Small Geometric Variations Research Articles

Validation of finite-element-simulated orthodontic forces produced by thermoplastic aligners: Effect of aligner geometry and creep

PurposeFinite element (FE) models for determining the orthodontic forces delivered by clear aligners often lack validation. The aim of this study was to develop and validate accurate FE models for clear aligners, considering the small but important geometrical variations from the thermoforming process and the creep behavior of the aligner material. Methods and materialsThe tooth misalignment considered was a 2.4° torque aberration (rotation about the mesial-distal axis at the level of the center of resistance) of the maxillary left central incisor. FE models were created from Micro-CT scans of a model dental arch and five nominally identical aligners with the aforementioned misfit. Fitting of the aligners onto the dental arch was simulated using Abaqus's Interference Fit function, followed by surface-to-surface frictional interaction. Stress relaxation of the aligner material was measured using double-cantilever beam bending and modeled with a Prony series. The assembled FE models were validated by comparing the predicted forces and moments delivered to the maxillary left central incisor with experimental data, obtained with a custom-built but fully calibrated apparatus. ResultsGood agreement between prediction and measurement was obtained for both the short- and long-term forces and moments. In the short-term, i.e., after 30 s, the dominant force in the labial-lingual direction had a maximum difference of 2.9% between experiment and simulation, and the dominant moment about the mesial-distal axis had a maximum difference of 8.3%. In the long-term, i.e., after 4 h, the experimental and numerical forces had a maximum difference of 8.4%. There were statistically significant differences in the forces delivered among the nominally identical aligners, which were predicted by the geometrically accurate FE models and attributed to the variations in the points of contact between the aligners and the dental arch. The decay in force applied was affected by both the viscoelastic material behavior and friction between the aligner and arch. ConclusionFor accurate prediction of the forces and moments delivered by thermoplastic aligners, FE models that can accurately capture the point contacts between the aligners and the underlying teeth are essential. Stress relaxation of the aligners could be adequately modeled using the Prony series to represent the temporal changes of their elastic modulus.

Investigation of tyre rim protectors on the aerodynamics of a passenger vehicle

The wheels of a passenger vehicle contribute to a significant part of the vehicle’s aerodynamic drag. The previous research has shown that the flow is sensitive to small geometrical variations of the tyre, such as its shoulder profile and tread pattern. This work investigates the effect of altering the tyre profile in the transition region between the tyre and the rim by adding a so-called rim protector. Full-scale wind tunnel tests capturing forces, flow fields and surface pressures were conducted for three tyre variants in combination with two rim configurations on a crossover SUV. With a low rim protector, the forces and flow fields were similar to the reference tyre without a rim protector for both rims. With a wide, protruding, rim protector on the open rim, a larger and more outwashed front wheel wake was obtained with differences in the vortex structures, resulting in a drag penalty of 0.017CD\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0.017~C_D$$\\end{document}. The altered front wheel wake reduced the shielding of the rear wheel, resulting in differences in the rear wheel wake and base pressure. With a closed rim, the differences with the wide rim protector were much smaller with only a slight drag increase compared to the reference, demonstrating that there can be a strong interaction between the tyre and rim design.

Sensitivity of cross-sectional compliance to manufacturing tolerances for wind turbine blades

Abstract. Wind turbine blades are complex structures and, despite advancements in analysis techniques, differences persist between predictions of their elastic response and experimental results. This undermines confidence in the ability to reliably design and certify novel blade designs that include self-regulating features like bend–twist coupling. To address these discrepancies, this study investigates the influence of manufacturing tolerances on the compliance properties of blade cross-sections, focusing specifically on a previously disregarded feature: the trailing edge bondline. To conduct this investigation, the validated cross-sectional modelling tools BECAS and VABS are used to demonstrate that even small geometric variations can have significant influence on cross-sectional stiffness properties. The results are further examined and substantiated through the utilisation of 3D finite element models, adopting both shell and solid elements. We reaffirm that an accurate geometric representation of the cross-section is necessary to adequately capture the shear flow within it and assure accurate predictions on cross-sectional stiffness properties, providing updated guidelines for designers in industry.

Mach–Zehnder-like interferometry with graphene nanoribbon networks

We study theoretically electron interference in a Mach–Zehnder-like geometry formed by four zigzag graphene nanoribbons arranged in parallel pairs, one on top of the other, such that they form intersection angles of 60∘. Depending on the interribbon separation, each intersection can be tuned to act either as an electron beam splitter or as a mirror, enabling tuneable circuitry with interfering pathways. Based on the mean-field Hubbard model and Green’s function techniques, we evaluate the electron transport properties of such eight-terminal devices and identify pairs of terminals that are subject to self-interference. We further show that the scattering matrix formalism in the approximation of independent scattering at the four individual junctions provides accurate results as compared with the Green’s function description, allowing for a simple interpretation of the interference process between two dominant pathways. This enables us to characterize the device sensitivity to phase shifts from an external magnetic flux according to the Aharonov–Bohm effect as well as from small geometric variations in the two path lengths. The proposed devices could find applications as magnetic field sensors and as detectors of phase shifts induced by local scatterers on the different segments, such as adsorbates, impurities or defects. The setup could also be used to create and study quantum entanglement.

Experiments on the dynamics of aspirating cantilevered pipes concurrently subjected to reverse external axial flow

The dynamics of a hanging cantilevered pipe conveying fluid upwards (i.e. aspirating fluid) and concurrently subjected to a partially confined (annular) reverse external flow over its upper portion has been investigated experimentally in the present parametric study. The influence of annular confinement, pipe length, eccentric placement of the outer wall of the annulus relative to the central pipe, and a constriction at the inlet or outlet of the outer rigid casing on the system was examined for different external/internal flow velocity ratios, particularly Uo/Ui = 0.015 – 0.80. This study is primarily motivated by its application in solution-mined caverns, specifically for the hydrocarbon storage mode. Two different dynamical behaviours were observed; therefore, the results were categorized into two groups: low Uo/Ui (0.015 – 0.06) and high Uo/Ui (0.20 – 0.80). First-mode flutter was found to be the mode of instability of the aspirating pipe, for all flow velocity ratios, followed by the development of mixed-mode motions at higher flow velocities, for all configurations of the system. Even though the bifurcation diagram trends remained qualitatively unaltered for almost all cases, the onset of instability, amplitude of oscillations, and excitation of mixed-mode motions were affected, suggesting sensitivity of the system to small geometrical variations. The nature of the oscillatory motions appeared to generally be near-intermittent and disordered, with minor variations for different parameters.

The Strong Sensitivity of the Characteristics of Binary Stochastic Neurons Employing Low Barrier Nanomagnets to Small Geometrical Variations

Binary stochastic neurons (BSNs) are excellent activators for machine learning. An ideal platform for implementing them are low- or zero-energy-barrier nanomagnets (LBMs) possessing in-plane anisotropy (e.g. circular or slightly elliptical disks) whose fluctuating magnetization encodes a probabilistic (p-) bit. Here, we show that such a BSN's activation function, the pinning current (which pins the output to a particular binary state), and the response time – all exhibit strong sensitivity to very slight geometric variations in the LBM's cross-section. A mere 1% change in the diameter of a circular nanomagnet in any arbitrary direction can alter the response time by a factor of ∼4 at room temperature and a 10% change can alter the pinning current by a factor of ∼2. All this causes large device-to-device variation which is detrimental to integration. We also show that the energy dissipation is lowered but the response time is increased by replacing a circular cross-section with a slightly elliptical one and then encoding the p-bit in the magnetization component along the major axis. Encoding the p-bit in the magnetization component along the minor axis has the opposite effect. The energy-delay-product, however, is relatively independent of whether the cross-section is a circle or an ellipse and which magnetization component encodes the p-bit in the case of the ellipse.

Investigation of Tyre Pattern Effect on the Aerodynamics of a Passenger Vehicle

Abstract The wheels of a passenger vehicle are one of the major contributors to the total aerodynamic drag, making their aerodynamic performance a considerable factor for the overall energy efficiency of the vehicle. Previous studies have shown that the complex flow field created by the wheels is sensitive to small geometrical variations of the tyre and that features such as shoulder profile and tread pattern can have a significant impact on drag and lift. In this study, the DrivAer model is used to evaluate the flow fields and aerodynamics of four tyre tread patterns with two rim designs. Full-scale wind tunnel tests were conducted where forces, surface pressures and flow fields were measured. Numerical simulations were also performed to aid the analysis. Using a slick tyre as the reference, it was found that rain grooves typically reduced the drag, whereas the effect of lateral grooves was dependent on the rim configuration. For the lift forces, the largest lift variations were obtained for the front lift which, in general, was reduced by rain grooves and increased by lateral grooves, most notably for the closed rim. The importance of considering the parasitic lift force acting on the wheel drive units when comparing experiments and simulations was demonstrated.

Robustness of Binary Stochastic Neurons Implemented With Low Barrier Nanomagnets Made of Dilute Magnetic Semiconductors

Binary stochastic neurons (BSNs) are excellent hardware accelerators for machine learning. A popular platform for implementing them are low- or zero-energy barrier nanomagnets possessing in-plane magnetic anisotropy (e.g. circular disks or quasi-elliptical disks with very small eccentricity). Unfortunately, small geometric variations in the lateral shapes of such nanomagnets can produce large changes in the BSN response times if the nanomagnets are made of common metallic ferromagnets (Co, Ni, Fe) with large saturation magnetization. Additionally, the response times are also very sensitive to initial conditions. Here, we show that if the nanomagnets are made of dilute magnetic semiconductors with much smaller saturation magnetization, then the variability in their response times (due to shape variations and variation in the initial condition) is drastically suppressed. This significantly reduces the device-to-device variation, which is a serious challenge for large scale neuromorphic systems.

Aerothermal Effect of Cavity Welding Beads on a Transonic Squealer Tip

Abstract High-pressure turbine blade tips are critical for gas turbine performance and are sensitive to small geometric variations. For this reason, it is increasingly important for experiments and simulations to consider real geometry features. One commonly absent detail is the presence of welding beads on the cavity of the blade tip, which are an inherent by-product of the blade manufacturing process. This paper therefore investigates how such welds affect the Nusselt number, film cooling effectiveness and aerodynamic performance. Measurements are performed on a linear cascade of high-pressure turbine blades at engine realistic Mach and Reynolds numbers. Two cooled blade tip geometries were tested: a baseline squealer geometry without welding beads, and a case with representative welding beads added to the tip cavity. Combinations of two tip gaps and several coolant mass flow rates were analyzed. Pressure sensitive paint was used to measure the adiabatic film cooling effectiveness on the tip, which is supplemented by heat transfer coefficient measurements obtained via infrared thermography. Drawing from all of this data, it is shown that the weld beads have a generally detrimental impact on thermal performance, but with local variations. Aerodynamic loss measured downstream of the cascade is shown to be largely insensitive to the weld beads.

Incommensurate vibro-acoustic performance due to in-process blank holder force variation during deep drawing process

Single-stage forming is widely used in automobile industry due to less cycle times, cost-effectiveness and ease of implementation. The continuously adaptable blank holder force (BHF) systems help produce defect-free components during the deep drawing process. However, this manufacturing process induces a significant amount of variability both at geometry and functional performance of the component. A systematic investigation of the effect of small geometrical changes on the vibro-acoustic properties is carried out using a combination of simulations and experiments. The influence of BHF and friction coefficient on vibro-acoustic properties is investigated through forming simulations. The forming analysis results—geometry profile and thinning—are used as an input to predict the vibro-acoustic behaviour of the formed component. The small geometric profile and thickness variations are significant and affect radiated noise-directivity pattern and sound power levels by 1.4 dB. Two physical components are manufactured using a single-stage deep drawing process. The natural frequencies and mode shapes obtained in free-free boundary conditions vary between the two components up to 20% for the first six flexible modes. The sound power levels between the actual parts varied by 2 dB(A). Finally, it is shown that the vibro-acoustic variability is more pronounced at higher frequencies.

Using a Time‐Based Subarray Method to Extract and Invert Noise‐Derived Body Waves at Long Beach, California

AbstractThe reconstruction of body waves from the cross‐correlation of random wavefields has recently emerged as a promising approach to probe the fine‐scale structure of the Earth. However, because of the nature of the ambient noise field, the retrieval of body waves from seismic noise recordings is highly challenging and has only been successful in a few cases. Here, we use seismic noise data from a 5,200‐node oil‐company survey to reconstruct body waves and determine the velocity structure beneath Long Beach, California. To isolate the body wave energy from the ambient noise field, we divide the entire survey into small‐aperture subarrays and apply a modified double‐beamforming scheme to enhance coherent arrivals within the cross‐correlated waveforms. The resulting beamed traces allow us to identify clear refracted P waves traveling between different subarray pairs, which we then use to construct a high‐resolution 3D velocity model of the region. The inverted velocity model reveals velocity variations of the order of 3% and strong lateral discontinuities caused by the presence of sharp geologic structures such as the Newport‐Inglewood fault (NIF). Additionally, we show that the resolution that is achieved through the use of high‐frequency body waves allows us to illuminate small geometric variations of the NIF that were previously unresolved with traditional passive imaging methods.

Reliability and Scalability of p-Bits Implemented With Low Energy Barrier Nanomagnets

Probabilistic (p-) bits implemented with low energy barrier nanomagnets (LBMs) have recently gained attention because they can be leveraged to perform some computational tasks very efficiently. Although more error-resilient than Boolean computing, p-bit based computing employing LBMs is, however, not completely immune to defects and device-to-device variations. In some tasks (e.g. binary stochastic neurons for machine learning and p-bits for population coding), extended defects, such as variation of the LBM thickness over a significant fraction of the surface, can impair functionality. In this paper, we have examined if unavoidable geometric device-to-device variations can have a significant effect on one of the most critical requirements for probabilistic computing, namely the ability to "program" probability with an external agent, such as a spin-polarized current injected into the LBM. We found that the programming ability is fortunately not lost due to reasonable device-to-device variations. The little variation in the probability versus current characteristic that reasonable device variability causes can be suppressed further by increasing the spin polarization of the current. This shows that probabilistic computing with LBMs is robust against small geometric variations, and hence will be "scalable" to a large number of p-bits.

Performance analysis of waveguide-mode resonant optical filters with stochastic design parameters.

The performance of optical filters with resonant waveguide gratings is investigated numerically in a stochastic context, assuming random fluctuations of various design variables. Specifically, we derive stochastic models based on polynomial chaos expansions, whose involved coefficients are obtained by computing spectral projections via sparse-grid quadrature. The latter exploits purely deterministic results from a rigorous coupled-wave analysis solver and requires less simulation data than standard Monte Carlo (MC) techniques. The statistical moments of the filter's spectral response are calculated reliably, as the comparison against reference results from MC analysis verifies, and the extraction of the Sobol indices reveals the structure's sensitivity with respect to specific design parameters. Moreover, the present analysis clearly points out that neglecting even small geometric variations in the filter design may produce misleading conclusions regarding the corresponding performance, with undesirable consequences in real-life applications.

Computing parametrized solutions for plasmonic nanogap structures

The interaction of electromagnetic waves with metallic nanostructures generates resonant oscillations of the conduction-band electrons at the metal surface. These resonances can lead to large enhancements of the incident field and to the confinement of light to small regions, typically several orders of magnitude smaller than the incident wavelength. The accurate prediction of these resonances entails several challenges. Small geometric variations in the plasmonic structure may lead to large variations in the electromagnetic field responses. Furthermore, the material parameters that characterize the optical behavior of metals at the nanoscale need to be determined experimentally and are consequently subject to measurement errors. It then becomes essential that any predictive tool for the simulation and design of plasmonic structures accounts for fabrication tolerances and measurement uncertainties.In this paper, we develop a reduced order modeling framework that is capable of real-time accurate electromagnetic responses of plasmonic nanogap structures for a wide range of geometry and material parameters. The main ingredients of the proposed method are: (i) the hybridizable discontinuous Galerkin method to numerically solve the equations governing electromagnetic wave propagation in dielectric and metallic media, (ii) a reference domain formulation of the time-harmonic Maxwell's equations to account for arbitrary geometry variations; and (iii) proper orthogonal decomposition and empirical interpolation techniques to construct an efficient reduced model. To demonstrate effectiveness of the models developed, we analyze geometry sensitivities and explore optimal designs of a 3D periodic coaxial nanogap structure.

Secondary instabilities modulate cortical complexity in the mammalian brain

Disclosing the origin of convolutions in the mammalian brain remains a scientific challenge. Primary folds form before we are born: they are static, well defined and highly preserved across individuals. Secondary folds occur and disappear throughout our entire lifetime: they are dynamic, irregular and highly variable among individuals. While extensive research has improved our understanding of primary folding in the mammalian brain, secondary folding remains understudied and poorly understood. Here, we show that secondary instabilities can explain the increasing complexity of our brain surface as we age. Using the nonlinear field theories of mechanics supplemented by the theory of finite growth, we explore the critical conditions for secondary instabilities. We show that with continuing growth, our brain surface continues to bifurcate into increasingly complex morphologies. Our results suggest that even small geometric variations can have a significant impact on surface morphogenesis. Secondary bifurcations, and with them morphological changes during childhood and adolescence, are closely associated with the formation and loss of neuronal connections. Understanding the correlation between neuronal connectivity, cortical thickness, surface morphology and ultimately behaviour, could have important implications on the diagnostics, classification and treatment of neurological disorders.

The Impact of Geometric Variation on Compressor Two-Dimensional Incidence Range

An important question for a designer is how, in the design process, to deal with the small geometric variations which result from either the manufacture process or in-service deterioration. For some blade designs geometric variations will have little or no effect on the performance of a row of blades, while in others their effects can be significant. This paper shows that blade designs which are most sensitive are those which are susceptible to a distinct switch in the fluid mechanisms responsible for limiting blade performance. To demonstrate this principle, the sensitivity of compressor 2D incidence range to manufacture variations is considered. Only one switch in mechanisms was observed, the onset of flow separation at the leading edge. This switch is only sensitive to geometric variations around the leading edge, 0–3% of the suction surface. The consequence for these manufacture variations was a 10% reduction in the blade's positive incidence range. For this switch, the boundary in the design space is best defined in terms of the blade pressure distribution. Blade designs where the acceleration exceeds a critical value just downstream of the leading edge are shown to be robust to geometric variation. Two historic designs, supercritical blades and blades with sharp leading edges, though superior in design intent, are shown to sit outside this robust region and thus, in practice, perform worse. The improved understanding of the robust, region of the design space is then used to design a blade capable of a robust, 5% increase in operating incidence range.

Practical SVBRDF capture in the frequency domain

Spatially-varying reflectance and small geometric variations play a vital role in the appearance of real-world surfaces. Consequently, robust, automatic capture of such models is highly desirable; however, current systems require either specialized hardware, long capture times, user intervention, or rely heavily on heuristics. We describe an acquisition setup that utilizes only portable commodity hardware (an LCD display, an SLR camera) and contains no moving parts. In particular, a laptop screen can be used for illumination. Our setup, aided by a carefully constructed image formation model, automatically produces realistic spatially-varying reflectance parameters over a wide range of materials from diffuse to almost mirror-like specular surfaces, while requiring relatively few photographs. We believe our system is the first to offer such generality, while requiring only standard office equipment and no user intervention or parameter tuning. Our results exhibit a good qualitative match to photographs taken under novel viewing and lighting conditions for a range of materials.

Wave scattering by randomly shaped objects

We propose a new methodology for the evaluation of the scattered radiation by objects of uncertain shape. The uncertainties are handled by treating them as random fields. The analysis is not restricted to small geometric variations, such as in modeling of rough surfaces. Due to its efficiency and accuracy we employ the Stochastic Galerkin method. We combine this later method with a specially suited domain decomposition procedure, with which we obtain a spectrally global convergence rate. The key idea is to split the equation system with respect to the spatial position of the boundaries, and consider the interface fields as the unknown quantities. This approach preserves the governing equations, allowing us to obtain the projections of the classical integral representation of the solution. The original unbounded domain of interest is transformed to a bounded domain, while the far-field radiation condition is automatically satisfied. Discretization is accomplished by standard numerical integration, which coincides with a collocation scheme. We conclude by showing the inherent connection of the integral representation to the formulation of the problem in terms of boundary integrals.

An Efficient Perturbative Approach for Finite-Element Analysis of Microwave Devices Exhibiting Small Geometrical Variations

An innovative method for fast analysis of geometrical variations in electromagnetic wave problems is proposed. The method is based on a perturbative approach applied to the solution of the linear integro-differential operator of the electromagnetic problem in presence of small domain modifications. This approach has been embedded in a classical finite-element framework to achieve a very fast technique for field evaluation in synthesis or tolerance investigation of microwave passive devices. The proposed technique can handle geometrical variations without the need of re-meshing the domain and without any deformation of the original mesh of the problem.

Uncertainty in the Multielemental Quantification by Total-Reflection X-ray Fluorescence: Theoretical and Empirical Approximation

Nowadays, the subject of the quality assurance of the analytical results is acquiring more and more importance. This work presents a basic theoretical and empirical approximation to the expanded uncertainty associated to the TXRF measurements. Two theoretical models has been proposed and compared systematically with the empirical expanded uncertainty obtained. The main consequences derived of this work are the following; theoretical model B explains with a high degree of agreement the empirical expanded uncertainties associated to the TXRF measurements, while theoretical model A explains partially the instrumental repeatability of the TXRF system. On the other hand, an unexpected U-behavior has been found for the empirical uncertainty in TXRF measurements whose explanation can be due to the sum of several sources of uncertainty not considered like variations of the Compton background or the nonlinearity of the Si(Li) detector quantum efficiency. Additionally, it has been shown that the roughness and small geometrical variations of the sample depositions are the more important uncertainty sources in the experimental TXRF measurements.