Direction Of Curvature Research Articles

A class of new tuned primal subdivision schemes with high-quality limit surface in extraordinary regions

We propose a unified tuning framework for primal subdivision schemes that are generalizations of odd-degree uniform B-spline surfaces for unstructured quadrilateral meshes of arbitrary topology. The subdivision of the resulting tuned primal subdivision (TPS) schemes is performed through efficient repeated local refinement operations. One level of subdivision of TPS-schemes is decomposed into one step of simple topological splitting plus an additional series of repeated local smoothing operations. The unified tuning framework optimizes subdivision rules for both topological splitting and smoothing operations near extraordinary vertices by minimizing the curvature fluctuation of the second-order characteristic maps of the respective TPS-scheme. To validate the limit surface quality of TPS-schemes in extraordinary regions, a mesh-independent metric is also devised to estimate local curvature variation in addition to highlight lines and direct curvature evaluation. With (p - 1)/2 steps of smoothing operations in each level of subdivision, the respective TPS-scheme is termed as a degree-p scheme that produces global C p -1 limit surfaces everywhere except at a finite number of extraordinary positions where near- G 2 continuity is achieved. The limit surface of TPS-schemes in extraordinary regions also exhibits appealing highlight lines, and the larger the number of smoothing operations applied in each level of subdivision, the better the final limit surface quality. One of the key advantages of the proposed tuning framework for TPS-schemes is that the optimization of relevant subdivision rules is performed by tuning structured operations of topological splitting and repeated smoothing that involve direct neighbors of an extraordinary vertex only without the need of tuning large subdivision stencils. All subdivision operations of TPS-schemes are local, involving one-ring of neighboring vertices only, which is efficient for high-degree surface subdivision and convenient for practical implementation. Numerical examples also validate the superiority of TPS-schemes over other state-of-the-art subdivision methods in terms of both highlight lines and various curvature measures.

Static analysis of masonry polygonal domes with membrane forces

Masonry polygonal domes are parts of several historic monuments and masonry buildings. The analysis of polygonal domes with a static approach is here presented, considering the structure made of vault cells and ribs. The vaults are portions of a cylindrical surface with single curvature in the meridian direction, and translation of the generatrix curve in the direction of the cylinder axis. The system is divided into rigid elements with interfaces. The first part of the work regards the geometry of the rigid elements, in particular the angles that characterize the shape of these. Then the equilibrium equations applied to every element are presented, with a procedure to calculate the membrane response for the self-weight in a non-redundant system, under symmetry conditions. The sum of the solution for the vaults is combined with effects of the weight of ribs and radial walls. The use of the equilibrium solution for pointed domes, domes with a lantern and oculus or additional load to the dome self-weight is shown. A limit analysis static approach is formulated calculating the maximum load relative to the equilibrium of the rigid elements considering the interfaces tensile strength and limited cohesion and friction for the shear resistance.

Determination of Velocities of Thread Axis Points When Interacting with a Direct Large Curvature Taking into Account the Deformation in the Contact Zone

The theoretical study of the process of the movement of the thread, which is deformed in the contact zone with the guide, from the point of view of determining the speed, is of great importance for solving a number of specific applied problems. When determining the speed, it was assumed that the start of the Lagrangian and Euler coordinates coincided. Taking into account that the crumpling of the thread in the contact zone occurs at forces much lower than the forces required to stretch the thread, the thread was considered as non-extensible. To determine the law of the distribution of the speed of the points of the thread, an independent vector, which is always connected to the main triangle, was introduced into consideration. The relationship between the vector of total curvature and the vector of absolute angular velocity is obtained. The obtained values of the speed at an arbitrary point of the axis of the thread as a function of the deformation vector, which determines the degree of twisting of the thread in the contact zone. The obtained results can be used to study various technological processes in the sewing, knitting, and textile industries, where the movement of the thread takes place along the guide surface of great curvature.

A point cloud segmentation algorithm based on multi-feature training and weighted random forest

Abstract Point cloud segmentation is the process of dividing point cloud data into a series of coherent subsets according to its attributes. It has been widely used in target recognition, digital protection of cultural relics, medical research and other fields. To improve the classification accuracy of point cloud and achieve accurate segmentation of objects or scenes, a point cloud segmentation algorithm based on multi–features training and weighted random forest (RF) is proposed. Firstly, the feature vector composed of 3D coordinate value, RGB value, echo intensity, point cloud density, normal direction and average curvature is used to train the SVM classifier, and the ‘one–to–one’ strategy is adopted to achieve the initial multivariate rough segmentation of point cloud. Then, the maximum information coefficient and sample correlation coefficient (SCC) are used to evaluate the correlation of the decision tree, and the decision tree is weighted accordingly to build a weak correlation weighted RF, so as to achieve further accurate segmentation of the point cloud. The experiment verifies the effectiveness of the proposed algorithm by segmenting the outdoor scene point cloud data model. The results show that the segmentation algorithm based on multi–features training and weighted RF can achieve accurate point cloud segmentation, and is an effective point cloud segmentation method.

A two-layered cross-ply laminate model for a single-ply satin woven fabric composite under thermal loads

The dominant fiber direction of a single-ply satin woven fabric is different depending on whether it is the upper or lower side. This affects the thermal distortion of laminates and principal curvature directions. Therefore, we propose a two-layered cross-ply laminate model for a single-ply satin woven fabric composite to consider the dominant fiber directions. To verify our model, we derive analytical solutions of antisymmetric angle-ply laminates under thermal loads for the conventional and proposed models. By comparing the analytical solutions with experimental results of unidirectional and satin woven fabric composites, we confirm that the proposed model accurately predicts the principal curvature direction.

Efficient single-mode operation in a 10 dB/m absorption very-large-mode-area ytterbium-doped optical fiber via curvature-induced mode filtering

In this paper we report our findings on the design, manufacturing and testing of low numerical aperture active step-index optical fibers with very large mode area, operating in a truly single-mode regime. Our approach to efficiently filter higher-order modes in the core relies on applying curvature in a specific direction at a given diameter on a specially designed fiber containing boron-doped silica rods on both sides of the core. The fabricated ytterbium-doped fibers exhibit a mode field diameter of 32μm, a cladding pump absorption of 10 dB/m and were designed for use in a compact monolithic configuration due to its all-solid nature and its 14 cm targeted bend diameter.

How the zebra got its stripes: Curvature-dependent diffusion orients Turing patterns on three-dimensional surfaces.

Many animals have patterned fur, feathers, or scales, such as the stripes of a zebra. Turing models, or reaction-diffusion systems, are a class of mathematical models of interacting species that have been successfully used to generate animal-like patterns for many species. When diffusion of the inhibitor is high enough relative to the activator, a diffusion-driven instability can spontaneously form patterns. However, it is not just the type of pattern but also the orientation that matters, and it remains unclear how patterns are oriented in practice. Here, we propose a mechanism by which the curvature of the surface influences the rate of diffusion, and can recapture the correct orientation of stripes on models of a zebra and of a cat in numerical simulations. Previous work has shown how anisotropic diffusion can give stripe forming reaction-diffusion systems a bias in orientation. From the observation that zebra stripes run around the direction of highest curvature, that is around the torso and legs, we apply this result by modifying the anisotropic diffusion rates based on the local curvature. These results show how local geometry can influence the reaction dynamics to give robust, global-scale patterns. Overall, this model proposes a coupling between the system geometry and reaction-diffusion dynamics that can give global control over the patterning by using only local curvature information. Such a model can give shape and positioning information in animal development without the need for spatially dependent morphogen gradients.

Heuristic estimation of river bathymetry in braided streams using digital image processing

AbstractMeasurement of river bathymetry has been revolutionized by high‐resolution remote sensing that combines UAV platforms with SfM‐MVS photogrammetry. Mapping inundated and exposed areas simultaneously are possible using either two‐media refraction correction or some form of the Beer–Lambert Law to estimate water depths. If, as in turbid glacially‐fed braided streams, the bed is not visible then traditional survey techniques (e.g. differential GPS systems) are required. As an alternative, here we test whether the spatial distribution of water depths in a shallow braided stream can be modelled from basic planimetric data and used to estimate inundated zone bathymetry. We develop heuristic rules using; (1) distance from the nearest river bank; (2) total inundated width along a line tangential to the local flow direction; (3) local curvature magnitude and direction; and distance from the nearest flow (4) divergence and (5) convergence regions. We parameterize them using a sample of measured water depths in stepwise multiple linear regressions and validate them using independent data. Resulting water depth distribution maps explain between 50% and 60% of the measured water depth spatial variability when compared to independent data. After incorporating modelled water depths into digital elevation models (DEMs) of exposed areas, we show that the developed method is suitable for volumetric change calculations in both dry and inundated areas.

Hydrogen-Bonding-Regulated Morphology Control and the Impact on the Antibacterial Activity of Cationic π-Amphiphiles.

This manuscript describes the synthesis, self-assembly, and antibacterial properties of naphthalene-diimide (NDI)-derived cationic π-amphiphiles. Three such asymmetric NDI derivatives with a nonionic hydrophilic wedge and a guanidine group in the two opposite sides of the NDI chromophore were considered. They differ by a single functional group (hydrazide, amide, and ester for NDI-1, NDI-2, and NDI-3, respectively), located in the linker between the NDI and the hydrophilic wedge. For NDI-1, the H-bonding among the hydrazides regulated unilateral stacking and a preferential direction of curvature of the resulting supramolecular polymer, producing an unsymmetric polymersome with the guanidinium groups displayed at the outer surface. NDI-3, lacking any H-bonding group, exhibits π-stacking without any preferential orientation and generates spherical particles with a relatively poor display of the guanidium groups. In sharp contrast to NDI-1, NDI-2 exhibits an entangled one-dimensional (1D) fibrillar morphology, indicating the prominent role of the H-bonding motif of the amide group and flexibility of the linker. The antibacterial activity of these assemblies was probed against Staphylococcus aureus (Gram-positive) and Escherichia coli (Gram-negative). NDI-1 showed the most promising antibacterial activity with a minimum inhibitory concentration (MIC) of ∼7.8 μg/mL against S. aureus and moderate activity (MIC ∼ 125 μg/mL) against E. coli. In sharp contrast, NDI-3 did not show any significant activity against the bacteria, suggesting a strong impact of the H-bonding-regulated directional assembly. NDI-2, forming a fibrillar network, showed moderate activity against S. aureus and negligible activity against E. coli, highlighting a significant impact of the morphology. All of these three molecules were found to be compatible with mammalian cells from the 3-[4,5-dimethylthiazol-2-yl]-2,5-diphenyl-tetrazolium bromide (MTT) and hemolysis assay. The mechanistic investigation by membrane polarization assay, live/dead fluorescence assay, and microscopy studies confirmed the membrane disruption mechanism of cell killing for the lead candidate NDI-1.

Exploring potential energy surfaces to reach saddle points above convex regions.

Saddle points on high-dimensional potential energy surfaces (PES) play a determining role in the activated dynamics of molecules and materials. Building on approaches dating back more than 50 years, many open-ended transition-state search methods have been developed to follow the direction of negative curvature from a local minimum to an adjacent first-order saddle point. Despite the mathematical justification, these methods can display a high failure rate: using small deformation steps, up to 80% of the explorations can end up in a convex region of the PES, where all directions of negative curvature vanish, while if the deformation is aggressive, a similar fraction of attempts lead to saddle points that are not directly connected to the initial minimum. In high-dimension PES, these reproducible failures were thought to only increase the overall computational cost, without having any effect on the methods' capacity to find all saddle points surrounding a minimum. Using activation-relaxation technique nouveau (ARTn), we characterize the nature of the PES around minima, considerably expanding on previous knowledge. We show that convex regions can lie on activation pathways and that not exploring beyond them can introduce significant bias in the saddle-point search. We introduce an efficient approach for traversing the convex regions, almost eliminating exploration failures, while multiplying by almost 10 the number of identified unique and connected saddle points as compared to the standard ARTn, thus underlining the importance of correctly handling convex regions for completeness of saddle point explorations.

Curvature Footprints of Transmembrane Proteins in Simulations with the Martini Force Field.

Membranes play essential roles in biological systems and are tremendously diverse in the topologies and chemical and elastic properties that define their functions. In many cases, a given membrane may display considerable heterogeneity, with localized clusters of lipids and proteins exhibiting distinct characteristics compared to adjoining regions. These lipid-protein assemblies can span nanometers to micrometers and are associated with cellular processes such as transport and signaling. While lipid-protein assemblages are dynamic, they can be stabilized by coupling between local membrane composition and shape. Due to the inherent difficulty in resolving atomistic details of membrane proteins in their native lipid environments, these complexes are notoriously challenging to study experimentally; however, molecular dynamics (MD) simulations might be a viable alternative. Here, we aim to assess the utility of coarse-grained (CG) MD simulations with the Martini force field for studying membrane curvature induced by transmembrane (TM) proteins that are reported to generate local curvature. The direction and magnitude of curvature induced by five different TM proteins, as well as certain lipid-protein and protein-protein interactions, were found to be in good agreement with available reference data.

Study of methods for predicting the stability of preparatory workings in the mines of Western Donbas

Purpose. Analysis of the effectiveness and feasibility of existing methods for predicting preparatory workings. Research methodology. The research was conducted using an analytical method (analysis, explanation, synthesis, comparison) and statistical data processing method. Research results. The conducted research allowed determining that the coal-bearing sedimentary massif of the Western Donbas, as a result of complex tectonic movements, is characterized by developed and intensive tectonic disturbances of a ruptural and plicative nature. The appearance of plicative disturbances in the hanging wall of the coal seam, accompanied by an increase in their thickness, leads to the concentration of stresses in the areas of disturbances caused by approaching the mining face. Regional plicative disturbances cause the formation of zones of anomalous activity in the intact mining massif. In addition to gravitational forces affecting the geological structure, tectonic stresses directed along the bedding plane are added to this phenomenon. Tectonic stresses are oriented in the direction of the main curvatures of the natural surface of rock deposition and depend on their magnitude. Geological deviations of various types are key indicators of anomalies in the tectonic environment and zones of reduced strength in an intact mining massif. These anomalies can result from the complex interaction of geological processes, including tectonic activity, water flow activity, and other natural factors. These deviations become fundamental factors contributing to the occurrence of gas-dynamic phenomena and rockfalls during the preparatory mining stage. Scientific novelty. The regularity of the interaction of geomechanical parameters of elements of the "layered massif – excavation support" system has been established. Practical significance. Studying methods for predicting the stability of preparatory workings allows for the development of effective excavation support systems according to geological conditions and prevents possible accidents and rockfalls in mining working areas.

Effect of Wave Dark Matter on Equal Mass Black Hole Mergers

For dark matter to be detectable with gravitational waves from binary black holes, it must reach higher than average densities in their vicinity. In the case of light (wavelike) dark matter, the density of dark matter between the binary can be significantly enhanced by accretion from the surrounding environment. Here we show that the resulting dephasing effect on the last ten orbits of an equal mass binary is maximized when the Compton wavelength of the scalar particle is comparable to the orbital separation, 2π/μ∼d. The phenomenology of the effect is different from the channels that are usually discussed, where dynamical friction (along the orbital path) and radiation of energy and angular momentum drive the dephasing, and is rather dominated by the radial force (the spacetime curvature in the radial direction) towards the overdensity between the black holes. While our numerical studies limit us to scales of the same order, this effect may persist at larger separations and/or particle masses, playing a significant role in the merger history of binaries. Published by the American Physical Society 2024

Which Coverages of Arc-Shaped Proteins Are Required for Membrane Tubulation?

Arc-shaped BIN/Amphiphysin/Rvs (BAR) domain proteins generate curvature by binding to membranes and induce membrane tubulation at sufficiently large protein coverages. For the amphiphysin N-BAR domain, Le Roux et al., Nat. Commun. 2021, 12, 6550, measured a threshold coverage of 0.44 ± 0.097 for nanotubules emerging from the supported lipid bilayer. In this article, we systematically investigate membrane tubulation induced by arc-shaped protein-like particles with coarse-grained modeling and simulations and determine the threshold coverages at different particle-particle interaction strengths and membrane spontaneous curvatures. In our simulations, the binding of arc-shaped particles induces a membrane shape transition from spherical vesicles to tubules at a particle threshold coverage of about 0.5, which is rather robust to variations of the direct attractive particle interactions or spontaneous membrane curvature in the coarse-grained model. Our study suggests that threshold coverages of around or slightly below 0.5 are a general requirement for membrane tubulation by arc-shaped BAR domain proteins.

The architectural application of shells whose boundaries subtend a constant solid angle

Surface geometry plays a central role in the design of bridges, vaults and shells, using various techniques for generating a geometry which aims to balance structural, spatial, aesthetic and construction requirements.In this paper we propose the use of surfaces defined such that given closed curves subtend a constant solid angle at all points on the surface and form its boundary. Constant solid angle surfaces enable one to control the boundary slope and hence achieve an approximately constant span-to-height ratio as the span varies, making them structurally viable for shell structures. In addition, when the entire surface boundary is in the same plane, the slope of the surface around the boundary is constant and thus follows a principal curvature direction. Such surfaces are suitable for surface grids where planar quadrilaterals meet the surface boundaries. They can also be used as the Airy stress function in the form finding of shells having forces concentrated at the corners.Our technique employs the Gauss-Bonnet theorem to calculate the solid angle of a point in space and Newton's method to move the point onto the constant solid angle surface. We use the Biot-Savart law to find the gradient of the solid angle. The technique can be applied in parallel to each surface point without an initial mesh, opening up for future studies and other applications when boundary curves are known but the initial topology is unknown.We show the geometrical properties, possibilities and limitations of surfaces of constant solid angle using examples in three dimensions.

Drivers of Morphogenesis: Curvature Sensor Self-Assembly at the Membrane.

This review examines the relationships between membrane chemistry, curvature-sensing proteins, and cellular morphogenesis. Curvature-sensing proteins are often orders of magnitude smaller than the membrane curvatures they localize to. How are nanometer-scale proteins used to sense micrometer-scale membrane features? Here, we trace the journey of curvature-sensing proteins as they engage with lipid membranes through a combination of electrostatic and hydrophobic interactions. We discuss how curvature sensing hinges on membrane features like lipid charge, packing, and the directionality of membrane curvature. Once bound to the membrane, many curvature sensors undergo self-assembly (i.e., they oligomerize or form higher-order assemblies that are key for initiating and regulating cell shape transformations). Central to these discussions are the micrometer-scale curvature-sensing proteins' septins. By discussing recent literature surrounding septin membrane association, assembly, and their many functions in morphogenesis with support from other well-studied curvature sensors, we aim to synthesize possible mechanisms underlining cell shape sensing.

Artificial intelligence warm-start approach: optimizing the generalization capability of QAOA in complex energy landscapes

To address the issue of the quantum approximate optimization algorithm frequently encountering local minima and the cost of parameter optimization within complex non-convex optimization energy landscapes, we consider a warm-start method. This approach leverages the characteristics of transition states in the enhanced optimizer, specifically descending along unique negative curvature directions, to find smaller local minima. Our research results indicate that with the assistance of an enhanced pre-training structure of the AlphaZero AI model, the initialization generalization ability of the new optimizer is significantly enhanced across various test sets. We train on 2-SAT training sets with clause densities between α ≈ 2.6 and α ≈ 2.89, and transfer to more complex test sets. Additionally, the average residual energy density in transfer learning consistently remains below 0.01, even achieving a high transfer success probability of 98% in hard instances with α ≈ 3.7. The search efficiency, pre-trained by ensemble learning, was significantly enhanced, while only requiring simple interpolation of a few transition points to transfer on the global optimal solutions at higher sample clause densities.

“Visible range curvature fiber-optic sensor with low strain-temperature dependence”

This manuscript introduces and demonstrates a visible curvature fiber optic sensor using an all-fiber Mach-Zehnder interferometer. The all-fiber interferometer was constructed using an in-line optical fiber sandwich structure, utilizing fibers specifically designed for the visible range. We demonstrate the reproducibility of the curvature sensor fabricating several distinct interferometers. These devices were subjected to curvature testing, exhibiting suitable wavelength shifts and achieving a maximal sensitivity of −10.44 nm/m−1. The hysteresis analysis shows minimal path deviation, and the statistical ANOVA analysis reveals a consistent mean trend with a minimal Prob > F value of 9.30472 × 10−55. Consequently, the hysteresis analysis indicates that the error in the curvature direction has a minimal impact on the measurement, and the low Prob > F value ensures that the curvature measurements cannot overlap. Then, accurate and high reproducibility of the curvature measurements can be expected. The results validate that the optical fiber structure is among the limited approaches to phase modulation interference within the visible range, representing a competitive alternative for curvature measurement.

Artificial Intelligence in Medical Imaging: Analyzing the Performance of ChatGPT and Microsoft Bing in Scoliosis Detection and Cobb Angle Assessment.

Open-source artificial intelligence models (OSAIM) find free applications in various industries, including information technology and medicine. Their clinical potential, especially in supporting diagnosis and therapy, is the subject of increasingly intensive research. Due to the growing interest in artificial intelligence (AI) for diagnostic purposes, we conducted a study evaluating the capabilities of AI models, including ChatGPT and Microsoft Bing, in the diagnosis of single-curve scoliosis based on posturographic radiological images. Two independent neurosurgeons assessed the degree of spinal deformation, selecting 23 cases of severe single-curve scoliosis. Each posturographic image was separately implemented onto each of the mentioned platforms using a set of formulated questions, starting from 'What do you see in the image?' and ending with a request to determine the Cobb angle. In the responses, we focused on how these AI models identify and interpret spinal deformations and how accurately they recognize the direction and type of scoliosis as well as vertebral rotation. The Intraclass Correlation Coefficient (ICC) with a 'two-way' model was used to assess the consistency of Cobb angle measurements, and its confidence intervals were determined using the F test. Differences in Cobb angle measurements between human assessments and the AI ChatGPT model were analyzed using metrics such as RMSEA, MSE, MPE, MAE, RMSLE, and MAPE, allowing for a comprehensive assessment of AI model performance from various statistical perspectives. The ChatGPT model achieved 100% effectiveness in detecting scoliosis in X-ray images, while the Bing model did not detect any scoliosis. However, ChatGPT had limited effectiveness (43.5%) in assessing Cobb angles, showing significant inaccuracy and discrepancy compared to human assessments. This model also had limited accuracy in determining the direction of spinal curvature, classifying the type of scoliosis, and detecting vertebral rotation. Overall, although ChatGPT demonstrated potential in detecting scoliosis, its abilities in assessing Cobb angles and other parameters were limited and inconsistent with expert assessments. These results underscore the need for comprehensive improvement of AI algorithms, including broader training with diverse X-ray images and advanced image processing techniques, before they can be considered as auxiliary in diagnosing scoliosis by specialists.

A Mach-Zehnder-based optical fiber sensor enables multi-directional and wide-range curvature sensing with the assistance of CNN

In this work, wide-range curvature sensing in multiple directions was achieved by combining a Mach-Zehnder-based optical fiber sensor (OFS) with convolutional neural networks (CNNs). The experimental results show that the curvature sensitivity of the proposed sensor is − 8.8320 nm/m−1 in the range of 0–3.1171 m−1. The application of CNNs significantly improves the measurement range to 0–10.4167 m−1, and the sensor can realize measurements over a wide curvature range in four directions. The accuracy of the measurements can still be guaranteed despite a sudden decrease in the number of wavelength sampling points, and curvature direction recognition was realized. Further, OFSs can achieve a wide range of curvature sensing in 12 directions by taking full advantage of the information contained in the transmission spectrum. The proposed technique is highly versatile and conducive to the popularization of OFSs in the field of curvature measurement.