Curvature Of Curve Research Articles

Spirals of Riemann’s Zeta-Function — Curvature, Denseness and Universality

AbstractThis paper deals with applications of Voronin’s universality theorem for the Riemann zeta-function $\zeta$ . Among other results we prove that every plane smooth curve appears up to a small error in the curve generated by the values $\zeta(\sigma+it)$ for real t where $\sigma\in(1/2,1)$ is fixed. In this sense, the values of the zeta-function on any such vertical line provides an atlas for plane curves. In the same framework, we study the curvature of curves generated from $\zeta(\sigma+it)$ when $\sigma>1/2$ and we show that there is a connection with the zeros of $\zeta'(\sigma+it)$ . Moreover, we clarify under which conditions the real and the imaginary part of the zeta-function are jointly universal.

A yield curvature model considering axial compression ratio

This study proposed a yield curvature prediction model considering axial compression ratio with exponential function which is improved on the basis of the specification effective yield curvature prediction model. Parametric moment–curvature curves approach was used to verify that the yield curvature is greatly affected by the section size, the yield strength of longitudinal steel bar and the axial compression ratio. On the basis, the yield curvature under different levels was obtained by Xtract and parametric moment–curvature curves approach, the result shows that with the increase of axial compression ratio, the yield curvature also increases, which is roughly a linear relationship. Subsequently, combined with the specification and considering the influence of axial compression ratio, a new yield curvature prediction model is proposed based on a massive sample space obtained by parametric moment–curvature curves approach. Moreover, by comparing with the experimental database of PEER, the accuracy of new prediction model is verified, and the result shows that the new prediction model is suitable for estimating yield curvature of square section columns.

Flexural performance of V-shaped RC folded plates: The role of plate thickness and fiber hybridization

Reinforced concrete folded plates (RC-FPs) are frequently used in structures such as industrial buildings, hangars, swimming pools, and sports halls due to their high load-bearing capacity, low self-weight, economic advantages, and architectural appearance. However, experimental studies on the reinforced concrete (RC) behavior of these new-generation structural members are very limited. For this purpose, this article investigated the effect of plate thickness and fiber hybridization on the flexural performance of V-shaped RC-FPs produced from self-compacting concrete (SCC). With this study, the experimental moment–curvature tool was used for the first time to evaluate the flexural performance of V-shaped RC-FP. A total of sixteen large-scale V-shaped RC-FP specimens with different plate thicknesses (50, 60, 70, and 80 mm) and fiber hybridization (single, binary, and ternary) were manufactured and subjected to a four-point loading after a 90-day curing period. After the experimental load–deflection and moment–curvature curves were obtained, load-bearing capacity, toughness, curvature ductility, and effective flexural stiffness values were calculated and also showed in the crack patterns for all large-scale V-shaped RC-FPs. The empirical equations with high-precision have been developed using multiple linear regression analysis for predicting the load-bearing capacity, toughness, curvature ductility, and effective flexural stiffness of V-shaped RC-FPs based on the parameters of plate thickness and fiber hybridization. Consequently, the use of hybrid fiber-reinforced SCC in the production of V-shaped RC-FPs exhibited superior properties in terms of flexural performance and crack behavior, as well as allowing for accelerated erection of the roof carrier system, resulting in significantly reducing construction time and costs. Also, fiber reinforcement rather than an increase in plate thickness induced significant increases in the flexural performance values of the V-shaped RC-FPs, while ternary fiber hybridization was the best.

Determination of the Equivalent Thickness of a Taiko Wafer Using ANSYS Finite Element Analysis

The successful handling of large semiconductor wafers is crucial for scaling up their production. Early-stage warpage control allows the prevention of undesirable asymmetric warpage, known as wafer bifurcation or buckling. Indeed, even in a gravity-free environment, thinning an 8″ or 12″ semiconductor wafer can result in warpage and bifurcation. To mitigate this issue, the taiko method, which involves creating a thicker ring region around the rim of the wafer, has been widely used. Previous research has focused on the theoretical factors affecting the warpage of a backside metalized taiko wafer. This work extends the case to a front-side metalized taiko wafer and introduces the concept of the equivalent thickness of a taiko wafer. The equivalent thickness of a taiko wafer, influenced by the ring region, lies in between the thickness of the central region and that of the annular region. Because of the limited number of taiko wafers that can be produced on a production line, modelling can be beneficial. In this work we compared the results of a developed analytical model with those obtained from a finite element analysis (FEA) approach with ANSYSY® Mechanical Enterprise 2022/R2 software to model the equivalent thickness of a taiko wafer. We investigated the curvature as a function of the stress of the metal layer, considering key design factors such as the substrate region thickness, the thickness of the thin metal film, the step height, and the width of the ring region. By systematically varying the thickness of the central region of the taiko wafer, we explored the curvature as a function of stress induced by thermal load in the linear regime and determined the slopes in the linear region of the curvature vs. stress curves. The aim of this study is to identify regularities and similarities with the Stoney equation and investigate the validity of the analytical approach for the case of a taiko substrate. The results show that there is a good agreement between the analytical model of a taiko wafer and the numerical analysis gained by the FEA methods.

A C3 continuous double circumscribed corner rounding method for five-axis linear tool path with improved kinematics performance

Abstract Corner rounding methods have been widely developed to pursue the smooth motions of machine tools. However, most corner rounding methods, which adopt the double inscribed transitions, still remain an inherent issue of retaining large curvatures of transition curves. Even for those double circumscribed transitions-based methods with relatively small curvatures, they also constrain excessively the transition lengths and are limited to a low-order continuity, deteriorating the feedrate and jerk of machine tools. For addressing these problems, a C3 continuous double circumscribed corner rounding (DCCR) method is proposed for five-axis linear tool path. In this method, the C3 continuous double circumscribed B-splines are specially designed to round the corners of tool position and tool orientation, whose transition lengths are analytically determined by jointly constraining the approximation errors, overlaps elimination, and parameter synchronization. Moreover, the excessive constrains of transition lengths imposed by traditional methods are alleviated by fully considering the effects of overlaps and parameter synchronization, and the jerk of rotary axes is also limited with a high-order continuity. Compared to the existing double inscribed corner rounding (DICR) and DCCR methods, experiment results demonstrate that our method can improve further the feedrate while limiting the jerk of machine tools.

Lane Detection Algorithm in Curves Based on Multi-Sensor Fusion

Identifying lane markings is a key technology in assisted driving and autonomous driving. The traditional sliding window lane detection algorithm has good detection performance in straight lanes and curves with small curvature, but its detection and tracking performance is poor in curves with larger curvature. Large curvature curves are common scenes in traffic roads. Therefore, in response to the problem of poor lane detection performance of traditional sliding window lane detection algorithms in large curvature curves, this article improves the traditional sliding window algorithm and proposes a sliding window lane detection calculation method, which integrates steering wheel angle sensors and binocular cameras. When a vehicle first enters a bend, the curvature of the bend is not significant. Traditional sliding window algorithms can effectively detect the lane line of the bend and provide angle input to the steering wheel, enabling the vehicle to travel along the lane line. However, as the curvature of the curve increases, traditional sliding window lane detection algorithms cannot track lane lines well. Considering that the steering wheel angle of the car does not change much during the adjacent sampling time of the video, the steering wheel angle of the previous frame can be used as input for the lane detection algorithm of the next frame. By using the steering wheel angle information, the search center of each sliding window can be predicted. If the number of white pixels within the rectangular range centered around the search center is greater than the threshold, the average of the horizontal coordinate values of these white pixels will be used as the horizontal coordinate value of the sliding window center. Otherwise, the search center will be used as the center of the sliding window. A binocular camera is used to assist in locating the position of the first sliding window. The simulation and experimental results show that compared with traditional sliding window lane detection algorithms, the improved algorithm can better recognize and track lane lines with large curvature in bends.

Automatic surface mesh generation by a binary-tree method

In order to realize the automation of surface mesh generation for arbitrary complex models, this paper proposes a binary-tree method (BTM) which can generate discontinuous grids. Compared with continuous grids, the adjacency relationship between discontinuous grids generated by BTM is more flexible, so it is easier to discretize “dirty” geometry without geometry repair than continuous grids. The BTM can adaptively generate meshes by features based on the curvature of curves and surfaces, and thus it does not need to construct a sizing field. Anisotropic meshes can also be directly generated by selecting the direction of subdividing meshes. Moreover, according to the periodic characteristics of periodic surfaces, the topological structure of the initial mesh can be designed to achieve mesh generation on periodic surfaces. Successful numerical examples are used to illustrate the effectiveness and robustness of the presented methods for meshing various types of geometric surfaces and reveal the excellent performance of the BTM. In addition, the BTM has been employed by the dual interpolation boundary face method (DiBFM) to solve 3D problems.

Ell -convex Legendre curves and geometric inequalities

In this paper we consider ell -convex Legendre curves, which are natural generalizations of strictly convex curves. We generalize various optimal geometric inequalities, isoperimetric inequality, Bonnesen’s inequality and Green–Osher inequality, for strictly convex curves to ones for ell -convex Legendre curves. Moreover we generalize the inverse curvature curve flow for this class of Legendre curves and prove that it always converges to a compact soliton after rescaling. Unlike in the class of regular curves, there are infinitely many compact solitons, which include circles and astroids.

Research on improved driver model based on vehicle-road security situation under large curvature curves

Unreasonable path planning will make the vehicle prone to traffic accidents when driving at a limited maximum speed in the case of the low-speed situation and large curvature curve conditions. Considering the defects of neural network model based on the data-driven may cause unexpected results, an improved driver model was proposed to enhance driving safety. In this paper, the Dempster/Shafer evidence theory was used to detect critical features of lane lines for situation detection. And an observer was established to observe and analyze the model output based on the vehicle space motion safety and driving stability characteristics. Then, an optimizer was established to optimize the output and provide the optimal driving trajectory according to the analyzed situations. Finally, it is verified that the proposed algorithm can help the vehicle safely pass the ample curvature curves by the simulation platform and real vehicle in the laboratory.

Classification method of shale gas analytic stages and its application

China is rich in shale gas resources, and improving the oil recovery of shale gas wells is one of the hot issues in the current research. The production of shale gas wells releases shale gas by reducing formation pressure by repeated fracturing. In this paper, the curvature of shale desorption efficiency curve is analyzed to study the pressure suitable for formation shale gas release. According to the inflection point and stagnation point of the curvature curve, the starting pressure, sensitive pressure and turning pressure are obtained. the curvature curve can be divided into four stages: sensitive desorption, rapid desorption, slow desorption and inefficient desorption. In actual exploitation, shale desorption cannot go through all four desorption stages, and can be determined according to the ratio of V_{L} /P_{L}. When the ratio is greater than 2.59, there are four integral stages in shale desorption, and the larger the ratio is, the longer the sensitive desorption stage is. At 1.0–2.59, there are three stages of desorption; at 0.54–1, there are only two stages; below 0.54, there are only low efficiency stage. The isothermal adsorption study on the core samples of the Upper Paleozoic in Yulin area of Ordos Basin shows that the shale of the Upper Paleozoic in the study area has more starting pressure and turning pressure, and less sensitive pressure, and the ratio of V_{L} /P_{L} is between 0.5 and 2.0. Generally, the isotherm adsorption curve can be divided into three stages: fast desorption, slow desorption and low efficiency desorption. The low efficiency desorption stage contributes the most to the productivity of Upper Paleozoic shale in this area, and the slow desorption is supplementary. According to the desorption stage and pressure node in shale mining, the formation pressure can be appropriately reduced to improve shale gas recovery efficiency.

The Differential Equations of Conformable Curve in IR^2

In this paper, we get some characterizations of conformable curve in R^2. We investigate the conformable curve in R^2. We define the tangent vector of the curve using the conformable derivative and the arc parameter s. Then, we get the Frenet formulas with conformable frames. Moreover, we define the location vector of conformable curve according to Frenet frame in the plane R^2. Finally, we obtain the differential equation characterizing location vector and curvature of conformable curve in the plane R^2.

Calculation of harrington function (desirability function) values under interval determination of its arguments

Purpose of work. Development of proposals for desirability function calculation by interval arithmetic method. Obtained results. A connection was shown between multiple-criterial (vector) optimization problem and calculation of Harrington function (desirability function) values. Generalized desirability function was shown to be treated as a multiplicative convolution of partial desirabilities. Using golden section properties, a connection was discerned between hierarchy analysis methods and calculation of desirability function values. In this case the distribution of probable desirability function values among intervals determined in accordance with golden mean rule does coincide with values obtained by expert method. Application of golden proportion enables increasing the number of intervals; thus, it may prove convenient in improvement of Harrington function sensitivity. Conclusions. For partial desirability function in its explicit form such geometric characteristics were determined as values of tangent, curvature of curve and center of curvature coordinates. For a necessary averaged desirability system obtaining process control, such characteristics were determined in general and explicit form as partial desirability elasticity, generalized desirability elasticity relative to partial desirability, generalized desirability elasticity relative to a variable that has physical sense and respective dimension depending on particular subject area and affects partial desirability value. To determine the boundary value of one partial desirability being substituted for another partial desirability, the rate of substitution function and boundary rate of substitution elasticity function were established. Due to errors emerging in determination of desirability function values application of interval analysis methods was proposed. Application of interval numbers as presented in hyperbolic form was shown for calcutaion of partial and generalized desirability, A partial power series sum was determined relative to a variable presented in hyperbolic form. Suggestions. The method of calculation of Harrington function (desirability function) values at interval determination of arguments was shown to be eventually used in development of specifications and preliminary design of complicated engineering аnd organizational systems.

Scoliosis and Kyphosis Prevalence in Turner Syndrome: A Retrospective Review at a Pediatric Tertiary Care Medical Center.

The prevalence of major coronal and sagittal spinal curves (scoliosis and kyphosis) in Turner syndrome (TS) is not well established due to limited reporting. The relationship between growth hormone (GH) therapy and its effect on TS spinal curve incidence is also not well established. A retrospective chart review of 306 TS patients from 2007 to 2021 evaluated major coronal and sagittal spinal curves, progression of the curve, and treatment with GH. Statistical significance (defined as P <0.05) between curvature rates and curve progression was compared between GH-treated patients and non-GH-treated patients using a χ 2 or Fisher exact test when appropriate. Thirty-seven of 306 (12%) TS patients had a radiographically relevant spinal deformity. Twenty-seven of 37 (73%) had mild; 4 of 37 (11%) had moderate, and 6 of 37 (16%) had severe curves. Of those with severe, 4 underwent spinal fusion, 1 was treated with bracing, and 1 was braced before a cardiovascular-related death. Regarding GH use among TS patients, 190 of 306 (62%) used GH versus 116 of 306 (38%) who did not. Of those with a spinal curve, 24 of 37 (65%) used GH compared with 13 of 37 (35%) who did not. On univariate analysis, GH therapy was not a risk factor for the diagnosis of a major spinal curve, a more severe degree of the curve at the time of diagnosis, or spinal curve progression ( P >0.05 for all). This is the largest single institution retrospective review of a TS cohort known to the authors assessing spinal curve prevalence and relation to GH treatment and demonstrates a TS spinal curve rate of 12% (37/306). Four of six (11%) TS patients with a severe curve underwent corrective spine fusion. There was no relationship between the use of GH and the presence of a spinal curve or curve progression. Further study is warranted to determine risk factors for curve progression. Level III. This retrospective case series serves to review and address the prevalence of spinal deformity in TS patients and whether GH impacts worsening deformity.

On special singular curve couples of framed curves in 3D Lie groups

In this paper, we introduce Bertrand and Mannheim curves of framed curves, which are a special singular curve in 3D Lie groups. We explain the conditions for framed curves to be Bertrand curves and Mannheim curves in 3D Lie groups. We give relationships between framed curvatures and Lie curvatures of Bertrand and Mannheim curves of framed curves. In addition, we obtain the characterization of Bertrand and Mannheim curves according to the various frames of framed curves in 3D Lie groups.

Shape monitoring method of submarine cable based on fiber Bragg grating

Submarine cables are crucial in the transmission of electricity between coastal islands. Compared with terrestrial cables, submarine cables operate under harsher environments and thus their probability of failure is higher. Therefore, the effective monitoring of submarine cables is necessary to prevent related accidents. Quasi-distributed sensing technology based on fiber Bragg gratings converts the sensing information into discrete curvature information according to the pure bending theory and subsequently reconstructs the shape of the submarine cable using discrete curvature interpolation and curve reconstruction algorithms. The fiber Bragg grating sensor is placed on the landing cable section to analyze the reconstruction effect and error, demonstrating the feasibility of the method for submarine cable monitoring. Finally, the monitoring results in extreme weather reveal potential safety hazards in the submarine landing cable.

Global toolpath smoothing for CNC machining based on B-spline approximation with tool tip position adjustment

B-spline curve approximation is widely used for fitting linear toolpaths to improve machining quality and efficiency in CNC machining. For a high-quality smoothing method, the control of both approximation error and curve curvature needs to be taken into account. To reduce the maximum curve curvature while meeting the precision requirements, a B-spline approximation scheme with tool tip position adjustment is proposed in this paper. Toolpaths are first divided into several subdivisions according to the discrete curvature of each tool tip point. For subdivisions that need adjustment, tool tip positions are adjusted to minimize the maximum discrete curvature. An existing approximation method named energy-term-incorporated progressive and iterative approximation for least square fitting (ELSPIA) is selected and improved to fit the adjusted toolpaths and lower the chord errors. For improving the numerical stability of the ELSPIA method, the way of searching appropriate foot point parameters is discussed in this paper. Deviation expansion factors of tooltip points are also defined to make the ELSPIA method suitable for fitting the adjusted toolpaths. Both simulations and experimental studies are conducted to prove that the proposed method can significantly decrease the maximum curvature of fitted B-spline curves and improve the machining efficiency without exceeding the tolerance. For example, experimental results show that for the tested butterfly and rabbit toolpaths, the proposed method can improve the machining efficiency by 2.61% and 2.37%, compared with the ELSPIA method without tool tip position adjustment.

On polyharmonic helices in space forms

In this article, we study polyharmonic curves of constant curvature where we mostly focus on the case of curves on the sphere. We classify polyharmonic curves of constant curvature in three-dimensional space forms and derive an explicit family of polyharmonic curves on the sphere. Our results give new insights into the geometric structure of higher order variational problems.

Research and implementation of variable-domain fuzzy PID intelligent control method based on Q-Learning for self-driving in complex scenarios.

In the control of the self-driving vehicles, PID controllers are widely used due to their simple structure and good stability. However, in complex self-driving scenarios such as curvature curves, car following, overtaking, etc., it is necessary to ensure the stable control accuracy of the vehicles. Some researchers used fuzzy PID to dynamically change the parameters of PID to ensure that the vehicle control remains in a stable state. It is difficult to ensure the control effect of the fuzzy controller when the size of the domain is not selected properly. This paper designs a variable-domain fuzzy PID intelligent control method based on Q-Learning to make the system robust and adaptable, which is dynamically changed the size of the domain to further ensure the control effect of the vehicle. The variable-domain fuzzy PID algorithm based on Q-Learning takes the error and the error rate of change as input and uses the Q-Learning method to learn the scaling factor online so as to achieve online PID parameters adjustment. The proposed method is verified on the Panosim simulation platform.The experiment shows that the accuracy is improved by 15% compared with the traditional fuzzy PID, which reflects the effectiveness of the algorithm.

The radial curvature of plane curves

The radial curvature of plane curves

Bond of Seawater Scoria Aggregate Concrete to Stainless Reinforcement

This study investigates the bond between seawater scoria aggregate concrete (SSAC) and stainless reinforcement (SR) through a series of pull-out tests. A total of 39 specimens, considering five experimental parameters—concrete type (SSAC, ordinary concrete (OC) and seawater coral aggregate concrete (SCAC)), reinforcement type (SR, ordinary reinforcement (OR)), bond length (3, 5 and 8 times bar diameter), concrete strength (C25 and C30) and concrete cover thickness (42 and 67 mm)—were prepared. The typical bond properties (failure pattern, bond strength, bond-slip curves and bond stress distribution, etc.) of seawater scoria aggregate concrete-stainless reinforcement (SSAC-SR) specimen were systematically studied. Generally, the failure pattern changed with the concrete type used, and the failure surface of SSAC specimen was different from that of OC specimen. SSAC enhanced the bond strength of specimen, while its effect on the deformation of SSAC-SR was negative. On average, the peak slip of SSAC specimens was 20% lower while the bond strength was 6.7% higher compared to OC specimens under the similar conditions. The effects of variables on the bond strength of SSAC–SR in increasing order are concrete type, bond length, concrete strength and cover thickness. The bond-slip curve of SSAC-SR specimen consisted of micro-slipping, slipping and declining stages. It can be obtained that SSAC reduced the curve curvature of bond-slip, and the decline of curve became steep after adopting SR. The typical distribution of bond stress along bond length changed with the types of concrete and reinforcement used. Finally, a specific expression of the bond stress-slip curve considering the effects of various variables was established, which could provide a basis for the practical application of reinforced SSAC.