Curvature Estimation Research Articles

Estimation of anisotropic bending rigidities and spontaneous curvatures of crescent curvature-inducing proteins from tethered-vesicle experimental data.

The Bin/amphiphysin/Rvs (BAR) superfamily proteins have a crescent binding domain and bend biomembranes along the domain axis. However, their anisotropic bending rigidities and spontaneous curvatures have not been experimentally determined. Here, we estimated these values from the bound protein densities on tethered vesicles using a mean-field theory of anisotropic bending energy and orientation-dependent excluded volume. The dependence curves of the protein density on the membrane curvature are fitted to the experimental data for the I-BAR and N-BAR domains reported by C. Prévost et al. Nat. Commun., 2015, 6, 8529 and F.-C. Tsai et al. Soft Matter, 2021, 17, 4254-4265, respectively. For the I-BAR domain, all three density curves of different chemical potentials exhibit excellent fits with a single parameter set of anisotropic bending energy. When the classical isotropic bending energy is used instead, one of the curves can be fitted well, but the others exhibit large deviations. In contrast, for the N-BAR domain, two curves are not well fitted simultaneously the anisotropic model, although it is significantly improved compared to the isotropic model. This deviation likely suggests a cluster formation of the N-BAR domains.

Codimension four regularity of generalized Einstein structures

We establish codimension 4 regularity of noncollapsed sequences of metrics with bounds on natural generalizations of the Ricci tensor. We obtain a priori $$L^2$$ curvature estimates on such spaces, with diffeomorphism finiteness results and rigidity theorems as corollaries.

Integrating flexibility-based curvature with quasi-static features induced by traffic loads for high-resolution damage localization in bridges

Curvature is one of the most popular damage-sensitive features in vibration-based structural health monitoring applications, typically calculated from identified modal features. While the relevant strategic or historical importance of bridges may justify dense sensor networks, a limited budget is generally assigned to monitor “minor” viaducts, thus involving inexpensive devices or extremely sparse sensing solutions. Modal parameters can only be obtained at instrumented locations. Thereby, damage assessment methods based on identified features typically have a low spatial resolution, especially when using low-cost monitoring setups with a modest number of sensing devices. This paper proposes an original identification method for the curvature of bridges based on sparse acceleration measurements that can be collected using standard accelerometers. The raw acceleration signal is processed through a particular filter bank that extracts dynamic and quasi-static signal components. The first components are employed to identify modal parameters, from which sparse yet robust estimates of the structural curvature are retrieved. On the other hand, the quasi-static acceleration generated by the structural deflection induced by traffic load is used to identify the curvature influence lines of the bridge, which are fused with modal estimates using a Kalman filter. The state variable of the analyzed system, representing a dense curvature profile of the structure subjected to concentrated loads, can be used as a damage-sensitive feature for high-resolution damage localization. The method is applied to a steel truss bridge subject to different damage configurations.

Estimation of the Horizontal Curvature of the Railway Track Axis with the Use of a Moving Chord Based on Geodetic Measurements

Estimation of the Horizontal Curvature of the Railway Track Axis with the Use of a Moving Chord Based on Geodetic Measurements

Time Zero Regularity of Ricci Flow

Abstract We consider the problem of when a smooth Ricci flow, for positive time, that attains smooth initial data in a weak sense must be smooth down to the initial time. We obtain curvature estimates for an example where this fails that was given in [26]. We prove a positive result in the case that the flow satisfies a lower ${ {\textrm {K}_{\textrm {IC}_1}}}$ curvature bound, equivalent to a lower Ricci bound in three dimensions. As an application, we prove that Gromov–Hausdorff limits of WPIC1 manifolds are WPIC1.

Estimation of Curvature of Real and Interpoled Images

Estimation of Curvature of Real and Interpoled Images

Assessment of a Point-Cloud Volume-of-Fluid method with sharp interface advection

Multiphase flows are ubiquitous in nature and industry. In order to fully describe multiphase systems, simulation approaches must be able to handle the interfaces separating the different phases properly. The Volume of Fluid (VOF) approach is widely used by researchers and engineers due to its intrinsic ability to conserve volume and handle large interface topology changes. A common problem that occurs in VOF Methods relates to the calculation of interfacial tension forces in the momentum equations while resolving a sharp interface. Common methods based on the gradients of the volume fraction field may lack accuracy due to the curvature and normal vector estimates through an abrupt transition. To address these points, the present work introduces a new proposal, where the VOF method based on a cloud of points for interface curvatures computation (PC-VOF) is extended by the coupling with the sharp-interface advection algorithm isoAdvector, implemented in the open source suite OpenFOAM®. The coupled method performs better than the ones implemented in the original solvers in a number of benchmark cases from the literature. It is shown to significantly reduce the spurious currents and also presents more stable and accurate results, especially for irregular triangular meshes.

Curvature estimates for the continuity method

We obtain curvature estimates for long-time solutions of the continuity method on compact Kähler manifolds with semi-ample canonical line bundles. In this setting, initiated in [G. La Nave and G. Tian, A continuity method to construct canonical metrics, Math. Ann. 365(3) (2016) 911–921; Y. A. Rubinstein, Some discretizations of geometric evolution equations and the Ricci iteration on the space of Kähler metrics, Adv. Math. 218(5) (2008) 1526–1565], we adapt arguments from [F. T.-H. Fong and Y. Zhang, Local curvature estimates of long-time solutions to the Kähler–Ricci flow, Adv. Math. 375 (2020) 107416] for the Kähler–Ricci flow to this setup. As an application, we derive curvature bounds for general metrics on product manifolds.

Development of a Method for Fast Assessment of Protein Solubility Based on Ultrasonic Dispersion and Differential Centrifugation Technology.

Protein solubility is very important for protein crystallization, bioprocess development, and protein application. In this study, a method based on the stability of a protein dispersion system is proposed for fast assessment of protein solubility, which mainly involves ultrasonic dispersion, differential centrifugation, and spectral measurement (UDDCS) and curvature estimation. The appropriate ultrasonic time and centrifugal time were experimentally determined at first. The results show that the relationship between the standard deviation and the protein concentrations originally added accords with the modified exponential equation, and the corresponding concentration of the maximum curvature point is defined as the solubility of the protein. Lysozyme solubility data in NaCl aqueous solutions and zein solubility data in ethanol aqueous solutions are selected to verify the UDDCS method by comparing the data obtained by the UDDCS method and the results from references, and the results indicate that the UDDCS method is reliable, universal, and time-saving. Finally, measurements of zein solubility in NaOH solution and casein solubility in urea aqueous solution were conducted as test cases by the UDDCS method.

An approximated volume of fluid method with the modified height function method in the simulation of surface tension driven flows

Surface tension in two-phase flow problems plays a dominant role in many micro-flow phenomena and has an important influence on the development of flow instability phenomena that contain free surfaces. In this study, the multi-moment finite volume method is extended for direct numerical simulation of two-phase flow problems. A constraint interpolation profile–CSL (semi-Lagrangian) scheme is used for discretization of the advection part in the momentum equation. A compact volume of fluid method–approximated piecewise linear calculation method without flux limiter is proposed for capturing the moving interface. For modeling the surface tension accurately, the logic in curvature estimation is redesigned based on the height function (HF) method. The isolated volumetric fractions that may reduce accuracy in HF integration are excluded, and the numerical solution shows that the accuracy in the curvature estimation is improved for a coarse mesh. The present method is implemented with a parallel block-structured adaptive mesh refinement (BAMR) strategy; thus, the computational cost can be reduced significantly. Numerical tests show that the present BAMR solver is capable of reproducing the theoretical predictions of capillary wave instability problems with high accuracy. The simulation of droplet collisions further demonstrates the accuracy of the surface tension model. Finally, we extend it to the liquid jet atomization. The wavy disturbance, film breakup, liquid filament pinch-off, and droplet generation are well reproduced. The droplet size distribution satisfies the experimental measurement and theoretical predictions power-law. BAMR shows a huge advantage in computational efficiency than the traditional Cartesian grid. The findings of this study can help for a better understanding of the micro-mechanism of surface tension driven flows.

High-order level set reinitialization for multiphase flow simulations based on unstructured grids

Reinitialization is essential to maintaining the accuracy of the level set method at capturing interfaces. In this paper, a high-order reinitialization method for the level set function which has previously been developed for structured grids was extended to unstructured grids. The proposed method involves constructing a stencil of an unstructured grid to define a high-order polynomial that approximates a piecewise segment of the interface. Then, the closest point method is adopted to estimate the signed distance function at grid points. The proposed method was validated by solving some benchmark problems of static cases and then the evolution of moving interfacial problems subject to prescribed velocity fields for various grid resolutions consisting of triangular elements. The accuracy of the proposed method was evaluated for computing geometric quantities such as the normal vector and curvature field. The proposed method proved to have high-order accuracy for estimating not only the signed distance function but also geometric quantities for a smooth interface. Finally, a local correction procedure was developed to apply the proposed method to level set problems involving the interface with kinks. The proposed method can accurately estimate normal vector and curvature fields including singularities both for static cases and for dynamic cases where an interface experiences topological changes. • High-order reinitialization of level set method on unstructured grid is developed. • We conduct a high-order estimation of normal vector and curvature on unstructured grid. • We propose a local correction procedure to manage kinks in level set method. • We successfully solve level set problems involving topological changes with kinks.

Curvature estimates for 4-dimensional complete gradient expanding Ricci solitons

Abstract In this paper, we derive curvature estimates for 4-dimensional complete gradient expanding Ricci solitons with nonnegative Ricci curvature (outside a compact set K). More precisely, we prove that the norm of the curvature tensor Rm {\mathrm{{Rm}}} and its covariant derivative ∇ ⁡ Rm {\nabla\mathrm{{Rm}}} can be bounded by the scalar curvature R by | Rm | ≤ C a ⁢ R a {|\mathrm{{Rm}}|\leq C_{a}R^{a}} and | ∇ ⁡ Rm | ≤ C a ⁢ R a {|\nabla\mathrm{{Rm}}|\leq C_{a}R^{a}} (on M ∖ K {M\setminus K} ), for any 0 ≤ a < 1 {0\leq a<1} and some constant C a > 0 {C_{a}>0} . Moreover, if the scalar curvature has at most polynomial decay at infinity, then | Rm | ≤ C ⁢ R {|\mathrm{{Rm}}|\leq CR} (on M ∖ K {M\setminus K} ). As an application, it follows that if a 4-dimensional complete gradient expanding Ricci soliton ( M 4 , g , f ) {(M^{4},g,f)} has nonnegative Ricci curvature and finite asymptotic scalar curvature ratio then it has finite asymptotic curvature ratio, hence admits C 1 , α {C^{1,\alpha}} asymptotic cones at infinity ( 0 < α < 1 ) {(0<\alpha<1)} according to Chen and Deruelle (2015).[21].

Gingival shape analysis using surface curvature estimation of the intraoral scans

BackgroundDespite many advances in dentistry, no objective and quantitative method is available to evaluate gingival shape. The surface curvature of the optical scans represents an unexploited possibility. The present study aimed to test surface curvature estimation of intraoral scans for objective evaluation of gingival shape.MethodsThe method consists of four main steps, i.e., optical scanning, surface curvature estimation, region of interest (ROI) definition, and gingival shape analysis. Six different curvature measures and three different diameters were tested for surface curvature estimation on central (n = 78) and interdental ROI (n = 88) of patients with advanced periodontitis to quantify gingiva with a novel gingival shape parameter (GS). The reproducibility was evaluated by repeating the method on two consecutive intraoral scans obtained with a scan-rescan process of the same patient at the same time point (n = 8).ResultsMinimum and mean curvature measures computed at 2 mm diameter seem optimal GS to quantify shape at central and interdental ROI, respectively. The mean (and standard deviation) of the GS was 0.33 ± 0.07 and 0.19 ± 0.09 for central ROI using minimum, and interdental ROI using mean curvature measure, respectively, computed at a diameter of 2 mm. The method’s reproducibility evaluated on scan-rescan models for the above-mentioned ROI and curvature measures was 0.02 and 0.01, respectively.ConclusionsSurface curvature estimation of the intraoral optical scans presents a precise and highly reproducible method for the objective gingival shape quantification enabling the detection of subtle changes. A careful selection of parameters for surface curvature estimation and curvature measures is required.

Morphometric features of drug-resistant essential tremor and recovery after stereotactic radiosurgical thalamotomy.

Essential tremor (ET) is the most common movement disorder. Its neural underpinnings remain unclear. Here, we quantified structural covariance between cortical thickness (CT), surface area (SA), and mean curvature (MC) estimates in patients with ET before and 1 year after ventro-intermediate nucleus stereotactic radiosurgical thalamotomy, and contrasted the observed patterns with those from matched healthy controls. For SA, complex rearrangements within a network of motion-related brain areas characterized patients with ET. This was complemented by MC alterations revolving around the left middle temporal cortex and the disappearance of positive-valued covariance across both modalities in the right fusiform gyrus. Recovery following thalamotomy involved MC readjustments in frontal brain centers, the amygdala, and the insula, capturing nonmotor characteristics of the disease. The appearance of negative-valued CT covariance between the left parahippocampal gyrus and hippocampus was another recovery mechanism involving high-level visual areas. This was complemented by the appearance of negative-valued CT/MC covariance, and positive-valued SA/MC covariance, in the right inferior temporal cortex and bilateral fusiform gyrus. Our results demonstrate that different morphometric properties provide complementary information to understand ET, and that their statistical cross-dependences are also valuable. They pinpoint several anatomical features of the disease and highlight routes of recovery following thalamotomy.

An Efficient Corner Detector Using Ratio of Center Distance of Symmetric Contour Technique

Feature detection is one of the basic research topics in the fields of image processing and corner that has been widely applied on vehicle detection, UAV image matching, camera calibration and so on. Particularly, a fast corner detector is of much benefit to many real-time tasks. A novel discrete curvature estimation method for corner detection based on the ratio of center distances of symmetric contour (RCDSC) is proposed in this paper. Benefiting from calculating the Euclidean distance twice only to estimate the discrete curvature at each point on a contour, RCDSC is much fast compared with other corner detectors. In addition, by choosing a relatively large radius of region of support and employing relative distance instead of absolute distance for constructing corner response function, RCDSC is also much robust to noises and local variations of contour. Extensive experiments exhibit the effectiveness and the efficiency of RCDSC in terms of average repeatability (AR), accuracy (ACU) and localization error (LE).

Horizontal curvature estimation of tram tracks using OpenStreetMap

For analysing, understanding and predicting the track/train-dynamics in order to develop comfortable and sustainable vehicles a sufficient description of the track course and conditions are key requirements. Not only the track irregularities but also the horizontal curvature affects the vehicle dynamics strongly. Nearly all cities owning light rail systems have gradually established the light rail traffic. By reasons of building density, road transportation infrastructure, and progress of the overall urban planning, the light rail infrastructure was constrained to the pre-existing environment. Thus, the track course is mainly optimized for efficient space use but not for best possible vehicle dynamics. To be able to analyse the track layout of tram networks at a bigger scale, an appropriate methodology that allows acquiring track course data is needed, which is the main objective of this paper. For this purpose, an open data approach was developed by the authors utilizing OpenStreetMap (OSM) to derive the horizontal track curvature based on geodata. This groundbreaking approach improves the state of the art since professional geodetic measurements of light rail tracks are generally rarely publicly available, cost-intensive and their preprocessing can potentially be time consuming. The outcome is a simple, robust, and fast approach that was validated using already existing reference track data which was available to the authors. Additionally, an error estimation of the methodology was carried out. Using a quadratic error function, the median standard deviation of the curvature can be determined and used to rate the exactness of the estimated curvature depending on its magnitude. In this approach, the curvature estimations exactness is generally high for small curve radii and decreases for bigger radii. Therefore it can be concluded that the field of application is especially promising for light rail infrastructure. But also for mainline tracks the new method can be used as a rough estimate, if no curvature data is at hand.

Homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds

We show that homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds, using that they admit periodic, integrally minimal foliations by homogeneous hypersurfaces. For the geometric flow induced by the orbit-Einstein condition, we construct a Lyapunov function based on curvature estimates which come from real GIT.

Performance Evaluation of Track Curvature Sensor for Curvature Estimation in a Curved Section of Railway Tracks

Active railway vehicles such as tilting trains and active steering bogies are being developed to improve the curve running performance of railway vehicles. In this case, a technology for sensing a curve and extracting curve information such as a curvature in real time is required. The existing railway curve detection technology has the disadvantage of requiring many calibration processes through test driving and being affected by running speed. In order to overcome these disadvantages, this paper proposes a very simple and efficient curvature estimation method. A curvature sensor prototype was manufactured and a test run was performed on the test track. As a test result compared with the track inspection data, the minimum deviation was 0.8%, the maximum deviation was 4.0% and the average deviation was 2.8%, showing good curvature measurement performance. It was also confirmed that the effect of the running speed was very small and the accuracy was high in the small curve with a large curvature. Therefore, the developed curvature measurement sensor is expected to be used very practically in the field of curvature detection and curvature extraction to control the vehicle in the curve section.

Four-dimensional generalized Ricci flows with nilpotent symmetry

We study solutions to generalized Ricci flow on four-manifolds with a nilpotent, codimension 1 symmetry. We show that all such flows are immortal, and satisfy type III curvature and diameter estimates. Using a new kind of monotone energy adapted to this setting, we show that blowdown limits lie in a canonical finite-dimensional family of solutions. The results are new for Ricci flow.

Curvature estimates for stable minimal surfaces with a common free boundary

The minimal surfaces meeting in triples with equal angles along a common boundary naturally arise from soap films and other physical phenomena. They are also the natural extension of the usual minimal surfaces. In this paper, we consider the multiple junction surface and show the Bernstein’s Theorem still holds for the stable multiple junction surfaces in some special cases. The key part is to derive the \(L^p\) estimates of the curvature for multiple junction surfaces.