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Tip-enhanced Raman spectroscopy (TERS) has gained great attentions for sensitive characterization and super-resolution chemical imaging of various materials. The performance of TERS is mainly affected by the probe geometry, such as the diameter of the tip apex, surface roughness, etc. In this regard, the fabrication of a sharp apex from metal wire is the one of the most important factor for TERS experiments. Conventionally, the electrochemical etching is commonly used technique for fabricating those metallic probes. To avoid the surface defects, the pulsed bias was commonly employed in the electrochemical etching process. However, it would make the fabrication system to be complex and sophisticated. Here, we report an simple automated electrochemical etching systems using DC bias for the efficient fabrication of TERS probes. With our optimized condition for DC electrochemical etching, gold probes with a clean surface and a radius of curvature below 200 nm can be obtained with yield of 85%. The fabricated metallic probe is used to detect the brilliant cresyl blue (BCB) molecules on the gold film, and it is confirmed that the enhancement factor is about 3,400.

Purpose To describe an open-source, reproducible, step-by-step method to design sum-of-segments thick intraocular lens (IOL) calculation formulas, and to evaluate a formula built using this methodology. Design Retrospective, multicenter case series Methods A set of 4242 eyes implanted with Finevision IOLs (PhysIOL, Liege, Belgium) was used to devise the formula design process and build the formula. A different set of 677 eyes from the same center was kept separate to serve as a test set. The resulting formula was evaluated on the test set as well as another independent data set of 262 eyes. Results The lowest standard deviation (SD) of prediction errors on Set 1 were obtained with the PEARL-DGS formula (±0.382 D), followed by K6 and Olsen (±0.394 D), EVO 2.0 (±0.398 D), RBF 3.0, and BUII (±0.402 D). The formula yielding the lowest SD on Set 2 was the PEARL-DGS (±0.269 D), followed by Olsen (±0.272 D), K6 (±0.276 D), EVO 2.0 (±0.277 D), and BUII (±0.301 D). Conclusion Our methodology achieved an accuracy comparable to other state-of-the-art IOL formulas. The open-source tools provided in this article could allow other researchers to reproduce our results using their own data sets, with other IOL models, population settings, biometric devices, and measured, rather than calculated, posterior corneal radius of curvature or sum-of-segments axial lengths.

This study aimed to compare ProGlider (Dentsply Sirona, Ballaigues, Switzerland) and R-Pilot (VDW, Munich, Germany) instruments in terms of their cyclic fatigue resistance using an artificial stainless steel canal showing an abrupt apical curvature, torsional resistance according to the ISO specification, and topographic changes on the instrument surface after glide path management in mesial canals of mandibular first molars with the abrupt curvature selected based on their micro-computed tomographic examination.Eighty instruments were used: 40 ProGlider (size 0.16, .02v taper) and 40 R-Pilot (size 0.125, .04 taper) instruments. The cyclic fatigue resistance was tested in a static test model using an artificial canal with an abrupt apical curvature (angle of curvature of 90° and radius of curvature of 2 mm). The torsional resistance test was performed according to ISO 3630-1 specifications. To determine surface topography of the unused and used instruments, mesial root canals of mandibular molars with an abrupt apical curvature were selected to prepare a glide path with either the ProGlider or R-Pilot instrument. An optical profilometer and scanning electron microscopy were used to determine the surface properties. Normally distributed torsional and cyclic resistance data were analyzed using the Student t test, whereas quantitative data obtained by the optical profilometer were analyzed with the Kruskal-Wallis H test with a 5% significance threshold.The R-Pilot showed significantly higher cyclic fatigue and torsional resistance than the ProGlider (P .05). Angular deflection values were similar between instruments (P .05). Measurements made from the blade area showed that the surface roughness values of the ProGlider were larger. Cutting blade measurements showed that unused instruments had significantly greater roughness values than used ones (P .05). Although there was a 14% increase between the blade edge radii of the used and unused R-Pilot instruments, this difference was determined as 61% in ProGlider instruments.The R-Pilot exhibited greater cyclic fatigue strength than the ProGlider when tested in an artificial canal with an inner diameter of 1.0 mm and an abrupt apical curvature. Torsional resistance of the R-Pilot was higher than the ProGlider, but the angular deflection values were similar. Glide path preparation in a mesial root canal with an abrupt apical curvature did not increase the surface roughness of both instruments but resulted in a greater blade edge radius.

An adaptive clamping method (SGD-MS) based on the radius of curvature is designed to alleviate the local optimal oscillation problem in deep neural network, which combines the radius of curvature of the objective function and the gradient descent of the optimizer. The radius of curvature is considered as the threshold to separate the momentum term or the future gradient moving average term adaptively. In addition, on this basis, we propose an accelerated version (SGD-MA), which further improves the convergence speed by using the method of aggregated momentum. Experimental results on several datasets show that the proposed methods effectively alleviate the local optimal oscillation problem and greatly improve the convergence speed and accuracy. A novel parameter updating algorithm is also provided in this paper for deep neural network.

Air pneumatic compression is a concept used for management of venous disease, including oedema. A typical air pneumatic compression device (PCD) consists of an inflatable sleeve composed of either single or multiple pressure chambers that encircle a limb. The aim of this research was to develop a mathematical model to predict the pressure applied by an air pneumatic device to an irregular cross-sectional lower limb manikin. The radius of curvature at any cross-section of the lower limb (i.e. calf (gastrocnemius), tibial crest (anterior edge of the tibia bone)) is irregular, and differs amongst individuals and populations. The effectiveness of air pneumatic devices is difficult to predict with these irregular cross sections. A theoretical model was developed to calculate pressure applied by compression sleeves on a lower leg manikin and results compared against experimental pressure exerted on the manikin by a silicone-based PCD. This prediction was made at each of three positions. The theoretical model developed based on elliptical shaped forms predicted the pressure more accurately for the ankle to above ankle position, whereas the model based on circular shaped forms predicted the pressure more accurately for below the calf to below the knee position. Refinements to the theoretical model to predict the pressure applied by PCD are recommended.

Breast cancer affects one out of eight women. Ultrasound (US) plays an important role in the diagnostic workflow, especially during the biopsy phase, in which tissue is extracted from the lesion for further analysis. The extension from 2D to 3D US acquisitions has multiple benefits including enhanced lesion localization and improved registration with MRI data. Current commercial 3D US systems lack the ability to preserve the breast's original shape. Robotic US scanners follow tailored trajectories and produce high quality volumes by accurate localization of 2D slices captured with a conventional linear probe. Current methods require a patient specific model to plan the scanning trajectory. In this study we investigate how to change the direction of the scanning trajectory based on US feedback, such that no patient specific model is required to perform a scan. In our method, the scanning trajectory is kept tangent to the breast based on confidence maps of the US images and an estimation of current radius of curvature of the surface. We evaluated our approach on a realistic breast phantom. The robot revolves around the breast without prior knowledge of its shape. In ten scans, the RMS error between the probe's scanning plane and the breast's surface normal is 12.6° out-of-plane, and 4.3° in-plane. A 3D US reconstruction shows the acquired data. This is a step forward to fully autonomous, high quality robotic US volume acquisitions.

The paper presents a comparative theoretical analysis of the movements of the curved rods of various curvature forms, which can be applied as tools for ultrasonic treatment of holes in fragile materials. It has been shown that the traditional processing of holes by an ultrasonic method is based on the use of straight rods, in which the amplitudes of displacements on the working – free end corresponds to the value of displacements at the point of its attachment to the ultrasonic oscillation concentrator. Supplementing the configuration of a straight rod with a curvilinear shape in the form of a circular arc or a spiral twisted by one turn will allow obtaining additional displacements caused by the elastic properties of a section with a curved shape. The paper considers several calculated schemes of a curvilinear rod bounded by angles j equal to p/2, p and 2p, fferent direction of the external force action. The obtained results have shown that an increase in the circular arc angle leads to a corresponding increase in the elastic displacement index of the rod free end. In this case, the total displacements of the rod free end will be made from displacements caused by vibrations of the acoustic system and the displacements of a curved thin rod from an external force. Calculations have established that the magnitude of the elastic displacements of curved rods is influenced by the shape and magnitude of the angle, the direction of the external force, the radius of curvature, the rigidity of the cross section. The considered schemes of thin rods with curvilinear sections can find practical application in ultrasonic oscillatory systems for processing small-diameter holes in fragile materials. This increases the intensity of tool oscillations and improves the process performance.

A clump moving through the intracluster medium of a galaxy cluster can drive a bow shock trailed by a bullet-like core. In some cases, such as in the prototypical Bullet cluster, X-rays show a gas bullet with a protruding head and pronounced shoulders. We point out that these features, while difficult to explain without dark matter (DM), naturally arise as the head of the slowed-down gas is gravitationally pulled forward toward its unhindered DM counterpart. X-ray imaging thus provides a unique, robust probe of the offset, collisionless DM, even without gravitational lensing or other auxiliary data. Numerical simulations and a toy model suggest that the effect is common in major mergers, is often associated with a small bullet-head radius of curvature, and may lead to distinct bullet morphologies, consistent with observations., Comment: 9 pages, 3 figures, comments welcome

A highly dispersive, diffractive optical element is designed and realized for an extremely high spectral resolution spectroscopy for exoplanet telescope application. Our design uses an annular Fresnel hologram to transform incident starlight directly into a spectrogram. The recording of the hologram is accomplished using two spherical waves of different radius of curvature. The resultant hologram consists of an annular grating structure with a gradually shrinking period as a function of increasing radius. The variable period not only could bring the incoming star-light into focus, but also exhibits a large on-axis chromatic behavior. We demonstrate a dispersion of wavelength 430–700 nm over 190 mm on-axis distance, leading to a super fine spectral resolution 0.0266 nm at wavelength 515 nm for a detector size of 20 µm.

Zirconia ceramics are widely used in medical and dental industry due to their excellent biocompatibility and aesthetics. In this respect, stereolithography apparatus (SLA) is popular method for 3D printing of ceramic suspensions. However, deformation and cracking of SLA-printed ceramics caused by residual stress seriously limit their application in clinical dentistry. In this investigation, 75 wt. % ZrO2 suspensions were successfully prepared, and ZrO2 ceramic composites were produced via SLA 3D printing. Special attention was paid to the establishment of theoretical model of residual stress in SLA. According to results, the development of residual stress in SLA-printed ceramics depended on various parameters such as laser power, scanning speed, and radius of curvature, as well as linear shrinkage, stress wave, and pure bending stress. The variations of surface residual stress at different laser beam powers, scan speeds, and radii of curvature were found to be consistent with that predicted theoretically. The errors between the theoretical and experimental value were 2.8%, 1.4%, 4.3%, 5.3%, and 4.2%, respectively, when the laser beam powers increased in turn. The errors between the theoretical and the experimental value were 2.5%, 3.9%, 2.8%,2.4%, and 3.8%, respectively, when the scan speeds increased in turn. Thus, theoretical model established was proved high accuracy and conformity to 3D printing standards.

In this paper, a Stokes-Brinkman model is developed to study a transverse flow through a rough curved channel containing a porous medium. The analytical expression of the flow rate, for a given mean pressure drop, is obtained as a function of the parameters specifying the surface roughness, the channel permeability and the channel radius of curvature. The study shows that the transverse flow through the porous curved channel is decreased by the surface roughness. Further to that, we have shown that the surface roughness has greater impact on the rough curved channel flow, when compared to a straight rough channel flow with the same permeability. The Stokes and Darcian flow limits pertaining to the rough curved channel flow have been examined, and it is found that the roughness effect is relatively significant in the Stokes flow limit.

To avoid degradation of material properties, high equipment investment, low efficiency, and potential safety issues caused by conventional technologies like line heating, multi-point plate forming, and explosive forming, a new die-less single-tool multi-point plate forming (DS-MPF) technology is proposed. In DS-MPF, a moving bar is used as a single forming tool and combined with horizontal and vertical motions relative to the plate. To reduce forming force component from the membrane stress, simple support boundary condition is preferred to avoid the plate edge being bent, trimmed, or thinning after being formed. However, this boundary may easily cause instability of the forming process and worse geometric accuracy of a formed part if an unsuitable toolpath is employed. In this paper, the forming mechanism and toolpath design principle are clarified to develop this new technology. Numerical and experimental forming case from an 8-mm SS400 steel plate into a spherical surface with a radius of curvature of 1000 mm was performed to validate the new technology and its design principle. The strain analysis of results shows DS-MPF tends to be a local forming method. The formed plate normally has local positive bending strain at the tool-contacted area and limited negative bending strain at the tool-uncontacted area between adjacent strokes. Forming a 3D curved shape with high geometric accuracy in DS-MPF can be achieved with appropriate control of the local bending strain produced in each stroke, stroke position, and forming sequence.

The simplified analysis of the initial jetless stage of high-speed drop impingement onto a convex solid surface recently proposed by Burson-Thomas et al. (2019) has been extended to a concave surface with the radius of curvature larger than the drop radius. An approximate approach has also been proposed to incorporate the surface curvature into Heymann’s analysis (1969) based on the Rankine–Hugoniot equations. It has been shown that the simplified analysis predicts a significantly longer initial stage than Heymann’s analysis. As opposed to the convex surface, the duration of the initial jetless stage and the corresponding size of the contact area for the concave surface are larger than for the flat one. For both convex and concave surfaces, the effect of the surface curvature is significant when the radii of curvature of the surface and the drop are nearly equal, and is almost absent if the ratio of the radii is more than 10.

A functional sessile droplet containing buoyant colloids (ubiquitous in applications like chemical sensors, drug delivery systems, and nanoreactors) forms self-assembled aggregates. The particles initially dispersed over the entire drop-flocculates at the center. We attribute the formation of such aggregates to the finite radius of curvature of the drop and the buoyant nature of particles. Initially, larger particles rise to the top of the droplet (due to higher buoyancy force), and later the smaller particles join the league, leading to the graded size distribution of the central aggregate. This can be used to segregate polydisperse hollow spheres based on size. The proposed scaling analysis unveils insights into the distinctive particle transport during evaporation. However, the formation of prominent aggregates can be detrimental in applications like spray painting, sprinkling of pesticides, washing, coating, lubrication, etc. One way to avoid the central aggregate is to spread the droplets completely (contact angle ~ 00), thus theoretically creating an infinite radius of curvature leading to uniform deposition of buoyant particles. Practically, this requires a highly hydrophilic surface, and even a small inhomogeneity on the surface would pin the droplet giving it a finite radius of curvature. Here, we demonstrate using non-intrusive vapor mediated Marangoni convection (Velocity scale ~ O(1 0 3) higher than the evaporation-driven convection) can be vital to an efficient and on-demand manipulation of the suspended micro-objects. The interplay of surface tension and buoyancy force results in the transformation of flow inside the droplet leads to spatiotemporal disbanding of agglomeration at the center of the droplet.

Creeping ultrasonic waves are used in echo flaw detection of near-surface and near-bottom zones of metal products of plane-parallel or cylindrical shape. The creeping (lateral) waves are also used in testing products by the time-of-flight diffraction method as the earliest (reference) signal, followed by the useful signals of waves diffracted on metal discontinuities. The purpose of this study is to evaluate the ability of the creeping wave to propagate over a concave metal surface. We have studied experimentally the attenuation of the amplitude of a creeping wave with the distance upon wave propagation over concave metal surfaces of different radii. The velocity of propagation of the creeping wave does not depend on the radius of curvature and equals to the velocity of the bulk longitudinal wave. The results obtained provide the possibility of using the time-of-flight diffraction method in control of the objects with concave surfaces, in particular, for in-tube testing.

A method is proposed for determining the radius of curvature of transition curves in satellite-teeth profiles of planetary gears with internal engagement. The teeth are cut by a tool with a modified initial contour and are characterized by high flexural strength. The radii of curvature of tooth profiles cut by a standard tool and nonstandard (gear-shaping and rack) tools are compared.

Abnormal voltages such as electrostatic, constant current, and strong electromagnetic signals can erroneously trigger operation of MEMS pyrotechnics and control systems in a fuze, which may result in casualties. This study designs a solid-state micro-scale switch by combining the corona gas discharge theory of asymmetric electric fields and Peek’s Law. The MEMS switch can be transferred from "off" to "on" through the gas breakdown between the corona electrodes. In the model, one of the two electrodes is spherical and the other flat, so a non-uniform electric field is formed around the electrodes. The theoretical work is as follows. First, the relation among the radius of curvature of the spherical electrode, the discharge gap, and the air breakdown voltage is obtained; to meet the low voltage (30–60 V) required to drive the MEMS switch, the radius of curvature of the spherical electrode needs to be 10–50 μm and the discharge gap between the two electrodes needs to be 9–11 μm. Second, the optimal ratio e is introduced to parameterize the model. Finally, the corona discharge structural parameters are determined by comparing the theoretical and electric field simulation results. The switch is then fabricated via MEMS processing. A hardware test platform is built and the performing chip tested. It is found that when the electrode gap is 9 μm, the electrostatic voltage is at least 37.3 V, with an error of 2.6% between the actual and theoretical air breakdown voltages. When the electrode gap is 11 μm, the electrostatic voltage is at least 42.3 V, with an error of 10.5% between the actual and theoretical air breakdown voltages. Both cases meet the design requirements.

This paper proposes a method of quality for the uneven removal caused by the change of the radius of curvature in the aspheric surface polishing and finishing. This method uses a polishing disk and a bonnet as polishing devices, two kinds of aspheric parts as workpieces with a concave surface and a convex surface respectively. By deriving the model of pressure and velocity at different positions, the equation between dwell time and curvature radius on the elliptical generatrix of aspheric workpiece could be obtained from the famous Preston equation on polishing material removal. According to the dwell time on the different path points, the movement of the robot could be controlled. In this way, only the dwell time of the path points on the elliptical generatrix needs to be calculated, rather than the entire aspheric surface. By measuring the values of surface roughness in the polishing of concave and convex aspheric surfaces, the experimental results verify that the method could improve the processing efficiency.

The diffusion of single micron-sized Brownian square platelets on cylindrical surfaces with different radii of curvature in the presence of depletion attractions was studied experimentally by video microscopy. The translational motion of a square is found to be diffusive along the axial direction of the cylinder but sub-diffusive along the circumferential direction due to the confinement induced by gravity, while its rotational motion displays a sub-diffusive behavior due to the confinement induced by orientation-dependent depletion attractions. Such a confinement effect decreases as the radius of curvature increases and can be tuned both through surface curvatures and/or depletion attractions. Our work provides a new way to control the translational and rotational dynamics of anisotropic particles through curved surfaces in the presence of depletion attractions.

A theoretical formula for calculating the global shear buckling strength of curved corrugated steel webs (CSWs) under simply support conditions was derived. Their geometric parameters, namely the corrugation depth-to-web thickness ratio, web slenderness, and radius of curvature, which influence the elastic shear buckling strength, were also assessed. The computational error of the formula for the shear buckling of a curved CSW was verified to be within 2% using finite element analysis. Increasing the corrugation depth-to-web thickness ratio and decreasing web slenderness significantly reduced the elastic shear buckling strength. On the contrary, reducing the height of the web or increasing the web thickness had the opposite effect. Although the radius of curvature has little influence on the shear strength of a curved CSW, it significantly impacts the buckling mode. The results provide a theoretical reference for the design and application of curved CSW bridges.

In order to obtain the MEFP with smaller divergence angle for the apply in the destruction of unexploded ordnance, LS-DYNA numerical simulation software was used to simulate the formation process and motion state of the projectile formed by the integrated MEFP warhead. The influence of the parameters of the liner (thickness, radius of curvature) and the initiation mode (single and multi-point initiation) on the formation characteristics of MEFP were studied. After the optimization design of warhead, the simulation model of MEFP interact with shell-covered cylindrical charge was established to estimate the damage power. The optimized MEFP has small divergence angle and can detonate the shell charge with a thickness of 10 mm.

With significant progress being made toward improving endoscope technology such as capsule endoscopy and robotic endoscopy, the development of advanced strategies for manipulating, controlling, and more generally, easing the accessibility of these devices for physicians is an important next step. This article presents an autonomous navigation strategy for use in endoscopy, utilizing a state-dependent region estimation approach to allow for multimodal control design. This region estimator is evaluated for its accuracy in predicting yaw angle of the camera relative to the lumen center, and for estimating the location of the camera based on overall haustra morphology within the colon. To assess the utility of this region estimator, multimodal control is used to allow for autonomous navigation of the Endoculus, a robotic capsule endoscope, within a benchtop, to-scale, simulated colon. The estimation approach is presented and tested, demonstrating successful tracking of fixed velocity rotations at speeds up to $40^\circ$ /s and allowing for curve anticipation approximately 10 cm before entering a curved section of the simulator. Finally, the multimodal control strategy utilizing this estimator is tested within the simulator over a variety of anatomic configurations. This strategy proves successful for navigation in both straight sections of this simulator and in tightly curved sections as small as 8 cm radius of curvature, with average velocities reaching 2.61 cm/s in straight sections and 0.99 cm/s in curved sections.

We investigated the optimal surface structure of an n-type Si substrate for Si-Al bonding (which prevents high-energy barrier formation) using simulation by the phase field method. The surface structure of the substrate contained a groove to suppress regrowth layer formation at the bottom of the groove. We determined the appropriate width and depth of the groove to effectively suppress the regrowth layer. The features of the regrowth layer suppression mechanism were clarified as the following: narrowing the groove caused the Al concentration to increase inside the groove and, in turn, decreased the degree of supercooling of the Si-Al liquid. However, when the groove was too narrow, the radius of curvature at the bottom of the groove decreased, and the equilibrium melting point of the Si-Al liquid rose due to the Gibbs–Thomson effect. On the other hand, the narrow groove increased the Al concentration, leading to decrease of the equilibrium melting point of the Si-Al liquid. This implies that there is always an optimum value for the width and the depth of the groove by which the regrowth layer is effectively suppressed through forming the groove in the Si surface for the Si-Al bonding process. Any groove morphology with the growth ratio (the ratio of the regrowth layer at the bottom to that at the top of the groove) less than 0.3 is appropriate to achieve good ohmic contact; however, it is considered that the groove with periodic length of 9.4 μm and aspect ratio around 0.2 is the best because of the ease of manufacturing.

To determine the stress–strain curve of a ductile material up to the fracture from a tensile test, the necking contour is measured by an optical measurement technique. The radius of the minimal cross-sectional area and the radius of curvature are used as input for analytical necking corrections of the stress–strain curve, as well as for finite element inverse simulations. Due to the increasing surface roughness that develops during testing, a precise determination of the specimen contour is very challenging. This is crucial, since the second derivative is required for estimating the radius of curvature. A dedicated contour-tracking algorithm was developed to deal with the surface roughness and a specimen painted white with black background was found to provide enough contrast. The new algorithm was implemented in a software, which is made available as open source. Tests were made for an isotropic, commercially pure aluminum alloy and for an axisymmetric, peak aged AA6082 alloy, based on image recording by a digital camera and synchronized force measurements. Modeling by finite element simulations was performed to assess the accuracy of analytical corrections of the stress–strain curves by inverse modeling and for designing a robust contour-tracking algorithm.

An algorithm for solving the problem of local shape errors of optical surfaces correcting by a small-sized ion beam, based on the matrix representation is presented. The algorithm involves searching for points that rise relative to the average height on the surface, where exposure to an ion beam of a given shape will lead to a decrease in the RMS deviation of the surface shape from the calculated one. It is shown that the new approach makes it possible to significantly expand the range of spatial frequencies, in which the height of relief can be reduced using the given ion beam size, and provides better results than the method of minimizing the functional of convolution of the ion beam and the surface map. Moreover, the new approach does not lead to appearance of shape errors (concentric structure) defined by the ion beam size and scanning step. An experiment for minimizing of local surface shape errors based on an etching map calculated using new approach was done. Matrix algorithm allowed in one procedure to reduce surface shape errors for a concave spherical optical element made of fused silica with a diameter D = 100 mm and a radius of curvature R = −137.5 mm in the RMS by more than 3 times. The initial RMS was 4.5 nm, RMS after treatment is 1.36 nm.

The pneumatic system is frequently operated in the high air velocity region, which aggravates the power consumption and erosion of bend, and the dynamic analysis of particles in bends with different radius of curvature in a horizontal-vertical pneumatic conveying system is necessary. This experimental study focuses on the particle motion characteristic of bend on the horizontal-vertical pneumatic conveying in terms of on pressure drop, particle velocity, power spectral characteristics of particle fluctuation velocity, the energy distribution of the proper orthogonal decomposition (POD) modes, time coefficients of POD, and spatial mode of POD mode during flowing through bends. The results indicate that the particle rope is the large-scale motion of particles containing high energy, which dominates the motion of particles in the bend, and the suppression of small-scale motion leads to the low pressure drop in a large radius ratio of the bend.