Equivalent Ellipse Research Articles

Casing Wear Log Using a Prewear Ellipse Shape from Ultrasonic Logging Data

Summary The inspection of casing integrity is an important field of study regarding well safety assessment. In casing design, casing wear prediction is usually performed with a torque and drag model calibrated with laboratory simulation results. The availability of ultrasonic logging data makes it possible to calibrate these models, correlating actual conditions with similar equipment, operations, and trajectory. This work presents an accurate methodology that quantifies casing wear under a certain uncertainty level using data from ultrasonic logging tools. An ellipse equation is adopted to estimate the prewear condition of the cross section, and then it is applied to calculate wear. Also, a methodology to generate synthetic tube cross sections with prescribed ovality, eccentricity, and groove wear, with any intensities and locations, is presented. A model error analysis is carried out to compare the accuracy of the proposed strategy with others found in the literature. A statistical error analysis shows how the measurement noise is related to the estimated wear. This provides the level of uncertainty of the response, which can improve the right interpretation of data. Results demonstrate that the strategy successfully achieves an adequate quantification and can be applied to estimate casing wear profiles, under an admissible uncertainty tolerance.

Numerical study on hydraulic fracture-cavity interaction in fractured-vuggy carbonate reservoir

In a fractured-vuggy carbonate reservoir (FVCR) are distributed many irregular natural fractures and cavities. They are the main oil/gas storage bodies. To stimulate such a reservoir, it is desired to connect the hydraulic fractures (HF) to them. To study the interaction mechanism between HFs and cavities in this paper, the natural fracture is modeled by the element partition method and the cavity is described by an ellipse equation at first. The surrounding fractured zone of a cavity is considered. Then the local and wellbore-nearby HF-cavity interactions are studied. It shows that the magnitude of in-situ stress has significant impact on their interaction due to the stress concentration surrounding a cavity. The higher in-situ stress leads to a stronger repulsion of a cavity to HF. The pore pressure and the surrounding fractured zone of a cavity can relieve the stress concentration, which facilitates the HF-cavity connection. The distributed natural fractures have the leading effect on HF direction when the in-situ stress difference is small. Next, the interaction between HF and cavity cluster is studied. It suggests that the injection mode has significant impact on the generation of fracture network. If the injection rate is adjusted properly, a complex fracture network can be generated. These findings help to deeply understand the HF-cavity interaction and provide valuable references for the HF treatment design in FVCR.

Displacement calculation method for homodyne interferometers based on spatial phase delay of beams

Based on the spatial phase delay of beams, a displacement measurement method is proposed for homodyne interferometers. In this method, two detectors are arranged in the interference spot to collect signals. Based on the algorithm of least squares fitting the parameters of the ellipse equation, the relative phase of the signals is solved to calculate the displacement. The proposed method uses optical fiber bundles for beam reception, which is more compact in structure than the traditional quadrature phase calculation method, and eliminates polarization mixing. The spatial delay phase in the method can be any unknown constant, which makes it more applicable in practice. The feasibility of this method is verified by ZEMAX simulations and experiments. The experimental results show that the 3σ of errors without the effect of power noise and vibration is 7.2 nm.

Towards Real-time pose estimation of the Mitral Valve Robot under C-arm X-ray Fluoroscopy.

Mitral regurgitation (MR) is a condition caused by a deformity in the mitral valve leading to the backflow of blood into the left atrium. MR can be treated through a minimally invasive procedure and our lab is currently developing a robot that could potentially be used to treat MR. The robot would carry a clip that latches onto the valve's leaflets and closes them to minimize leakage. The robot's accurate localization is needed to navigate the clip to the leaflets successfully. This paper discusses algorithms used to track the clip's position and orientation under real-time using C-arm fluoroscopy. The positions are found through a deep learning semantic segmentation framework and the pose is found by calculating its bending and rotational angles. The robot's bending angle and the clip's rotational angle is found through an equivalent ellipse algorithm and an SVM classifier, respectively, and were validated by comparing orientations obtained from an electromagnetic tracker. The bending angle calculation has an average error of 7.7° and the rotational angle calculation is 76% for classifying them into five classes. Execution times are within 100ms and hence this could be a promising approach in real-time pose estimation.

Experimental studies and theoretical analysis of the residual properties of three-span small-scale continuous concrete slabs after a fire

This study investigated the effect of travelling fire scenarios, span–thickness ratios, and recurring ages on the post-fire residual behaviour of small-scale continuous reinforced concrete slabs. The mechanical performance of five fire-damaged continuous slabs and one reference slab were investigated, including load–deflection curves, concrete and reinforcement strains, cracking patterns, and failure modes, and the observations were compared with those discussed in companion papers. In addition to considering the boundary restraint and failure criteria, this study proposed a simple ellipse equation to determine the tensile membrane action region and residual ultimate loads of concrete slabs at the limit state. The results indicated that the travelling fire scenario, including the fire direction and time delay, had a slight effect on the residual behaviour of fire-damaged slabs with larger span–thickness ratios. For fire-damaged slabs with larger span–thickness ratios, flexural failure easily occurred with sufficient development of the tensile membrane action. The proposed ellipse method can be used to accurately determine the residual ultimate loads of fire-damaged continuous slabs with large span–thickness ratios.

A Moments View of Climatology and Variability of the Asian Summer Monsoon Anticyclone

AbstractA comprehensive investigation of the climatology of and interannual variability and trends in the Asian summer monsoon anticyclone (ASMA) is presented, based on a novel area and moments analysis. Moments include centroid location, aspect ratio, angle, and “excess kurtosis” (measuring how far the shape is from elliptical) for an equivalent ellipse with the same area as the ASMA. Key results are robust among the three modern reanalyses studied. The climatological ASMA is nearly elliptical, with its major axis aligned along its centroid latitude and a typical aspect ratio of ~5–8. The ASMA centroid shifts northward with height, northward and westward during development, and in the opposite direction as it weakens. New evidence finding no obvious climatological bimodality in the ASMA reinforces similar suggestions from previous studies using modern reanalyses. Most trends in ASMA moments are not statistically significant. ASMA area and duration, however, increased significantly during 1979–2018; the 1958–2018 record analyzed for one reanalysis suggests that these trends may have accelerated in recent decades. ASMA centroid latitude is significantly positively (negatively) correlated with subtropical jet-core latitude (altitude), and significantly negatively correlated with concurrent ENSO; these results are consistent with and extend previous work relating monsoon intensity, ENSO, and jet shifts. ASMA area is significantly positively correlated with the multivariate ENSO index 2 months previously. These results improve our understanding of the ASMA using consistently defined diagnostics of its size, geometry, interannual variability, and trends that have not previously been analyzed.

Analysis of heat and mass transfer on the peristaltic flow in a duct with sinusoidal walls: Exact solutions of coupled PDEs

This research article uncovers a novel mathematical model that interprets the peristaltic flow in elliptic duct with heat and mass transfer for the first time. A unique mathematical technique is introduced in this study that provides exact analytical solutions for partial differential equations. The Cartesian coordinate system is used in the present analysis and the non-circular form of duct is attained by considering equation of ellipse in the boundary conditions. The temperature, concentration and velocity profile are exactly computed and analyzed through graphical results. The axially symmetric flow behaviour is revealed by the graphical outcomes. Concentration, velocity and temperature profiles have parabolic shapes and axially symmetric behaviour.

An elliptical blade is not a true ellipse, but a superellipse–Evidence from two Michelia species

The shape of leaf laminae exhibits considerable diversity and complexity that reflects adaptations to environmental factors such as ambient light and precipitation as well as phyletic legacy. Many leaves appear to be elliptical which may represent a ‘default’ developmental condition. However, whether their geometry truly conforms to the ellipse equation (EE), i.e., (x/a)2 + (y/b)2 = 1, remains conjectural. One alternative is described by the superellipse equation (SE), a generalized version of EE, i.e., |x/a|n +|y/b|n = 1. To test the efficacy of EE versus SE to describe leaf geometry, the leaf shapes of two Michelia species (i.e., M. cavaleriei var. platypetala, and M. maudiae), were investigated using 60 leaves from each species. Analysis shows that the majority of leaves (118 out of 120) had adjusted root-mean-square errors of < 0.05 for the nonlinear fitting of SE to leaf geometry, i.e., the mean absolute deviation from the polar point to leaf marginal points was smaller than 5% of the radius of a hypothesized circle with its area equaling leaf area. The estimates of n for the two species were ˂ 2, indicating that all sampled leaves conformed to SE and not to EE. This study confirms the existence of SE in leaves, linking this to its potential functional advantages, particularly the possible influence of leaf shape on hydraulic conductance.

RETRACTED ARTICLE: Urban air pollution resolution and basketball training optimization based on time convolution network

The optimization of basketball training service rate ball playing position angular impact is extremely large. Neck structure construction curve analysis effective area individual model, sphere ball-like mathematical model, angle sum and angle, angle-dependent, angle-wise mathematical model, selection-appropriate numbers angle. Nonlinear Heterosexual Ellipse Equation (NHEE) analyzes basketball’s free throw choice kinematics parameters while determining which learning process has a major impact if one succeeds. Basketball knee curve shows statistical analysis that helps to determine the success of basketball training curve analysis. NHEE uses a set of different measures of curve fit given during basketball practice.

An analytical method for determining the tensile membrane action of RC slab panels

This paper presents a newly developed method for determining the influence of tensile membrane action on the ultimate loading capacity of a two-way RC concrete slab. In this method, more realistic membrane action and two failure criteria of a slab panel are established. The developed method has been validated against the test results and good agreement is achieved. Compared to the tensile membrane action region obtained from the FEM (Vulcan), the assumptions about the focus of the ellipse equation proposed within the present method are reasonable and accurate. The present method can be used for predicting the ultimate loads and failure modes of the two-way simply supported RC slabs at large deflections. The research indicates that the in-plane shear force has considerable effect on the prediction of ultimate loads of the slabs and neglecting the in-plane shear force results the overestimated the concrete corner strains.

A SURVEY OF TEACHERS' OPINIONS ABOUT IMPLEMENTING REALISTIC MATHEMATICS EDUCATION IN TEACHING THE TOPICS OF THE ELLIPSE EQUATION

&lt;p&gt;Realistic Mathematics Education (RME) is an instructional theory that has been implemented in many countries around the world to link mathematics to real-world situations. The effectiveness of implementing RME in mathematics education is highly dependent on the role of teachers. This study was conducted with 64 high school teachers to survey their understanding and perspectives on RME and the status of RME implementation in teaching the topics of ellipse equation. Through qualitative analyzing the survey results, the study found that teachers are interested in RME, although the percentage of teachers formally trained in this theory was not high. Besides, the survey shows that it is necessary to help teachers overcome difficulties and improve the frequency and effectiveness of RME application in teaching mathematics.&lt;/p&gt;&lt;p&gt; &lt;/p&gt;&lt;p&gt;&lt;strong&gt;Article visualizations:&lt;/strong&gt;&lt;/p&gt;&lt;p&gt;&lt;img src="/-counters-/edu_01/0841/a.php" alt="Hit counter" /&gt;&lt;/p&gt;

A Visual-Based Angle Measurement Method Using the Rotating Spot Images: Mathematic Modeling and Experiment Validation

An angle measurement method based on the rotating spot images and machine vision technology is proposed. This method abandons the traditional coding disk but uses image sensor to capture the images of a spot rotating synchronously with the measured shaft. Assuming the center of the rotation shaft is fixed, the mathematic model of the trajectory of the spot images is an ellipse. N spot images are used to fit the ellipse equation, where the eccentric angle of the ellipse is the measured rotation angle. The basic algorithms and a compact lensless transmission angle measurement structure are also proposed. The simulation and experiment results are verified the feasibility of the measurement method, where the 5.4” accuracy can be obtained and a random collection of N ≥ 36 spot images is recommended. Since the shape of the ellipse trajectory does not affect the measurement accuracy, this method allows the spot disk to be non-concentric with the rotating shaft, and allows the spot disk to be non-parallel to the image sensor. Therefore, the proposed method can achieve precision measurement under non-precision installation.

Application of equivalent circle and ellipse for pore shape modeling in crack growth problem: A numerical investigation in microscale

Cracks and pores are common discontinuities in geomaterials and control their mechanical behaviors, which are vital parameters for stability of geosystems. Due to experimental complexities to implement and study of micro-behaviors of porous materials, numerical investigation such as the eXtended Finite Element Method (XFEM) is of great importance to understand the mechanism of the crack growth and propagation. Among all parameters, pore shape has a significant effect on the crack path, which has not yet been fully investigated. In fact, due to difficulty and complexity even in numerical models, the real pore shapes are often assumed as equivalent circular pores. However, the circle has a uniform surface and, consequently, mechanical properties of the simulated model is not what happens in reality. An alternative is to use equivalent ellipse due to its smaller cross-section, capability to locate at different angles and having various aspect ratios─ the ratio of small to large radii. In this paper, the effect of elliptical and circular pore shapes on the crack growth is numerically modeled and compared to each other. To this end, we defined α and β as the angle of horizontal axis relative to the large diameter of the ellipse (α) and the line connecting the centers of two porosities (β). These angles have been used to study the effect of pore shape and arrangement on the failure process. Finally, using elliptical and circular pore shapes, real rock samples (sandstone and carbonate) were analyzed. Results showed that in identical size of the elliptical front pores, the stress intensity factor increases more than 50% by increasing α angle from 0 to 90 degrees. This is quite the opposite for elliptical side pores where the stress intensity decreases about 11%. In addition, β angle variations are more effective than α angle on crack growth parameters. Also in real samples, the elliptical shape provides more valid crack paths than the circular shape. Also, predictions of the fracture parameters are better matched with the real model using elliptical pores.

Rock Particle Motion Information Detection Based on Video Instance Segmentation.

The detection of rock particle motion information is the basis for revealing particle motion laws and quantitative analysis. Such a task is crucial in guiding engineering construction, preventing geological disasters, and verifying numerical models of particles. We propose a machine vision method based on video instance segmentation (VIS) to address the motion information detection problem in rock particles under a vibration load. First, we designed a classification loss function based on Arcface loss to improve the Mask R-CNN. This loss function introduces an angular distance based on SoftMax loss that distinguishes the objects and backgrounds with higher similarity. Second, this method combines the abovementioned Mask R-CNN and Deep Simple Online and Real-time Tracking (Deep SORT) to perform rock particle detection, segmentation, and tracking. Third, we utilized the equivalent ellipse characterization method for segmented particles, integrating with the proportional calibration algorithm to test the translation and detecting the rotation by calculating the change in the angle of the ellipse’s major axis. The experimental results show that the improved Mask R-CNN obtains an accuracy of 93.36% on a self-created dataset and also has some advantages on public datasets. Combining the improved Mask R-CNN and Deep SORT could fulfill the VIS with a low ID switching rate while successfully detecting movement information. The average detection errors of translation and rotation are 5.10% and 14.49%, respectively. This study provides an intelligent scheme for detecting movement information of rock particles.

A didactic proposal for the construction of the ellipse

The purpose of the present is to propose the construction of the ellipse in a didactic way in which the work deals with the exposure of a specific methodology for the 3rd year of high school when dealing with ellipse content. Followed by the results of the realization of a workshop aimed at the construction of the ellipse in a didactic way, constructed with low cost material, thereby proposing the teaching of mathematics in a more pleasant and effective way, where the ellipse equations were defined with the theoretical concept and afterwards, the gardener's method was used to construct this curve in a terrain, using ropes and civil construction fasteners, so that the student could concretize and apply this content in practice. After that, it was used for construction in the classroom using thread threads or thin strings to make the tracing and to finish it used the Geogebra software to finish the work showing the perfection of the curve explained in the classroom. The didactic process carried out showed a real interest of the students mainly with the use of the field practice. In conclusion, teaching mathematics in a didactic and interactive way provides a favorable environment for learning, stimulating students with a critical sense and an investigative spirit.

An aggregate gradation detection method based on multi-view information fusion

In this study, the morphologies of the aggregate in multiple views were analysed during the falling of particles to calculate aggregate gradation. Four types of characterisation parameters were selected to extract the multi-view information of aggregate particles in five views. Based on the multi-view information, the aggregate particles were classified using principal component analysis and a probabilistic neural network. An aggregate equivalent volume characterisation method was formulated to calculate the aggregate mass, whereby the aggregate volume was converted into the aggregate mass by the least-squares method. The experimental results show that the proposed aggregate sieving method can effectively realise the gradation classification of aggregates. Considering the product of the maximum area and the minimum equivalent Feret ellipse minor axis as the equivalent volume, the calculated aggregate mass yielded a good correlation with the actual aggregate mass. Compared with single-view information, multi-view information can improve the accuracy and repeatability of gradation calculations. The use of multi-view information to calculate aggregate gradation can reduce manpower and improve detection efficiency, which is important for applications in the construction industry.

Aggregate Particle Size Calculation Based on Optimized Equivalent Ellipse

The precise calculation of the aggregate size is crucial for detecting aggregate gradation. Therefore, the aim of this study was to propose a method for calculating aggregate particle size. First, a series of image-processing methods, such as filtering, enhancement, segmentation, and morphology, were implemented to obtain a binary image. Consequently, a method for determining the particle shape and correcting the particle size was devised. The aggregate particles are divided into four categories, i.e., rectangle, ellipse, diamond, and triangle, according to three parameters: compact factor, projected contour, and distance distribution from edge point to centre of mass. The corresponding correction coefficient of each category based on the equivalent elliptical minor axis was then calculated, and the grading accuracy of the corrected particle size was analyzed. The accuracy of the particle size classification obtained by the method of aggregate particle shape determination and particle size correction proposed in this paper is 80.7 %.

An analogous ellipse equation for describing the coupling relationship of friction and adhesion between a probe tip and graphene

Frictional and adhesive properties of two-dimensional (2D) materials play a key role in determining the performance of micro-nano electromechanical systems (M/NEMS). In this study, a coupling relationship between the lateral force (Fl) and the adhesive force (Fa) of a probe tip sliding on graphene is investigated by molecular dynamics (MD) simulations and a continuum modeling approach. Our results show that the coupling effect of van der Waals (vdW) interactions (between tip/graphene and graphene/substrate) and the bending energy of graphene dominate the coupling relationship. An analogous ellipse equation is proposed to describe the coupling relationship between the interfacial friction and adhesion based on the periodic interaction potential between a probe tip and the lattice of graphene, which is independent of the probe tip type. This study should be of great importance for understanding the interaction mechanism between probe tips and 2D materials on different substrates.

Measurement-Based Electric Arc Furnace Model Using Ellipse Formula

This paper proposes a mathematical model of an electric arc furnace (EAF) system based on the voltage and current (V–I) field data. The proposed method is formulated using the ellipse equation, which is derived from the measurement profile of real EAF systems. This paper also presents the harmonics and power-pattern information corresponding to the smelting processes (boring, melting, and refining) in order to realistically design an EAF for potential industrial applications. The third harmonic component significantly affects the shape of the V–I curve in realistic EAF systems, while the periodic power fluctuation is closely associated with the size of the ellipse. These characteristics can be formulated and designed by the proposed method, and even in the absence of the V–I profile, an EAF model can be generated using the generalized information provided in this paper. The electrical phenomenon in the proposed method is mathematically verified using the PSCAD/EMTDC software.

Graph-analytical method of load mode analysis of ferromagnetic current stabilizer

In this paper we consider the application of graph-analytical method for the analysis of the load regime of ferromagnetic current stabilizer. It is proved that under active load the current of the ferromagnetic stabilizer and magnetic flux are related by the ellipse equation where the axes coincide with the axes of coordinate system. The advantage of the proposed method is that it is possible to use an experimentally obtained characteristic.