Arc Of Circle Research Articles

Constructing a model of the axis form in a S-shaped riser of a cultivator paw

When cultivating the soil, a force of resistance to the movement of cultivator paw acts on it. It has a variable value and causes a moment of force applied to the riser of the paw. Under the action of the moment, the elastic axis of the riser changes its shape. This affects the position of the paw in the soil. The form of an S-shaped riser whose elastic axis consists of two circle arcs has been considered in this study. During cultivator operation, one part of the riser bends, increasing the curvature of the elastic axis, and the other, on the contrary, unbends, that is, its curvature decreases. The modeling of the shape of the elastic axis of the paw riser is based on the theory of resistance of materials, according to which the curvature of the elastic axis of the cantilevered band is directly proportional to the applied moment and inversely proportional to its stiffness. If the shape of the cross-section of the riser along its entire length is unchanged and the properties of the metal are also the same, then the stiffness is constant. In the case of small deflections of the band, the linear theory of bending is used, but the deflections in the riser are significant, so the nonlinear theory has been used for this case. At the same time, it is taken into account that the elastic axis of the riser already has an initial curvature, the sign of which changes after passing through the point of connection of the component arcs. To model the shape of the elastic axis of the S-shaped paw riser, the deformation of the arcs of the circles that form this paw was calculated separately. Numerical integration methods were used to find the shape of the deformed elastic axes of both parts of the riser. They were connected into a whole and a deformed elastic axis of the S-shaped riser was obtained. Two variants of the riser with different lengths of their elastic axis, but the same height and the same angle of entry into the soil, were considered. The combination of the component arcs of the riser shows that, under the action of the same force, the deviation from the specified movement depth for one riser is 2 cm, and for the other – 4 cm.

Reliable comparison of multi-directional mechanical properties for biomimetic circle arc honeycombs

Abstract Compared to straight honeycombs, curved honeycombs derived from biomimetic strategies typically exhibit superior mechanical properties and a broader tunable range. Consequently, there has been a surge in research focusing on curved honeycombs. However, few studies have concurrently designed multiple honeycombs for reliable comparisons, and little attention has been given to isotropy. In this study, circle arc walls were introduced to replace the straight walls of five classical honeycombs, thereby creating representative curved honeycombs for analysis. The numerical modeling method in ANSYS software was validated by experimentally testing 3D printed specimens of circle arc honeycombs. At the same mass and under loading conditions in different directions, it was found that the Young's modulus, yield strength, Poisson's ratio, and energy absorption of circle arc hexagon (CAH), circle arc square (CAS), circle arc triangle (CAT), circle arc re-entrant (CAR), and circle arc double-V (CAD) were assessed. Both experimental and numerical results revealed that CAH demonstrates superior energy absorption while maintaining a high degree of isotropy, characterized by all isotropic factors below 0.1 in mechanical properties. Notably, CAD exhibits a Negative Poisson's ratio (NPR) effect across all loading directions. These results provide benchmarks for future studies on curved honeycombs and guide further research in this field.

Examining the influence of 2.5-D ultra-low velocity zone morphology on ScP waveforms and estimated elastic parameters

Summary Ultra-low velocity zones (ULVZs) have been identified as regions of extremely low velocity anomalies in the Earth's lowermost mantle using seismic observations from reflected, refracted, and diffracted arrivals along the mantle side of the core-mantle boundary (CMB). Estimation of ULVZ geometrical (i.e., shape and size) and elastic (i.e., velocity and density) parameters with uncertainties is crucial in understanding the role of ULVZs in the ongoing dynamic processes within the Earth's mantle; however, these parameters are still poorly known due to uncertainties and tradeoffs of the seismically resolved ULVZ geometries and elastic parameters. Computation of synthetic waveforms for 2-D and 3-D ULVZs shapes is currently computationally feasible, but past studies utilize higher dimensional waveform modeling of mostly only low-frequency diffracted waves. Most studies focusing on high-frequency core-reflected waveforms (e.g., ScP) still use 1-D modeling approaches to determine ULVZ properties. This approach might lead to wrong results if the imaged structures have inherently 3-D geometries. This study investigates high-frequency synthetic ScP waveforms for various 2.5-D ULVZ geometries showing that additional seismic arrivals are generated even when the ScP geometrical ray path does not directly strike the location of the ULVZ. The largest amplitude additional phases in the 2.5-D models are post-cursor arrivals that are generated at the edges of the finite-length ULVZs. These newly identified ScP post-cursors can arrive within the ScsP post-cursor time window traditionally analyzed in 1-D ULVZ studies. These post-cursors might then be misidentified or constructively/destructively interfere with the ScsP postcursor, leading to incorrect estimation of ULVZ parameters. In this study we investigate the bias introduced by the 2.5-D morphologies on the 1D estimated ULVZ elastic properties in a Bayesian waveform inversion scheme. We further expand the Bayesian method by including the data noise covariance matrix in the inversion and compare it to an autoregressive noise model that was utilized in previous studies. From the application to the observed ScP data, we find that the new approach converges faster, particularly for the inversion of data from multiple events, and the new algorithm retrieves ULVZ parameters with more realistic uncertainties. The inversion of 2.5-D synthetic ScP waveforms suggests that the retrieved ULVZ parameters can be misleading with unrealistically high confidence if we do not consider the data noise covariance matrix in the inversion. Our new approach can also retrieve the shape of a multi-dimensional Gaussian ULVZ if its length is 12o or longer in the great circle arc direction. However, 2.5-D synthetic waveforms show additional waveform complexity which can constructively interfere with the ScP wavefield. Hence, in many cases the estimation of ULVZ properties using 1-D forward modeling can provide incorrect ULVZ parameters. Hence previous ULVZ modeling efforts using 1-D parameter estimation methods may be incorrect.

Medium-voltage feeder blocks division method considering source-load uncertainty and characteristics complementary clustering

Existing feeder block division methods fail to consider the complementary characteristics and uncertainty between power sources and loads, which result in excessive feeder blocks, low inter-block balance, and significant disparity in net load peak-valley difference. To address these issues, a medium-voltage feeder block division method that considers the uncertainty and complementary characteristics of sources and loads is proposed. Firstly, based on the probability density characteristics of sources and loads, an uncertainty model of DG output and load demand is established. Secondly, considering the constraints of block maximum load rate and feeder non-crossing, a feeder block division model is established. Additionally, a set of center circles is defined, and based on this, an improved K-means clustering algorithm is proposed. The initial clustering centers based on the center circles is set, and the clustering centers based on the arcs of the center circles corrected. And the weighted distances between power sources and clustering centers are calculated. An algorithm flow for improved K-means clustering feeder block division is designed accordingly. Finally, the case studies show that the result of block division is improved.

COMPARATIVE STUDY REGARDING TWO CONSTRUCTIVE SOLUTIONS FOR CONICAL WORM FROM PUMP CONSTRUCTION

In this paper two constructive solutions for central conical worm from composition of helical compressor are analyzed. First is a worm with cycloid frontal profile and the second one is a worm with circle arc frontal profile. The conjugated worm for the conical rotor is determined based on the fundamental theorems of surface enwrapping. Afterward, the area between the flanks of lobes for drive and driving worms are calculated in sections perpendicular to the axis of driving worm. For equals dimensions of worms it is estimated the volume included between the drive and driving worms, as determining factor defining the compressor flow.

Crosswalk between the PROMIS physical function CAT and PROMIS upper extremity CAT v1.2 in a hand surgery population

BackgroundThere is no gold standard patient-reported outcome measure (PROM) in hand surgery. As a result, a diverse array of PROM instruments have been utilized across centers over time. Lack of score interchangeability limits the ability to compare or conglomerate scores when new instruments are introduced. Our aim was to develop a linkage for the PROMIS UE CAT v1.2 and PROMIS PF CAT scores and develop crosswalk tables for interconversion between these PROMs.MethodsRetrospective review was conducted to identify adult (≥ 18y) patients seen by orthopaedic hand surgeons at a single academic tertiary care hospital who had completed PROMIS UE CAT v1.2 and PROMIS PF CAT score at the same visit. For those with multiple visits, only one randomly selected visit was included in the analyses. Pearson’s correlation was calculated to determine the linear relationship between the scores. Linkage from PF to UE was performed utilizing several commonly utilized equating models (identity, mean, linear, equipercentile and circle-arc methods). The performance of the models was assessed using intraclass correlation (ICC) between observed PROMIS UE CAT v1.2 and estimated PROMIS UE CAT v1.2 scores generated using the model as well as Root Mean Square Error (RMSE). The model chosen as the ‘best’ was further assessed for population invariance using root expected mean squared difference (REMSD) where < 0.08 were considered good.ResultsOf 10,081 included patients, mean age was 48.3 (SD = 17.0), and 54% were female (5,477/10,081). Mean UE CAT v1.2 and PF CAT scores were 37 (SD = 9.8) and 46 (SD = 10.0), respectively. There was a strong correlation between the scores (Pearson correlation r = 0.70). All methods performed acceptably (ICC ≥ 0.66 and RMSE < = 7.52 for all). The equipercentile method had the highest ICC (ICC = 0.70 (95% CI 0.69–0.71)) while the mean and circle arc methods had the lowest RMSE. The circle arc method is the most reliable with the smallest standard error and has satisfactory population invariance across age group (REMSD 0.065) and sex (REMSD 0.036).ConclusionsCrosswalk tables to be used for bidirectional conversion between scores were created.Level of evidence: III.

Statistical Inference in Circular Structural Model and Fitting Circles to Noisy Data

It is well known that commonly used algorithms for circle fitting perform poorly when sampling distribution of the points is not symmetric with respect to the circle center, for example, when the points are sampled from a circle arc. To overcome this difficulty we introduce and study a parametric circular structural model. In this model the points on the circumference are assumed to be sampled according to the von Mises distribution with unknown concentration and mean direction parameters. We develop maximum likelihood and method of moments estimators of the circle center and radius, and study their statistical properties. In particular, we show that the proposed maximum likelihood estimator is asymptotically normal and efficient. We also develop a test of uniformity for the sampling distribution along the circle. Based on the derived theoretical results we propose a numerically stable circle fitting algorithm, investigate its accuracy in a simulation study, and illustrate its behavior in a real data example. Supplementary materials for this article are available online.

A Numerical Analysis on the Performance and Optimization of the Savonius Wind Turbine for Agricultural Use

Given the state of the world nowadays, renewable energy is becoming more and more essential rendering wind turbine electricity quite important. Its shape and the fact that the Savonius vertical axis wind turbine runs at relatively low wind speeds with high torque values makes it suitable for practical uses such as that of an irrigation system in agriculture industry. This paper utilizes numerical research with Computational Fluid Dynamics (CFD) to investigate the performance of a vertical-axis wind turbine. The ANSYS CFD program was engaged to construct the simulations during the pre- and post-processing stages. Wind speed remained constant while the angular velocity was altered to enable analysis of the flow through the wind turbine. Because of its mechanical simplicity, the primary profile of a semicircle has remained a typical option for turbines that generate high torque based on drag force. The effects of using elliptical curves and the fluctuation in thickness along the profile chord were both examined in this study. Equivalently, an attempt to optimize the rotor's design was made. After the performance of a numerical simulation, a geometry consisting of simple circle arcs was developed, with a 10.9% improvement in the power coefficient, analogous to prior optimizations with more complicated geometries. The numerical results derived include the torque coefficient evolution throughout a full rotation as well as the distribution of vorticity magnitude at different rotor points.

The use of complex structure splines in roadway design

Objectives. The aim of the work is to develop the theory of spline-approximation of a sequence of points on a plane for using compound splines with a complex structure. In contrast to a simple spline (e.g., polynomial), a compound spline contains repeating bundles of several elements. Such problems typically arise in the design of traces for railroads and highways. The plan (projection on the horizontal plane) of such a trace is a curve consisting of a repeating bundle of elements “line + clothoid + circle + clothoid ...,” which ensures continuity not only of curve and tangent but also of curvature. The number of spline elements, which is unknown, should be determined in the process of solving the design problem. An algorithm for solving the problem with respect to the spline, which consists of arcs conjugated by straight lines, was implemented and published in an earlier work. The approximating spline in the general case is a multivalued function, whose ordinates may be limited. Another significant factor that complicates the problem is the presence of clothoids that are not expressed analytically (in a formula). The algorithm for determining the number of elements of a spline with clothoids and constructing an initial approximation was also published earlier. The present work considers the next stage of solving the spline approximation problem: optimization using a nonlinear programming spline obtained at the first stage by means of the dynamic programming method.Methods. A new mathematical model in the form of a modified Lagrange function is used together with a special nonlinear programming algorithm to optimize spline parameters. In this case, it is possible to calculate the derivatives of the objective function by the spline parameters in the absence of its analytical expression through these parameters.Results. A mathematical model and algorithm for optimization of compound spline parameters comprising arcs of circles conjugated by clothoids and lines have been developed.Conclusions. The previously proposed two-step scheme for designing paths of linear structures is also suitable for the utilization of compound splines with clothoids.

Vision-based measurement method for geometric dimensions of PVC pipe end faces

This study introduces a vision-based expedited methodology for assessing various geometric circular dimensions on the termini of PVC conduits. The process commences with delineating pipe profiles using the EDPF algorithm for edge detection. Successive steps employ a radius-constrained weighted circular approximation algorithm to form provisional circular profiles from closed-edge segments. These profiles are refined using a rapid circle arc fitting algorithm for multiple open-edge sections. Noise circles are sifted out with the Number of False Alarms algorithm, and upon calibration with actual dimensions, these profiles are quantified into physical sizes of the conduit's terminal geometries. Empirical evidence from the methodology demonstrates an ability to measure the circular dimensions with a mean accuracy rate surpassing 99.2%.

Матрица расстояний между российскими регионами и её использование в экономическом анализе

The spatial factor plays an important role in solving many practical problems of modern economics — from the analysis of trade and migration to the study of the dynamics of regional prices and the spread of epidemics. At the same time, the method of calculating the distance matrix plays a very important role. Countries and even regions are not point objects, and economic activity in them is distributed all over the territory, but the distance is measured between two points. In addition, the distance between points can be calculated along a straight line (great circle arc), roads and railways, or by some synthetic method. Special attention is paid to the regions without railroad connection. The paper considers the main problems of distance matrix construction and possible ways to solve them. As a result, we recommend a distance matrix that can be used by all specialists in spatial economics.

Words are delicious

Words are delicious

Assessment of mathematical model for elliptical excision: solving the doubt about vertex angle and predicting postoperative wound length

BackgroundElliptical excision is the most commonly used method for small benign tumour excision and primary closure. However, elliptical excision remains the topic of debate. The aim of this study was to explore the relationship among postoperative incision, vertex angle, and the length and width of fusiform excision through a mathematical model.MethodsWe collected data from fusiform circle excisions performed at the author’s hospital (101 cases). The measured values were applied to the mathematical model formula for statistical analysis.ResultsThe functional relationships among the length, width, arc, and angle of the fusiform circle were obtained. The mean apical tangent angle was 100.731°±15.782°, and the mean apical inner angle was 50.366°±7.891°. There was no significant difference between the preoperatively designed arc length preoperative and the postoperative incision length (P < 0.001). The apical vertex push-out distance equals half of the value of the fusiform length subtracted from arc.ConclusionsThe mathematical model can be used to design the incision for ellipse fusiform excision to predict the final wound length.

Mean convergence of Fourier–Akhiezer–Chebyshev series

We prove mean convergence of the Fourier series in Akhiezer–Chebyshev polynomials in Lp, p>1, using a weighted inequality for the Hilbert transform in an arc of the unit circle.

Combined approximation algorithms for interactive design of road routes in CAD

Objectives. The aim of the work is to create algorithms for approximating a sequence of points on a plane by arcs of clothoids and circles. Such a problem typically arises in the design of railroad and highway routes. The plan (projection onto a horizontal plane) of the road route is a curve (spline) consisting of a repeating bundle of elements “straight line + clothoid arc + circle arc + clothoid arc + ...”. Such a combination of elements provides continuity not only for the curve and its tangent, but also for the curvature. Since the number of spline elements is not known in advance, and their parameters are subject to restrictions, there is no mathematically consistent algorithm for this problem. The two-stage scheme for solving the problem is developed at RTU MIREA only for a spline with lines and circles (i.e., without clothoid elements). At the first stage, the scheme uses dynamic programming to determine the number of spline elements. At the second stage, the scheme optimizes parameters of the spline using nonlinear programming. This scheme has yet to be implemented for a spline with clothoids due to a significantly more complicated nature of this problem. Therefore, the design of route plans in existing computer aided design (CAD) systems is carried out in interactive mode using iterative selection of elements. In this regard, it makes sense to develop mathematically consistent algorithms for element-by-element approximation.Methods. The problem of element-by-element approximation by a circle and a clothoid is formalized as a lowdimensional non-linear programming problem. The objective function is the sum of squared deviations from the original points. Since a clothoid can only be represented in Cartesian coordinates by power series, there are difficulties in calculating the derivatives of the objective function with respect to the desired parameters of the spline elements. The proposed mathematically consistent algorithm for calculating these derivatives is based on the integral representation of the Cartesian coordinates of the points of the clothoid as functions of its length.Results. A mathematical model and algorithms have been developed for approximating a sequence of points on a plane by clothoids and circles using the method of nonlinear programming. A second-order algorithm is implemented with the calculation and inversion of the matrix of second derivatives (Hesse matrix).Conclusions. For approximation by circles and clothoids using nonlinear programming, it is not necessary to have an analytical expression of the objective function in terms of the required variables. The proposed algorithms make it possible to calculate not only the first, but also the second derivatives in the absence of such expressions.

Planning and control of the ship curvilinear route

The possibility of applying the traditional navigation parameters used in pilotage (bearing and distance), as well as their sum and difference for planning and controlling the ship curvilinear route in coastal waters is being investigated. Mathematical apparatus is based on the classical navigation methods such as the theory of isolines, the lines of position, the principles of route planning, as well as the approximation of the curvilinear route. The mathematical justification of the circle arcs, ellipse and hyperbola used as the approximation lines of both the ship curvilinear route and the control isolines is given. The methods for estimating the vessel approaching to the point of the beginning and end of the turn and for controlling the ship movement along the planned path by measuring the navigational parameters are proposed. The problems of the physical and mathematical feasibility of the route arising at the junction points of the straight and curvilinear parts of the ship route are recommended to be resolved on the principles of transition curves (clothoids), considering the maneuvering characteristics of the vessel. The main theses of the research are supported by the graphical interpretation while the given expressions are ready for practical application. The formalization of the proposed methods in both automatic navigation systems and autonomous ship control systems will allow the navigator on the bases of the configuration of the relative position of landmarks and the ship curvilinear route to solve the problems of processing relevant navigation information in coastal and congested waters more efficiently in conjunction with the traditional pilotage methods, which is especially important for advanced autonomous navigation.

Ship voyage optimisation considering environmental forces using the iterative Dijkstra's algorithm

ABSTRACT The original Dijkstra's algorithm requires the weight map for the network to find the optimum path; however, the change of weights due to temporal change in the met-ocean parameters makes it difficult to use this algorithm for ship navigation; hence, the path was discretised into a limited number of segments and an iterative scheme was developed in which the weight of network was determined based on the environmental condition at the time of ship navigation. A container trip from the Chabahar port in the Gulf of Oman to the Mumbai port in eastern India was studied. The objective was to minimize the fuel consumption. The results showed a decrease of ∼6 tons in the amount of fuel consumption and the total costs in the optimal path were 4.76% less than the path of the great circle arc. The proposed model is simple and effective to be run for operational route optimization.

Theorems for Arcs of Different Circles Having Same Arc-Angles with Application in Concave and Convex Structures

Theorems for Arcs of Different Circles Having Same Arc-Angles with Application in Concave and Convex Structures

Theorems for Arcs of Different Circles Having Same Arc-Angles with Application in Concave and Convex Structures

Theorems for Arcs of Different Circles Having Same Arc-Angles with Application in Concave and Convex Structures

Spin-dependent transmission in curved graphene superlattice

We investigate spin-dependent transmission in a curved graphene superlattice of N cells where each one is made up of four regions. The first is concave, and the third is convex, two arcs of circles separated by a distance d from flat graphene sheets. The tunneling analysis allows us to determine all transmission and reflection channels associated with our system. As a result, we show that the number of cells acts by decreasing the transmissions with the same spin. We predict a solid spin-filtering effect when d and N are sufficiently large. Finally, it is determined that the degree and duration of suppression of the transmissions with the same spin over a range of energy are controllable using d.