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Studying ionic wind is crucial for deepening our comprehension of electrical discharge processes and refining their application in industrial technologies. This research investigates the behavior of needle–needle electrode using high-speed schlieren imaging techniques, focusing on the dynamics of ionic wind and its influence on spark discharge channel formation. Observations indicate that the ionic wind generated during corona discharge provides a structured pathway that significantly guides the development of spark discharge channels, particularly evident in horizontal configurations. Our findings reveal that the velocity and density of the ionic wind increase with decreasing curvature radius of the needle tip, thereby enhancing its guiding effect. Furthermore, the spark discharge channel forms through the convergence of positive and negative streamers, which meet near the cathode, leading to substantial disturbances in the surrounding flow field post-discharge. This research highlights the intricate relationship between corona and spark discharges, demonstrating the critical role of ionic wind in influencing discharge channel morphology and offering insights for future applications in plasma and electrostatic-based technologies. [ABSTRACT FROM AUTHOR]

The curvature of soft interfaces plays a crucial role in determining their mechanical and thermodynamic properties, both at macroscopic and microscopic scales. In the case of air/water interfaces, particular attention has recently focused on water microdroplets, due to their distinctive chemical reactivity. However, the specific impact of curvature on the molecular properties of interfacial water and interfacial reactivity has so far remained elusive. Here, we use molecular dynamics simulations to determine the effect of curvature on a broad range of structural, dynamical, and thermodynamical properties of the interface. For a droplet, a flat interface, and a cavity, we successively examine the structure of the hydrogen-bond network and its relation to vibrational spectroscopy, the dynamics of water translation, rotation, and hydrogen-bond exchanges, and the thermodynamics of ion solvation and ion-pair dissociation. Our simulations show that curvature predominantly impacts the hydrogen-bond structure through the fraction of dangling OH groups and the dynamics of interfacial water molecules. In contrast, curvature has a limited effect on solvation and ion-pair dissociation thermodynamics. For water microdroplets, this suggests that the curvature alone cannot fully account for the distinctive reactivity measured in these systems, which are of great importance for catalysis and atmospheric chemistry. [ABSTRACT FROM AUTHOR]

Biological lipid membranes are generally asymmetric, not only with respect to the composition of the two membrane leaflets but also with respect to the state of mechanical stress on the two sides. Computer simulations of such asymmetric membranes pose unique challenges with respect to the choice of boundary conditions and ensemble in which such simulations are to be carried out. Here, we demonstrate an alternative to the usual choice of fully periodic boundary conditions: The membrane is only periodic in one direction, with free edges running parallel to the single direction of periodicity. In order to maintain bilayer asymmetry under these conditions, nanoscale "sticky tapes" are adhered to the membrane edges in order to prevent lipid flip-flop across the otherwise open edge. In such semi-periodic simulations, the bilayer is free to choose both its area and mean curvature, allowing for minimization of the bilayer elastic free energy. We implement these principles in a highly coarse-grained model and show how even the simplest examples of such simulations can reveal useful membrane elastic properties, such as the location of the monolayer neutral surface. [ABSTRACT FROM AUTHOR]

The topology of the applied magnetic field is an important design aspect of Hall thrusters. For modern Hall thrusters, the magnetic field topology most often features curved lines with a concave (negative) curvature upstream of the field's peak and a convex (positive) curvature downstream. Additionally, the advent of the magnetic shielding technique has resulted in Hall thruster designs with non-conventional field topologies that exhibit high degrees of concavity upstream of the field's peak. In this article, a detailed study is carried out on the effects that the magnetic field curvature has on the plasma discharge in a 2D configuration representative of a Hall thruster's radial–azimuthal cross section. The analyses are performed for discharges of three propellants of high applied interest: xenon, krypton, and argon. For each propellant, high-fidelity electrostatic reduced-order particle-in-cell (PIC) simulations are performed with various degrees of positive and negative curvatures of the magnetic field. Corresponding 1D radial PIC simulations are also performed for xenon to compare the observations against the 2D results. Most notably, it is observed that the instability spectra in the positive-curvature cases are mostly dominated by electron cyclotron drift instability, whereas the modified two stream instability is dominant in the negative-curvature cases. The distributions of electron and ion temperatures, in particular, as well as the contribution of various mechanisms to electrons' cross-field transport show notable variations between the positive and negative curvature values. Finally, the field curvature is observed to majorly influence the ion beam divergence along the radial and azimuthal coordinates. [ABSTRACT FROM AUTHOR]

The aggregation of dipolar chains driven by thermal fluctuations in an external strong (electric or magnetic) field is investigated theoretically. We discover a new simple electrostatic mechanism that rationalizes the counter-intuitive lateral coalescence of dipolar chains. There, we first demonstrate that two bent dipolar chains can either attract or repel each other depending if they possess similar or opposite curvatures, respectively. Upon bending, dipolar chains become the siege of polarization-induced local charges that in turn lead to quadrupolar couplings. This striking feature is then exploited to understand our conducted Monte Carlo simulations at finite temperature where thermal fluctuations cause local curvatures in the formed dipolar chains. The related quadrupolar attractive mode with correlated chain-curvatures is clearly identified in the simulation snapshots. Our findings shed new light on a longstanding problem in soft matter and related areas. [ABSTRACT FROM AUTHOR]

The microscopic processes involving droplet impact and interaction on spatially curved surfaces remain unclear. In this study, we implement a dynamic contact angle model with adjusted upper and lower limits into a simulation of droplet motion, constructing a three-dimensional numerical model to depict the dynamics and heat transfer characteristics of symmetric double droplets impacting plane, concave, and convex cylindrical, and concave and convex spherical surfaces. The processes of droplet spreading, retraction, rebound, splitting, and heat transfer are elaborated, revealing the role of surface curvature during impact. Our results show that different curvatures significantly affect the flow morphology of the flow dividing line. For the two main curvatures of the surface, the curvature in the direction of droplet arrangement predominates. Positive curvature promotes spreading and repels the liquid phase, while negative curvature promotes agglomeration and attracts the liquid phase. Extreme situations arise when both positive and negative curvatures occur simultaneously. Regarding heat transfer, the overall heat transfer rate is mainly determined by the spread area, and the heat transfer performance of convex surfaces is better than that of plane or concave surfaces. Residual bubbles increase heat transfer inhomogeneity, but different surfaces do not show significant variability. Additionally, the heat flow intensity in the central interaction region has the following relationship with its rebound height and is independent of the overall heat transfer intensity. [ABSTRACT FROM AUTHOR]

In this study, we determine a new type comprehensive frame, which is called the generalized Frenet‐type frame in three‐dimensional Lie groups with Myller configurations, and it includes several special and classical type frames for Euclidean 3‐space and three‐dimensional Lie groups. After constructing this new comprehensive frame, we obtain derivative formulas with the help of the Lie curvature. In addition, we define some special type curves. The geometry of versor fields along a curve with Frenet‐type frame in three‐dimensional Lie groups with Myller configurations is a generalization of the usual theory of curves. Since this particular relationship, the osculating‐type and rectifying‐type curves with Frenet‐type frame in three‐dimensional Lie groups with Myller configurations include some special cases for osculating and rectifying curves in different spaces. [ABSTRACT FROM AUTHOR]

A new definition of entropy is introduced using a model that simulates an expanding space-time compatible with the fundamental principle of cosmology. The entropy is obtained by mean of a state function that measures the variation of the space-time normal curvature, from a highly compressed space to a lower compressed space. The defined entropy leads to work out a new understanding of the earliest conditions that last for a period estimated to 380,000 years after the Big Bang. It leads to understand via a short period of inflation the process that generates the uniform distribution of matter and energy at the surface of the last scattering. It involves gravitational singularities in a process of gradual decompression propitious to the incubation of matter recombination, and it allows to trace back gravity origin. [ABSTRACT FROM AUTHOR]

In this paper, we establish a generalized Wintgen inequality for quaternionic bi-slant submanifolds and QR-submanifolds (with minimal codimension) in quaternion space forms. We also aim to characterize the second fundamental form of those submanifolds for which the equality cases can hold. Finally, we provide examples of submanifolds embedded in quaternion space forms to support our results. [ABSTRACT FROM AUTHOR]

Multi-focus image fusion has wide applications in the field of computer vision. This research work presents a two-fold multi-focus image fusion framework in spatial domain. Firstly, the salient features of the focused regions in multi-focus images are detected using Gaussian curvature filter (GCF) and range filtering. The initial focus detection map is then refined using morphological filters. Experiments have shown that the proposed method is fast and robust when compared with latest multi-focus fusion schemes. [ABSTRACT FROM AUTHOR]

The shape estimation technique can help solve the end positioning or grasping control of soft robots. However, there is a lack of sensing and modeling techniques for accurate deformation estimation and soft robots with axial elongation, e.g., pneumatic soft actuators (PSAs). This paper presents a shape-self-sensing pneumatic soft actuator (SPSA) with integrated liquid-metal piecewise curvature sensors (LMCSs). Two types of LM composite (Ga-In-Sn/Ga2O3 composites for the sensor and Ga-In-Sn/NdFeB/Ni for the electronic wire) were used to build the strain sensor network. Furthermore, a piecewise variable curvature (PVC) model was developed to predict the bending deformation of the soft actuator. A two-SPSAs-based gripper was built to test the identification performance of LMCSs. The results indicate that SPSA could perform contact and size identification using the PVC model. In addition, the K-nearest neighbors (KNN) algorithm was used to classify the shape of the targets. Finally, the circular, triangular, and square targets were identified with an accuracy rate of 93.3%. The work was expected to be applied to the size and shape perception and deformation planning of soft robots. [ABSTRACT FROM AUTHOR]

This paper presents a quantitative analysis of the nonlinearities of the positive predictive value (PPV) and its effect in evaluating two-class pattern classification models with imbalanced datasets. The analysis is made through an expression of the PPV as a function of two other classification ratios that are invariant to the data imbalance —the true positive rate (TPR) and false positive rate (FPR), and σ — the imbalance ratio (IR) of the dataset such that PPV = σ TPR/(σ TPR + FPR). The curvatures of PPV in the three-dimensional TPR–FPR– σ space are studied using the Hessian matrix, from which a saddle-shaped 3D surface in the space is revealed. This paper explores the nonlinear behaviors of PPV around the critical points, identified at FPR = σ TPR on the saddle surface, along with its scaling and sensitivity issues as performance measurements in model evaluation. The effect of the nonlinearities of PPV for the F1 and MCC metrics on imbalanced datasets is also studied. It is warned through the results of this study that the evaluations of classification models could be misleading if without an awareness and understanding of the nonlinearities associated with the PPV and its relevant metrics on imbalanced datasets. [ABSTRACT FROM AUTHOR]

In this paper, the well‐posedness of Cauchy's problem of fractional Schrödinger equations with a power‐type nonlinearity on n‐dimensional manifolds with nonnegative Ricci curvature is studied. Under suitable volume conditions, the local solution with initial data in H[n2]+1 will blow up in finite time no matter how small the initial data is, which follows from a new weight function and ODE inequalities. Moreover, the upper‐bound of the lifespan can be estimated. [ABSTRACT FROM AUTHOR]

In this paper, we investigate Ricci–Yamabe solitons (RYSs) and gradient Ricci–Yamabe solitons (gradient RYSs) in generalized Robertson–Walker (GRW) spacetimes. At first, we prove that if a GRW spacetime admits a RYS, then it becomes a perfect fluid spacetime (PFS) and the divergence of the Weyl tensor vanishes. Also, a GRW spacetime admitting a RYS is of Petrov type I , D or O and in case of four dimension, the spacetime turns into a Robertson–Walker spacetime. Next, we show that if a GRW spacetime of constant scalar curvature admits a gradient RYS, then it becomes a PFS and the divergence of the Weyl tensor vanishes. [ABSTRACT FROM AUTHOR]

Recently, a variety of microenvironmental biophysical stimuli have been proved to play a crucial role in regulating cell functions. Among them, morpho-physical cues, like curvature, are emerging as key regulators of cellular behavior. Changes in substrate curvature have been shown to impact the arrangement of Focal Adhesions (FAs), influencing the direction and intensity of cytoskeleton generated forces and resulting in an overall alteration of cell mechanical identity. In their native environment, cells encounter varying degrees of substrate curvature, and in specific organs, they are exposed to dynamic changes of curvature due to periodic tissue deformation. However, the mechanism by which cells perceive substrate curvature remains poorly understood. To this aim, a micro-pneumatic device was designed and implemented. This device enables the controlled application of substrate curvature, both statically and dynamically. Employing a combined experimental and simulative approach, human adipose-derived stem cells were exposed to controlled curvature intensity and frequency. During this exposure, measurements were taken on FAs extension and orientation, cytoskeleton organization and cellular/nuclear alignment. The data clearly indicated a significant influence of the substrate curvature on cell adhesion processes. These findings contribute to a better understanding of the mechanisms through which cells perceive and respond to substrate curvature signals. This work is our contribution to the comprehension of substrate curvature's function as a crucial regulator of cell adhesion at the scale of focal adhesions and cell mechanical identity. In recent years, a large body of knowledge is continuously growing providing comprehension of the role of various microenvironmental biophysical stimuli in regulating cell functions. Nevertheless, little is known about the role of substrate curvature, in particular, when cells are exposed to this stimulus in a dynamic manner. To address the role of substrate curvature on cellular behavior, a micro-pneumatic device was designed and implemented. This device enables the controlled application of substrate curvature, both statically and dynamically. The experiment data made it abundantly evident that the substrate curvature had a major impact on the mechanisms involved in cell adhesion. [Display omitted] [ABSTRACT FROM AUTHOR]

Aim Methodology Results Conclusions To evaluate the agreement between six currently available periapical radiography‐based methods for measuring the root canal curvatures in mesial roots of mandibular first molars, assessed by two examiners with different proficiency levels.Non‐endodontically treated mesial roots of 41 human mandibular first molars were radiographed using the parallelling technique. Two independent observers (a specialist in endodontics and radiology and a final‐year dental student) assessed their root canal curvature using the methodologies described by Schneider (1971, Oral Surgery, Oral Medicine, Oral Pathology and Oral Radiology, 32, 271), Weine (1982, Endodontic therapy), Berbert and Nishiyama (1994, Revista Gaúcha de Odontología, 356), Luiten et al. (1995, Journal of Endodontics, 21, 26), Hankins and ElDeeb (1996, Journal of Endodontics, 22, 123) and Pettiette et al. (1999, Journal of Endodontics, 25, 230). Intra‐ and inter‐examiner reliability was assessed using the intraclass correlation coefficient. The differences in curvature angle measured by the different methods were compared using the one‐way anova for repeated measures test, followed by Tukey's post hoc analysis. The effect was calculated using the Cohen's d method. To determine the agreement between methods, the Bland–Altman analysis was used. The significance level was set at 5%.Agreement for the observers was excellent (>0.81) for the six methods considered. For the angle comparisons between methods, the maximum differences were for Schneider versus Weine (35.77°) and Luiten versus Hankins (35.14°), whilst the highest percentage of angles with a difference >10° were Weine versus Luiten and Berbert versus Pettiette (90%) and the comparison Weine versus Hankins presented with the lowest frequency (15%). Excellent agreement was found for five comparisons: Weine versus Luiten (0.940), Berbert versus Pettiette (0.917), Weine versus Pettiette (0.907), Luiten versus Pettiette (0.904) and Berbert versus Luiten (0.812). Compared to Schneider's method, the other methods showed a tendency of increasing difference as the angles became more acute. The other methods exhibited linear differences, remaining constant for smaller and larger angles.Reliability was excellent for all methods assessed separately. Maximum differences in curvature angles were found when comparing Schneider versus Weine and Luiten versus Hankins. Excellent agreement was found for Weine versus Luiten, Berbert versus Pettiette, Weine versus Pettiette, Luiten versus Pettiette and Berbert versus Luiten. In the presence of dilacerations, the method by Schneider was less sensitive. [ABSTRACT FROM AUTHOR]

In this paper we propose a weaker version of Penrose's much heeded Strong Cosmic Censorship (SCC) conjecture, asserting inextendability of maximal Cauchy developments by manifolds with Lipschitz continuous Lorentzian metrics and Riemann curvature bounded in Lp. Lipschitz continuity is the threshold regularity for causal structures, while curvature bounds rule out infinite tidal accelerations, arguing for physical significance of this weaker SCC conjecture. The main result of this paper, under the assumption that no extensions exist with higher connection regularity W loc 1 , p , proves in the affirmative this SCC conjecture with bounded curvature for p sufficiently large, (p > 4 to address uniform bounds, p > 2 without uniform bounds). [ABSTRACT FROM AUTHOR]

We prove the local Lipschitz continuity of sub-elliptic harmonic maps between certain singular spaces, more specifically from the 푛-dimensional Heisenberg group into CAT ⁡ ( 0 ) \operatorname{CAT}(0) spaces. Our main theorem establishes that these maps have the desired Lipschitz regularity, extending the Hölder regularity in this setting proven in [Y. Gui, J. Jost and X. Li-Jost, Subelliptic harmonic maps with values in metric spaces of nonpositive curvature, Commun. Math. Res. 38 (2022), 4, 516–534] and obtaining same regularity as in [H.-C. Zhang and X.-P. Zhu, Lipschitz continuity of harmonic maps between Alexandrov spaces, Invent. Math. 211 (2018), 3, 863–934] for certain sub-Riemannian geometries; see also [N. Gigli, On the regularity of harmonic maps from RCD ⁢ ( K , N ) \mathrm{RCD}(K,N) to CAT ⁢ ( 0 ) \mathrm{CAT}(0) spaces and related results, preprint (2022), https://arxiv.org/abs/2204.04317; and A. Mondino and D. Semola, Lipschitz continuity and Bochner–Eells–Sampson inequality for harmonic maps from RCD ⁡ ( k , n ) \operatorname{RCD}(k,n) spaces to CAT ⁡ ( 0 ) \operatorname{CAT}(0) spaces, preprint (2022), https://arxiv.org/abs/2202.01590] for the generalisation to RCD spaces. The present result paves the way for a general regularity theory of sub-elliptic harmonic maps, providing a versatile approach applicable beyond the Heisenberg group. [ABSTRACT FROM AUTHOR]

This paper studies the convergence of the proximal point method for quasiconvex functions in finite dimensional complete Riemannian manifolds. We prove initially that, in the general case, when the objective function is proper and lower semicontinuous, each accumulation point of the sequence generated by the method, if it exists, is a limiting critical point of the function. Then, under the assumptions that the sectional curvature of the manifold is bounded above by some non negative constant and the objective function is quasiconvex we analyze two cases. When the constant is zero, the global convergence of the algorithm to a limiting critical point is assured and if it is positive, we prove the local convergence for a class of quasiconvex functions, which includes Lipschitz functions. [ABSTRACT FROM AUTHOR]

Meander bends are one of the most common morphological features of rivers. Their formation is the result of interactions between bank erosion and several other river characteristics, such as the bed topography resulting from bank erosion, sinuosity, channel flow, and riffle-pool sequencing. Many studies have emphasized proportional relationships between channel widths and different aspects of meander morphology, such as wavelength, curvature of the radius, and belt width. These relationships have been studied for bankfull level width in high-order channels. It is not clear how such relationships vary in low-order headwater streams. This research addresses those gaps in low-order streams of which little is known. Field surveys were conducted in nine meander bends of a low-order alluvial channel in Virginia. The results suggest that in a low-order channel, the ratios of width with wavelength, the radius of curvature, and belt width are mostly similar between the meanders' beginning and tail endpoints. The stream also has similar meander morphologic characteristics and ratios as anticipated from the literature on high-order streams. [ABSTRACT FROM AUTHOR]

The cochlea, situated within the inner ear, is a spiral-shaped, liquid-filled organ responsible for hearing. The physiological significance of its shape remains uncertain. Previous research has scarcely addressed the occurrence of transverse flow within the cochlea, particularly in relation to its unique shape. This study aims to investigate the impact of the geometric features of the cochlea on fluid dynamics by characterizing transverse flow induced by harmonically oscillating axial flow in square ducts with curvature and torsion resembling human cochlear anatomy. We examined four geometries to investigate curvature and torsion effects on axial and transverse flow components. Twelve frequencies from 0.125 Hz to 256 Hz were studied, covering infrasound and low-frequency hearing, with mean inlet velocity amplitudes representing levels expected for normal conversation or louder situations. Our simulations show that torsion contributes significantly to transverse flow in unsteady conditions, and that its contribution increases with increasing oscillation frequency. Curvature alone has a small effect on transverse flow strength, which decreases rapidly with increasing frequency. Strikingly, the combined effect of curvature and torsion on transverse flow is greater than expected from a simple superposition of the two effects, especially when the relative contribution of curvature alone becomes negligible. These findings may be relevant to understanding physiological processes in the cochlea, including metabolite transport and wall shear stress. Further studies are needed to investigate possible implications for cochlear mechanics. [ABSTRACT FROM AUTHOR]

Motivated by constructions appearing in mirror symmetry, we study special representatives of complexified Kähler classes, which extend the notions of constant scalar curvature and extremal representatives for usual Kähler classes. In particular, we provide a moment map interpretation, discuss a possible correspondence with compactified Landau–Ginzburg models, and prove existence results for such special complexified Kähler forms and their large volume limits in certain toric cases. [ABSTRACT FROM AUTHOR]

The texture mapping technique based on irregular surfaces is widely used in many fields such as film and television, industry and games, etc. In order to adapt to the rapid development in the field of computer graphics and further enhance the uniformity and effectiveness of the texture mapping effect, a triangular mesh simplified texture mapping technique based on the optimized spring-fingertip is proposed. Firstly, a complex two-dimensional graph is established through the spring-fingertip model, which is parameterized and normalized to reduce the deformation of the texture; subsequently, the concept of triangular mesh simplification is introduced to optimize the model timeliness, which replaces the traditional way of folding the edges; finally, the weight of each edge is further analyzed through local curvature calculation. In order to verify the effectiveness of the texture mapping method, simulation and analysis experiments are done, and the experimental results show that the accuracy of the model reaches 99.25%, which is an average improvement of 7.19% relative to the remaining four models. Therefore, the texture mapping model based on optimized triangular mesh effectively improves the realism of the mapping effect and reduces the computational burden of the model. [ABSTRACT FROM AUTHOR]

Because of their curvature, age, track type and maintenance history, metro tracks should be inspected periodically during the planning horizon. Metro companies operate track geometry cars to periodically collect measurement data from the tracks by crossing the urban rail transit network. Optimizing the schedule for the track geometry car is a challenge: in addition to minimizing travelling distance, the inspection time interval of the same line should be arranged as equally as possible within the planning horizon. This article proposes a mathematical model for the track geometry car routing problem with periodic demands (TGCRP-PD). To effectively address this problem, a memetic algorithm-based metaheuristic is adopted. The proposed solution approach is applied to a real-world case. The numerical results show that the proposed method could save a dead mileage of 295.016 km (accounting for 48.882%) and greatly improve the level of service intervals. [ABSTRACT FROM AUTHOR]

We give a new formula for the Lichnerowicz Laplacian on normal homogeneous spaces in terms of Casimir operators. We derive some practical estimates and apply them to the known list of non-symmetric, compact, simply connected homogeneous spaces G / H with 퐺 simple whose standard metric is Einstein. This yields many new examples of Einstein metrics which are stable in the Einstein–Hilbert sense, which have long been lacking in the positive scalar curvature setting. [ABSTRACT FROM AUTHOR]

Let (M , g) be a noncompact, connected, complete Riemannian three-manifold with nonnegative Ricci curvature satisfying Ric ≥ ε ⁢ tr ⁡ (Ric) ⁢ g for some ε > 0 . In this note, we give a new proof based on inverse mean curvature flow that (M , g) is either flat or has non-Euclidean volume growth. In conjunction with the work of J. Lott [On 3-manifolds with pointwise pinched nonnegative Ricci curvature, Math. Ann.388 (2024), 3, 2787–2806] and of M.-C. Lee and P. Topping [Three-manifolds with non-negatively pinched Ricci curvature, preprint (2022), https://arxiv.org/abs/2204.00504], this gives an alternative proof of a conjecture of R. Hamilton recently proven by A. Deruelle, F. Schulze, and M. Simon [Initial stability estimates for Ricci flow and three dimensional Ricci-pinched manifolds, preprint (2022), https://arxiv.org/abs/2203.15313] using Ricci flow. [ABSTRACT FROM AUTHOR]

For every complete and minimally immersed submanifold f : M n → S n + p whose second fundamental form satisfies | A | 2 ≤ n ⁢ p / (2 ⁢ p − 1) , we prove that it is either totally geodesic, or (a covering of) a Clifford torus or a Veronese surface in S 4 , thereby extending the well-known results by Simons, Lawson and Chern, do Carmo & Kobayashi from compact to complete M n . We also obtain the corresponding result for complete hypersurfaces with non-vanishing constant mean curvature, due to Alencar & do Carmo in the compact case, under the optimal bound on the umbilicity tensor. In dimension n ≤ 6 , a pinching theorem for complete higher-codimensional submanifolds with non-vanishing parallel mean curvature is proved, partly generalizing previous work by Santos. Our approach is inspired by the conformal method of Fischer-Colbrie, Shen & Ye and Catino, Mastrolia & Roncoroni. [ABSTRACT FROM AUTHOR]

Purpose: Autostereoscopic displays have become increasingly common, but their impact on ocular dimensions remains unknown. We sought to identify changes in the crystalline lens dimensions induced by autostereoscopic three‐dimensional (3D) viewing. Methods: Forty young adults (age: 22.6 ± 2.0 years, male/female: 15/25) were consecutively enrolled and randomly divided into two groups (3D and two‐dimensional [2D] viewing groups) to watch a 30‐min movie clip displayed in 3D or 2D mode on a tablet computer. The lens thickness (LT), diameter, curvature, decentration and tilt were measured with anterior segment optical coherence tomography under both non‐accommodating (static) and accommodating conditions. Results: In the static condition, the LT decreased by 0.03 ± 0.03 mm (p < 0.001) and the anterior radius of curvature (ARC) increased by 0.49 ± 0.59 mm (p = 0.001) post‐3D viewing. In contrast, following 2D viewing, the ARC decreased by 0.23 ± 0.25 mm (p = 0.001). Additionally, the increase in the steep ARC post‐3D viewing was greater in high‐myopic eyes than low to moderate myopic eyes (p = 0.04). When comparing the accommodative with the static (non‐accommodative) condition, for 3D viewing the lens decentration decreased (−0.03 ± 0.05 mm, p = 0.02); while for 2D viewing, the posterior curvature radius (−0.14 ± 0.20 mm, p = 0.006) and diameter (−0.13 ± 0.20 mm, p = 0.01) decreased. Conclusions: Viewing with the autostereoscopic 3D tablet could temporally decrease the thickness and curvature of the lens under non‐accommodating conditions. However, its long‐term effect requires further exploration. [ABSTRACT FROM AUTHOR]

The compressor transition duct transfers the air from the low-pressure compressor to the high-pressure compressor. An aircraft always experiences off-design conditions except for level flight conditions during aircraft range. So, to throw some light on the performance of transition ducts under off-design conditions, this paper presents its performance assessment numerically for uniform and swirl flow cases under varying Mach numbers (M). This analysis reveals that a higher Mach number provokes an adverse pressure gradient and non-uniformity. In the uniform flow, the non-uniformity attains a maximum value of 0.04366 near the inner wall, which indicates the presence of a highly distorted flow near the inner wall; however, its maximum value is 0.03661 near to the outer wall in the swirl flow. Also, the pressure recovery reduces with an increased Mach number. Notably, as the Mach number increasesfrom the design point, the pressure coefficient along the convex curvature significantly drops to the lowest point of −0.65015 and −0.79324 for uniform and swirl flow, respectively. Consequently, the inner wall experiences a large adverse pressure gradient (−0.90822) compared to the decreasing Mach number from the design point for the uniform flow, whereas it is experienced by the outer wall in the case of swirl flow (−0.94729). [ABSTRACT FROM AUTHOR]

This paper presents different non-polynomial hybrid models in the framework of Carrera's Unified Formulation for the bending of a magneto-electric shell with variable radii of curvature. The shell's middle surface is graphed by a parametric surface. Differential Geometry is employed for evaluating the Lamé Parameters and Radius of Curvature. The mechanical displacements are modeled in the context of an equivalent single layer by sinusoidal, hyperbolic, and tangential models. The electrical and magnetic scalar potential functions are written by a polynomial thickness function in the framework of Layerwise theory. The shell panels are subjected to mechanical, electrical, and magnetic loads. The governing equations are obtained by the Principle of Virtual Displacement. The correspondent partial differential equations are discretized by Chebyshev-Gauss-Lobatto grid distribution and solved by the so-called Differential Quadrature Method. The classical Lagrange polynomial is employed as the basis function for the method. The stresses, electrical displacement, and magnetic induction are recovered by the three-dimensional (3D) equilibrium equations. A comparative analysis with 3D solutions provided in the literature is performed for a square plate and a doubly curved shallow shell panel and remarkable results are obtained. So, the validated models are further used to study shells with variable radii of curvature; specifically, for helicoid, ellipsoid, and catenoid panels. [ABSTRACT FROM AUTHOR]

Consider a symmetric space G/H with simple Lie group G. We demonstrate that when G/H is not irreducible, it is necessarily even dimensional and noncompact. Furthermore, the subgroup H is also both noncompact and non-semisimple. Additionally, we establish that the only G-invariant connection on G/H is the canonical connection. On the other hand, we show that if G/H has an odd dimension, it must be irreducible, and the subgroup H must be semisimple. Finally, we present an explicit example, and we show that there exists no other torsion-free G-invariant connection on a symmetric space G/H with semisimple Lie group G which has the same curvature as the canonical one. [ABSTRACT FROM AUTHOR]

In this note, we prove a family of sharp weighed inequalities which involve weighted k-th mean curvature integral and two distinct quermassintegrals for closed hypersurfaces in \mathbb {R}^n. This inequality generalizes the corresponding result of Wei and Zhou [Bull. Lond. Math. Soc. 55 (2023), pp. 263–281] where their proof is based on earlier results of Kwong-Miao [Pacific J. Math. 267 (2014), pp. 417–422; Commun. Contemp. Math. 17 (2015), p. 1550014]. Here we present a proof which does not rely on Kwong-Miao's results. [ABSTRACT FROM AUTHOR]

This paper studies the combinatorial Calabi flow for circle patterns with obtuse exterior intersection angles on surfaces of finite topological type. By using a Lyapunov function, we show that the flow exists for all time and converges exponentially fast to a circle pattern metric with prescribed attainable curvatures. This provides an algorithm to search for the desired circle patterns. [ABSTRACT FROM AUTHOR]

The aim of this paper is to prove some results about almost Yamabe soliton and almost Ricci-Bourguignon soliton with special soliton vector field. In fact, we prove that every compact non-trivial almost Ricci-Bourguignon soliton with constant scalar curvature is isometric to a Euclidean sphere. Then we show that every compact almost Ricci-Bourguignon soliton whose soliton vector field is divergence-free is Einstein and its soliton vector field is Killing. Finally, we prove that a complete almost Ricci-Bourguignon soliton (M, g, V, λ, ρ) has V as the contact vector field of a contact manifold M with metric g and its Reeb vector field is geodesic, then it becomes a Ricci-Bourguignon soliton and g has constant scalar curvature. In particular, if V is strict, then g is a compact Sasakian Einstein. [ABSTRACT FROM AUTHOR]

We construct a fundamental piece of the boundary of the maximal globally hyperbolic development (MGHD) of Cauchy data for the multi-dimensional compressible Euler equations, which is necessary for the local shock development problem. For an open set of compressive and generic H 7 initial data, we construct unique H 7 solutions to the Euler equations in the maximal spacetime region below a given time-slice, beyond the time of the first singularity; at any point in this spacetime, the solution can be smoothly and uniquely computed by tracing both the fast and slow acoustic characteristic surfaces backward-in-time, until reaching the Cauchy data prescribed along the initial time-slice. The future temporal boundary of this spacetime region is a singular hypersurface, containing the union of three sets: first, a co-dimension-2 surface of "first singularities" called the pre-shock; second, a downstream hypersurface called the singular set emanating from the pre-shock, on which the Euler solution experiences a continuum of gradient catastrophes; third, an upstream hypersurface consisting of a Cauchy horizon emanating from the pre-shock, which the Euler solution cannot reach. We develop a new geometric framework for the description of the acoustic characteristic surfaces which is based on the Arbitrary Lagrangian Eulerian (ALE) framework, and combine this with a new type of differentiated Riemann variables which are linear combinations of gradients of velocity, sound speed, and the curvature of the fast acoustic characteristic surfaces. With these new variables, we establish uniform H 7 Sobolev bounds for solutions to the Euler equations without derivative loss and with optimal regularity. [ABSTRACT FROM AUTHOR]

We propose a notion of stability for constant k$k$‐mean curvature hypersurfaces in a general Riemannian manifold and we give some applications. When the ambient manifold is a Space Form, our notion coincides with the known one, given by means of the variational problem. [ABSTRACT FROM AUTHOR]

Let d≥3$d\ge 3$ be an integer. For a holomorphic d$d$‐web W$\mathcal {W}$ on a complex surface M$M$, smooth along an irreducible component D$D$ of its discriminant Δ(W)$\Delta (\mathcal {W})$, we establish an effective criterion for the holomorphy of the curvature of W$\mathcal {W}$ along D$D$, generalizing results on decomposable webs due to Marín, Pereira, and Pirio. As an application, we deduce a complete characterization for the holomorphy of the curvature of the Legendre transform (dual web) LegH$\mathrm{Leg}\mathcal {H}$ of a homogeneous foliation H$\mathcal {H}$ of degree d$d$ on PC2$\mathbb {P}^{2}_{\mathbb {C}}$, generalizing some of our previous results. This then allows us to study the flatness of the d$d$‐web LegH$\mathrm{Leg}\mathcal {H}$ in the particular case where the foliation H$\mathcal {H}$ is Galois. When the Galois group of H$\mathcal {H}$ is cyclic, we show that LegH$\mathrm{Leg}\mathcal {H}$ is flat if and only if H$\mathcal {H}$ is given, up to linear conjugation, by one of the two 1‐forms ω1d=yddx−xddy$\omega _1^{d}=y^d\mathrm{d}x-x^d\mathrm{d}y$, ω2d=xddx−yddy$\omega _2^{d}=x^d\mathrm{d}x-y^d\mathrm{d}y$. When the Galois group of H$\mathcal {H}$ is noncyclic, we obtain that LegH$\mathrm{Leg}\mathcal {H}$ is always flat. [ABSTRACT FROM AUTHOR]

Laboratory experiments and numerical simulations were performed to explore the influence of intersection geometry on fluid flow and solute transport in fractures. Fractures were engraved and sealed into an acrylic plate and two orthogonal intersections with different geometry were constructed. The effects of curvature and relative shear displacement at intersections on preferential flow and solute transport were investigated. By solving the Navier–Stokes (NS) equation, the fluid mixing and solute distribution were predicted. The results showed that the geometric characteristics at the intersection have a significant effect on the preferential flow and solute distribution. The results agreed well with the experimental results, in terms of flow direction, preferential flow rate, and heterogeneous solute distribution. With an increase in curvature, the flow difference between the two outlets increases gradually. Increasing curvature can reduce the preferential flow and weaken the inhomogeneity of solute distribution. An increase of relative shear displacement decreases the pressure gradient and flow rate at the entrance of the two branch fractures, and thereby increases preferential flow and inhomogeneity of solute distribution. The results provide a basis and reference for further exploring the relationship between the geometric characteristics of fracture intersections and flow behaviors. [ABSTRACT FROM AUTHOR]

The renewed focus on eye growth in preterm‐born children was primarily triggered by Danish cohort studies, including the Copenhagen Project, which focused on children born from 1959–1961. The retinotoxic effects of excessive oxygen on premature neonates had long been clarified and therapeutically adjusted for. Later, ultrasound oculometry and keratometry established that ocular size deficits, linked to development, also occurred in normally developing children, not just frail outliers. This indicated that general catch‐up had not been achieved. This paper discusses whether one early segment of eye development does not occur in preterm, and here even in more robust neonates, without later compensation. [ABSTRACT FROM AUTHOR]

In this work, we prove a compactness theorem on the space of all Hamiltonian stationary Lagrangian submanifolds in a compact symplectic manifold with uniform bounds on area and total extrinsic curvature. This generalizes the compactness theorems in Chen and Warren [J. Differential Geom. 126 (2024), pp. 65–97] and Chen and Ma [Var. Partial Differential Equations 60 (2021), Paper No. 75, 23]. [ABSTRACT FROM AUTHOR]

We prove polynomial decay of correlations for geodesic flows on a class of nonpositively curved surfaces where zero curvature only occurs along one closed geodesic. We also prove that various statistical limit laws, including the central limit theorem, are satisfied by this class of geodesic flows. [ABSTRACT FROM AUTHOR]

L ν operator is an important extrinsic differential operator of divergence type and has profound geometric settings. In this paper, we consider the clamped plate problem of L ν 2 operator on a bounded domain of the complete Riemannian manifolds. A general formula of eigenvalues of L ν 2 operator is established. Applying this general formula, we obtain some estimates for the eigenvalues with higher order on the complete Riemannian manifolds. As several fascinating applications, we discuss this eigenvalue problem on the complete translating solitons, minimal submanifolds on the Euclidean space, submanifolds on the unit sphere and projective spaces. In particular, we get a universal inequality with respect to the L I I operator on the translating solitons. Usually, it is very difficult to get universal inequalities for weighted Laplacian and even Laplacian on the complete Riemannian manifolds. Therefore, this work can be viewed as a new contribution to universal estimate. [ABSTRACT FROM AUTHOR]

In the realm of five-axis Computer Numerical Control (CNC) machining, the challenge of minimizing velocity, acceleration, and jerk fluctuations has prompted the development of various local corner smoothing methods. However, existing techniques often rely on symmetrical spline curves or impose pre-set transition length constraints, limiting their effectiveness in reducing curvature and maintaining velocity at critical corners. To comprehensively address these limitations comprehensively, a novel approach for local smoothing of five-axis linear toolpaths is presented in this paper. The proposed method introduces two asymmetrical B-splines at corners, effectively smoothing both the tool-tip position in the workpiece coordinate system and the tool orientation in the machine coordinate system. To fine-tune transition curve scales and minimize velocity disparities between adjacent corners, an overlap elimination scheme is employed. Furthermore, the two-step strategy emphasizes the synchronization of tool-tip position and tool orientation while considering maximal approximation error. The outcome is a blended five-axis toolpath that significantly reduces curvature extremes in the smoothed path, achieving reductions ranging from 36.28 % to 45.51 %. Additionally, the proposed method streamlines the interpolation process, resulting in time savings ranging from 5.68 % to 8.78 %, all the while adhering to the same geometric and kinematic constraints. [ABSTRACT FROM AUTHOR]

This paper presents the details of the analyses which were conducted to study the effects of steel reinforcing bars with unintended high strength on the behaviors of reinforced concrete (RC) columns. The influence of these bars on the column strength and strength-reduction factors were investigated. The former was studied with the help of column axial load-moment interaction diagrams, while a reliability analysis was carried out for the latter. Four different column cross sections reinforced with reinforcement ratios varying from 1 to 4% were included in the analysis. Other variables included concrete compressive and reinforcing bar yield strengths. The effects of the aforementioned variables were also considered on the development length of the reinforcing bars in tension and compression. It was found that the use of reinforcing bars with unintended high strength could change column behavior to compression-controlled at a lesser axial load level, which is accompanied by a reduction in the curvature capacity. Modifications have been suggested to control the negative effects of unintended high strength of bars on the column behavior and bar development length. Strength-reduction factors for RC sections ranging from compression-controlled to tension-controlled regions have also been proposed, which differ from those suggested by the prevalent code of practice. [ABSTRACT FROM AUTHOR]

In contrast to the conventional etching that makes nanoparticles rounder and our previous sharpening etching mode that causes serrated edges, here, we developed a new boring etching mode that targets the faces of Au nanoplates to make holes. The critical factors are the pre-incubation step with the ligand 2-mercapto-5-benzimidazolecarboxylic acid (MBIA) and the subsequent removal of excess ligands in the solution. Thus, etching is focused onto the few sites with initial loss of ligands, which cannot be quickly replaced. The choice of ligand MBIA is also of importance, as it carries negative charge and repels each other. Its inability of forming a dense layer probably plays a critical role in the site-selectivity for faces, because ligands at the higher curvature edges and corners are expected to have less repulsion. The etching results from the comproportionation reaction between Au3+ and Au0 in the nanoplates, where Br− coordination to Au and the extra stabilization from cetyltrimethylammonium bromide (CTAB) are essential. We believe that the ability of boring holes is an important tool for future synthetic designs. [ABSTRACT FROM AUTHOR]

We prove an analogue statement to an estimate by De Lellis–Müller in R 3 on the standard Minkowski lightcone. More precisely, we show that under some additional assumptions, any spacelike cross section of the standard lightcone is W 2 , 2 -close to a round surface provided the trace-free part of a scalar second fundamental form A is sufficiently small in L 2 . To determine the correct intrinsically round cross section of reference, we define an associated 4-vector, which transforms equivariantly under Lorentz transformations in the restricted Lorentz group. A key step in the proof consists of a geometric, scaling invariant estimate, and we give two different proofs. One utilizes a recent characterization of singularity models of null mean curvature flow along the standard lightcone by the author, while the other is heavily inspired by an almost-Schur lemma by De Lellis–Topping. [ABSTRACT FROM AUTHOR]