adjust the Young’s modulus of the original lattice and obtain a drop up to 90 % with 0.3 vol fraction, which can be expected to match soft trabecular bones. Interestingly, the resulting structures show elastic anisotropy and slip-induced deformation. The proposed approaches can be applied to biomedical applications and used to adjust lattice properties for use in energy, aerospace, and optics.

Recent evidence shows that the curvature of porous scaffold plays a significant role in guiding tissue regeneration. However, the underlying mechanism remains controversial to date. In this study, we developed an in silico model to simulate the effect of surface curvature on the osteoconduction of scaffold implants, which comprises the primary aspects of bone regeneration. Selective laser melting was used to manufacture a titanium scaffold with channels representative of different strut curvatures for in vivo assessment. The titanium scaffold was implanted in the femur condyles of rabbits to validate the mathematical model. Simulation results suggest that the curvature affected the distribution of growth factors and subsequently induced the migration of osteoblast lineage cells and bone deposition to the locations with higher curvature. The predictions of the mathematical model are in good agreement with the in vivo assessment results, in which newly formed bone first appeared adjacent to the vertices of the major axes in elliptical channels. The mechanism of curvature‐guided osteoconduction may provide a guide for the design optimization of scaffold implants to achieve enhanced bone ingrowth. [ABSTRACT FROM AUTHOR]

To address the problem of low overall machining efficiency of free-form surfaces and difficulty in ensuring machining quality, this paper proposes a MATLAB-based free-form surface division method. The surface division is divided into two stages: Partition area identification and area boundary determination. In the first stage, the free-form surface is roughly divided into convex, concave, and saddle regions according to the curvature of the surface, and then the regions are subdivided based on the fuzzy c-means clustering algorithm. In the second stage, according to the clustering results, the Voronoi diagram algorithm is used to finally determine the boundary of the surface patch. We used NURBS to describe free-form surfaces and edit a set of MATLAB programs to realize the division of surfaces. The proposed method can easily and quickly divide the surface area, and the simulation results show that the proposed method can shorten machining time by 36% compared with the traditional machining method. It is proved that the method is practical and can effectively improve the machining efficiency and quality of complex surfaces.

The organization and shape of the microstructural elements of trabecular bone govern its physical properties, are implicated in bone disease, and serve as blueprints for biomaterial design. To devise fundamental structure-property relationships and design truly bone-mimicking biomaterials, it is essential to characterize trabecular bone structure from the perspective of geometry, the mathematical study of shape. Using micro-CT images from 70 donors at five different sites, we analyze the local and global geometry of human trabecular bone in detail, respectively by quantifying surface curvatures and Minkowski functionals. We find that curvature density maps provide distinct and sensitive shape fingerprints for bone from different sites. Contrary to a common assumption, these curvature maps also show that bone morphology does not approximate a minimal surface but exhibits a much more intricate curvature landscape. At the global (or integral) perspective, our Minkowski analysis illustrates that trabecular bone exhibits other types of anisotropy/ellipticity beyond interfacial orientation, and that anisotropy varies substantially within the trabecular structure. Moreover, we show that the Minkowski functionals unify several traditional morphometric indices. Our geometric approach to trabecular morphometry provides a fundamental language of shape that could be useful for bone failure prediction, understanding geometry-driven tissue growth, and the design of bone-mimicking tissue scaffolds. The architecture of trabecular bone is key in determining bone properties, and is often a starting point for the design of bone-substitutes. Despite the substantial history of bone morphometry, a fundamental characterization of trabecular bone geometry is still lacking. Therefore, we introduce a robust framework to quantify local and global trabecular bone geometry, which we apply to hundreds of micro-CT scans. Our approach relies on quantifying surface curvatures and Minkowski functionals, which are the most fundamental local and global shape quantifiers. Our results show that these shape metrics are sensitive to differences between bone types and unify traditional metrics within a single mathematical framework. This geometrical framework could also be useful to design bone-mimicking scaffolds and understand geometry-driven tissue growth. [Display omitted] [ABSTRACT FROM AUTHOR]

This paper reports the results from a direct numerical simulation of an initially turbulent boundary layer passing over a wall-mounted "speed bump" geometry. The speed bump, represented in the form of a Gaussian distribution profile, generates a favorable pressure gradient region over the upstream half of the geometry, followed by an adverse pressure gradient over the downstream half. The boundary layer approaching the bump undergoes strong acceleration in the favorable pressure gradient region before experiencing incipient or very weak separation within the adverse pressure gradient region. These types of flows have proved to be particularly challenging to predict using lower-fidelity simulation tools based on various turbulence modeling approaches and warrant the use of the highest fidelity simulation techniques. The present direct numerical simulation is performed using a flow solver developed exclusively for graphics processing units. Simulation results are utilized to examine the key phenomena present in the flowfield, such as relaminarization/stabilization in the strong acceleration region succeeded by retransition to turbulence near the onset of adverse pressure gradient, incipient/weak separation and development of internal layers, where the sense of streamwise pressure gradient changes at the foot, apex and tail of the bump. [ABSTRACT FROM AUTHOR]

Due to the increasing energy cost, the efficiency of the industrial dryer as the energyintensive processes should be improved. The designer should optimize the design parameters of industrial drying equipment to achieve the minimum drying energy consumption. SST k-ω turbulence model is used to simulate a real geometry for industrial drying applications. For the optimization of the impinging round jet, the specific drying energy consumption is set as the objective function to be minimized. The jet to surface distance, jet to jet spacing, jet inlet velocity, jet angle, and surface velocity are chosen as the design parameters. The SHERPA search algorithm is used to search for the optimal point from the weighted sum of all objectives method. One correlation is developed and validated for the specific drying energy consumption. It is found that the SST k-ω turbulence model succeeded with reasonable accuracy in reproducing the experimental results. The minimum specific energy consumption correlates with high values of the jet to jet spacing, jet angle, and surface velocity and low values of the nozzle to surface distance and jet inlet velocity. The agreement in the prediction of the specific drying energy consumption between the numerical simulation and correlation is found to be reasonable and all the data points deviate from the correlation by less than 7%. [ABSTRACT FROM AUTHOR]

Thermal protection effect of reactive fire protection systems on small‐scale steel components with curved surfaces Intumescent fire protection coatings, also referred to as reactive fire protection systems, are often used to protect steel components from heating up too quickly in the event of a fire. The products are particularly suitable due to profile‐following application as well as the comparatively low coating thickness. If exposed to fire, the intumescent coating foams up and forms a thermal protective layer around the steel profile. This slows down the heating of the steel and delays the temperature‐related loss of strength, which improves the fire resistance of the steel component. From fire tests it is known that the performance of intumescent coatings on steel profiles with a curved surface is usually worse than on comparable components with a flat surface. The following article presents the theoretical background as well as the results from fire tests on small‐scale specimens to show the influence of surface curvature on the thermal protective effect of intumescent fire protection coatings. The systematic investigations show that with increasing surface curvature, the performance of the intumescent coating tends to decrease. When assessing the thermal protective effect of an intumescent coating, the surface curvature of a steel component should be considered. Focusing solely on the profile factor of a steel profile is generally not sufficient. The research forms the basis for the development of screening tests to assess the suitability of intumescent coatings for curved surfaces, enabling a pre‐selection of products for this application. [ABSTRACT FROM AUTHOR]

Biological tissues comprise complex structural environments known to influence cell behavior via multiple interdependent sensing and transduction mechanisms. Yet, and despite the predominantly nonplanar geometry of these environments, the impact of tissue-size (milliscale) curvature on cell behavior is largely overlooked or underestimated. This study explores how concave, hemicylinder-shaped surfaces 3-50 mm in diameter affect the migration, proliferation, orientation, and differentiation of C2C12 myoblasts. Notably, these milliscale cues significantly affect cell responses compared with planar substrates, with myoblasts grown on surfaces 7.5-15 mm in diameter showing prevalent migration and alignment parallel to the curvature axis. Moreover, surfaces within this curvature range promote myoblast differentiation and the formation of denser, more compact tissues comprising highly oriented multinucleated myotubes. Based on the similarity of effects, it is further proposed that myoblast susceptibility to substrate curvature depends on mechanotransduction signaling. This model thus supports the notion that cellular responses to substrate curvature and compliance share the same molecular pathways and that control of cell behavior can be achieved via modulation of either individual parameter or in combination. This correlation is relevant for elucidating how muscle tissue forms and heals, as well as for designing better biomaterials and more appropriate cell-surface interfaces. [ABSTRACT FROM AUTHOR]

Conformal Geometric Algebra (CGA) provides a unified representation of both geometric primitives and conformal transformations, and as such holds significant promise in the field of computer graphics. In this paper we implement a simple ray tracer in CGA with a Blinn–Phong lighting model, before putting it to use to examine ray intersections with surfaces generated from the direct interpolation of geometric primitives. General surfaces formed from these interpolations are rendered using analytic normals. In addition, special cases of point-pair interpolation, which might find use in graphics applications, are described and rendered. A closed form expression is found for the derivative of the square root of a scalar plus 4-vector element with respect to a scalar parameter. This square root derivative is used to construct an expression for the derivative of a pure-grade multivector projected to the blade manifold. The blade manifold projection provides an analytical method for finding the normal line to the interpolated surfaces and its use is shown in lighting calculations for the ray tracer and in generating vertex normals for exporting the evolved surfaces as polygonal meshes. [ABSTRACT FROM AUTHOR]

Surface curvature affects adhesion forces, deformations of surfaces in contact, leakage of mechanical seals, friction, wear, paintability, and electrical conductivity. However, potential benefits of surface curvature have not yet been fully utilized. One problem is the lack of comparison data helping to make an informed decision on the selection of curvature characterization method. In this paper, five multiscale curvature characterization methods, namely Nowicki, Bigerelle-Nowicki, Gleason-Heron, Kalin, and Bartkowiak are compared. The comparison was conducted on large image databases of computer-generated fractal surfaces, sine waves and real engineering surfaces. Specifically, the methods were evaluated for their ability to differentiate between surfaces that: (i) exhibit increasing curvature complexity, (ii) have varying curvatures at a single scale, and (iii) represent minute multiscale curvature changes encountered in real engineering applications. The results obtained indicate that the Bigerelle-Nowicki method exhibits the best overall performance.

A mathematical model for synthesis of the initial tooth contour of a gear in terms of the reduced curvature of the working surfaces is proposed. The form of the initial tooth contour corresponding to high performance is determined for machining equipment. [ABSTRACT FROM AUTHOR]

Jet impingements enhance the heat and mass transfer rate in industrial drying machines. The designer should optimize the design parameters of industrial drying equipment to achieve maximum heat transfer rate. The heat transfer between multiple jets and a moving curved surface is more difficult to study due to the changing boundaries and the effect of surface curvature but is also very relevant in industrial drying applications. SST k-ω turbulence model is used to simulate a real geometry for industrial drying applications. The SST k-ω turbulence model succeeded with reasonable accuracy in reproducing the experimental results. The jet to surface distance, jet to jet spacing, jet inlet velocity, jet angle, and surface velocity are chosen as the design parameters. For the optimization of the impinging round jet, the average Nu number on the moving curved surface is set as the objective functions to be maximized. The SHERPA search algorithm is used to search for the optimal point from the weighted sum of all objectives method. One correlation is developed and validated for the average Nu number. It is found that the maximum average Nu number correlates with high values of jet inlet velocity (Vj), jet angle (ϑ) and jet to jet spacing (S/d) and low values of the jet to surface distance (H/d) and relative surface velocity (VR). The agreement in the prediction of the average Nu number between the numerical simulation and correlation is found to be reasonable and all the data points deviate from the correlation by less than 4%. [ABSTRACT FROM AUTHOR]

Matching, clustering, and retrieving 3D CAD models of mechanical components based on their shape are useful for many CAD/CAM applications such as design reuse, variant process planning and group technology. Surfaces are the prominent elements of the B-Rep (Boundary Representation) CAD model, but the current methods of similarity assessment are not centered on the surfaces and lack an accurate description of their geometric features. In order to solve the problem of retrieval and clustering of B-Rep models more efficiently, the concept of "most crucial surface" is proposed and its corresponding characteristics are studied in detail. The contribution of our approach is that surfaces are the major shape determinants of the B-Rep model, and the distribution of Carosati curvatures is the optimum shape features of surfaces. First, the surface elements are extracted from the STEP (Standard for Exchange of Product Model) files of the B-rep models, and the distribution of minimum, Gauss and Carosati surface curvatures are converted into the shape feature space by the wavelet transform, the Fourier transform, and the grouping calculation. Thus we characterize the B-Rep model as a histogram with surfaces as bins, and then compare and cluster the B-Rep models by the bipartite matching algorithm or the earth mover's distance. The surface-based methods are evaluated with the four effectiveness indices in the clustering experiment of the NDR (National Design Reservoir) data, and the results indicated that the grouping method for the surface Carosati curvatures has a highly competent matching and clustering performance. [ABSTRACT FROM AUTHOR]

Objective  The auditory brain stem implant (ABI) is a neuroprosthesis placed on the surface of the cochlear nucleus (CN) to provide hearing sensations in children and adults who are not candidates for cochlear implantation. Contemporary ABI arrays are stiff and do not conform to the curved brain stem surface. Recent advancements in microfabrication techniques have enabled the development of flexible surface arrays, but these have only been applied in animal models. Herein, we measure the surface curvature of the human CN and adjoining regions to assist in the design and placement of next-generation conformable clinical ABI arrays. Three-dimensional (3D) reconstructions from ultrahigh T1-weighted brain magnetic resonance imaging (MRI) sequences and histologic reconstructions based on postmortem adult human brain stem specimens were used. Design  This is a retrospective review of radiologic data and postmortem histologic axial sections. Setting  This is set at the tertiary referral center. Participants  Data were acquired from healthy adults. Main Outcome Measures  The main outcome measures are principal curvature values (Kmin and Kmax) and global radius of curvature. Results  The CN was successfully extracted and rendered as a 3D surface in all cases. Significant curvatures of the CN in both histologic and radiographic reconstructions were found with global radius of curvature ranging from 2.08 to 8.5 mm. In addition, local curvature analysis revealed that the surface is highly complex. Conclusion  Detailed rendering of the human CN is feasible using histology and 3D MRI reconstruction and highlights complex surface topography that is not recapitulated by contemporary stiff ABI arrays. [ABSTRACT FROM AUTHOR]

Size-controlled synthesis of two-dimensional (2D) catalysts with low stacking numbers and small nanoflake lengths is crucial for promoting the catalytic performance in diverse heterogeneous catalysis. Herein, we report a facile and general "surface curvature-confined synthesis" strategy to modulate the slab lengths and stacking numbers of 2D transition metal sulfides by controlling the strain induced by different surface curvature of supports. An efficient NiMo sulfide with shorter slab length (average 3.71 nm), less stacking number (1–2 layers) and more edge active sites is synthesized onto ZSM-5 zeolites with the average size of 100 nm, which shows superior kHDS value of dibenzothiophene (14.05 × 10−7 mol/(g·s)), enhanced stability up to 80 h, and high direct desulfurization selectivity (> 95%). This design concept is also proved to be generally applicable to modulate the slab lengths and stacking numbers of other 2D catalysts such as MoS2 and WS2 nanoflakes, which shows great potentials for developing more ultrasmall 2D catalysts with controlled sizes and excellent catalytic activities. [ABSTRACT FROM AUTHOR]

Carbon nanotubes can affect the self-assembly of amyloid beta peptides (A β) related to neurodegenerative diseases. We use molecular dynamics (MD) to investigate the effects of carbon nanotubes (CNT) on the conformational evolution of monomeric A β 1-42 peptide. The chirality of CNT varies from (10, 10), (15, 15), (20, 20) and (25, 25) that corresponds to declining curvatures. We show that the adhesion of peptide on CNT surface leads to internal structures predisposes to collapse, which might be reasonable methods to impede the initial nucleation and self-assembly. Adsorption induce the loss of the peptides' native structures. Adsorption and subsequent denaturation accompanies by a loss of surface hydration of peptide. When the curvature of CNT decreases, peptide spread almost completely over the CNT surface. Conversely, peptide will wrap around the CNT when the curvature of CNT is high. Peptide adsorption onto CNT also reduces their α -helical content and β -sheet ratio, indicating that the CNT significantly affect the formation of α -helical structures while inducing random coil conformations. The arrangement of peptides on CNT surface relates to the affinity of various amino acids onto CNT. These insights provide useful information for understanding the binding and winding tendency of peptides on carbon nanostructures' surface. Image 1 [ABSTRACT FROM AUTHOR]

The energy approach to the study of a hydroelastic system consisting of an elastic blood vessel, viscous fluid flow, and an aneurysm has been developed to evaluate the various energy components of the system: viscous flow dissipation energy and the stretching and bending energies of the aneurysm wall. To calculate the total energy of the system, we have developed a computing complex including commercial and free software and self-developed modules. The performance of the complex has been tested on model geometric configurations and configurations corresponding to blood vessels with cerebral aneurysms of real patients and reconstructed by angiographic images. The calculated values of the Willmore functional characterizing the shell bending energy are consistent with theoretical data. [ABSTRACT FROM AUTHOR]