Search

This study considered the effect of shear deformation in the bending model, which was important to assess of the plate buckling loads according to changes in the thickness. The buckling of square, skew, and perforated plates was studied with the rotation gradient (curvature) and the deflection gradient in the in the geometrical nonlinearity (GNL) effect using the BEM. The importance of the curvatures appeared when the thickness-to-span ratio reached 0.05 and increased for thicker plates in several cases. The present boundary elements formulation used the gradient of the displacements instead of second derivatives in the GNL, which disregarded the relation between the in-plane forces derivatives consequently. The singularities related to the differentiation process to obtain the BIEs for the gradient of displacements and for the stresses were reduced with using the tangent differential operator. [ABSTRACT FROM AUTHOR]

In order to realize the automation of surface mesh generation for arbitrary complex models, this paper proposes a binary-tree method (BTM) which can generate discontinuous grids. Compared with continuous grids, the adjacency relationship between discontinuous grids generated by BTM is more flexible, so it is easier to discretize "dirty" geometry without geometry repair than continuous grids. The BTM can adaptively generate meshes by features based on the curvature of curves and surfaces, and thus it does not need to construct a sizing field. Anisotropic meshes can also be directly generated by selecting the direction of subdividing meshes. Moreover, according to the periodic characteristics of periodic surfaces, the topological structure of the initial mesh can be designed to achieve mesh generation on periodic surfaces. Successful numerical examples are used to illustrate the effectiveness and robustness of the presented methods for meshing various types of geometric surfaces and reveal the excellent performance of the BTM. In addition, the BTM has been employed by the dual interpolation boundary face method (DiBFM) to solve 3D problems. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to investigate the influence of smooth curvature distributions on the self-noise of a low Reynolds number aerofoil and to unveil the flow mechanisms in the phenomenon. Design/methodology/approach: In this paper, large Eddy simulation (LES) approach was performed to investigate the unsteady aerodynamic performance of both the original aerofoil E387 and the redesigned aerofoil A7 in a time-dependent study of boundary layer characteristics at Reynolds number 100,000 and angle of attack (AoA) 4-degree. The aerofoil A7 is redesigned from E387 by removing the irregularities in the surface curvature distributions and keeping a nearly identical geometry. Flow vorticity magnitude of both aerofoils, along with the spectra of the vertical fluctuating velocity component and noise level, are analysed to demonstrate the bubble flapping process near the trailing edge (TE) and the vortex shedding phenomenon. Findings: This paper provides quantitative insights about how the flapping process of the laminar separation bubble (LSB) within the boundary layer near the TE affects the aerofoil self-noise. It is found that the aerofoil A7 with smooth curvature distributions presents a 10% smaller LSB compared to the aerofoil E387 at Reynolds number 100,000 and AoA 4-degree. The LES results also suggest that curvature distribution smoothing leads to a 6.5% reduction in overall broadband noise level. Originality/value: This paper fulfils an identified need to reveal the unknown flow structure and the boundary layer characteristics that resulted in the self-noise reduction phenomenon yielded by curvature distribution smoothing. [ABSTRACT FROM AUTHOR]

Most font editors offer curvature-related tools. One of these tools is the visualization of curvature via curvature combs. Another tool is the so-called harmonization, which makes the curvature continuous along paths. An implementation of both tools in METAPOST will be presented. Curvature-optimized paths already play a significant role in METAFONT and METAPOST and therefore example METAPOST paths will be examined for their curvature behavior. [ABSTRACT FROM AUTHOR]

Although a surface parametrization by orthogonal curvilinear coordinates offers many benefits, ways to construct them are not immediate. The utility of lines of curvature for constructing such representations globally is severely limited by the presence of umbilical points, but a collection of local parametrizations may suffice in applications. Here we develop a practical method to obtain a local reparametrization of a piecewise parametric surface model by consistently accurate lines of curvature coordinates. Our analysis of possible instabilities occurring at an isolated umbilical point indicates that a slight modification of the original patches may suffice to ensure that the configuration of the reparametrized surface always stays regular. We give explicit representations of differential geometric quantities which are particularly useful in treating finite element formulations defined on surfaces. [ABSTRACT FROM AUTHOR]

The cell-based smoothed radial point interpolation method in conjunction with a second order cone programming is proposed for kinematic limit analysis of rigid-perfectly plastic thin plates in this paper. The transverse displacement field is interpolated by the radial point interpolation method (RPIM) and no rotational degrees of freedom are involved. The gradient smoothing technique is utilized to construct smoothed curvature field in every smoothing domain and there is no need to compute the second derivatives of shape functions. The rotational boundary conditions are satisfied in the process of curvature smoothing and the translational boundary conditions can be directly enforced without any special treatment. The limit analysis problem of thin plates is formulated by minimizing the dissipation power subject to a set of equality constraints and this minimization problem can be expressed easily as a standard second order cone programming. It is testified from the computational results that the proposed procedure can provide reasonable and satisfactory upper bound limit load multipliers for thin plates. [ABSTRACT FROM AUTHOR]

The axial buckling behavior is determined for an elastic beam or rod which has a uniform curvature in its natural state, is straightened by pure bending, and clamped at its ends. Buckling can be either identical to the classical two-dimensional behavior determined by Euler, or it can be three-dimensional involving twist and deflection out of the plane of natural curvature depending on the bending and torsional stiffnesses and the natural curvature. While the classical two-dimensional buckling behavior of Euler's elastica is stable under applied load, the three-dimensional buckling behavior can be stable or unstable. Theoretical and experimental examples are presented illustrating the full range of possibilities. [ABSTRACT FROM AUTHOR]

A patent has been issued for a camera optical lens developed by Aac Optics (Changzhou) Co. Ltd. The lens is designed to meet the increasing demands for high-quality imaging, particularly in terms of night scene photography and background blur. The lens incorporates a free-form surface, which allows for better correction of aberrations and improved imaging quality. The patent provides detailed specifications and claims for the camera optical lens, including requirements for focal lengths, curvature radii, and thicknesses of various lens components. For more information, the patent can be accessed using the provided URL. [Extracted from the article]

A recent report from the College of Electrical and Control Engineering discusses new research on nanowires and their potential applications in various fields such as gas sensing, switchgear, and biomedicine. The study focuses on the influence of the curvature radius of the cathode on the micro-corona discharge process. The researchers propose a gas model to describe the discharge dynamics and investigate the effects of the nanowire radius on discharge current, electric field, ionization reaction rate, and charged particle characteristics. The findings suggest that the curvature radius affects the discharge intensity differently depending on the gap and voltage conditions. Increasing the curvature radius can enhance the coupling process and increase the discharge current, particularly at small gaps or low voltages. [Extracted from the article]

A patent application for a dual optic, curvature changing accommodative intraocular lens (IOL) has been filed by inventors David Borja, Lauren Gerardi, and Shinwook Lee. The lens is designed to replace the natural lens in the eye and provide accommodation for both near and far vision. The IOL utilizes a fluid optic body and a second optic body connected by struts, which can change the curvature of the lens in response to the contraction and relaxation of the ciliary muscles. This technology aims to provide a safe and stable solution for patients with cataracts or presbyopia. [Extracted from the article]

A recent study conducted in Lima, Peru investigated and compared the morphological features of keratoconus (KC) and normal eyes using anterior segment optical coherence tomography (OCT). The study found that KC eyes displayed an asymmetric bowtie pattern in the Sagittal and Tangential curvature maps, while normal eyes showed a symmetric bowtie pattern. There were significant differences in the variables measured between the Gaussian, Tangential, and Sagittal maps in both normal and KC groups. The study concluded that the Tangential maps were more sensitive in discriminating between KC and normal eyes compared to the Gaussian maps. [Extracted from the article]

A patent application has been submitted for a system that recommends the curvature of transseptal needles based on patient anatomy. The transseptal puncture technique is used in various cardiac procedures, and the curvature of the needle can affect its approach to the interatrial septum. The system uses an anatomical map to determine the spatial relationship between the access vessel and the target puncture location, and it can recommend a preferred needle shape or a custom needle shape for individual patients. The system aims to improve the accuracy and efficiency of transseptal puncture procedures. [Extracted from the article]

A recent study conducted by researchers from Fujian Medical University in China examined the long-term survival benefits of laparoscopic spleen-preserving splenic hilar lymphadenectomy (LSPSHL) for patients with advanced proximal gastric cancer (APGC) without greater curvature invasion. The study, which followed 536 patients for at least 5 years, found that laparoscopic total gastrectomy with LSPSHL improved prognosis and reduced recurrence rates compared to standard treatment. The researchers recommend further multicenter studies to validate these findings. This research was published in JAMA Surgery and was funded by Fujian Province Medical 'Dual High' Construction Funding and Fujian Research and Training Grants for Young and Middle-aged Leaders in Healthcare. [Extracted from the article]

MEDICREA International, a company based in France, has been issued a patent for a method of producing the ideal curvature of a rod of vertebral osteosynthesis material used to support a patient's vertebral column. The method involves receiving a model defining the curvature of the rod based on a pre-operative X-ray of the patient's vertebral column, and producing the rod using computer-aided design. The curvature of the rod is determined based on various measurements and criteria, such as the lumbar lordosis and the position of the apex point. The patent provides detailed claims and a system for implementing the method. This information may be useful for researchers and professionals in the field of bone diseases and conditions, spinal curvatures, and musculoskeletal diseases and conditions. [Extracted from the article]

A preprint abstract from biorxiv.org discusses the role of membrane curvature in the formation of contact sites between the endoplasmic reticulum (ER) and the plasma membrane (PM) in cardiomyocytes. The study suggests that PM curvature plays a role in the formation of these contact sites, and the junctophilin family of proteins is involved in this process. The study also identifies a family of proteins called Eps15-homology domain containing proteins (EHDs) that interact with junctophilins and facilitate their tethering to curved PM. These findings provide insights into the spatial regulation of ER-PM contacts through PM curvature modulation. [Extracted from the article]

A recent study conducted by researchers at the University of California Davis focused on the biomechanical engineering of the knee joint. The study aimed to determine the variations in the radii of curvature of the articular surfaces of the femoral condyles in the sagittal plane. Using high-resolution CT scans, 3D models of the femur were created, and the radii of curvature were measured at different degrees of flexion. The results showed that the medial and lateral femoral condyles exhibited multi-radius of curvature sagittal profiles, with a decrease in radius at specific flexion angles. The study concluded that the flexion-extension axis of the knee is not strictly fixed due to variations in the anterior-posterior positions of the centers of curvature. This research provides valuable insights for the design of femoral components that restore native knee kinematics. [Extracted from the article]

• An efficient unstructured surface mesh generation method has been proposed for arbitrary regions with tiny features or crack defects. • A novel type of meshing template has been proposed to solve the problem of entity boundary fitting of the outside-in grid-based method. • The proposed meshing method is invariably achievable to implement based on an easily accessible and reliable way. • The proposed meshing method can guarantee the convergence of high-quality mesh generation under any circumstances. • Several realistic geometries with cracks or proximity features are applied to demonstrate the validity, accuracy, and robustness of the proposed method. An efficient unstructured quadrilateral-dominated surface mesh generation algorithm is presented to generate high-quality surface elements for arbitrary geometry with tiny features or crack defects. For complex entities with proximity features, a novel type of meshing template has been proposed to solve the problem of entity boundary fitting of the outside-in grid-based method. The algorithm also works for regions with proximity features, as well as for arbitrary geometry with one or multiple cracks. The procedure incorporates aspects of well-known meshing techniques, but includes some original and efficient processes. The refinement field is constructed according to mesh size, boundary curvature, surface curvature and other geometry features. In order to effectively generate the core mesh, a fast intersection algorithm between topological elements and the solid boundary is established, which improves the efficiency of intersection calculation. The geometry-based techniques are employed for boundary matching of the core mesh. The method has been successfully employed in conjunction with the dual interpolation boundary face method (DiBFM). Several realistic geometries with cracks or proximity features are applied to demonstrate the accuracy and validity of the proposed approach. [ABSTRACT FROM AUTHOR]

Size regulation in living organisms is a major unsolved problem in developmental biology. This is due to the intrinsic complexity of biological growth, which simultaneously involves genetic, biochemical, and mechanical factors. In this article, we propose a novel theoretical framework that explores the role of incompatibility, the geometric source of residual stress in a growing body, as a possible regulator of size termination during development. We explore this paradigm both at the level of a model 2D cell, and at the level of continuous tissues. After establishing a parallel between incompatibility and the shape parameter of vertex models, we show that incompatibility-driven growth leads to size control in a model 2D cell. We then extend the same paradigm to the level of continuous bodies, where incompatibility is measured by the Ricci curvature of the growth tensor. By using the model 2D cell as a template, we now derive an evolutionary law for the growth tensor with curvature fixed at a physiological value. When the analysis is specialised to radial symmetry (discs and spheres), this model captures the salient features observed in Drosophila wing discs and multicellular spheroids: these systems have a target size and build up residual stresses that cause the tissue to open in response to a radial cut, with the cut edges curling outward. The theory proposed in this work suggests that incompatibility in a growing biological tissue is potentially controllable at the cell level, and that incompatibility-driven growth provides an effective method of controlling global information (stress, size) through local geometric controls. [ABSTRACT FROM AUTHOR]

The article focuses on the optical principles behind the distortion and reflection of images in curved mirrors, specifically convex mirrors. It explains how the curvature of a mirror alters the angles of reflected light, resulting in distorted images. It mentions that the experiment involves using an aluminum soda can, mirror film, and a felt-tip pen to demonstrate how stretched images can be reflected accurately in a convex mirror.

Purpose: The purpose of this study is to investigate the Cattaneo-Christov double diffusion, multiple slips and Darcy-Forchheimer's effects on entropy optimized and thermally radiative flow, thermal and mass transport of hybrid nanoliquids past stretched cylinder subject to viscous dissipation and Arrhenius activation energy. Design/methodology/approach: The presented flow problem consists of the flow, heat and mass transportation of hybrid nanofluids. This model is featured with Casson fluid model and Darcy-Forchheimer model. Heat and mass transportations are represented with Cattaneo-Christov double diffusion and viscous dissipation models. Multiple slip (velocity, thermal and solutal) mechanisms are adopted. Arrhenius activation energy is considered. For graphical and numerical data, the bvp4c scheme in MATLAB computational tool along with the shooting method is used. Findings: Amplifying curvature parameter upgrades the fluid velocity while that of porosity parameter and velocity slip parameter whittles down it. Growing mixed convection parameter, curvature parameter, Forchheimer number, thermally stratified parameter intensifies fluid temperature. The rise in curvature parameter and porosity parameter enhances the solutal field distribution. Surface viscous drag gets controlled with the rising of the Casson parameter which justifies the consideration of the Casson model. Entropy generation number and Bejan number upgrades due to growth in diffusion parameter while that enfeeble with a hike in temperature difference parameter. Originality/value: To the best of the authors' knowledge, this research study is yet to be available in the existing literature. [ABSTRACT FROM AUTHOR]

Graph neural networks (GNNs) have achieved great success in many graph-based tasks. Much work is dedicated to empowering GNNs with adaptive locality ability, which enables the measurement of the importance of neighboring nodes to the target node by a node-specific mechanism. However, the current node-specific mechanisms are deficient in distinguishing the importance of nodes in the topology structure. We believe that the structural importance of neighboring nodes is closely related to their importance in aggregation. In this paper, we introduce discrete graph curvature (the Ricci curvature) to quantify the strength of the structural connection of pairwise nodes. We propose a curvature graph neural network (CGNN), which effectively improves the adaptive locality ability of GNNs by leveraging the structural properties of graph curvature. To improve the adaptability of curvature on various datasets, we explicitly transform curvature into the weights of neighboring nodes by the necessary negative curvature processing module and curvature normalization module. Then, we conduct numerous experiments on various synthetic and real-world datasets. The experimental results on synthetic datasets show that CGNN effectively exploits the topology structure information and that the performance is significantly improved. CGNN outperforms the baselines on 5 dense node classification benchmark datasets. This study provides a deepened understanding of how to utilize advanced topology information and assign the importance of neighboring nodes from the perspective of graph curvature and encourages bridging the gap between graph theory and neural networks. The source code is available at https://github.com/GeoX-Lab/CGNN. [ABSTRACT FROM AUTHOR]

The paper discusses the relationships between electrical quantities, such as voltages, currents, and frequency, and geometrical ones, namely curvature and torsion. The proposed approach is based on the Frenet frame utilized in differential geometry and provides a general framework for the definition of the time derivative of electrical quantities in stationary as well as transient conditions. As a byproduct, the proposed approach unifies and generalizes the time- and phasor-domain frameworks. Other noteworthy results are a new interpretation of the link between frequency and the time derivatives of voltage and current; and a definition of the rate of change of frequency that includes the novel concept of “torsional frequency.” Several numerical examples based on balanced, unbalanced, harmonically-distorted and transient voltages illustrate the findings of the paper. [ABSTRACT FROM AUTHOR]

In this paper, we study the coarse Ricci curvature of inhomogeneous random graph on vertex set [ n ] ≔ { 1 , 2 , ... , n }. In this graph, each pair of vertices (i , j) forms an edge independently with probability λ n α g i n , j n for some function g (x , y) ∈ (0 , 1 ] , constants λ > 0 and α ∈ [ 0 , 1 ]. We derive the asymptotic coarse Ricci curvature of this random graph. Phase transition phenomenon exists as α varies from zero to one. [ABSTRACT FROM AUTHOR]

Axisymmetric beading instabilities in soft, elongated cylinders have been observed in a plethora of scenarios, ranging from cellular nanotunnels and nerves in biology to swollen cylinders and electrospun fibers in polymer physics. One of the common geometrical features that can be seen in these systems is the finite wavelength of the emerging pattern. However, modelling studies often predict that the instability has an infinite wavelength, which can be associated with localized necking or bulging. In this paper, we consider a soft elastic cylinder with a thin coating that resists bending, as described by the Helfrich free energy functional. The bending stiffness and natural mean curvature of the coating are two novel features whose competition against bulk elasticity and capillarity is investigated. For intermediate values of the bending stiffness, a linear stability analysis reveals that the mismatch between the current and natural mean curvature of the coating can lead to patterns emerging with a finite wavelength. This analysis creates a continuous bridge between the classical solutions of the shape equation obtained from the Helfrich functional and a curvature-controlled zero-wavemode instability, similar to the one induced by the competition between bulk elasticity and capillarity. A weakly non-linear analysis predicts that the criticality of the bifurcation depends on the controlling parameter, with both supercritical and subcritical bifurcations possible. When capillarity is introduced, the criticality of the bifurcation changes in a non-trivial way. • We study axisymmetric beading in elastic cylinders with a thin coating. • Curvature incompatibility can lead to patterns emerging with finite wavelength. • Highly curved coatings lead to an infinite-wavelength elastocapillary-like pattern. • The emerging pattern can have localized amplitude modulations. • The pattern can be controlled by stretching, bending, and capillarity. [ABSTRACT FROM AUTHOR]

A recent study conducted at the National Traffic Injury Rehabilitation Hospital in South Korea focused on assessing the preservation of lumbar lordotic curvature (LLC) in everyday sitting conditions. The researchers used an inertial measurement system to compare the magnitude and maintenance of LLC across different sitting conditions, such as verbal instructions, chair type, and desk task types. The study found that sitting upright and using an office chair were associated with better preservation of LLC, while keyboard tasks had the largest impact on LLC. These findings suggest that strategies such as using an office chair and preferring computer work may help preserve LLC. [Extracted from the article]

A recent study conducted by researchers at Tehran University of Medical Sciences aimed to evaluate the effectiveness of two novel eyelid curvature measurements in distinguishing between normal eyes and different severities of blepharoptosis (droopy eyelids). The study analyzed the upper eyelid curvature of patients with unilateral blepharoptosis and compared it to normal controls. The results showed that the area circularity index (ACI) based on area measurements was able to differentiate blepharoptosis patients from normal controls and from each other. The researchers suggest that including data from the fellow normal eyes in the form of ratio indices may improve the accuracy of these measurements. [Extracted from the article]

Alcon Inc. has been issued a patent for a dual optic, curvature changing accommodative intraocular lens (IOL). The lens is designed to replace the natural lens in the eye and provide accommodation for both near and far vision. The lens utilizes the movement of the capsular bag and the contraction and relaxation of the ciliary muscles to change the shape and curvature of the lens, allowing for focusing on different distances. This technology aims to provide a safe and stable solution for patients with cataracts or presbyopia. [Extracted from the article]

Researchers at Shaanxi Provincial People's Hospital in China have conducted a study on the curvature characteristics of the talus trochlea in people from northern China. They collected computed tomography scanning data from 61 specimens and constructed a three-dimensional model. The study found significant differences in talus curvatures among different areas, with the posterior area having a larger radius of curvature than the anterior area. The researchers recommend considering these characteristics when designing the talus component in total ankle replacement surgery. The full study can be accessed in the Journal of Orthopaedic Surgery and Research. [Extracted from the article]

A study conducted at Zhejiang University in Hangzhou, China, examined the changes in posterior corneal asphericity (AQ) after two different surgical procedures for myopia: femtosecond laser-assisted in situ keratomileusis (FS-LASIK) and small incision lenticule extraction (SMILE). The study found that both procedures resulted in a significant increase in the posterior corneal Q-value, with no significant differences between the two approaches. However, patients with moderate myopia had lower increases in Q-value and smaller AQ-values compared to those with high myopia. The study suggests that both FS-LASIK and SMILE procedures can affect the posterior corneal asphericity, and the degree of change depends on the severity of myopia. [Extracted from the article]

A patent application has been filed for a method of treating abnormal bone curvature using a generative adversarial network (GAN). The GAN is trained using treatment data from multiple patients, including radiologic images and orthotic usage. The trained GAN can then identify abnormal bone curvature in new patients and generate artificial radiologic images to track the progress of treatment. The patent application does not specify a company or institution associated with the invention. [Extracted from the article]

Researchers from Delft University of Technology in the Netherlands have developed a deep learning framework to design artificial microstructures with specific surface curvatures. This framework can be applied to various topological features, such as tubular, membranous, and particulate structures. The researchers demonstrated the framework's ability to mimic the curvature profiles of trabecular bone, spinodoid topologies, and periodic nodal surfaces for use in bio-scaffolds and implants. The study also highlighted the role of curvature in redistributing bending and membrane strain energies. This research was supported by the China Scholarship Council. [Extracted from the article]

A recent report from the State University of New York (SUNY) Albany discusses the application of the Frenet-Serret apparatus, which is used to determine the local geometry of curves in three-dimensional space, to quantum-mechanical evolutions. The researchers propose a quantum version of the Frenet-Serret apparatus to quantify the bending and twisting of quantum curves traced by dynamically evolving state vectors. They show that their proposed curvature and torsion coefficients align with those in existing literature, and they explore the statistical structure of quantum theory using these concepts. The research includes examples with nonzero curvature and nonvanishing torsion, as well as applications to different degrees of entanglement in quantum states. [Extracted from the article]

In this article, we investigate the temporal evolution of arbitrary, simple, closed two-dimensional (2D) and three-dimensional (3D) interfaces under motion driven by mean curvature up to a singularity. To facilitate this investigation, we propose a novel Allen–Cahn (AC) model with a time-dependent interfacial thickness parameter. The original AC equation was developed to model the phase separation of a binary mixture. It is well known that a level set or interface of the solution of the AC equation obeys the dynamics of motion by curvature as the interfacial thickness parameter approaches zero. Generally, it is difficult to find a closed-form analytic solution of the AC equation with any initial condition. Therefore, we need to estimate the solution of the AC equation through computational approaches such as finite difference method (FDM), finite element method (FEM), Fourier-spectral method (FSM), and finite volume method (FVM). Any simple, closed curves and convex surfaces eventually shrink to a point due to motion by mean curvature. Therefore, it becomes necessary to use adaptive mesh techniques to resolve this small size problem. However, even though we use adaptive mesh techniques, we still confront the relatively thick interfacial transition layer when the curves or interfaces become very small. To avoid this problem, we can start with a very small mesh size for a small value of the interfacial parameter, which results in an extremely high computational cost even when using adaptive mesh techniques. To resolve these issues, we present the AC equation with a time-dependent interfacial parameter and develop an adaptive mesh refinement system. To show the superior performance of the proposed mathematical equation and its computational algorithm, we present various numerical experiments and investigate the motion by mean curvature up to the singularity of curves in 2D space and interfaces in 3D space. [ABSTRACT FROM AUTHOR]

In this paper, we investigate numerically the dynamic snap-through motion of a shallow arch micro-beam that is electrostatically excited through three separated electrodes. It is excited by a dc voltage and a time-varying signal with a frequency tuned near its first in-plane frequency in both initial curvature and initial-counter curvature configurations. A reduced-order model based on the Galerkin method is utilized to discretize the governing equation of motion and to analyze the static and dynamic responses of the micro-beam. The phase portraits obtained from simulations reveal the presence of a stable response that oscillates back and forth around single and double equilibria until it eventually settles in a steady state zone near the first equilibrium point or encloses both equilibria. This can be tracked using a Long-Time Integration (LTI) and recording the time–history signal for a long period. Remarkably, this behavior can be controlled by adjusting the initial operating conditions mainly the signal frequency. We also observe the emergence of a chaotic attractor in the vicinity of the resonance frequency when the shallow arch beam is excited while it is in its initial-counter curvature. The simulated FFTs indicate the presence of the chaotic attractor in the vicinity of primary resonance due to dynamic snap-through motion or large excitation between two equilibria. We observed the existence of periodic orbits with single loop (P-1) and an full chaotic behavior around the two equilibria. The existence of this phenomenon can be attributed to the fact that the excitation voltage is positioned close to the snap-through threshold. [ABSTRACT FROM AUTHOR]

A study conducted at a surgical center in Draper, Utah compared changes in the posterior curvature and the posterior-anterior radii ratio of the cornea one year after laser eye surgeries for myopia. The study included 199 eyes from 119 patients who underwent laser in situ keratomileusis (LASIK), photorefractive keratectomy (PRK), or small incision lenticule extraction (SMILE). The researchers found that the change in the posterior-anterior radii ratio did not differ between the surgery groups, and the posterior cornea exhibited flattening after LASIK, SMILE, and PRK. The study provides valuable information for individuals considering these surgical treatments for myopia. [Extracted from the article]

According to a preprint abstract from biorxiv.org, researchers have discovered a conserved mechanism for the internalization of G-protein coupled receptors (GPCRs). This mechanism involves the insertion of an amphipathic helix 8 (H8) into the inner leaflet of lipid membranes, which drives endocytosis of the receptors. The strength of H8 membrane insertion predicts the rate of constitutive internalization of GPCRs. This research provides insights into the cellular signaling and trafficking of transmembrane receptors. Please note that this preprint has not yet undergone peer review. [Extracted from the article]

A study conducted by researchers at Siksha 'O' Anusandhan Deemed to be University in Odisha, India, aimed to investigate the correlation between central corneal thickness (CCT) and refractive error, corneal curvature, and axial length. The study included 612 patients aged 18 to 40 with myopia, hypermetropia, or emmetropia. The results showed that CCT was thicker in hypermetropia and thinner in myopia compared to emmetropia. Additionally, the cornea tends to become steeper and thinner with increasing age. The study provides valuable insights into the relationship between CCT and refractive errors. [Extracted from the article]

A recent study conducted by researchers at the University of California explores the relationship between curvature and the genesis of premature ventricular complexes (PVCs) in individuals with long QT syndrome. The study utilizes computer simulations to investigate the effects of curvature on PVC genesis under long QT conditions. The findings suggest that the curvature of the repolarization gradient (RG) border region plays a significant role in promoting or suppressing PVCs, depending on the source and sink conditions. Additionally, the study examines the effects of wavefront curvature and concludes that PVCs are promoted by convex wavefronts but suppressed by concave wavefronts. The research highlights the importance of considering the geometry of the RG border in understanding the risk of arrhythmias in cardiac diseases. [Extracted from the article]

New research from the University of Balear Island in Palma de Mallorca, Spain, explores the preference for curved contours in visual stimuli, known as the curvature effect. The study suggests that this preference is not solely based on geometric features, but also influenced by individual and contextual factors. The researchers propose a multidimensional approach to understanding contour preference, taking into account perceptual and hedonic evaluations, as well as personal traits and cognitive preferences. The findings prompt a reevaluation of past research and offer insights for future studies in psychology and aesthetics. [Extracted from the article]

A patent application by inventor Homayoun Bagherinia has been made available online for a method/system that improves the registration of corresponding optical coherence tomography (OCT) data sets. The method involves generating multiple image pairs from the OCT volumes and identifying characteristic features in each pair. These features are used to define registration transformation parameters, allowing for the accurate alignment of the OCT data sets. The method also includes the use of multiple derived maps from a single base map to identify retinal landmarks that may not be detectable in low-quality OCT data. The invention aims to improve the reliability of registering pairs of OCT data sets taken at different times. The patent application is assigned to Carl Zeiss Meditec Inc. [Extracted from the article]

A study conducted by researchers from Zhejiang University School of Medicine in China examined the distribution of refractive status in school-age children with different corneal curvatures (CC) and the correlation between CC and refractive status. The study included 2,214 grade 4 children in Hangzhou who were screened for myopia. The results showed that children with lower corneal curvature (LCC) had a lower incidence of myopia and longer axial length (AL). The study suggests that low CC can mask the reduction of spherical equivalent (SE) and the growth of AL, and that AL growth is faster before the onset of myopia. [Extracted from the article]

Researchers at National Cheng Kung University Hospital conducted a study on the associations between femoral 3D curvature and sagittal imbalance of the spine in spinal surgery. The study aimed to determine if subjects with sagittal imbalance exhibit greater femoral bowing compared to subjects with sagittal balance, and if there are associations between femoral bowing and compensatory mechanisms of the lower extremity in subjects with sagittal imbalance. The study found that greater femoral bowing is observed in subjects with sagittal imbalance and knee flexion compared to the balanced population, and that knee flexion and femoral obliquity angle are associated with femoral curvature. Further research is needed to investigate the cause-and-effect relationship between sagittal imbalance, compensatory mechanisms of the lower extremity, and femoral bowing. [Extracted from the article]

Assisting end users to identify desired results from a large dataset is an important problem for multi-criteria decision making. To address this problem, top- k and skyline queries have been widely adopted, but they both have inherent drawbacks, i.e., the user either has to provide a specific utility function or faces many results. The k -regret minimization query is proposed, which integrates the merits of top- k and skyline queries. Due to the NP-hardness of the problem, the k -regret minimization query is time consuming and the greedy framework is widely adopted. However, formal theoretical analysis of the greedy approaches for the quality of the returned results is still lacking. In this paper, we first fill this gap by conducting a nontrivial theoretical analysis of the approximation ratio of the returned results. To speed up query processing, a sampling-based method, S toc P res G reed , is developed to reduce the evaluation cost. In addition, a theoretical analysis of the required sample size is conducted to bound the quality of the returned results. Finally, comprehensive experiments are conducted on both real and synthetic datasets to demonstrate the efficiency and effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Shape analogy is a key technique in analyzing time series. That is, time series are compared by how much they look alike. This concept has been applied for many years in geometry. Notably, none of the current techniques describe a time series as a geometric curve that is expressed by its relative location and form in space. To fill this gap, we introduce Shape-Sphere , a vector space where time series are presented as points on the surface of a sphere. We prove a pseudo-metric property for distances in Shape-Sphere. We show how to describe the average shape of a time series set using the pseudo-metric property of Shape-Sphere by deriving a centroid from the set. We demonstrate the effectiveness of the pseudo-metric property and its centroid in capturing the ' shape ' of a time series set, using two important machine learning techniques, namely: Nearest Centroid Classifier and K-Means clustering, using 85 publicly available data sets. Shape-Sphere improves the nearest centroid classification results when the shape is the differentiating feature while keeping the quality of clustering equivalent to current state-of-the-art techniques. [ABSTRACT FROM AUTHOR]

A general approach based on a natural basis function expansion to cancel the temperature-curvature of the base-emitter voltage in the bipolar transistors embedded in bandgap references is presented. The proposed method can be applied to the widely used Banba, Kuijk, and Brokaw structures to build references with sub-ppm/°C temperature coefficients. Current version and voltage version embodiments based on a self-bootstrapping concept are provided. Error sources that can potentially affect the reference performance are analyzed and their effects on the temperature coefficient are minimized after trimming. Monte Carlo simulation results confirm that after calibration, temperature drift performance is within the design/trimming target 0.5 ppm/°C. A partially integrated Kuijk-based prototype reference has been designed and fabricated in a 65nm UMC process. Measurement results demonstrated a 1.5 ppm/°C temperature coefficient over a temperature range of 0 °C to 80 °C with a low-cost two-temperature trimming method. With additional trimming, 0.8 ppm/°C performance was achieved. [ABSTRACT FROM AUTHOR]

In this paper, we propose an adaptive knot placement algorithm for B-Spline curve approximation to dense and noisy 2D data points. The proposed algorithm is based on a heuristic rule for knot placement. It consists in constructing a distribution knot function by blending geometric criteria such as discrete derivatives, discrete angular variations and curvature. It has been successfully compared to three well known methods for approximating various noisy functions and sets of data in handwriting context. [ABSTRACT FROM AUTHOR]

• We propose an on-line Pareto front shape estimation strategy for adaptive selection. We use achievement scalarizing function to locate the pivotal point, which can best characterize the curvature of Pareto front. Then the curvature of Pareto front can be approximately obtained according to the ratio of distances. • An adaptive scalarizing function based fitness evaluation, which can guarantee the Pareto optimality, is presented. According to the estimated curvature of Pareto front, we select a proper indicator to maximize the convergence. • A new similarity measure named dimensionality margin distance for diversity is proposed which can eliminate the abnormality and improve the discrimination of MaOPs. Compared to the existing methods, the proposed approach shows a better consistency especially in high-dimensional and those with abnormal values. Evolutionary algorithms have been proven to be effective in solving multi-objective optimization problems. However, their performance deteriorates progressively in handling many-objective optimization problems due to the sensitivity upon the curvature of Pareto front, as well as the implicit evaluation on similarity in high dimensionality. This paper proposes an on-line Pareto front curvature estimator for an adaptive selection, in which the achievement scalarizing function is used to identify the pivotal solution to extrapolate the geometric information. Then an adaptive scalarizing function based fitness assessment, which guarantees the Pareto optimality, is presented. The diversity of the Pareto optimal solutions is also ensured by introducing a novel similarity metric. Finally, an extensive experimental analysis is presented to corroborate the analytical result by evaluating problems with various types of Pareto fronts. The experimental results substantiate the efficacy of the results with competitive performance. [ABSTRACT FROM AUTHOR]

Purpose: The pin fin is applied into a Lamilloy cooling structure which is broadly used in the leading edge region of the modern gas turbine vane. The purpose of this paper is to investigate effects of the layout, diameter and shape of pin fins on the flow structure and heat transfer characteristics in a newly improved Lamilloy structure at the leading edge region of a turbine vane. Design/methodology/approach: A numerical method is applied to investigate effects of the layout, diameter and shape of pin fins on the flow structure and heat transfer characteristics in a newly improved Lamilloy structure at the leading edge of a turbine vane. The diverse locations of pin fins are Lp = 0.35, 0.5, 0.65. The diameter of the pin fins varies from 8 mm to 32 mm. Three different ratios of root to roof diameter for pin fins are also investigated, i.e. k = 0.5, 1, 2. The Reynolds number ranges from 10,000 and 50,000. Results of the flow structures, heat transfer on the target surface and pin fin surfaces, and friction factor are studied. Findings: The heat transfer on the pin fin surface gradually decreases and then increases as the location of the pin fins increases. Increasing the diameter of the pin fins causes the heat transfer on the pin fin surface to gradually increase, while a lower value of the friction factor occurs. Besides, the heat transfer on the pin fin surface at a small root diameter increases remarkably, but a slight heat transfer penalty is found at the target surface. It is also found that both the Reynolds analogy performance and the thermal performance are increased compared to the baseline whose diameter and normalized location of pin fins are set as 16 and 0.5 mm, respectively. Social implications: The models provide a basic theoretical study to deal with nonuniformity of the temperature field for the turbine vane leading edge. The investigation also provides a better understanding of the heat transfer and flow characteristics in the leading edge region of a modern turbine vane. Originality/value: This is a novel method to adopt pin fins into a Lamilloy cooling structure with curvature. It presents that the heat transfer of the pin fin surface in a pin-fin Lamilloy cooling structure with curvature can be significantly increased by changing the parameters of the pin fins which may lead to various flow behavior. In addition, the shape of the pin fin also shows great influence on the heat transfer and flow characteristics. However, the heat transfer of the target surface shows a small sensitivity to different layouts, diameter and shape of pin fin. [ABSTRACT FROM AUTHOR]

A recent study conducted at the University of Regensburg in Germany explored the association between genes related to oral clefts and the curvature of maxillary lateral incisors. The researchers analyzed panoramic radiographs and DNA from 231 patients and found trends suggesting that certain genetic polymorphisms in BMP2 and BMP4 may be involved in the root curvature of these teeth. The study concluded that BMP2 and BMP4 genes might play a role in the curvature of maxillary lateral incisors. This research has been peer-reviewed and published in The Cleft Palate-Craniofacial Journal. [Extracted from the article]

Petals and leaves are usually curled and exhibit intriguing morphology evolution upon growth, which contributes to their important biological functions. To understand the underlying morphoelastic mechanism and to determine the crucial factors that govern the growth-induced instability patterning in curved petals and leaves, we develop an active thin shell model that can describe variable curvatures and spontaneous growth, within the framework of general differential geometry based on curvilinear coordinates and hyperelastic deformation theory. Analytical solutions of distinguished growing shapes such as saddle surface and cylindrical mode are then derived. We reveal distinct morphological evolutions of doubly curved leaves/petals with different curvatures κ x (along the main vein) and κ y (perpendicular to the main vein) upon differential growth. Compared to the flat (zero curvature) configuration, leaves/petals with longitudinal curvature κ x experience a global bending deformation. With the increase of growth strain, the leaf/petal undergoes a coupling behavior of edge wrinkling and global bending deformation, associated with a pitchfork bifurcation. Conversely, the transverse curvature κ y does not lead to significant bending behavior, but results in delayed critical buckling threshold and reduced wrinkling amplitude. Physical insights into curvature effects on morphology evolutions are further provided by the analysis of nonlinear competition between bending and membrane energies. Moreover, we explore the effect of vein constraint on pattern formation, showing that, unlike the edge wrinkling observed in leaves with strong vein constraint, those with weak vein constraint are prone to grow into a saddle shape, consistent with analytical solutions. The results uncover the intricate interplay between configurational curvature and vein confinement on plant morphogenesis, providing fundamental insights into a variety of growing shapes of curled petals and leaves. • We have uncovered the intricate interplay between curvature and vein confinement on morphogenesis of curled petals and leaves. • We have developed an active thin shell model that can describe variable curvature and spontaneous growth. • Analytical solutions of distinguished growing shapes including saddle, elliptic hyperbolic, and cylindrical modes are obtained. • Physical insights into configurational curvature effects on morphology evolutions are provided by the nonlinear competition between bending and membrane energies. • The results could help design biomimetic deployable structures that quantitatively harness active shape morphing and surface instabilities. [Display omitted] [ABSTRACT FROM AUTHOR]