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This paper introduces a new high-sensitivity curvature fiber sensor based on a miniature two-path Mach–Zehnder interferometer (MTP-MZI). The sensor is fabricated by coupling and fusing the multimode fiber (MMF) with the single-mode fiber (SMF) using arc fusion technology (AFT), resulting in a centimeter-level two-path MZI structure. The sensor represents an innovative approach to MZI coupling technology, which reduces device size, simplifies manufacturing, and lowers costs. In curvature-sensing experiments, the MTP-MZI sensor achieves a maximum curvature sensitivity of −96.70 dB/m−1 in the curvature range of 0.0418 m−1 to 0.0888 m−1, which is an extremely high sensitivity among intensity-modulated curvature sensors. Additionally, temperature-sensing measurements of the MTP-MZI sensor show a maximum temperature sensitivity of 212 pm/°C in the range of 30 °C to 70 °C, which is low temperature sensitivity and solves the cross-sensitivity problem. Thanks to the miniature two-path structure of the MTP-MZI, it provides a new perspective for developing multidimensional and multiparameter measurement methods in MZI fiber sensors. [ABSTRACT FROM AUTHOR]

In high-strength steel (HSS), shear edge failure due to stretch flangeability is a serious problem. Shear edge failure is strongly affected by the cutting methods. As countermeasures, cut-off punching and double punching of the entire circumference have conventionally been considered. However, it has not been shown whether these processes can be applied to the stretch-flange-forming part of the outer circumference of automotive parts. In this study, the effect of the punching allowance and the method of improving the double punching process on the outer circumferences of automotive parts were investigated using hot-rolled HSS sheets. The results of hole expansion tests and observations of shear edge faces and metal flow show that partial double punching reduces the rigidity of the cut-off side and increases the collapse probability. Also, the crack propagation caused by high tensile stress near the upper cutting edge is accelerated. In comparison with double punching of the entire circumference of a 590 MPa-class or 780 MPa-class HSS sheet, in partial double punching, the stretch flangeability is improved and the hole expansion test value is 1.5 times that of double punching when the cut off amount is greater than the thickness. However, it is considered that the stiffness of the cut-off side varies depending on the curvature and the thickness of the plane, and the effect of such variations will be confirmed in a wide range of curvature and thickness in the future. [ABSTRACT FROM AUTHOR]

In this study, we propose a new toothed gear for mechanical transmissions built from a satellite wheel with two toothed conical crowns, one of which conjugates with a fixed central conical wheel mounted in the transmission housing and the other with a movable conical wheel installed on the flange of the driven shaft. The satellite wheel is mounted on the inclined portion of the crankshaft and performs spherospatial motion around a fixed point. When the crankshaft rotates, the teeth of the wheels engage with spherospatial interaction in two lateral gearings of the satellite wheel, yielding kinematic ratios dependent on the correlation of the number of teeth. The teeth of the satellite wheel are used with circular arc profiles, and the teeth of the central wheel have flank profiles with variable curvatures increasing continuously from the root to the tip, so that, in meshing, the teeth form multipair contacts with convex–concave geometry with a small difference in flank curvatures. The flank profile geometry and pairs of teeth simultaneously engage depending on the configurational parameters of the gearing and can use up to 100% of pairs of simultaneously conjugated teeth. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the holonomy group of n-dimensional projective Finsler metrics of constant curvature. We establish that in the spherically symmetric case, the holonomy group is maximal, and for a simply connected manifold it is isomorphic to D i f f o (S n - 1) , the connected component of the identity of the group of smooth diffeomorphism on the n - 1 -dimensional sphere. In particular, the holonomy group of the n-dimensional standard Funk metric and the Bryant–Shen metrics are maximal and isomorphic to D i f f o (S n - 1) . These results are the firsts describing explicitly the holonomy group of n-dimensional Finsler manifolds in the non-Berwaldian (that is when the canonical connection is non-linear) case. [ABSTRACT FROM AUTHOR]

We consider smooth Riemannian surfaces whose curvature K satisfies the relation Δ log | K - c | = a K + b away from points where K = c for some (a , b , c) ∈ R 3 , which we call generalized Ricci surfaces. We prove some isometric immersion theorems allowing points where K = c using properties of log-harmonic functions. For instance, we obtain a characterization of Riemannian surfaces that locally admit minimal isometric immersions, possibly with umbilical points, into a 3-dimensional Riemannian manifold of constant sectional curvature. We also give an application to convex affine spheres. Finally, we study compact generalized Ricci surfaces: we obtain topological obstructions and construct examples. [ABSTRACT FROM AUTHOR]

In this study, the highly nonlinear and multi-scale flame-turbulence interactions prevalent in turbulent premixed flames are examined by using direct numerical simulation (DNS) datasets to understand the effects of increase in pressure and changes in the characteristic scale ratios at high pressure. Such flames are characterized by length-scale ratio (ratio of integral length scale and laminar thermal flame thickness) and velocity-scale ratio (ratio of turbulence intensity and laminar flame speed). A canonical test configuration corresponding to an initially laminar methane/air lean premixed flame interacting with decaying isotropic turbulence is considered. We consider five cases with the initial Karlovitz number of 18, 37, 126, and 260 to examine the effects of an increase in pressure from 1 to 10 atm with fixed turbulence characteristics and at a fixed Karlovitz number, and the changes to characteristic scale ratios at the pressure of 10 atm. The increase in pressure for fixed turbulence characteristics leads to enhanced flame broadening and wrinkling due to an increase in the range of energetic scales of motion. This further manifests into affecting the spatial and state-space variation of thermo-chemical quantities, single point statistics, and the relationship of heat-release rate to the flame curvature and tangential strain rate. Although these results can be inferred in terms of an increase in Karlovitz number, the effect of an increase in pressure at a fixed Karlovitz number shows differences in the spatial and state-space variations of thermo-chemical quantities and the relationship of the heat release rate with the curvature and tangential strain rate. This is due to a higher turbulent kinetic energy associated with the wide range of scales of motion at atmospheric pressure. In particular, the magnitude of the correlation of the heat release rate with the curvature and the tangential strain rate tend to decrease and increase, respectively, with an increase in pressure. Furthermore, the statistics of the flame-turbulence interactions at high pressure also show sensitivity to the changes in the characteristic length- and velocity-scale ratios. The results from this study highlight the need to accurately account for the effects of pressure and characteristic scales for improved modeling of such flames. [ABSTRACT FROM AUTHOR]

In this paper, we prove the following geometric inequalities in the Euclidean space Rn(n⩾3)$\mathbb {R}^n \ (n\geqslant 3)$, which are weighted Alexandrov–Fenchel type inequalities, ∫Σr2αHkdμ⩾ωn−1∫ΣHldμωn−1n−1−k+2αn−1−l,for0⩽l

In nonsmooth stochastic optimization, we establish the nonconvergence of the stochastic subgradient descent (SGD) to the critical points recently called active strict saddles by Davis and Drusvyatskiy. Such points lie on a manifold M, where the function f has a direction of second-order negative curvature. Off this manifold, the norm of the Clarke subdifferential of f is lower-bounded. We require two conditions on f. The first assumption is a Verdier stratification condition, which is a refinement of the popular Whitney stratification. It allows us to establish a strengthened version of the projection formula of Bolte et al. for Whitney stratifiable functions and which is of independent interest. The second assumption, termed the angle condition, allows us to control the distance of the iterates to M. When f is weakly convex, our assumptions are generic. Consequently, generically, in the class of definable weakly convex functions, SGD converges to a local minimizer. Funding: The work of Sholom Schechtman was supported by "Région Ile-de-France". [ABSTRACT FROM AUTHOR]

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We study an almost Yamabe soliton (Mn, g, V, ρ) and obtain various conditions on V in terms of infinitesimal harmonic transformation, 2-Killing, and an inequality, to show that V is Killing. In addition, we have provided characterizations of a 2-Killing vector field V on any Riemannian manifold in terms of the strain tensor and divergence of V. [ABSTRACT FROM AUTHOR]

In this paper, we give the flag curvature formula of general (α, β)-metrics of Berwald type. We study conformally related (α, β)-metrics, especially general (α, β)-metrics that are conformally related to invariant (α, β)-metrics. Also, a necessary and sufficient condition for a Finsler metric conformally related to an (α, β)-metric is given and conformally related Douglas Randers metrics are studied. Finally, we present some examples of conformally related (α, β)-metrics. [ABSTRACT FROM AUTHOR]

This study focuses on exploring the effects of geometrical imperfections and different analysis methods on the optimum design of Double-Layer Grids (DLGs), as used in the construction industry. A total of 12 notable metaheuristics are assessed and contrasted, and as a result, the Slime Mold Algorithm is identified as the most effective approach for size optimization of DLGs. To evaluate the influence of geometric imperfections and nonlinearity on the optimal design of real-size DLGs, the optimization process is carried out by considering and disregarding geometric nonlinearity while incorporating three distinct forms of geometrical imperfections, namely local imperfections, global imperfections, and combinations of both. In light of the uncertain nature of geometrical imperfections, probabilistic distributions are used to define these imperfections randomly in direction and magnitude. The results demonstrate that it is necessary to account for these imperfections to obtain an optimal solution. It's worth noting that structural imperfections can increase the maximum stress ratio by up to 70%. The analysis also reveals that the initial curvature of members has a more significant impact on the optimal design of structures than the nodal installation error, indicating the need for greater attention to local imperfection issues in space structure construction. [ABSTRACT FROM AUTHOR]

Diameter estimates for Kähler metrics are established which require only an entropy bound and no lower bound on the Ricci curvature. The proof builds on recent PDE techniques for L∞$L^\infty$ estimates for the Monge–Ampère equation, with a key improvement allowing degeneracies of the volume form of codimension strictly greater than one. As a consequence, we solve the long‐standing problem of uniform diameter bounds and Gromov–Hausdorff convergence of the Kähler–Ricci flow, for both finite‐time and long‐time solutions. [ABSTRACT FROM AUTHOR]

Energetic electron precipitation (EEP) during substorms significantly affects ionospheric chemistry and lower‐ionosphere (<100 km) conductance. Two mechanisms have been proposed to explain what causes EEP: whistler‐mode wave scattering, which dominates at low latitudes (mapping to the inner magnetosphere), and magnetic field‐line curvature scattering, which dominates poleward. In this case study, we analyzed a substorm event demonstrating the dominance of curvature scattering. Using ELFIN, POES, and THEMIS observations, we show that 50–1,000 keV EEP was driven by curvature scattering, initiated by an intensification and subsequent earthward motion of the magnetotail current sheet. Using a combination of Swarm, total electron content, and ELFIN measurements, we directly show the location of EEP with energies up to ∼1 MeV, which extended from the plasmapause to the near‐Earth plasma sheet (PS). The impact of this strong substorm EEP on ionospheric ionization is also estimated and compared with precipitation of PS (<30 keV) electrons. Plain Language Summary: During magnetospheric substorms, energetic electrons in the Earth's plasma sheet (PS), the night‐side magnetosphere region filled by hot plasma, precipitate to the ionosphere. Energetic electron precipitation (EEP) affects the density, temperature, and composition of the ionosphere. However, the exact process that causes such precipitation is not well understood due to observational constraints. The challenge lies in simultaneously measuring the EEP properties at the ionosphere and the plasma and wave properties in the PS. We analyze a fortuitous satellite conjunction during a substorm, during which EEP was simultaneously captured by ELFIN, Swarm, and POES at low altitudes, and THEMIS in the equatorial PS. EEP was observed to extend across a broad equatorial domain, projecting into a wide ionospheric region and encompassing the PS region and a significant portion of the inner magnetosphere. High‐energy‐resolution measurements from ELFIN reveal that the main driver of precipitation is the scattering of energetic electrons by strongly curved magnetic field lines in the PS, as opposed to the more commonly suggested scattering mechanisms associated with wave‐particle interactions. We also show that the EEP drastically altered the ionization profile of the ionosphere. Key Points: We investigate the radial location of energetic (50–1,000 keV) electron precipitation (EEP) during a substormWe compare the impact of plasma sheet electron precipitation (<30 keV) and EEP (50–1,000 keV) on the altitudinal profile of ionizationOur results underscore the key role of curvature scattering in energetic electron precipitation during substorms [ABSTRACT FROM AUTHOR]

In this paper, the motion of strictly convex closed plane curves under dissipative hyperbolic mean curvature flow is studied. The hyperbolic Monge–Amp è$$ \overset{\grave }{e} $$re equation is derived by using the support function. The short‐time existence of the flow is proved, and some evolution equations are derived. Furthermore, according to different initial velocities, we discuss the expansion and contraction of the dissipative hyperbolic curvature flow; that is, if the initial velocity v˜0<−α2ω0(θ)$$ {\tilde{v}}_0<-\frac{\alpha }{2}{\omega}_0\left(\theta \right) $$, the flow will converge to the limit curve at a finite time; if the initial velocity v˜0=−α2ω0(θ)$$ {\tilde{v}}_0&#x0003D;-\frac{\alpha }{2}{\omega}_0\left(\theta \right) $$, the flow will converge to a point t→∞$$ t\to \infty $$; if the initial velocity −−α2ω0(θ)0$$ {\tilde{v}}_0\left(\theta \right)>0 $$, the flow will expand to a limit curve as t→∞$$ t\to \infty $$. [ABSTRACT FROM AUTHOR]

In this paper, we study the interesting open problem of classifying the minimal Lagrangian submanifolds of dimension n in complex space forms with semi-parallel second fundamental form. First, we completely solve the problem in cases n = 2, 3, 4. Second, supposing further that the scalar curvature is constant for n ≥ 5, we also give an answer to the problem by applying the classification theorem of [F. Dillen, H. Li, L. Vrancken and X. Wang, Lagrangian submanifolds in complex projective space with parallel second fundamental form, Pacific J. Math. 255 (2012) 79–115]. Finally, for such Lagrangian submanifolds in the above problem with n ≥ 3, we establish an inequality in terms of the traceless Ricci tensor, the squared norm of the second fundamental form and the scalar curvature. Moreover, this inequality is optimal in the sense that all the submanifolds attaining the equality are completely determined. [ABSTRACT FROM AUTHOR]

In this work, we study a functional involving the generalized scalar curvatures and prove a spherical sphere theorem under some pinching condition of this quantity. As an application, we define a new invariant on 3-dimensional manifolds and use it to study the topology of manifolds. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel curvature tensor called the 풦-curvature tensor, which is formed by combining the Weyl tensor and the 풲2-curvature tensor. It is proved that a semi-Riemannian manifold with traceless 풦-curvature tensor is Einstein, while a 풦-curvature flat semi-Riemannian manifold exhibits constant sectional curvature. We show that a space-time with traceless 풦-curvature tensor or 풦-curvature flat represents dark energy era. A semi-Riemannian manifold with divergence-free 풦-curvature tensor is Weyl harmonic. In a space-time where the 풦-curvature tensor is of divergence-free, both the isotropic pressure and energy density are constants. Under certain conditions, it is shown that a pseudo-풦-symmetric semi-Riemannian manifold reduces to a pseudo-Riemannian manifold. It is demonstrated that pseudo-풦-symmetric space-times can be regarded as generalized Robertson–Walker (GRW) space-times. Finally, a concrete example of pseudo-풦-symmetric semi-Riemannian manifolds is presented. [ABSTRACT FROM AUTHOR]

In [Phys. Rev. D 107, 104008 (2023)], we reported a novel exact closed-form solution which describes asymptotically flat spacetimes in pure ℛ 2 gravity. The solution is Ricci scalar flat, viz. ℛ ≡ 0 everywhere. Whereas any metric with a null Ricci scalar would trivially satisfy the ℛ 2 vacuo field equation, ℛ (ℛ μ ν − 1 4 g μ ν ℛ) + g μ ν □ ℛ − ∇ μ ∇ ν ℛ = 0 , in this paper, we shall show that our solution satisfies a "stronger" version of the ℛ 2 vacuo field equation, viz. ℛ μ ν − 1 4 g μ ν ℛ + ℛ − 1 (g μ ν □ ℛ − ∇ μ ∇ ν ℛ) = 0 , despite the term ℛ − 1 being singular. Even though ℛ identically vanishes, for our solution, the combinations ℛ − 1 ∇ μ ∇ ν ℛ and ℛ − 1 □ ℛ are free of singularity. This exceptional property sets our solution apart from the set of null-Ricci-scalar metrics and makes it a genuinely nontrivial solution. We further demonstrate that, as a member of a larger class of asymptotically de Sitter metrics, our solution is resilient against perturbations in the scalar curvature at largest distances, making it relevant for physical situations where the background deviates from asymptotic flatness. [ABSTRACT FROM AUTHOR]

Introduction: For decades, the saccadic system has been a favorite target of neurophysiologists seeking to elucidate the neural control of eye movements, partly because saccades are characterized by a set of highly stereotyped relationships between amplitude, duration, and peak velocity. There is a large literature describing the dynamics and trajectories of these movements in normal primates, but there are no similarly detailed analyses for subjects with infantile strabismus syndrome. Previous studies have shown the amplitudes and directions of saccades often differ for the two eyes in this disorder, but it is unknown whether a similar disconjugacy exists for duration. The present study was designed to determine whether or not saccade duration differs for the two eyes in strabismus, and whether there are abnormalities involving the trajectories of these movements. Methods: Dynamic analyses of saccade trajectories and durations were performed for two normal monkeys, two with esotropia and two with exotropia. The amount of curvature was compared for the two eyes. For each monkey with strabismus, the amount of curvature was compared to normal controls. Saccades were placed into 12 bins, based on direction; for each bin, the mean saccade duration was compared for the two eyes (duration disconjugacy). The duration disconjugacy for each bin was then compared for monkeys with strabismus, versus normal control animals. Results: Surprisingly, the amount of curvature was not consistently greater in subjects with pattern strabismus. However, saccade curvature differed for the two eyes by a significantly greater amount for all monkeys with strabismus, compared to normal controls. In addition, for a subset of saccades in subjects with strabismus, saccade duration differed for the two eyes by more than 10 ms, even when the animal was fully alert. Discussion: To the best of the author’s knowledge, this is the first study to show that, in strabismus, saccade durations can differ for the two eyes by an abnormally large amount. These data also suggest that, in monkeys with pattern strabismus, abnormal horizontal-vertical crosstalk in brainstem can lead to directional disconjugacy without significantly impairing component stretching. These results place important constraints on future attempts to model the neural mechanisms that contribute to directional disconjugacy in pattern strabismus. [ABSTRACT FROM AUTHOR]

We extend Vétois’ Obata-type argument and use it to identify a closed interval I n I_{n} , n ≥ 3 n\geq 3 , containing zero such that if a ∈ I n a\in I_{n} and ( M n , g ) (M^{n},g) is a compact conformally Einstein manifold with nonnegative scalar curvature and Q 4 + a ⁢ σ 2 Q_{4}+a\sigma_{2} constant, then it is Einstein. We also relax the scalar curvature assumption to the nonnegativity of the Yamabe constant under a more restrictive assumption on 푎. Our results allow us to compute many Yamabe-type constants and prove sharp Sobolev inequalities on compact Einstein manifolds with nonnegative scalar curvature. In particular, we show that compact locally symmetric Einstein four-manifolds with nonnegative scalar curvature extremize the functional determinant of the conformal Laplacian, partially answering a question of Branson and Ørsted. [ABSTRACT FROM AUTHOR]

Micro-corona devices could be extensively utilized in gas sensing, switchgear, biomedicine, and other fields. As the influence mechanism of the cathode curvature radius on micro-corona discharge dynamical processes is very important for performance optimization and the promotion of these devices, a micro-scale corona discharge gas model in a mixture of N2-O2 is proposed based on the fluid–chemical mixing method, which describes the dynamic process of the discharge at atmosphere and normal temperatures. To reveal the influence mechanism of the nanowire curvature radius on the micro-corona discharge, the effect of the cathode nanowire radius on the discharge current, electric field, ionization reaction rate, and charged particle characteristics at different gaps and voltages were determined. The findings indicate that the effect of curvature radius on discharge intensity varies under different gap and voltage conditions. Further analysis indicates that an increase in curvature radius reduces the electric field near the tip while increasing the ionization area and secondary emission area as well as the number of positive ions in the space, consequently affecting the coupling process between the collision ionization and the secondary emission. Especially under the conditions of either small gap or low voltage, a suitable increase in the curvature radius could promote the coupling process and then increase the discharge current. [ABSTRACT FROM AUTHOR]

Previous studies have reported sex differences in cortical gyrification. Since most cortical folding is principally defined in utero, sex chromosomes as well as gonadal hormones are likely to influence sex‐specific aspects of local gyrification. Classic congenital adrenal hyperplasia (CAH) causes high levels of androgens during gestation in females, whereas levels in males are largely within the typical male range. Therefore, CAH provides an opportunity to study the possible effects of prenatal androgens on cortical gyrification. Here, we examined the vertex‐wise absolute mean curvature—a common estimate for cortical gyrification—in individuals with CAH (33 women and 20 men) and pair‐wise matched controls (33 women and 20 men). There was no significant main effect of CAH and no significant CAH‐by‐sex interaction. However, there was a significant main effect of sex in five cortical regions, where gyrification was increased in women compared to men. These regions were located on the lateral surface of the brain, specifically left middle frontal (rostral and caudal), right inferior frontal, left inferior parietal, and right occipital. There was no cortical region where gyrification was increased in men compared to women. Our findings do not only confirm prior reports of increased cortical gyrification in female brains but also suggest that cortical gyrification is not significantly affected by prenatal androgen exposure. Instead, cortical gyrification might be determined by sex chromosomes either directly or indirectly—the latter potentially by affecting the underlying architecture of the cortex or the size of the intracranial cavity, which is smaller in women. [ABSTRACT FROM AUTHOR]

In [19] , Smoczyk showed that parabolic expansion of convex curves and hypersurfaces by the reciprocal of the harmonic mean curvature gives rise to a linear second order equation for the evolution of the support function, with corresponding representation formulae for solutions. In this article we obtain representation formula for the corresponding linear hyperbolic evolution equation for the support function of locally convex curves of general nonzero rotation number, finding some natural similarities and differences in behaviour of solutions as compared with the parabolic case. As applications, we consider linear hyperbolic flows that preserve length or generalised enclosed area of the evolving curve, flow of curves with Neumann boundary conditions inside cones and hyperbolic approaches to the Yau problem of flowing one curve to another. We also consider radial graphs evolving by similar linear equations and linear higher order hyperbolic equations. Our results may be compared with the corresponding parabolic cases consider by the first author, Schrader and Wheeler, in [17]. [ABSTRACT FROM AUTHOR]

The conventional circular waveguide 90° TE01 bend makes it difficult to achieve broadband because of the serious interference from TM11 mode. To solve this problem, the mode coupling characteristics in the hexagonal waveguides are investigated in this paper, and it is found that when the deformation amplitude is appropriate, not only the degradation between TE01 and TM11 is broken but other parasitic modes can be efficiently suppressed. Based on the analysis, an oversized broadband TE01 waveguide bend with variable curvature is proposed, and its transmission efficiency is over 95% from 8.5 to 11 GHz, while its structure length is only 26.16 times wavelength. Measurement results indicate that the S21 of the bend is about −0.4 dB from 8.5 to 11 GHz, and it works stably under a microwave output power of 1 MW. The consistency between theoretical calculations, simulation, and experiments indicates the feasibility of this novel TE01 bend. [ABSTRACT FROM AUTHOR]

We introduce the notion of conformal trajectories in three-dimensional Riemannian manifolds M3. Given a conformal vector field V ∈ 픛(M3), a conformal trajectory of V is a regular curve γ in M3 satisfying ∇γ′γ′ = qV × γ′, for some fixed nonzero constant q ∈ ℝ. In this paper, we study the conformal trajectories in the space forms ℝ3, 핊3 and ℍ3. For (non-Killing) conformal vector fields in 핊3 (respectively, in ℍ3), we prove that conformal trajectories have constant curvature and its torsion is a linear combination of trigonometric (respectively, hyperbolic) functions on the arc-length parameter. In the case of Euclidean space ℝ3, we obtain the same result for the radial vector field and characterizing all conformal trajectories. [ABSTRACT FROM AUTHOR]

In contemporary manufacturing, the processing of structural materials plays a pivotal role in enabling the creation of robust, tailor-made, and precise components suitable for diverse industrial applications. Nonetheless, current material forming technologies face challenges due to internal stress and defects, resulting in a substantial decline in both mechanical properties and processing precision. We herein develop a processing strategy toward graphene superstructure with a curvature gradient, which allows us to fabricate robust structural materials with meticulously designed functional shapes. The structure consists of an arc-shaped assembly of graphene nanosheets positioned at co-axial curvature centers. During the dehydration-based evaporate-casting process, the assembly is tightened via capillary effect, inducing local bending. By precisely tuning the axis-center distance and tilt angle, we achieve accurate control over the shape of obtained structure. Notably, internal stress is harnessed to reinforce a designed mortise and tenon structure, resulting in a high joining strength of up to ~200 MPa. This innovative approach addresses the challenges faced by current material forming technologies and opens up more possibilities for the manufacturing of robust and precisely shaped components. Through precise adjustments to the curvature gradient inherent in stacked graphene assembly walls, a highly controllable water casting process for self-shaping with an accuracy of ca. 10 μm is demonstrated for making shaped functional materials. [ABSTRACT FROM AUTHOR]

Flash floods stand as a substantial peril linked to climate change, imposing a severe menace to both human existence and built structures. This study aims to assess and compare the effectiveness of four distinct machine learning (ML) methodologies in the production of flood susceptibility maps (FSMs) in Ibaraki prefecture, Japan. Additionally, the investigation aims to examine the influence of excluding plan and profile curvature factors on the accuracy of the resulting maps. The dataset comprised 224 spots, consisting of 112 flooded and 112 non-flooded locations, and 11 environmental factors. The models were trained using 70% of the dataset, while the remaining 30% was utilized for model evaluation using the ROC curve method. The results indicated that both the ANN-MLP and SVR models achieved notable accuracy, with area under curve values of 95.23% and 95.83% respectively. An intriguing observation was made when the plan and profile curvature factors were excluded, as it led to an improvement in the accuracy of the ANN-MLP model, resulting in an accuracy of 96.7%. Furthermore, the generated FSMs were classified into five distinct hazard levels. The northern region of the maps predominantly exhibited very low and low hazard levels, while areas located in the southern region, closer to main streams, demonstrated considerably higher hazard levels categorized as very high and high. Ultimately, this study marks novel endeavor to investigate the impact of the curvature factor on the precision of machine learning algorithms in the creation of FSMs, which serve as fundamental tools for subsequent investigations. [ABSTRACT FROM AUTHOR]

Featured Application: Featured Application: Fire Dynamics Simulator Pyrosim. In the existing research on tunnel fires, researchers primarily focus on straight tunnels, neglecting the impact of curved sidewalls in curved tunnels. Based on the theory of smoke diffusion, a series of CFD numerical simulations was conducted using the Fire Dynamics Simulator to investigate the characteristics of smoke distribution in a curved highway tunnel. The results indicated that distinct smoke distribution characteristics were observed when a fire occurred in a curved tunnel compared with those observed in straight tunnels, with significant differences particularly evident for the radius of curvature of the tunnel below 1000 m. By comparing the smoke distribution characteristics from various fire source locations, the most unfavorable fire source locations within a curved tunnel were determined. High-temperature fire smoke bounds between the inner and outer walls of the tunnel, leading to the formation of multiple high-temperature zones in proximity to the fire source, rather than diffusing directly towards the exit in a linear tunnel. Additionally, based on an analysis of temperature, visibility, and CO concentration at characteristic heights, suitable locations for pedestrian crossings within the tunnel were deduced and an evacuation strategy for persons within the core fire area was proposed. The results can provide a reference for personal evacuation strategies in curved highway tunnel fire scenarios and the design of an adit for people passing in such tunnels. [ABSTRACT FROM AUTHOR]

Butler Matrix networks are well established as beamforming networks for phased antenna arrays. The challenge we address in this work is to cover the entire (advanced 5G or 6G) FR3 band (7–24 GHz) with a single network, while retaining low losses and minimal size. The employed multilayer topology is also well established; however, the matching between the utilized hybrid couplers and the phase shifters constitutes a major challenge for such a wideband operation. This is achieved herein by employing meander lines with appropriate curvature and introducing two distinct design methods for the Butler Matrix. The first method focuses on designing individual components separately, followed by their integration into the overall Butler Matrix structure. This approach is demonstrated through the design, prototyping, measurements, and validation of an 8 × 8 Butler Matrix beamformer, which operates across the 6–16 GHz band (FR3 Low). The second method introduces a wideband-matching technique which simplifies the implementation process by designing the Butler Matrix as a single, unified structure. This technique is applied to both 4 × 4 and 8 × 8 Butler Matrices, which are implemented and simulated for the low FR3 band. Both design methods result in wideband operation and compact size and meet the desired performance criteria. [ABSTRACT FROM AUTHOR]

The traditional Iterative Closest Point (ICP) algorithm often suffers from low computational accuracy and efficiency in certain scenarios. It is highly sensitive to the initial pose, has a poor ability to resist interference, and frequently becomes trapped in local optima. Extracting feature points accurately from partially overlapping points with weak three-dimensional features, such as smooth planes or surfaces with low curvature, is challenging using only the traditional ICP algorithm for registration. This research introduces a "First Rough then Precise" registration strategy. Initially, the target position is extracted in complex environments using an improved clustering method, which simultaneously reduces the impact of environmental factors and noise on registration accuracy. Subsequently, an improved method for calculating normal vectors is applied to the Fast Point Feature Histogram (FPFH) to extract feature points, providing data for the Sample Consistency Initial Algorithm (SAC-IA). Lastly, an improved ICP algorithm, which has strong anti-interference capabilities for partially overlapping point clouds, is utilized to merge such point clouds. In the experimental section, we validate the feasibility and precision of the proposed algorithm by comparing its registration outcomes with those of various algorithms, using both standard point cloud dataset models and actual point clouds obtained from camera captures. [ABSTRACT FROM AUTHOR]

In the past few decades, various techniques for structural damage identification based on dynamic properties have been widely studied, among which modal curvature is the research hotspot, due to its high sensitivity to local damage. To realize story-level structural damage identification of shear buildings, this paper first derives the patterns of variation in modal curvature of the damaged structure. Then, a new damage index sensitive to local damage called the Modal Curvature Change modified with Softmax (MCCSM for short), is proposed to improve the accuracy of structural damage identification. Afterward, the validity of the damage index is verified by a shaking table test of a scaled RC frame structure model and its corresponding numerical model. The research results show that the damage location indicated by MCCSM corresponds well with the damage phenomenon in the shaking table test and numerical simulation; compared with using the theoretical mode shape, the MCCSM index can give comparable damage identification results using the mode shape obtained through operational modal analysis from vibration time-history data, which proves the feasibility in engineering practices; through numerical simulation, it is proved that the MCCSM index is applicable in a wide range of damage cases with different story position, number of damaged story, and damage extent. [ABSTRACT FROM AUTHOR]

Programmable self-assembly has seen an explosion in the diversity of synthetic crystalline materials, but developing strategies that target "self-limiting" assemblies has remained a challenge. Among these, self-closing structures, in which the local curvature defines the finite global size, are prone to polymorphism due to thermal bending fluctuations, a problem that worsens with increasing target size. Here, we show that assembly complexity can be used to eliminate this source of polymorphism in the assembly of tubules. Using many distinct components, we prune the local density of off-target geometries, increasing the selectivity of the tubule width and helicity to nearly 100%. We further show that by reducing the design constraints to target either the pitch or the width alone, fewer components are needed to reach complete selectivity. Combining experiments with theory, we reveal an economical limit, which determines the minimum number of components required to create arbitrary assembly sizes with full selectivity. [ABSTRACT FROM AUTHOR]

This work investigates the well-posedness and optimal control of a sixth-order Cahn–Hilliard equation, a higher-order variant of the celebrated and well-established Cahn–Hilliard equation. The equation is endowed with a source term, where the control variable enters as a distributed mass regulator. The inclusion of additional spatial derivatives in the sixth-order formulation enables the model to capture curvature effects, leading to a more accurate depiction of isothermal phase separation dynamics in complex materials systems. We provide a well-posedness result for the aforementioned system when the corresponding nonlinearity of double-well shape is regular and then analyze a corresponding optimal control problem. For the latter, existence of optimal controls is established, and the first-order necessary optimality conditions are characterized via a suitable variational inequality. These results aim at contributing to improving the understanding of the mathematical properties and control aspects of the sixth-order Cahn–Hilliard equation, offering potential applications in the design and optimization of materials with tailored microstructures and properties. [ABSTRACT FROM AUTHOR]

It has been a widely-accepted belief that for a planar convex domain with two coordinate axes of symmetry, the location of maximal norm of gradient of torsion function is either linked to contact points of largest inscribed circle or connected to points on boundary of minimal curvature. However, we show that this is not quite true in general. Actually, we derive the precise formula for the location of maximal norm of gradient of torsion function on nearly ball domains in ℝn, which displays nonlocal nature and thus does not inherently establish a connection to the aforementioned two types of points. Consequently, explicit counterexamples can be straightforwardly constructed to illustrate this deviation from conventional understanding. We also prove that for a rectangular domain, the maximum of the norm of gradient of torsion function exactly occurs at the centers of the faces of largest (n - 1)-volume. [ABSTRACT FROM AUTHOR]

The elastic energy of a bending-resistant interface depends on both its geometry and its material composition. We consider such a heterogeneous interface in the plane, modeled by a curve equipped with an additional density function. The resulting energy captures the complex interplay between curvature and density effects, resembling the Canham--Helfrich functional. We describe the curve by its inclination angle, so that the equilibrium equations reduce to an elliptic system of second order. After a brief variational discussion, we investigate the associated nonlocal L²-gradient flow evolution, a coupled quasilinear parabolic problem. We analyze the (non)preservation of quantities such as convexity, positivity, and symmetry, as well as the asymptotic behavior of the system. The results are illustrated by numerical experiments. [ABSTRACT FROM AUTHOR]

The initiation of a positive corona discharge near a model hydrometeor in air is studied numerically. Hydrometeors in the form of an ellipsoid of revolution and a cylinder with two hemispheres at the ends are considered as models. Threshold characteristics (external electric field strength, particle charge) are obtained for hydrometers of various sizes and shapes at an atmospheric pressure of 0.4−1 atm. Analysis of the results of numerous calculation options shows that the threshold field strength at the top of the hydrometeor is determined by the curvature radius of the surface at this point and air pressure. A universal dependence of the reduced threshold field strength on the product of the curvature radius of the surface and air pressure is obtained. The simulation results indicate the possibility of initiating a corona discharge in a thundercloud from the top of a hydrometeor less than a centimeter long at a subthreshold reduced field strength of 10−15 kV∕(cm atm). [ABSTRACT FROM AUTHOR]

Introduction: Esophagogastroduodenoscopy (EGD) requires adequate air infusion. However, cases of poor gastrointestinal wall extension due to frequent eructation have been reported. Sufficient gastrointestinal wall extension can be achieved by applying cricoid pressure during EGD. Herein, we evaluated the frequency of cases with poor gastrointestinal wall extension and the efficacy and safety of applying cricoid pressure during EGD. Methods: This interventional study included patients who underwent EGD between January 2020 and December 2020 at the JA Akita Koseiren Yuri Kumiai General Hospital. Cases wherein folds of the greater curvature of the upper gastric body were not sufficiently extended during EGD were considered to have poor gastrointestinal wall extension. In such cases, air infusion was performed while applying cricoid pressure. This procedure was considered effective when gastric wall extension was achieved. Results: A total of 2,000 patients were enrolled and underwent upper gastrointestinal endoscopy; however, five were excluded because of upper gastrointestinal tract stenosis. Observation of gastric wall extension of the greater curvature in the upper gastric body with normal air insufflation was difficult in 113 (5.7%) cases. Applying cricoid pressure was effective in 93 (82.3%) patients with poor gastric wall extension. Sufficient gastric wall extension was achieved within an average of 12.8 s in cases where cricoid pressure application was effective. No adverse events were associated with cricoid pressure application. Conclusions: Cricoid pressure application for patients with poor gastric wall extension during EGD is useful for ensuring a sufficient field of view during observation of the gastric body. [ABSTRACT FROM AUTHOR]

In this paper, we aim at identifying the level sets of the gauge norm in the Heisenberg group ℍ n via the prescription of their (non-constant) horizontal mean curvature. We establish a uniqueness result in ℍ 1 under an assumption on the location of the singular set, and in ℍ n for n ≥ 2 in the proper class of horizontally umbilical hypersurfaces. [ABSTRACT FROM AUTHOR]

We study a family of invariants of compact metric spaces that combines the Curvature Sets defined by Gromov in the 1980 s with Vietoris–Rips Persistent Homology. For given integers k ≥ 0 and n ≥ 1 we consider the dimension k Vietoris–Rips persistence diagrams of all subsets of a given metric space with cardinality at most n. We call these invariants persistence sets and denote them as D n , k VR . We first point out that this family encompasses the usual Vietoris–Rips diagrams. We then establish that (1) for certain range of values of the parameters n and k, computing these invariants is significantly more efficient than computing the usual Vietoris–Rips persistence diagrams, (2) these invariants have very good discriminating power and, in many cases, capture information that is imperceptible through standard Vietoris–Rips persistence diagrams, and (3) they enjoy stability properties analogous to those of the usual Vietoris–Rips persistence diagrams. We precisely characterize some of them in the case of spheres and surfaces with constant curvature using a generalization of Ptolemy's inequality. We also identify a rich family of metric graphs for which D 4 , 1 VR fully recovers their homotopy type by studying split-metric decompositions. Along the way we prove some useful properties of Vietoris–Rips persistence diagrams using Mayer–Vietoris sequences. These yield a geometric algorithm for computing the Vietoris–Rips persistence diagram of a space X with cardinality 2 k + 2 with quadratic time complexity as opposed to the much higher cost incurred by the usual algebraic algorithms relying on matrix reduction. [ABSTRACT FROM AUTHOR]

In this particular article, our focus revolves around the establishment of a geometric inequality, commonly referred to as Chen's inequality. We specifically apply this inequality to assess the square norm of the mean curvature vector and the warping function of warped product slant submanifolds. Our investigation takes place within the context of locally metallic product space forms with quarter-symmetric metric connections. Additionally, we delve into the condition that determines when equality is achieved within the inequality. Furthermore, we explore a number of implications of our findings. [ABSTRACT FROM AUTHOR]

This article explores the Ricci tensor of slant submanifolds within locally metallic product space forms equipped with a semi-symmetric metric connection (SSMC). Our investigation includes the derivation of the Chen–Ricci inequality and an in-depth analysis of its equality case. More precisely, if the mean curvature vector at a point vanishes, then the equality case of this inequality is achieved by a unit tangent vector at the point if and only if the vector belongs to the normal space. Finally, we have shown that when a point is a totally geodesic point or is totally umbilical with n = 2 , the equality case of this inequality holds true for all unit tangent vectors at the point, and conversely. [ABSTRACT FROM AUTHOR]

Helicoidal surfaces of constant mean curvature were fully described by do Carmo and Dajczer. However, the obtained parameterizations are given in terms of somewhat complicated integrals, and as a consequence, not many examples of such surfaces are visualized. In this paper, by using these methods in some particular cases, we provide several interesting visualizations involving these surfaces, mostly as an isometric deformation of a rotational surface. We also give interpretations of some older results involving helicoidal surfaces, motivated by the work carried out by Malkowsky and Veličković. All of the graphics in this paper were created in Wolfram Mathematica. [ABSTRACT FROM AUTHOR]

We prove that for any two Riemannian metrics |$\sigma _{1}, \sigma _{2}$| on the unit disk, a homeomorphism |$\partial \mathbb{D}\to \partial \mathbb{D}$| extends to at most one quasiconformal minimal diffeomorphism |$(\mathbb{D},\sigma _{1})\to (\mathbb{D},\sigma _{2})$| with |$L^{1}$| Hopf differential. For minimal Lagrangian diffeomorphisms between hyperbolic disks, the result is known, but this is the first proof that does not use anti-de Sitter geometry. We show that the result fails without the |$L^{1}$| assumption in variable curvature. The key input for our proof is the uniqueness of solutions for a certain Plateau problem in a product of trees. [ABSTRACT FROM AUTHOR]

In this paper, we study the stability of the volume preserving mean curvature flow of closed hypersurfaces in the hyperbolic space. We prove that an L 2 -almost umbilical hypersurface will be deformed to a totally umbilical hypersurface along the flow. Our result removes the assumption on the mean curvature in the theorems of Huang-Lin-Zhang [Peking J. Math. (2023)] and Leng-Xu-Zhao [Int. J. Math. (2014)]. [ABSTRACT FROM AUTHOR]

By using some line integrals in terms of the radial m -Bakry–Émery and radial m -modified Bakry–Émery Ricci curvatures, we give various compactness criteria for complete Riemannian manifolds when m is a positive constant, a negative constant, or infinity. Our results not only guarantee the compactness of complete Riemannian manifolds allowing the presence of negative amounts of the radial m -Bakry–Émery and radial m -modified Bakry–Émery Ricci curvatures, but also give new Myers-type theorems via m -Bakry–Émery and m -modified Bakry–Émery Ricci curvatures even the line integrals are reduced to pointwise positive lower bounds on the m -Bakry–Émery and m -modified Bakry–Émery Ricci curvatures. The key ingredients in proving our results are Riccati inequalities obtained from Bochner–Weitzenböck formulas via m -Bakry–Émery and m -modified Bakry–Émery Ricci curvatures. [ABSTRACT FROM AUTHOR]

For every d ≥ 3 , we construct a noncompact smooth 푑-dimensional Riemannian manifold with strictly positive sectional curvature without isoperimetric sets for any volume below 1. We construct a similar example also for the relative isoperimetric problem in (unbounded) convex sets in R d . The examples we construct have nondegenerate asymptotic cone. The dimensional constraint d ≥ 3 is sharp. Our examples exhibit nonexistence of isoperimetric sets only for small volumes; indeed, in nonnegatively curved spaces with nondegenerate asymptotic cones, isoperimetric sets with large volumes always exist. This is the first instance of noncollapsed nonnegatively curved space without isoperimetric sets. [ABSTRACT FROM AUTHOR]

In this paper, we present a geometric perspective on how to quantify the bending and the twisting of quantum curves traced by state vectors evolving under nonstationary Hamiltonians. Specifically, relying on the existing geometric viewpoint for stationary Hamiltonians, we discuss the generalization of our theoretical construct to time-dependent quantum-mechanical scenarios where both time-varying curvature and torsion coefficients play a key role. Specifically, we present a quantum version of the Frenet–Serret apparatus for a quantum trajectory in projective Hilbert space traced out by a parallel-transported pure quantum state evolving unitarily under a time-dependent Hamiltonian specifying the Schrödinger evolution equation. The time-varying curvature coefficient is specified by the magnitude squared of the covariant derivative of the tangent vector | T 〉 to the state vector | Ψ 〉 and measures the bending of the quantum curve. The time-varying torsion coefficient, instead, is given by the magnitude squared of the projection of the covariant derivative of the tangent vector | T 〉 to the state vector | Ψ 〉 , orthogonal to | T 〉 and | Ψ 〉 and, in addition, measures the twisting of the quantum curve. We find that the time-varying setting exhibits a richer structure from a statistical standpoint. For instance, unlike the time-independent configuration, we find that the notion of generalized variance enters nontrivially in the definition of the torsion of a curve traced out by a quantum state evolving under a nonstationary Hamiltonian. To physically illustrate the significance of our construct, we apply it to an exactly soluble time-dependent two-state Rabi problem specified by a sinusoidal oscillating time-dependent potential. In this context, we show that the analytical expressions for the curvature and torsion coefficients are completely described by only two real three-dimensional vectors, the Bloch vector that specifies the quantum system and the externally applied time-varying magnetic field. Although we show that the torsion is identically zero for an arbitrary time-dependent single-qubit Hamiltonian evolution, we study the temporal behavior of the curvature coefficient in different dynamical scenarios, including off-resonance and on-resonance regimes and, in addition, strong and weak driving configurations. While our formalism applies to pure quantum states in arbitrary dimensions, the analytic derivation of associated curvatures and orbit simulations can become quite involved as the dimension increases. Thus, finally we briefly comment on the possibility of applying our geometric formalism to higher-dimensional qudit systems that evolve unitarily under a general nonstationary Hamiltonian. [ABSTRACT FROM AUTHOR]

The goal of this paper is to analyze sharp-type inequalities including the scalar and Ricci curvatures of bi-slant Riemannian submersions in complex space forms. Then, for bi-slant Riemannian submersion between a complex space form and a Riemannian manifold, we give inequalities involving the Casorati curvature of the space ker φ ∗ . Also, we mention some examples. [ABSTRACT FROM AUTHOR]

It is known that the Frenet–Serret apparatus of a space curve in three-dimensional Euclidean space determines the local geometry of curves. In particular, the Frenet–Serret apparatus specifies important geometric invariants, including the curvature and the torsion of a curve. It is also acknowledged in quantum information science that low complexity and high efficiency are essential features to achieve when cleverly manipulating quantum states that encode quantum information about a physical system. In this paper, we propose a geometric perspective on how to quantify the bending and the twisting of quantum curves traced by dynamically evolving state vectors. Specifically, we propose a quantum version of the Frenet–Serret apparatus for a quantum trajectory in projective Hilbert space traced by a parallel-transported pure quantum state evolving unitarily under a stationary Hamiltonian specifying the Schrödinger equation. Our proposed constant curvature coefficient is given by the magnitude squared of the covariant derivative of the tangent vector | T 〉 to the state vector | Ψ 〉 and represents a useful measure of the bending of the quantum curve. Our proposed constant torsion coefficient, instead, is defined in terms of the magnitude squared of the projection of the covariant derivative of the tangent vector | T 〉 , orthogonal to both | T 〉 and | Ψ 〉. The torsion coefficient provides a convenient measure of the twisting of the quantum curve. Remarkably, we show that our proposed curvature and torsion coefficients coincide with those existing in the literature, although introduced in a completely different manner. Interestingly, not only we establish that zero curvature corresponds to unit geodesic efficiency during the quantum transportation in projective Hilbert space, but we also find that the concepts of curvature and torsion help enlighten the statistical structure of quantum theory. Indeed, while the former concept can be essentially defined in terms of the concept of kurtosis, the positivity of the latter can be regarded as a restatement of the well-known Pearson inequality that involves both the concepts of kurtosis and skewness in mathematical statistics. Finally, not only do we present illustrative examples with nonzero curvature for single-qubit time-independent Hamiltonian evolutions for which it is impossible to generate torsion, but we also discuss physical applications extended to two-qubit stationary Hamiltonians that generate curves with both nonzero curvature and nonvanishing torsion traced by quantum states with different degrees of entanglement, ranging from separable states to maximally entangled Bell states. In the Appendix C, we examine the different curvature and torsion characteristics of the three qubit | GHZ 〉 and | W 〉 states under evolution by a quantum Heisenberg Hamiltonian. [ABSTRACT FROM AUTHOR]