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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]

BackgroundAs perception of penile curvature varies widely, we sought to understand how adults perceive curvature and how these opinions compare with those of patients with curvature, specifically Peyronie's disease (PD).AimTo investigate the perspectives of curvature correction from adults with and without PD, as well as differences within demographics.MethodsA cross-sectional survey was administered to adult patients and nonpatient companions in general urology clinics at 3 institutions across the United States. Men, women, and nonbinary participants were recruited. Patients were grouped as having PD vs andrology conditions without PD vs general urology conditions plus companions. The survey consisted of unlabeled 2-dimensional images of penis models with varying degrees of curvature. Participants selected images that they would want surgically corrected for themselves and their children. Univariable and multivariable analyses were performed to identify demographic variables associated with willingness to correct.OutcomesOur main outcome was to detect differences in threshold to correct curvature between those with and without PD.ResultsParticipants were grouped as follows: PD (n = 141), andrology (n = 132), and general (n = 302) . Respectively, 12.8%, 18.9%, and 19.9% chose not to surgically correct any degree of curvature (P = .17). For those who chose surgical correction, the mean threshold for correction was 49.7°, 51.0°, and 51.0° (P = .48); for their children, the decision not to correct any degree of curvature was 21.3%, 25.4%, and 29.3% (P = .34), which was significantly higher than correction for themselves (P

Maintaining lipid asymmetry across membrane leaflets is critical for functions like vesicular traffic and organelle homeostasis. However, a lack of molecular‐level understanding of the mechanisms underlying membrane fission and fusion processes in synthetic systems precludes their development as artificial analogs. Here, we report asymmetry induction of a bilayer membrane formed by an extended π‐conjugated molecule with oxyalkylene side chains bearing terminal tertiary amine moieties (BA1) in water. Autogenous protonation of the tertiary amines in the periphery of the bilayer by water induces anisotropic curvature, resulting in membrane fission to form vesicles and can be monitored using time‐dependent spectroscopy and microscopy. Interestingly, upon loss of the induced asymmetry by extensive protonation using an organic acid restored bilayer membrane. The mechanism leading to the compositional asymmetry in the leaflet and curvature induction in the membrane is validated by density functional theory (DFT) calculations. Studies extended to control molecules having changes in hydrophilic (BA2) and hydrophobic (BA3) segments provide insight into the delicate nature of molecular scale interactions in the dynamic transformation of supramolecular structures. The synergic effect of hydrophobic interaction and the hydrated state of BA1 aggregates provide dynamicity and unusual stability. Our study unveils mechanistic insight into the dynamic transformation of bilayer membranes into vesicles. [ABSTRACT FROM AUTHOR]

We show that taking account of bounded curvature reduces the threshold regularity of connection coefficients required for existence and uniqueness of solutions to the geodesic equation, to L p , one derivative below the regularity W 1 , p required if one does not take account of curvature. We prove curvature in L p gives local existence and curvature in W 1 , p gives uniqueness. Our argument is based on the authors' theory of the RT-equations for regularizing connections to optimal regularity by coordinate transformation. The incoming regularity is too low to formulate a weak version of the geodesic equation based on the standard method of multiplying by smooth test functions and integrating by parts, so alternatively, we define weak solutions by coordinate transformation, and we give an explicit procedure for mollifying the original connection such that the correct weak solution is indeed a limit of smooth solutions of the mollified equations in the original coordinates. This is an example where limits under suitable mollification are more fundamental than a weak formulation, indicative of more complicated PDE's in which the standard weak formulation of the equations does not adequately rule out unphysical solutions. Our results apply to general second order ODE's in which the lack of regularity can be isolated in the connection coefficients. The results apply to General Relativity. [ABSTRACT FROM AUTHOR]

We consider closed planar curves with fixed length and arbitrary winding number whose elastic energy depends on an additional density variable and a spontaneous curvature. Working with the inclination angle, the associated L 2 -gradient flow is a nonlocal quasilinear coupled parabolic system of second order. We show local well-posedness, global existence of solutions, and full convergence of the flow for initial data in a weak regularity class. [ABSTRACT FROM AUTHOR]

Metal curved panels are commonly used in engineering structures, but they may be more susceptible to damage under impact loads compared to flat panels. Polyurea coating has been proposed as a solution to improve impact resistance. Therefore, this study investigates the impact resistance performance of curved composite panels by applying polyurea coating to aluminum‐based panels with different curvatures. First, a numerical model of polyurea‐coated aluminum composite panels was established using the finite element software LS‐DYNA, and the sensitivity of model mesh and the numerical model validity were carried out. Then, the impact resistance performance of polyurea‐coated aluminum‐based flat panels was studied from the aspects such as deformation modes and energy dissipation, and the influence of polyurea layer thickness and coating position on the impact resistance performance of polyurea‐coated aluminum composite panels was analyzed. Based on the above results, numerical models of polyurea‐coated aluminum‐based curved panels under different curvatures are further established, and the impact resistance performance of composite curved panels and the structural forms for effective protection against impact loads are comprehensively analyzed. The research results indicate that double‐sided polyurea coating is the optimal coating method for both aluminum flat panels and aluminum curved panels. After the coating thickness reaches 4 mm, there is no significant improvement in the structural impact resistance performance. The impact deformation of curved panels can be divided into four stages: dynamic buckling, plastic indentation, rebound deformation, and vibration. The concave surface has strong impact and deformation resistance, and the convex surface has strong impact resistance. The research results have important theoretical implications for the safe engineering design of protective structures using metal curved panels. [ABSTRACT FROM AUTHOR]

This article describes a method for determining the geometric working volume of satellite positive displacement machines (pump and motor). The working mechanism of these machines is satellite mechanism consisting of two non-circular gears (rotor and curvature) and circular gears (satellites). Two variants of the satellite mechanism are presented. In the first mechanism, the rolling line of the rotor is a sinusoid "wrapped" around a circle. In the second mechanism, the rolling line of the rotor is a double sinusoid "wrapped" around a circle. A method for calculating the area of the working chamber as a function of the rotor rotation angle is presented, based on mathematical formulae of the rotor, the curvature and the satellite rolling lines. It has been shown that the second variant of the satellite mechanism is advantageously characterised by a larger difference between the maximum area of the working chamber and the minimum area of this chamber. New mathematical formulas have been proposed to calculate the area of the working chamber for any angle of rotation of the shaft (rotor) based on the maximum and minimum values of the area of this chamber. It was thus confirmed that the geometric working volume depends on the maximum and minimum area of a working chamber and on the height of the satellite mechanism. The analyses of the area of the working chamber were carried out both for the mechanism without gears (the area delimited by the rolling lines of the elements of the mechanism) and for the real mechanism with gears. Differences in the values of these fields were also detected. [ABSTRACT FROM AUTHOR]

It was proved by Jenkins [Arch. Rational Mech. Anal. 8 (1961), 181–206] that a smooth entire graph in {\mathbb {R}}^3 with vanishing anisotropic mean curvature must be a plane. By using a calibration argument and a stability inequality we show here a different self-contained proof of this result, which is still valid when the anisotropic mean curvature is constant. [ABSTRACT FROM AUTHOR]

Let G = (V , E) be a finite, combinatorial graph. We define a notion of curvature on the vertex set V via the inverse of the resistance distance matrix. We prove that this notion of curvature has a number of desirable properties. Graphs with curvature bounded from below by K > 0 have diameter bounded from above. The Laplacian L = D − A satisfies a Lichnerowicz estimate, there is a spectral gap λ 2 ≥ 2 K. We obtain matching two-sided bounds on the maximal commute time between any two vertices in terms of | E | ⋅ | V | − 1 ⋅ K − 1 . Moreover, we derive quantitative rates for the mixing time of the corresponding Markov chain and prove a general equilibrium result. [ABSTRACT FROM AUTHOR]

A pseudo-Riemannian Lie group is a connected Lie group endowed with a left-invariant pseudo-Riemannian metric of signature (p , q). In this paper, we study pseudo-Riemannian Lie groups (G , 〈 ⋅ , ⋅ 〉) with non-Killing left-invariant conformal vector fields. Firstly, we prove that if h is a Cartan subalgebra for a semisimple Levi factor of the Lie algebra g , then dim ⁡ h ≤ max ⁡ { 0 , min ⁡ { p , q } − 2 }. Secondly, we classify trans-Lorentzian Lie groups (i.e., min ⁡ { p , q } = 2) with non-Killing left-invariant conformal vector fields, and prove that [ g , g ] is at most three-step nilpotent. Thirdly, based on the classification of the trans-Lorentzian Lie groups, we show that the corresponding Ricci operators are nilpotent, and consequently the scalar curvatures vanish. As a byproduct, we prove that four-dimensional trans-Lorentzian Lie groups with non-Killing left-invariant conformal vector fields are necessarily conformally flat, and construct a family of five-dimensional ones which are not conformally flat. [ABSTRACT FROM AUTHOR]

Purpose: To review the literature on the topic, to suggest a common line of treatment applicable across a wide community of specialists, and to contribute in maintaining the high level of interest in this disease. Methods: A comprehensive and exhaustive review of the literature was performed, identifying hundreds of articles on the topic. Results: Peyronie's disease is a condition that has been recognized, studied, and treated for centuries; despite this, if one excludes surgery in cases in which the deformity is stable, no clear treatment (or line of treatment) is available for complete relief of signs and symptoms. Treatment options were divided into local, oral, and injection therapy, and a wide variety of drugs, remedies, and options were identified. Conclusions: Low-intensity extracorporeal shock wave therapy, vacuum therapy, penile traction therapy, phosphodiesterase type 5 inhibitors, hyaluronic acid, and collagenase of Clostridium histolyticum may be recommended only in specific contexts. Further studies on individual options or potential combinations are required. [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 this article, we attempt to solve Einstein field equations minimally coupled to a ϕ 2 scalar field in closed, flat, and open FLRW space-time during the inflationary era. To achieve this, we introduce an auxiliary function of cosmic time and derive the Hubble parameter, scalar field, and scale factor in terms of it. The universe undergoes remarkable accelerating expansion when the auxiliary function reaches a specific value. Additionally, we determine a lower bound on the scale factor at the onset of inflation for both open and closed cases. Finally, we estimate the mass of the inflaton and Hubble constant numerically. Our findings suggest that the scalar field oscillates after the inflationary period. [ABSTRACT FROM AUTHOR]

Trajectory tracking on a low-speed vehicle using the model predictive control (MPC) algorithm usually assumes a simple road terrain. This assumption does not correspond to the actual road situation, leading to low tracking accuracy. Therefore, a trajectory tracking method considering road curvature based on MPC is proposed in this paper. In this method, the controller can automatically switch between MPC types. Linear model predictive control (LMPC) is selected for small road curvatures, while nonlinear model predictive control (NMPC) is employed for large road curvatures. In addition, the NMPC algorithm in this work considers the effect of road curvature on tracking accuracy, making it suitable for tracking time-varying curvature roads. To verify the feasibility of the algorithm, simulation comparisons with the basic MPC model were carried out at different testing roads and vehicle longitudinal speeds. The results indicate that the method significantly improves trajectory tracking accuracy, all while ensuring real-time calculations. The intelligent switching capability of control models based on road curvature allows its application to track trajectories on arbitrarily complex roads. [ABSTRACT FROM AUTHOR]

In the current work, we study the geometry and topology of warped product Legendrian submanifolds in Kenmotsu space forms F 2 n + 1 (ϵ) and derive the first Chen inequality, including extrinsic invariants such as the mean curvature and the length of the warping functions. Additionally, sectional curvature and the δ-invariant are intrinsic invariants related to this inequality. An integral bound is also given in terms of the gradient Ricci curvature for the Bochner operator formula of compact warped product submanifolds. Our primary technique is applying geometry to number structures and solving problems such as problems with Dirichlet eigenvalues. [ABSTRACT FROM AUTHOR]

Single-cell RNA sequencing (scRNA-seq) enables dissecting cellular heterogeneity in tissues, resulting in numerous biological discoveries. Various computational methods have been devised to delineate cell types by clustering scRNA-seq data, where clusters are often annotated using prior knowledge of marker genes. In addition to identifying pure cell types, several methods have been developed to identify cells undergoing state transitions, which often rely on prior clustering results. The present computational approaches predominantly investigate the local and first-order structures of scRNA-seq data using graph representations, while scRNA-seq data frequently display complex high-dimensional structures. Here, we introduce scGeom, a tool that exploits the multiscale and multidimensional structures in scRNA-seq data by analyzing the geometry and topology through curvature and persistent homology of both cell and gene networks. We demonstrate the utility of these structural features to reflect biological properties and functions in several applications, where we show that curvatures and topological signatures of cell and gene networks can help indicate transition cells and the differentiation potential of cells. We also illustrate that structural characteristics can improve the classification of cell types. [ABSTRACT FROM AUTHOR]

Many researchers have widely applied shape descriptors to perform dimensional synthesis of mechanisms. This work investigates the path synthesis of planar four-bar linkages for closed and open curves using elliptical Fourier descriptors (EFDs). EFD is also a Fourier-based analysis method. Its Fourier coefficients of a coupler curve are obtained through separate Fourier expansion of the x and y components of the coupler curve rather than on a function. Elliptical Fourier descriptors are effective at describing complex curves with high curvature. A process has been developed for approximating non-periodic paths using EFD. By combining the process with the traditional EFD, a general method is established for the synthesis of four-bar linkages for open and closed curves in a single-step optimization process. The proposed approach offers an effective and efficient procedure in the path synthesis of four-bar linkages, providing a foundation for future research in the broader application of EFD in the dimensional synthesis of linkages. [ABSTRACT FROM AUTHOR]

We develop a conformal duality for space‐like graphs in Riemannian and Lorentzian three‐manifolds that admit a Riemannian submersion over a Riemannian surface whose fibers are the integral curves of a Killing vector field, which is time‐like in the Lorentzian case. The duality swaps mean curvature and bundle curvature and sends the length of the Killing vector field to its reciprocal while keeping invariant the base surface. We obtain two consequences of this result. On the one hand, we find entire graphs in Lorentz–Minkowski space L3$\mathbb {L}^3$ with prescribed mean curvature a bounded function H∈C∞(R2)$H\in \mathcal {C}^\infty (\mathbb {R}^2)$ with bounded gradient. On the other hand, we obtain conditions for the existence and nonexistence of entire graphs which are related to a notion of the critical mean curvature. [ABSTRACT FROM AUTHOR]

Background/Objectives: Lumbar lordotic curvature (LLC), closely associated with low back pain (LBP) when decreased, is infrequently assessed in clinical settings due to the spatiotemporal limitations of radiographic methods. To overcome these constraints, this study used an inertial measurement system to compare the magnitude and maintenance of LLC across various sitting conditions, categorized into three aspects: verbal instructions, chair type, and desk task types. Methods: Twenty-nine healthy participants were instructed to sit for 3 min with two wireless sensors placed on the 12th thoracic vertebra and the 2nd sacral vertebra. The lumbar lordotic angle (LLA) was measured using relative angles for the mediolateral axis and comparisons were made within each sitting category. Results: The maintenance of LLA (LLAdev) was significantly smaller when participants were instructed to sit upright (−3.7 ± 3.9°) compared to that of their habitual sitting posture (−1.2 ± 2.4°) (p = 0.001), while the magnitude of LLA (LLAavg) was significantly larger with an upright sitting posture (p = 0.001). LLAdev was significantly larger when using an office chair (−0.4 ± 1.1°) than when using a stool (−3.2 ± 7.1°) (p = 0.033), and LLAavg was also significantly larger with the office chair (p < 0.001). Among the desk tasks, LLAavg was largest during keyboard tasks (p < 0.001), followed by mouse and writing tasks; LLAdev showed a similar trend without statistical significance (keyboard, −1.2 ± 3.0°; mouse, −1.8 ± 2.2°; writing, −2.9 ± 3.1°) (p = 0.067). Conclusions: Our findings suggest that strategies including the use of an office chair and preference for computer work may help preserve LLC, whereas in the case of cueing, repetition may be necessary. [ABSTRACT FROM AUTHOR]

This work considers the non-convex finite-sum minimization problem. There are several algorithms for such problems, but existing methods often work poorly when the problem is badly scaled and/or ill-conditioned, and a primary goal of this work is to introduce methods that alleviate this issue. Thus, here we include a preconditioner based on Hutchinson's approach to approximating the diagonal of the Hessian and couple it with several gradient-based methods to give new 'scaled' algorithms: Scaled SARAH and Scaled L-SVRG. Theoretical complexity guarantees under smoothness assumptions are presented. We prove linear convergence when both smoothness and the PL-condition are assumed. Our adaptively scaled methods use approximate partial second-order curvature information and, therefore, can better mitigate the impact of badly scaled problems. This improved practical performance is demonstrated in the numerical experiments also presented in this work. [ABSTRACT FROM AUTHOR]

N‐coordinated Ni sites (NiNx) are effective catalysts for the electrochemical reduction of CO2 to CO. In most researches, modulating the coordination environment of Ni atoms is focused on to improve electrochemical CO2 reduction (ECR) performance. However, the influence of the carbon substrate's structure on the intrinsic activity of NiNx is seldom investigated. The highly curved surface of carbon nanotubes (CNT) may provide a unique curvature effect on NiNx. It is found that the Ni residues in CNT can be atomized to form NiNx sites on the surface of CNT (Ni‐N/CNT@covalent triazine framework [CTF]) through high‐temperature pyrolysis, using a soluble CTF nanosheet as N precursor. The π‐conjugated and ultrathin 2D structure of CTF enables closer interfacial contact between CTF and CNT, which avoids the formation of a thick carbon layer to maximize the curvature effect. Theoretical data reveal that the NiN3 configuration may act as a highly active ECR site, and the curvature effect from CNT can further tune the electronic structure of NiN3, thus improving the ECR kinetics. The Ni‐N/CNT@CTF‐based flow‐cell electrolyzer exhibits a jCO of 201 mA cm−2 at −0.9 V with a high FECO of 98%. [ABSTRACT FROM AUTHOR]

We study entire spacelike constant mean curvature hypersurfaces in Anti-de Sitter space of any dimension. First, we give a classification result with respect to their asymptotic boundary, namely we show that every admissible sphere |$\Lambda $| is the boundary of a unique such hypersurface, for any given value |$H$| of the mean curvature. We also demonstrate that, as |$H$| varies in |$\mathbb {R}$|⁠ , these hypersurfaces analytically foliate the invisible domain of |$\Lambda $|⁠. Finally, we extend Cheng-Yau Theorem to the Anti-de Sitter space, which establishes the completeness of any entire constant mean curvature hypersurface. [ABSTRACT FROM AUTHOR]

On a complete |$p$| -nonparabolic |$3$| -dimensional manifold with non-negative scalar curvature and vanishing second homology, we establish a sharp monotonicity formula for the proper |$p$| -Green function along its level sets for |$1

Stoney formula is widely used in advanced devices to estimate the residual stress of thin film/substrate system by measuring surface curvature. Many hypotheses including that thin film thickness is ignored are required, thus bringing significant error in characterizing the inhomogeneous residual stress distribution. In this article, arbitrary residual stresses on thin film/substrate structures with nonnegligible film thickness are modeled and characterized. We introduce nonuniform misfit strain and establish the governing equations including mismatched strain, displacements, and interfacial stresses based on the basic elastic theory. The parameterization method and the method of constant variation are used in the process of equation decoupling. The expressions between displacements, surface curvatures, and misfit strain are determined through decoupling calculations. By substituting misfit strain, residual stresses are expressed by parametric equation related to surface curvature. It further indicates that there is a "non-local" part between the film stress and curvature at the same point. Compared to neglecting the film thickness, the proposed method eliminate relative errors up to 58.3%, which is of great significance for stress measurement of thin films and substrates. [ABSTRACT FROM AUTHOR]

Background: Sir Roy Calne in 1976 described "Biliary reconstruction is the Achilles heel of liver transplantation," and it remains true. In some patients, such as those with short‐gut syndrome and concomitant biliary atresia, neither duct to duct nor Roux biliary reconstruction is feasible. Methods: We present a case of child's third liver transplant (LT), where an innovative extra‐anatomical biliary bypass was created using a sleeve from greater curvature of the stomach. Results: The patient is well nearly 10 years following the LT. Conclusions: This technique could prove to be an important addition to the armamentarium of a surgeon in difficult retransplants and in patients with short‐gut syndrome as it provides a viable option with good long‐term outcome. [ABSTRACT FROM AUTHOR]

To estimate the accurate position of the target, the geodesic curvature of the transmitter sensor is proposed in the present work. The geodesic curvature of the transmitter sensor traces the motion of a sensor as the shortest distance along a curved path, which measures the optimal distance on a curved path, accurate measurement of moving targets in an environment with complex geodesics, enhances the realism of the simulation, and underwater surveillance. Theorem 2.1 describes the geodesic curvature between the transmitter sensor and the target. A proposed non-cooperative moving target state measurement (NMTSM) algorithm quantifies the degradation of localization performance and mitigates the stratification effect and geodesic spreading losses. The localization error, localization error variance, and localization accuracy with respect to the number of anchor nodes are compared with standard methods. The proposed non-cooperative moving target state measurement (NMTSM) algorithm improves the localization performance by 33.46% and reduces position MSE by 35.46%, and velocity MSE by 38.86% up to 650 meters. It reduces the localization error by 32.23%, the localization error variance by 34.86% and improves the localization accuracy by 42.21%. The proposed algorithm is useful for the sub-aquatic Internet of Underwater Things (IoUT). [ABSTRACT FROM AUTHOR]

In this paper, we investigate the rigidity and vanishing properties of compact submanifolds with free boundary of arbitrary codimension in the unit ball. We first show that a minimal submanifold with free boundary in the unit ball satisfying a pointwise or integral curvature pinching condition on the second fundamental form is a flat equatorial disk. Then we prove a vanishing theorem for cohomology groups for submanifolds with free boundary in the unit ball under an integral curvature pinching condition on the trace‐free second fundamental form. [ABSTRACT FROM AUTHOR]

One of the main obstacles regarding Bakry–Emery curvature on graphs is that the results require a global uniform lower curvature bounds where no exception sets are allowed. We overcome this obstacle by introducing the perpetual cutoff method. As applications, we prove gradient estimates only requiring curvature bounds on parts of the graph. Moreover, we sharply upper bound the distance to the exception set for graphs having uniformly positive Bakry–Emery curvature everywhere but on the exception set. [ABSTRACT FROM AUTHOR]

This paper consists of two parts. The first part is devoted to the study of the Beltrami equation with a polar singularity in a circle centred at the origin, with a cut along the positive semiaxis. The coefficients of the equation have a first-order pole at the origin and do not belong to the class $ L_2(G). $ L 2 (G). Therefore, despite having a unique form, this equation is not covered in the analysis of I.N.Vekua [Generalized analytic functions. Nauka: Moscow; 1988. Russian] and needs to be independently studied. In the second part of the article, the coefficients of the equation are chosen so that the resulting solutions are continuous in a circle without a cut. These results can be used in the theory of infinitesimal bendings of surfaces of positive curvature with a flat point and in constructing a conjugate isometric coordinate system on a surface of positive curvature with a planar point. [ABSTRACT FROM AUTHOR]

In this paper we assume that a perfect fluid is the source of the gravitational field while analyzing the solutions to the Einstein field equations. With this new and innovative approach, we investigate some curvature properties of perfect fluid spacetimes. Firstly, we provide a necessary condition for a Lorentzian manifold to be a perfect fluid spacetime. We prove that a conformally flat perfect fluid space-time is a spacetime of quasi constant sectional curvature. Also, we acquire that a conharmonically flat perfect fluid spacetime represents the radiation era. Next, we show that if a stiff matter fluid obeys Yang's equations, then the vorticity of the fluid vanishes. Moreover, we find that if the Ricci tensor is Killing, then the perfect fluid spacetime is (i) expansion-free and shear-free, and its flow is geodesic, however, not necessarily vorticity-free, and (ii) σ and p are constant. Besides, we establish that Ricci semi-symmetric or Ricci symmetric perfect fluid spacetimes represent either dark matter era, or phantom era. Finally, we acquire that if a perfect fluid is Ricci symmetric, then either the spacetime represents a dark matter era, or a static spacetime. [ABSTRACT FROM AUTHOR]

In this paper we consider harmonic functions on gradient shrinking Ricci solitons with constant scalar curvature. A Liouville theorem is proved without using gradient estimate: any bounded harmonic function is constant on gradient shrinking Ricci solitons with constant scalar curvature. As an application, we show that the space of harmonic functions with polynomial growth has finite dimension. [ABSTRACT FROM AUTHOR]

In this article, we extend an unknottedness theorem for compact self-shrinkers to the mean curvature flow to shrinkers with finite topology and one asymptotically conical end, which conjecturally comprises the entire set of self-shrinkers with finite topology and one end. The mean curvature flow itself is used in the argument presented. [ABSTRACT FROM AUTHOR]

For a wide class of curvature energy functionals defined for planar curves under the fixed-length constraint, we obtain optimal necessary conditions for global and local minimizers. Our results extend Maddocks' and Sachkov's rigidity principles for Euler's elastica by a new, unified and geometric approach. This in particular leads to complete classification of stable closed p-elasticae for all p ∈ (1 , ∞) and of stable pinned p-elasticae for p ∈ (1 , 2 ] . Our proof is based on a simple but robust "cut-and-paste" trick without computing the energy nor its second variation, which works well for planar periodic curves but also extends to some non-periodic or non-planar cases. An analytically remarkable point is that our method is directly valid for the highly singular regime p ∈ (1 , 3 2 ] in which the second variation may not exist even for smooth variations. [ABSTRACT FROM AUTHOR]

We prove that three-dimensional electrostatic manifolds with divergence-free Bach tensor are locally conformally flat, provided that the electric field and the gradient of the lapse function are linearly dependent. Consequently, a three-dimensional electrostatic manifold admits a local warped product structure with a one-dimensional base and a constant curvature surface fiber. [ABSTRACT FROM AUTHOR]

Advances in quantitative biophysical techniques have allowed researchers to probe deeply into the mechanisms behind complex membrane remodeling phenomena. Despite their lack of structure, intrinsically disordered proteins have become widely recognized for their various biophysical functions over the past several years. These functions include membrane curvature sensing and membrane bending. The combination of nanofabricated substrates and live-cell systems has created a new avenue for biomimetic research that will vastly expand our ability to study protein interactions with curved membranes. Biological membranes are integral cellular structures that can be curved into various geometries. These curved structures are abundant in cells as they are essential for various physiological processes. However, curved membranes are inherently unstable, especially on nanometer length scales. To stabilize curved membranes, cells can utilize proteins that sense and generate membrane curvature. In this review, we summarize recent research that has advanced our understanding of interactions between proteins and curved membrane surfaces, as well as work that has expanded our ability to study curvature sensing and generation. Additionally, we look at specific examples of cellular processes that require membrane curvature, such as neurotransmission, clathrin-mediated endocytosis (CME), and organelle biogenesis. [ABSTRACT FROM AUTHOR]

Cognitive deficits are a core symptom of schizophrenia, but research on their neural underpinnings has been challenged by the heterogeneity in deficits' severity among patients. Here, we address this issue by combining logistic regression and random forest to classify two neuropsychological profiles of patients with high (HighCog) and low (LowCog) cognitive performance in two independent samples. We based our analysis on the cortical features grey matter volume (VOL), cortical thickness (CT), and mean curvature (MC) of N = 57 patients (discovery sample) and validated the classification in an independent sample (N = 52). We investigated which cortical feature would yield the best classification results and expected that the 10 most important features would include frontal and temporal brain regions. The model based on MC had the best performance with area under the curve (AUC) values of 76% and 73%, and identified fronto-temporal and occipital brain regions as the most important features for the classification. Moreover, subsequent comparison analyses could reveal significant differences in MC of single brain regions between the two cognitive profiles. The present study suggests MC as a promising neuroanatomical parameter for characterizing schizophrenia cognitive subtypes. [ABSTRACT FROM AUTHOR]