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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]

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]

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]

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]

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]

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]

Although much is known about the embryo during implantation, the architecture of the uterine environment in which the early embryo develops is not well understood. We employed confocal imaging in combination with 3D analysis to identify and quantify dynamic changes to the luminal structure of murine uterus in preparation for implantation. When applied to mouse mutants with known implantation defects, this method detected striking peri-implantation abnormalities in uterine morphology that cannot be visualized by histology. We revealed 3D organization of uterine glands and found that they undergo a stereotypical reorientation concurrent with implantation. Furthermore, we extended this technique to generate a 3D rendering of the cycling human endometrium. Analyzing the uterine and embryo structure in 3D for different genetic mutants and pathological conditions will help uncover novel molecular pathways and global structural changes that contribute to successful implantation of an embryo.

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.

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]

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]

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.

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]

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]

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]

In the milling process of automobile panel mold of hardened steel, the characteristic of free-form surface is one of the dominant factors for surface topography. In this paper, the trajectory of cutting edge is firstly modeled to analyze the residual height of the free-form surface in ball-end milling of hardened steel. Furthermore, the non-uniform rational B-splines (NURBS) surface reconstruction is utilized to generate the surface topography. Subsequently, the influences of surface curvature, lead angle, milling vibrations on the machined surface topography, and residual height are investigated, respectively. Finally, the accuracy of the surface topography and the roughness prediction model are validated by the milling experiments of free-form surface, where two-dimensional contour maps could be obtained. The simulation and experimental results demonstrate that the machined surface topography of hardened steel is fitted by means of NURBS surface reconstruction. In that manner, the effects of surface characteristics on the machined surface topography can be accurately predicted. [ABSTRACT FROM AUTHOR]

Though the importance of curvature continuity on compressor blade performances has been realized, there are two major questions that need to be solved, i.e., the respective effects of curvature continuity at the leading-edge blend point and the main surface, and the contradiction between the traditional theory and experimental observations in the effect of those novel leading-edge shapes with smaller curvature discontinuity and sharper nose. In this paper, an optimization method to design continuous-curvature blade profiles which deviate little from datum blades is proposed, and numerical and theoretical analysis is carried out to investigate the continuous-curvature effect on blade performances. The results show that the curvature continuity at the leading-edge blend point helps to eliminate the separation bubble, thus improving the blade performance. The main-surface curvature continuity is also beneficial, although its effects are much smaller than those of the blend-point curvature continuity. Furthermore, it is observed that there exist two factors controlling the leading-edge spike, i.e., the curvature discontinuity at the blend point which dominates at small incidences, and the nose curvature which dominates at large incidences. To the authors’ knowledge, such mechanisms have not been reported before, and they can help to solve the sharp-leading-edge paradox.

Tool orientation has an important effect on the surface quality of a free-form surface during ball end milling process, and the selection of tool orientation is important to ensure the surface quality. In this work, a series of milling experiments were performed by using a carbide ball end mill on a workpiece of TC17 titanium alloy. The purpose of this study was to determine the tool orientation producing optimal surface integrity. The results showed that the surface roughness in both directions was better when the rotational angle was within the range of 0°~90° and with a constant inclination angle. In addition, inclination angle had little effect on the roughness in the feed direction, whereas a much larger or smaller angle led to greater roughness in the step direction. The tool orientation strongly affected the surface morphology. Compressive residual stress was detected on all machined surfaces. The maximum surface residual stress was obtained when the rotational angle was 90°, and the surface residual stress decreased as the inclination angle increased. On this basis, four curved surface models with different curvatures were established according to the features of a blade, and the effects of inclination angle and cutter path orientation on surface integrity were studied. The results indicated that the surface roughness produced with an upward orientation varied more than that produced with a downward orientation for a steep curved surface; the value of the roughness was small for a horizontal orientation and when the machine surface was very smooth. The machined surface for a flat curved surface was smoother, and there were no obvious differences in surface morphology between the two cutter path orientations. For steep curved surfaces, the cutter path orientation had no obvious influence on the residual stress, and a greater value was obtained when the surface was much steeper. For flat curved surfaces, the residual stress had no obvious variation resulting from small changes of the inclination angle. [ABSTRACT FROM AUTHOR]

PEGylation on nanoparticles (NPs) is widely used to prevent aggregation and to mask NPs from the fast clearance system in the body. Understanding the molecular details of the PEG layer could facilitate rational design of PEGylated NPs that maximize their solubility and stealth ability without significantly compromising the targeting efficiency and cellular uptake. Here, we use molecular dynamics (MD) simulation to understand the structural and dynamic the PEG coating of mixed monolayer gold NPs. Specifically, we modeled gold NPs with PEG grafting densities ranging from 0–2.76 chain/nm 2 , chain length with 0–10 PEG monomers, NP core diameter from 5 nm to 500 nm. It is found that the area accessed by individual PEG chains gradually transits from a “mushroom” to a “brush” conformation as NP surface curvature become flatter, whereas such a transition is not evident on small NPs when grafting density increases. It is shown that moderate grafting density (∼1.0 chain/nm 2 ) and short chain length are sufficient enough to prevent NPs from aggregating in an aqueous medium. The effect of grafting density on solubility is also validated by dynamic light scattering measurements of PEGylated 5 nm gold NPs. With respect to the shielding ability, simulations predict that increase either grafting density, chain length, or NP diameter will reduce the accessibility of the protected content to a certain size molecule. Interestingly, reducing NP surface curvature is estimated to be most effective in promoting shielding ability. For shielding against small molecules, increasing PEG grafting density is more effective than increasing chain length. A simple model that includes these three investigated parameters is developed based on the simulations to roughly estimate the shielding ability of the PEG layer with respect to molecules of different sizes. The findings can help expand our current understanding of the PEG layer and guide rational design of PEGylated gold NPs for a particular application by tuning the PEG grafting density, chain length, and particle size. [ABSTRACT FROM AUTHOR]

One complication in interpreting indentation modulus measurements in inhomogeneous structural materials is the coupling between surface topography and material heterogeneity. Typically, the specimen surface is prepared to be as smooth and flat as possible, yet there are always limits to how flat a sample surface will be. Moreover, when a compositional interface is sensed mechanically, via a change in modulus, any non-flat surface topography near the interface is combined with the phase changes to influence the total elastic-modulus measurement. This paper uses a linear elastic finite element model to suggest how to decouple these two phenomena. Three axisymmetric models are presented: (1) convex and concave surfaces with material uniformity, (2) a flat surface with a lateral-graded material interface, and (3) convex and concave surfaces with a laterally-graded material interface. Using the exact Hertzian formulae, the indentation modulus is computed assuming that all the models have flat surfaces, like physical experiments often assume, and are elastically uniform. The results of (1) and (2), which have only a non-flat surface topography or material heterogeneity, are used to interpret (3), which has both. The competition between the contact radius and the distance from the indentation point to the material interface significantly influences the calculated elastic modulus. The flat-surface assumption can yield significant errors when extracting the elastic modulus in solids with pronounced curved surfaces. An empirical relation based upon contact pressure and displacement data is used to accurately extract the true material elastic modulus when both surface curvature and material interface are present. [ABSTRACT FROM AUTHOR]

In this paper, a predictive model of milling stability, which considers the surface curvature and the lead angle of the milling cutter, is proposed for milling of the panel die with sculptured surface. Firstly, influences of the radius of curvature and lead angle of milling cutter on uncut chip thickness are analyzed by exploring the curvature characteristics of sculptured surface. Subsequently, influence of the curvature characteristics of sculptured surface on chatter stability lobes in milling process is investigated by utilizing the full-discretization method. This analysis implies that the milling stability decreases with the increase in the radius of the die surface's curvature; the milling stability decreases with the increase in lead angle. The experimental results demonstrate that the prediction of chatter stability lobes could match well with the measured results on the change trend, where the maximum relative percent error is less than 11.1 % in stable milling. It is further validated that this method can effectively predict the chatter stability lobes of the domain in ball end milling of sculptured surface of die. [ABSTRACT FROM AUTHOR]

This article presents computational algorithms for the design, analysis, and optimization of airfoil aerodynamic performance. The prescribed surface curvature distribution blade design (CIRCLE) method is applied to a symmetrical airfoil NACA0012 and a non-symmetrical airfoil E387 to remove their surface curvature and slope-of-curvature discontinuities. Computational fluid dynamics analysis is used to investigate the effects of curvature distribution on aerodynamic performance of the original and modified airfoils. An inviscid-viscid interaction scheme is introduced to predict the positions of laminar separation bubbles. The results are compared with experimental data obtained from tests on the original airfoil geometry. The computed aerodynamic advantages of the modified airfoils are analyzed in different operating conditions. The leading edge singularity of NACA0012 is removed and it is shown that the surface curvature discontinuity affects aerodynamic performance near the stalling angle of attack. The discontinuous slope-of-curvature distribution of E387 results in a larger laminar separation bubble at lower angles of attack and lower Reynolds numbers. It also affects the inherent performance of the airfoil at higher Reynolds numbers. It is shown that at relatively high angles of attack, a continuous slope-of-curvature distribution reduces the skin friction by suppressing both laminar and turbulent separation, and by delaying laminar-turbulent transition. It is concluded that the surface curvature distribution has significant effects on the boundary layer behavior and consequently an improved curvature distribution will lead to higher aerodynamic efficiency. [ABSTRACT FROM AUTHOR]

Flames propagating along the sample edges (edge flame) will transform two-dimensional flame spread into three-dimensional flame spread, causing a significant interference with results of material flammability test. A potential method to minimize above effect is utilizing an inert wall to inhibit the side surface of sample with a designed air gap distance. In this work, the downward flame spread along the sample edge with various air gap distances is systematically studied. Cast PMMA with thicknesses from 0.4 to 2.5 mm were used as samples. The general trend of flame spread rate (FSR) at edge with respect to air gap distance can be summarized into three regimes: when the air gap distance is less than 2 mm, the edge flame is quenched by wall heat loss, and the overall flame spread behavior is two-dimensional. Then, the edge flame appears after the air gap distance exceeds 2 mm, resulting in a sharp increase in FSR. This critical air gap distance for the onset of edge flame is less sensitive to the sample thickness. Finally, as the air gap distance continues to increase, the FSR gradually approaches the asymptotic value of the uninhibited sample. With the increase in air gap distance, thermally-thin assumption loses validity as a result of the reduction in residence time of solid phase (larger FSR). To interpret the general trend of FSR with respect to air gap distance, a modified flame spread model based on conventional thermal theory is developed. The effect of air gap distance on flame spread along sample edge is characterized by two correction factors, one of which describes solid surface curvature at sample edge, the other of which is the effective flame temperature considering the heat loss from the spreading flame to the metal wall. The new model well reproduces the experimental results, and further supports the significance of heat loss in the trend of flame spread rate. This work helps to understand the flame spread mechanism under effects of solid surface curvature and heat loss, while also providing scientific support for optimization of material flammability testing standards. [ABSTRACT FROM AUTHOR]

The controlling mechanisms of the radiation extinction of the flame spreading over cylinders in low flow velocity conditions are investigated with an analytical approach. Attention is focused on the interaction among solid surface curvature, solid surface radiation, and gas-phase volumetric radiation heat loss in the flame spread process. The analysis uses a classical thermal model, which considers the heat balance on the unburned fuel surface near the flame front. A non-dimensional number that evaluates the effects of volumetric radiation heat loss and finite rate chemistry on the flame temperature is also proposed. It is found that solid surface radiation cannot be a dominant mechanism for the radiation extinction of a flame spreading over a thin cylinder. Furthermore, in the case of flame spread over a cylinder, flame spread rate significantly increases with decreasing opposed flow velocity due to curvature effect, thus the consideration of the relative gas flow velocity seen by the spreading flame becomes essential in low flow velocity conditions. However, when the volumetric radiation heat loss in the gas phase is taken into account in the thermal model, flame spread rate for a thin cylinder once increases with decreasing opposed flow velocity and then turns to decrease. As a result, the flame spread rate of a thin cylinder shows a peak value in low flow velocity conditions. This trend is in good agreement with previous microgravity experiments (Fujita et al., 2002 [1]). Moreover, the limit condition of flame spread appears as a bifurcation point where the stable and unstable solutions of flame spread rate coincide in the low flow velocity condition. The analytical results indicate that it is essential to consider the volumetric radiation heat loss in the gas phase to predict the flame spread over a curved surface in low flow velocity conditions. [ABSTRACT FROM AUTHOR]

In this work, the behavior of bovine serum albumin (BSA) interacting with zinc oxide (ZnO) particles functionalized with 3-mercaptopropionic acid (3-MPA) and without any coating has been investigated. Two kinds of ZnO particles of different size and morphology were obtained: microwires (MW) and nanoparticles (NP). The effect of surface modification on the fluorescence properties of ZnO was studied. Typical ZnO green emission due to defects was not observed in the functionalized NP spectrum. Structure alterations of the protein interacting with ZnO particles were evaluated by fluorescence spectroscopy and circular dichroism (CD). Though BSA structure was not significantly perturbed in any case, some conformational changes were observed for BSA interacting with not functionalized MW. [ABSTRACT FROM AUTHOR]

Local solid shape applies to the surface curvature of small surface patches--essentially regions of approximately constant curvatures--of volumetric objects that are smooth volumetric regions in Euclidean 3-space. This should be distinguished from local shape in pictorial space. The difference is categorical. Although local solid shape has naturally been explored in haptics, results in vision are not forthcoming. We describe a simple experiment in which observers judge shape quality and magnitude of cinematographic presentations. Without prior training, observers readily use continuous shape index and Casorati curvature scales with reasonable resolution. [ABSTRACT FROM AUTHOR]

Important three-dimensional spatial features such as depth and surface concavity can be difficult to convey clearly in the context of two-dimensional images. In the area of macromolecular visualization, the computer graphics technique of ray-tracing can be helpful, but further techniques for emphasizing surface concavity can give clearer perceptions of depth. The notion of diffusion accessibility is well-suited for emphasizing such features of macromolecular surfaces, but a method for calculating diffusion accessibility has not been made widely available. Here we make available a web-based platform that performs the necessary calculation by solving the Laplace equation for steady state diffusion, and produces scripts for visualization that emphasize surface depth by coloring according to diffusion accessibility. The URL is . [ABSTRACT FROM AUTHOR]

The leaf surface usually stays flat, maintained by coordinated growth. Growth perturbation can introduce overall surface curvature, which can be negative, giving a saddle-shaped leaf, or positive, giving a cup-like leaf. Little is known about the molecular mechanisms that underlie leaf flatness, primarily because only a few mutants with altered surface curvature have been isolated and studied. Characterization of mutants of the CINCINNATA-like TCP genes in Antirrhinum and Arabidopsis have revealed that their products help maintain flatness by balancing the pattern of cell proliferation and surface expansion between the margin and the central zone during leaf morphogenesis. On the other hand, deletion of two homologous PEAPOD genes causes cup-shaped leaves in Arabidopsis due to excess division of dispersed meristemoid cells. Here, we report the isolation and characterization of an Arabidopsis mutant, tarani (tni), with enlarged, cup-shaped leaves. Morphometric analyses showed that the positive curvature of the tni leaf is linked to excess growth at the centre compared to the margin. By monitoring the dynamic pattern of CYCLIN D3;2 expression, we show that the shape of the primary arrest front is strongly convex in growing tni leaves, leading to excess mitotic expansion synchronized with excess cell proliferation at the centre. Reduction of cell proliferation and of endogenous gibberellic acid levels rescued the tni phenotype. Genetic interactions demonstrated that TNI maintains leaf flatness independent of TCPs and PEAPODs. [ABSTRACT FROM AUTHOR]

Improved understanding of solid surface energy and its role in the overall mechanical properties is of great interest due to the emerging manufacturing techniques of nanostructures, coatings, and synthetic/biological bilayer–polymer hybrids. Continuum numerical modeling of surface stresses efficiently incorporates a zero-thickness membrane bonded to a bulk, intrinsically accounting for surface tension and surface elasticity. Compressive surface stresses are not possible in a purely membrane formulation, ignoring the surface flexural resistance. The extension of material surfaces to account for flexural resistance, i.e., the Steigmann–Ogden model, requires spatial derivatives of second order, posing significant challenges to standard discretization techniques. Hence, the effect of surface curvature resistance on the overall mechanical behavior of complex geometries remains elusive. Here, we develop a three-dimensional computational formulation of curvature-dependent surface energetics at finite strains using surface-enriched isogeometric analysis. Coupled with a hyperelastic bulk, bending-resistance of material surfaces furnishes a new physical length scale, i.e., the elastobending length. We quantify the effect of elastobending deformations for several numerical examples involving soft materials with thin coatings and liquid-shell surfaces, capturing budding-like behavior observed at cell membranes. Our results demonstrate a stiffer overall mechanical behavior when material surfaces resist bending deformations and illustrate how curvature effects lead to complex budding deformations at non-zero initial curvature states. The proposed methodology provides a robust computational foundation to help improve our understanding and mechanical characterization of soft solids, nanostructures, and biological membranes at small scales. [ABSTRACT FROM AUTHOR]

[Display omitted] • A microfluidic manipulation technology to control curvature of PLGA microspheres. • Osteogenesis of BMSCs was enhanced on the microspheres of curvature κ = 1/82.5 µm−1. • A novel lncRNA to regulate osteogenesis on spherical substrates via Lamin A. Microsphere-carriers have gained great interests as three-dimensional substrates for cultivation/expansion of tissue cells, required by cell-based therapy. However, how the microsphere curvature affects the cell proliferation/differentiation as well as the underlying signaling pathway of stem cells, and how to consequently regulate those cellular functionalities via manipulating microcarrier surface curvature, still remain to be explored. The current study was thus designed to develop a microfluidic manipulation technology to precisely control poly (lactic-co-glycolic) acid (PLGA) microsphere surface curvature, and subsequently to investigate the cellular responses and responding pathways of rat bone mesenchymal stem cells (BMSCs) cultured on these microspheres of predetermined curvature. A microfluidic device was developed to produce mono-distributed PLGA microspheres of diameters ranging from 52 µm to 250 µm, corresponding to curvatures (κ) from 1/26 µm−1 to 1/125 µm−1. BMSCs attachment and proliferation was evaluated on them and the one of κ = 1/82.5 µm−1 was shown to provide the most suitable microenvironment for cells to grow and undergo osteogenic differentiation. It was even found that F-actin cytoskeletal organization, nuclear distortion and expression of Lamin A were significantly enhanced by cells on the microcarriers of κ = 1/82.5 µm−1. Furthermore, a long non-coding RNA named lnc-LMNA, was found in this study to be the key factor associated with Lamin A to regulate osteogenic differentiation of BMSCs on spherical substrates. The current study thus provides a smart manipulation technology via microfluidic-manufacturing microcarriers to regulate cell functionalities, thereby enhancing desired therapeutic outcomes of cell-based regeneration or repair. [ABSTRACT FROM AUTHOR]