Curvature Model Research Articles

Biomechanical effects of over lordotic curvature after spinal fusion on adjacent intervertebral discs under continuous compressive load

BackgroundTo investigate the effects of over-lordotic curvature after lumbar fusion on the stress and deformations of the adjacent intervertebral discs under constant compressive loads. MethodsTwo-level ovine specimens—including three vertebral bodies with two discs—were divided into two groups: Group A (to observe external deformation) and Group B (to observe internal stress and deformations of the discs). Each group consisted of three models: a) intact model, b) increased stiffness + unchanged curvature fusion model, and c) increased stiffness + curvature fusion model. Models were tested at a vertebral pressure of 0.4 MPa for 30 min. Creep deformations and stress distributions in the superior adjacent intervertebral discs were analysed using finite element models. FindingsStiffness angle of the curvature model was increased by 5° and compared with the intact and stiffness models. In Group A, there was no significant deformation in the superior and adjacent intervertebral discs (P > 0.05), whereas creep deformations of the Group B discs increased significantly. Maximum deformations, with increases of approximately 3.7-fold and 2.8-fold in the vertical and horizontal directions, respectively, occurred at the anterior annulus fibrosus. The vertical and sagittal stress concentrations at the anterior annulus fibrosus had maximum differences of 1.0 MPa and 1.2 MPa, respectively. InterpretationsUnder a continuous compressive load, over-lordotic fusion significantly increases the stress and deformation gradient of the nucleus polposus and annulus fibrosus in the superior, adjacent intervertebral disc, increasing the risk of damage and secondary degeneration of these discs when subjected to daily static loads.

Evolutionarily unique mechanistic framework of clathrin-mediated endocytosis in plants

In plants, clathrin mediated endocytosis (CME) represents the major route for cargo internalisation from the cell surface. It has been assumed to operate in an evolutionary conserved manner as in yeast and animals. Here we report characterisation of ultrastructure, dynamics and mechanisms of plant CME as allowed by our advancement in electron microscopy and quantitative live imaging techniques. Arabidopsis CME appears to follow the constant curvature model and the bona fide CME population generates vesicles of a predominantly hexagonal-basket type; larger and with faster kinetics than in other models. Contrary to the existing paradigm, actin is dispensable for CME events at the plasma membrane but plays a unique role in collecting endocytic vesicles, sorting of internalised cargos and directional endosome movement that itself actively promote CME events. Internalized vesicles display a strongly delayed and sequential uncoating. These unique features highlight the independent evolution of the plant CME mechanism during the autonomous rise of multicellularity in eukaryotes.

The Euler spiral of rat whiskers.

This paper reports on an analytical study of the intrinsic shapes of 523 whiskers from 15 rats. We show that the variety of whiskers on a rat's cheek, each of which has different lengths and shapes, can be described by a simple mathematical equation such that each whisker is represented as an interval on the Euler spiral. When all the representative curves of mystacial vibrissae for a single rat are assembled together, they span an interval extending from one coiled domain of the Euler spiral to the other. We additionally find that each whisker makes nearly the same angle of 47∘ with the normal to the spherical virtual surface formed by the tips of whiskers, which constitutes the rat's tactile sensory shroud or "search space." The implications of the linear curvature model for gaining insight into relationships between growth, form, and function are discussed.

Multi-roll levelling method for longitudinal waves in metal sheet based on a coupled curvature integration model

Longitudinal waves are the main flatness defects of metal sheets. This defect is typically eliminated by repeated elastoplastic bending via a multi-roll leveller to make the residual curvature of the sheet as small as possible. Therefore, an effective mathematical model is important for the leveller design and levelling parameter adjustment. In this paper, based on the basic principle of multi-roll levelling for the longitudinal wave of a metal sheet, a geometric model of multi-roll levelling was established via the curvature integration method; a bending-moment curvature model was also established to account for the residual curvature of reverse bending and the difference between the elastic section and the elastoplastic section. A coupled curvature integration model was constructed by combining the two models to systematically describe the multi-roll levelling process, and the variation of the curvature, surface profile curve and plastic deformation rate of the sheet during levelling were discussed; the influence of the intermesh of the work rolls on the levelling effect of the longitudinal wave was analysed. The results show that there are infinite intermesh combinations of the first work roll and the last work roll that make the residual curvature of the sheet close to zero after levelling. The results also show that the residual curvature is much more sensitive to the variation of the first work roll than to the variation of the last work roll.

Research on curvature model and transmission characteristics of hollow micro-bottle resonator

提出了有关空心微瓶谐振腔的曲率变化模型并且研究了曲率对其传输特性的影响。仿真分析了微瓶谐振腔内回音壁模式的分布情况，随着曲率的增加，微瓶谐振腔对回音壁模式的束缚能力越强，使得内部光场能量也相应增加。通过控制熔接机的放电次数制得不同曲率的空心微瓶谐振腔，并且根据理想气体状态方程，推导了制备工艺中曲率模型，研究了空心微瓶谐振腔的曲率随放电次数的变化趋势。实验结果表明，曲率越大的空心微瓶谐振腔品质因子越高，可达到7.26×10⁵，该结论在提升谐振腔的品质因子方面具有重要价值。

A New Formulation of Coupling and Sliding Motions of Grain Boundaries Based on Dislocation Structure

A continuum model of the two dimensional low angle grain boundary motion and the dislocation structure evolution on the grain boundaries has been developed in [L. Zhang and Y. Xiang, J. Mech. Phys. Solids, 117 (2018), pp. 157--178]. The model is based on the motion and reaction of the constituent dislocations of the grain boundaries. The long-range elastic interaction between dislocations is included in the continuum model, and it maintains a stable dislocation structure described by Frank's formula for grain boundaries. In this paper, we develop a new continuum model for the coupling and sliding motions of grain boundaries that avoids the time-consuming calculation of the long-range elastic interaction. In this model, the long-range elastic interaction is replaced by a constraint of Frank's formula. The constrained evolution problem in our new continuum model is further solved by using the projection method. Effects of the coupling and sliding motions in our new continuum model and relationship with the classical motion by curvature model are discussed. The continuum model is validated by comparisons with discrete dislocation dynamics model and the early continuum model [L. Zhang and Y. Xiang, J. Mech. Phys. Solids, 117 (2018), pp. 157--178] in which the long-range dislocation interaction is explicitly calculated.

Research and analysis of stiffness-enhanced soft gripper

In view of the problems of low stiffness, small driving force and large balloon effect existing in the current soft actuator, this paper proposes an optimization method to enhance the overall stiffness of the soft gripper by using rigid components based on the multi-cavity soft pneumatic actuator. This paper introduces the main components of the actuator: the soft part poured by liquid silica gel, and the open rectangular rigid structures by 3D printed. The kinematics model of the finger is established based on the Piecewise Constant Curvature model(PCC). The bending performance of the enhanced stiffness gripper is verified by finite element analysis(FEA): the tip force of actuator increased with the increase of the number of rigid structures when the bending angle is constant. According to the and experimental data, the overall stiffness of soft gripper is increased by the rigid structure without affecting the flexibility of operation. And the maximum weight which can grasp is 3.4 times that of the traditional soft gripper, improved the grasping range of the soft gripper effectively.

A Novel Theoretical Approach for Estimation of Axial Crushing Behavior of Polygonal Hollow Sections

The aim of the present study was to introduce new crushing mechanisms in terms of crushing modes for estimating the crushing force and absorbed energy of polygonal thin walled metal sections subjected to axial progressive collapse. For this purpose, two models were developed. The first model, which has been extensively used before and named as “plastic hinge model” (PHM), was modified based on new crushing modes; and as the second, a novel model was introduced by the authors named as “induced curvature model” (ICM). The latter model was considered to be more realistic than the former due to consideration of metal sheet curvatures during progressive folding process, as well as including the hardening effect of the material during plastic deformation. All possible crushing modes for a typical polygonal section were considered and discussed by combining different crushing modes of the corner elements. New expressions for the absorbed energies and crushing force were presented based on the resulting crushing modes. To evaluate the validity and efficiency of the proposed models, a detailed FE simulation was conducted using LS-DYNA. Comparison of FEM, PHM and ICM results showed the superiority of the ICM over PHM.

Bending models of lipid bilayer membranes: Spontaneous curvature and area-difference elasticity

We present a computational study of bending models for the curvature elasticity of lipid bilayer membranes that are relevant for simulations of vesicles and red blood cells. We compute bending energy and forces on triangulated meshes and evaluate and extend four well established schemes for their approximation: Kantor and Nelson (1987), Jülicher (1996), Gompper and Kroll (1996) and Meyer et al. (2003), termed A, B, C, D. We present a comparative study of these four schemes on the minimal bending model and propose extensions for schemes B, C and D. These extensions incorporate the reference state and non-local energy to account for the spontaneous curvature, bilayer coupling, and area-difference elasticity models. Our results indicate that the proposed extensions enhance the schemes to account for shape transformation including budding/vesiculation as well as for non-axisymmetric shapes. We find that the extended scheme B is superior to the rest in terms of accuracy, and robustness as well as simplicity of implementation. We demonstrate the capabilities of this scheme on several benchmark problems including the budding-vesiculating process and the reproduction of the phase diagram of vesicles.

The C-Band All-Sky Survey (C-BASS): Simulated parametric fitting in single pixels in total intensity and polarization.

The cosmic microwave background (CMB) B-mode signal is potentially weaker than the diffuse Galactic foregrounds over most of the sky at any frequency. A common method of separating the CMB from these foregrounds is via pixel-based parametric-model fitting. There are not currently enough all-sky maps to fit anything more than the most simple models of the sky. By simulating the emission in seven representative pixels, we demonstrate that the inclusion of a 5 GHz data point allows for more complex models of low-frequency foregrounds to be fitted than at present. It is shown that the inclusion of the C-BASS data will significantly reduce the uncertainties in a number of key parameters in the modelling of both the galactic foregrounds and the CMB. The extra data allow estimates of the synchrotron spectral index to be constrained much more strongly than is presently possible, with corresponding improvements in the accuracy of the recovery of the CMB amplitude. However, we show that to place good limits on models of the synchrotron spectral curvature will require additional low-frequency data.

Kinematic Model and Real-Time Path Generator for a Wire-Driven Surgical Robot Arm with Articulated Joint Structure

This paper presents a forward kinematic model of a wire-driven surgical robot arm with an articulated joint structure and path generation algorithms with solutions of inverse kinematics. The proposed methods were applied to a wire-driven surgical robot for single-port surgery. This robot has a snake-like robotic arm with double segments to fit the working space in a single port and a joint structure to secure stiffness. The accuracy of the model is highly important because small surgical robot arms are usually controlled by open-loop control. A curvature model is widely used to describe and control a continuum robotic body. However, the model is quite different from a continuum robotic arm with a joint structure and can lead to slack of the driving wires or decreased stiffness of the joints. An accurate forward kinematic model was derived to fit the actual hardware structure via the frame transformation method. An inverse kinematic model from the joint space to the wire-length space was determined from an asymmetric model for the joint structure as opposed to a symmetric curvature model. The path generation algorithm has to generate a command to send to each actuator in open-loop control. Two real-time path generation algorithms that solve for inverse kinematics from the task space to the joint space were designed and compared using simulations and experiments. One of the algorithms is an optimization method with sequential quadratic programming (SQP), and the other uses differential kinematics with a PID (Proportional-Integral-Derivative) control algorithm. The strengths and weaknesses of each algorithm are discussed.

Fatigue resistance of ProTaper gold exposed to high-concentration sodium hypochlorite in double curvature artificial canal

This study aimed to evaluate and compare the fatigue resistance of ProTaper Gold (PTG) and ProTaper Universal (PTU) in artificial single and double curvature canals in 5% sodium hypochlorite (NaOCl) at body temperature (37 °C). PTG and PTU files (size F1) were subjected to fatigue tests in two different artificial ceramic canals. The single curvature model had a 60° curvature angle with a 5 mm radius. The double curvature model had a 60° curvature angle with a 5 mm radius and a second 30° curvature with a 2 mm radius. A file segment was introduced into the artificial canal and immersed in water or 5% NaOCl at 37 °C. The total number of cycles to fracture (NCF) was recorded. Data were analyzed using t-test and linear regression analysis. The NCF of all files was significantly influenced by the type of NiTi metal alloy (P < .01), canal curvatures (P < .01), and the environmental conditions (P < .05). PTG had higher fatigue resistance than PTU files in both single and double curvature canals (P < .05). The NCF of PTU files in 5% NaOCl was shorter than that in water (P < .05). The mean length of broken PTG was significantly shorter than those of PTU files in both single and double curvature canals (P < .01). The fatigue performance of PTG is better than that of PTU in both single and double curvature. Environmental conditions may affect the fatigue behavior of PTU files with single curvature.

Reachability Improvement of a Climbing Robot Based on Large Deformations Induced by Tri-Tube Soft Actuators.

Locomotion of soft-bodied organisms, such as amoeba, worms, and octopuses, is safe, robust, and adaptable and has great promise for applications in complex environments. While such organisms fully exploit the potential provided by their soft structures, engineering solutions commonly constrain soft deformation in favor of controllability. In this study, we study how soft deformations can enhance the climbing capabilities of a robot. We introduce a robot called Longitudinally Extensible Continuum-robot inspired by Hirudinea (LEeCH), which has few shape constraints. Inspired by real leeches, LEeCH has a flexible extensible body and two suction cups at the ends. It is capable of performing 3D climbing locomotion using two suction cups driven by vacuum pumps and tri-tube soft actuators which have only three DC motors. The large deformations occurring in LEeCH extend its workspace compared to robots based on constant curvature models, and we show successful locomotion transition from one surface to another at angles between 0° and 180° in experiment. We develop a model based on multibody dynamics to predict the nonlinear deformations of the robot, which we verify in the experiment. The model reveals a nondimensional morphological parameter, which relates the robot's shape to its mass, stiffness, and size. The workspace of LEeCH as a function of this parameter is studied in simulation and is shown to move beyond that of robots based on constant curvature models.

Holographic correspondence of F(R) gravity with/without matter fields

In this paper, we apply the holographic principle to the early universe, obtaining an inflation realization of holographic origin. First we show that under the consideration of extended infrared cutoffs, there exists a holographic correspondence of various F(R) (such as quadratic, cubic, exponential F(R) models) cosmological models in the absence of matter fields. Then we establish that such holographic correspondence is not only confined to the vacuum F(R) gravity but also can be extended to the higher curvature models along with matter fields. In the presence of matter field, in particular the second-rank antisymmetric Kalb-Ramond field, all the considered F(R) models lead to a viable inflationary phenomenology consistent with Planck 2018 constraints. We further extend our discussion of holographic correspondence to F(T) cosmological models.

Importance of outliers: A three-dimensional study of coarsening in α -phase iron

Grain coarsening behavior in an $\ensuremath{\alpha}$-phase iron sample is studied in three dimensions using high energy x-ray diffraction microscopy. 4971 grains that are entirely inside the sample are segmented in the initial state and 3905 remain after annealing. A matching procedure was used to track 3299 grains between the two states while the remainder were either consumed by neighbors or the tracking algorithm failed to correlate them. During the single annealing treatment, the average grain volume increased by 13%. Statistical analysis in each state yields subtle changes in the grain size and nearest neighbor number distributions. Correlating topological features with volume changes between states, the average behavior is seen to be consistent with an isotropic model of curvature driven coarsening, but the dispersion of volume changes in each topological class is comparable to the overall trend in the average behaviors. Thus, the topological characterizations used here are not predictive of the behavior of individual grains under the isotropic assumption. Examination of anecdotal cases allows understanding of some outliers but others appear counter to an isotropic theory.

A coupled THINC/QQ and LS framework for simulating incompressible free-surface flows with surface tension

In this paper, we propose a simple and accurate numerical framework for simulating incompressible free-surface flows with surface tension on fixed Eulerian grids. For capturing moving interfaces, we developed a novel interface capturing scheme by coupling the THINC/QQ (THINC method with quadratic surface representation and Gaussian quadrature) and LS (Level Set) method. The new scheme, so-called THINC/QQLS (coupled THINC/QQ and LS), possesses certain advantages, for instance, improving the accuracy of interface reconstruction, ensuring rigorous volume/mass conservation, and providing accurate LS field for computing surface tension force. In order to accurately calculate the interface curvature, we propose a simple and accurate curvature model. We verified the proposed THINC/QQLS scheme as well as the curvature model with classical benchmark tests and realistic free-surface flow simulations. Numerical results reveal that the proposed numerical framework can accurately capture free surfaces and provide an accurate approach for computing surface tension force and suppressing the parasitic currents.

Total curvature (TC) model and its alternating direction method of multipliers algorithm for noise removal

This paper develops a variational model for image noise removal using total curvature (TC), which is a high-order regularizer. The TC has the advantage of preserving image feature. Unfortunately, it also has the characteristics of nonlinear, non-convex and non-smooth. Consequently, the numerical computation with the curvature regularization is difficult. In order to conquer the computation problem, the proposed model is transformed into an alternating optimization problem by importing auxiliary variables. Furthermore, based on alternating direction method of multipliers, we design a fast numerical approximation iterative scheme for proposed model. Finally, numerous experiments are implemented to indicate the advantages of the proposed model in image edge preserving, image contrast and corners preserving. Meanwhile, the high computational efficiency of the designed model is verified by comparing with traditional models, including the total variation (TV) and total Laplace (TL) model.

Curvature models of conformally flat Walker (2,2)-manifolds

Four-dimensional conformally flat curvature models of signature [Formula: see text] are considered and complete classification of curvature tensor is obtained. Then, some remarks about Ivanov–Petrova and Walker–Ivanov–Petrova properties are stated.

Examination of the Effects of Curvature in Geometrical Space on Accuracy of Scaling Derived Projections of Plant Biomass Units: Applications to the Assessment of Average Leaf Biomass in Eelgrass Shoots.

Conservation of eelgrass relies on transplants and evaluation of success depends on nondestructive measurements of average leaf biomass in shoots among other variables. Allometric proxies offer a convenient way to assessments. Identifying surrogates via log transformation and linear regression can set biased results. Views conceive this approach to be meaningful, asserting that curvature in geometrical space explains bias. Inappropriateness of correction factor of retransformation bias could also explain inconsistencies. Accounting for nonlinearity of the log transformed response relied on a generalized allometric model. Scaling parameters depend continuously on the descriptor. Joining correction factor is conceived as the partial sum of series expansion of mean retransformed residuals leading to highest reproducibility strength. Fits of particular characterizations of the generalized curvature model conveyed outstanding reproducibility of average eelgrass leaf biomass in shoots. Although nonlinear heteroscedastic regression resulted also to be suitable, only log transformation approaches can unmask a size related differentiation in growth form of the leaf. Generally, whenever structure of regression error is undetermined, choosing a suitable form of retransformation correction factor becomes elusive. Compared to customary nonparametric characterizations of this correction factor, present form proved more efficient. We expect that offered generalized allometric model along with proposed correction factor form provides a suitable analytical arrangement for the general settings of allometric examination.

Census of bounded curvature paths

A bounded curvature path is a continuously differentiable piece-wise $$C^2$$ path with bounded absolute curvature connecting two points in the tangent bundle of a surface. These paths have been widely considered in computer science and engineering since the bound on curvature models the trajectory of the motion of robots under turning circle constraints. Analyzing global properties of spaces of bounded curvature paths is not a simple matter since the length variation between length minimizers of arbitrary close endpoints or directions is in many cases discontinuous. In this note, we develop a simple technology allowing us to partition the space of spaces of bounded curvature paths into one-parameter families. These families of spaces are classified in terms of the type of connected components their elements have (homotopy classes, isotopy classes, or isolated points) as we vary a parameter defined in the reals. Consequently, we answer a question raised by Dubins (Pac J Math 11(2):471–481, 1961).