Circular Contour Research Articles

Optical Möbius strips in isotropic random non-paraxial light

Abstract The statistics of Möbius strips with various topologies, formed by the axes of polarization ellipses as they are traced along a closed circular contour of small size passing through the center of a solitary circular polarization singularity line (C-line), have been investigated both analytically and numerically in a random isotropic electromagnetic field. Found are the analytical expressions for the joint probability density function of the differential characteristics of the random isotropic electromagnetic field, which allow for the determination of the topological properties of diagrams of polarization ellipses and the normal vectors to them, as well as the optical strips that arise in the space around C-lines.

A Circle Center Location Algorithm Based on Sample Density and Adaptive Thresholding

How to acquire the exact center of a circular sample is an essential task in object recognition. Present algorithms suffer from the high time consumption and low precision. To tackle these issues, we propose a novel circle center location algorithm based on sample density and adaptive thresholding. After obtaining circular contours through image pre-processing, these contours were segmented using a grid method to obtain the required coordinates. Based on the principle of three points forming a circle, a data set containing a large number of samples with circle center coordinates was constructed. It was highly probable that these circle center samples would fall within the near neighborhood of the actual circle center coordinates. Subsequently, an adaptive bandwidth fast Gaussian kernel was introduced to address the issue of sample point weighting. The mean shift clustering algorithm was employed to compute the optimal solution for the density of candidate circle center sample data. The final optimal center location was obtained by an iteration algorithm. Experimental results demonstrate that in the presence of interference, the average positioning error of this circle center localization algorithm is 0.051 pixels. Its localization accuracy is 64.1% higher than the Hough transform and 86.4% higher than the circle fitting algorithm.

A Rapid Head Organ Localization System Based on Clinically Realistic Images: A 3D Two Step Progressive Registration Method with CVH Anatomical Knowledge Mapping.

Rapid localization of ROI (Region of Interest) for tomographic medical images (TMIs) is an important foundation for efficient image reading, computer-aided education, and well-informed rights of patients. However, due to the multimodality of clinical TMIs, the complexity of anatomy, and the deformation of organs caused by diseases, it is difficult to have a universal and low-cost method for ROI organ localization. This article focuses on actual concerns of TMIs from medical students, engineers, interdisciplinary researchers, and patients, exploring a universal registration method between the clinical CT/MRI dataset and CVH (Chinese Visible Human) to locate the organ ROI in a low-cost and lightweight way. The proposed method is called Two-step Progressive Registration (TSPR), where the first registration adopts "eye-nose triangle" features to determine the spatial orientation, and the second registration adopts the circular contour to determine the spatial scale, ultimately achieving CVH anatomical knowledge automated mapping. Through experimentation with representative clinical TMIs, the registration results are capable of labeling the ROI in the images well and can adapt to the deformation problem of ROI, as well as local extremum problems that are prone to occur in inter-subject registration. Unlike the ideal requirements for TMIs' data quality in laboratory research, TSPR has good adaptability to incomplete and non-thin-layer quality in real clinical data in a low-cost and lightweight way. This helps medical students, engineers, and interdisciplinary researchers independently browse images, receive computer-aided education, and provide patients with better access to well-informed services, highlighting the potential of digital public health and medical education.

Measurement method of spherical radius size of differential planetary gear tooth surface based on 3D vision

Abstract In order to accurately measure the spherical radius dimensions of planetary gear tooth surfaces, we propose a non-contact measurement method based on 3D vision technology. Firstly, the point cloud data of the planetary gear captured by the laser 3D profiler is preprocessed, and the tooth surface point cloud is extracted. Next, based on the structural characteristics of the planetary gear tooth surface, a uniform slicing and sampling algorithm is used to extract circular contour points where the tooth surface point cloud intersects with the slicing planes. These points are then projected onto a two-dimensional plane, where an improved RANSAC algorithm is used to precisely fit each circular cross-section. Contour points associated with significant fitting errors are removed based on a set tolerance value. Finally, an improved differential evolution algorithm is used to perform a three-dimensional spherical fitting on the contour points that meet the tolerance criteria, achieving accurate measurement of the spherical radius of the planetary gear tooth surfaces. Experimental results demonstrate that the repeatability error of the proposed method is ±0.02 mm, with a maximum absolute error of 0.026 mm and an average measurement time of 4.76 s. The method exhibits high robustness and measurement accuracy, meeting practical engineering measurement requirements.

Interpolating bremsstrahlung function in ABJM model

In ABJM theory, enriched RG flows between circular 1/6 BPS bosonic and 1/2 BPS fermionic Wilson loops have been introduced in L. Castiglioni [L. Castiglioni, S. Penati, M. Tenser, and D. Trancanelli, Interpolating Wilson loops and enriched RG flows, .]. These flows are triggered by deformations corresponding to parametric 1/6 BPS fermionic loops. In this paper, we revisit the study of these operators, but instead of circular contours, we consider an interpolating cusped line and a latitude and study their RG flow in perturbation theory. This allows for the definition of a bremsstrahlung function away from fixed points. We generalize to this case the known cusp/latitude correspondence that relates the bremsstrahlung function to a latitude Wilson loop. We find that away from the conformal fixed points the ordinary identity is broken by the conformal anomaly in a controlled way. From a defect perspective, the breaking of the correspondence can be traced back to the appearance of an anomalous dimension for fermionic operators localized on the defect. As a by-product, we provide a brand new result for the two-loop cusp anomalous dimension of the 1/6 BPS fermionic and the 1/6 BPS bosonic Wilson lines. Published by the American Physical Society 2024

Results of the analytical solution of the problem of radial vibrations of disks of variable thickness

An analytical solution is obtained for the problem of radial vibrations of disks of variable thickness. A disk is considered that is rigidly fixed along the inner circular contour (ρ=0.2) and free on the outer contour (ρ=1). The thickness of the disk varies according to the law H=H0(ρν+μ+Cρν-μ)2, where H0,C,μ are arbitrary constants; ν is the Poisson's ratio. The exact solution of the problem is known only for H=const and H=1/ρ3. However, these solutions are not sufficient to study the vibrations of disks of other configurations. The proposed law of thickness variation H(ρ) allows us to obtain exact solutions to the problem at any value of the constant coefficients H0, C, μ, ν. By varying the values of these coefficients within a single given function, it is possible to set the disk profile of the desired appearance. The methods used to obtain these solutions are based on appropriate mathematical transformations of the original equation. The problem of disk oscillations is solved for four variants of thickness change. The natural frequencies for the first three forms of vibration are calculated. Comparison of the natural frequencies found for the three cases of the disk profile gently sloping indicates an increase in their values with an increase in the bending of the disk thickness. Based on the obtained eigenfunctions, the stresses were calculated and the nature of their distribution along the radial coordinate of the disk was determined. The strength of the disks under resonant radial vibrations was evaluated using a special criterion. It is found that the most limiting, i.e., destructive principal stress σ1=σr at the first (main) form of vibration should be chosen from the ratio σr≈0.79 [σ-1], where [σ-1] is the endurance limit of the disk material under uniform loading. The results obtained can be used to predict the stress-strain state of disks of variable profile under their radial vibrations

Multi-criteria parametric optimization of the displacement and weight of a shell of minimal surface on a circular contour consisting of two inclined ellipses under thermal and power loading with consideration of geometric nonlinearity

Thin shells are well suited to optimal design problems, and the finite element method and gradient descent method make it possible to solve inverse problems in structural and applied mechanics. The calculation process takes into account geometric nonlinearity. In modern numerical studies, a formulation taking into account geometric nonlinearity in the finite element method is used, namely, a stepwise loading procedure. It becomes necessary to take into account the relations between displacement vectors and their derivatives and strain increments. These relations help to determine the stiffness matrix of the finite element at each loading step, which leads to a qualitative study of real displacements in the structure. The geometrically nonlinear calculation of a shell of minimum surface on a circular contour consisting of two inclined ellipses in a multi-criteria parametric optimization is performed by the finite element method. The finite element method is a universal variational method that is focused on solving the most complex problems of elasticity theory and applied and structural mechanics using separate calculation complexes. Stiffness matrix - for the whole body is formed on the basis of the finite element stiffness matrix. The system of solving equations of the finite element method is formed using the Lagrange's variational principle, according to which the total potential energy P of a finite element model of a body in a state of stability and equilibrium has a minimum value. As part of the sensitivity analysis, gradients of the design variables of the structure, displacements in the form of partial derivatives of these characteristics along the design variables, and shell thickness are calculated. The sensitivity information serves as the basis for building an optimal design algorithm using the gradient descent method of the objective function. Standard multi-criteria parametric optimization allows for an average of 10% steel savings, with geometric nonlinearity increasing to 20%. At this study site, 24.4% of sheet steel was saved, which is a significant relative saving. This methodology of the authors shows high results for innovative design and production of steel thin shells in Ukraine and around the world, and also makes it possible to apply several types of optimization to one research object.

Femtosecond laser drilling 100 μm diameter micro holes with aspect ratios > 20 in a Nickel based superalloy

Micro holes with high aspect ratios are essential for the cooling performance of aero-engines. Challenges persist in deep hole drilling due to the escalating stringent requirements in terms of hole diameters, aspect ratios, and 3D profiles. In this study, we propose a two-step femtosecond laser drilling method to produce cylindrical micro holes with diameters of ∼100 μm, aspect ratios >20, and near-zero taper angle in Inconel 718 plates. In the first drilling period, the laser polarization trepanning method is used, yielding through-holes with aspect ratios >20 but undesired tapers and irregular shapes at the hole exit. A new method called laser spinning is then introduced in the second drilling period, proficiently decreasing taper angles to be < 0.05° and improving the irregular exit profiles into circular contours. Employing a rotating inclined laser beam, the laser spinning method facilitates deep hole drilling by enhancing laser penetration, solely resulting augmented hole diameters at the exit without compromising hole aspect ratios. The efficacy of this drilling approach is achieved through modifying the incident laser reflection on internal hole walls. Overall, the presented results and analyses hold great promise for high-quality deep hole drilling in opaque materials, particularly for products regarding aero-engines.

Manipulating plasmonic vortex based on meta-atoms with four rectangular slits.

In this paper, four rectangular slits with the same size and regular rotation angle are regarded as the meta-atom, arranged on circular contours, to create plasmonic vortex lenses (PVLs) solely based on the geometric phase. These PVLs can achieve the same purpose of exciting surface plasmon polariton (SPP) vortices with arbitrary combinations of topological charge (TC) when illuminated by circularly polarized (CP) light with different handedness as the traditional PVLs. Furthermore, they can generate SPP vortices with different TCs and specific constant or varying electric-field intensities when excited by linearly polarized (LP) light, which marks the first instance of this phenomenon solely through geometric phase manipulation. The TC can be dynamically altered by controlling the polarization order of the incident vector beam. These PVLs not only possess advantages in terms of device miniaturization and the creation of a more uniform vortex field, as compared to PVLs based on the transmission phase, but also offer a more straightforward design process in comparison to traditional structures that rely solely on the geometric phase.

Investigation of stochastic toolpath strategy in three-axis ball-end milling of 2D and free-form surfaces

The machining of free-form components by ball-end milling inherently produces surface error in the form of scallops. The objective of any free-form toolpath strategy is to balance productivity while minimizing scallop height to reduce surface error. Conventional machining strategies produce repeatable material patterns (constant scallop height) that may limit workpiece function in areas such as lubricity, directional anisotropy, and aesthetic appearance. These strategies also involve steady-state cuts, which allow accumulation of temperature, restrict the permissible depth and speed. In the present paper a novel complex stochastic toolpath strategy has been proposed that comprises pseudo-random circular contours concatenated into a smooth path. The approach enables continuous variation of chip load, force, and direction, and avoids conditions of continuous, periodic high cutting loads and heat accumulation. Based on initial testing, it has been observed that stochastic toolpaths are longer than conventional toolpaths. However, a decrease in average cutting loads enable reduction in cutting time with feed optimization. Additionally, the proposed strategy resulted in lower scallop height than conventional machining, thereby improving surface condition.

Six-Bar Linkages With Compliant Mechanisms for Programmable Mechanical Structures

Abstract Programmable mechanical structures are formed by autonomous and adaptive cells and can reproduce meshes known from the finite element method. Furthermore, they can change their structure not only through morphing, but also by self-reconfiguration of the cells. A crucial component of the cells, which can preserve the underlying geometry of a triangular mesh, are six-bar linkages. The main part of the present contribution concerns the six-bar linkages as a fully 3D-printable compliant mechanism where each revolute joint of the six-bar linkage is replaced with a notch flexure hinge with the circular contour. The utilization of notch flexure hinges presents two significant drawbacks. First, notch flexure hinges do not maintain the center of rotation. Second, although compliance is an inherent and desirable characteristic of flexural hinges, it gives rise to secondary or parasitic motion. The compliance subsequently lead to alterations in the underlying geometry of a triangular mesh. For self-reconfiguration of the cells, an efficient model is needed to predict the positioning errors. Therefore, the flexure hinge is represented by three distinct models, namely a finite element model, a beam model, and a simplified linearized model based on translational and rotational spring elements. These models are compared and evaluated in succession first to identify the parameters of the simplified model and later on, the simplified model is used to show the deviations of a medium-scaled programmable structure with respect to the idealized behavior. The current work brings us closer to both the development of programmable mechanical structures and the prediction of positioning errors during self-reconfiguration.

An accurate novel circular hole inspection method for sheet metal parts using edge-guided robust multi-view stereo

Sheet metal parts are frequently used in the industrial field, and the circular holes on these parts are commonly employed as assembly references. Therefore, precise measurement of these circular holes is essential. Because of the scratches, rust, and complex reflection around the edges, the measurement of circular holes on sheet metal parts is a challenging task. In this research, an accurate circular hole inspection method for sheet metal parts is proposed to realize online inspection using a multi-camera system. After capturing images in a single shot, edge detection is adopted to obtain sub-pixel circular hole contours. A new adaptive matching cost based on the descriptor of binary robust independent elementary features and bilinear normalized cross-correlation is introduced to the PatchMatch-based multi-view stereo method to obtain dense and accurate point clouds. To improve the accuracy and integrity of circular hole measurement, a new edge-guided multi-scale geometric consistency matching strategy is proposed accompanied by depth detail restoration. Finally, the points around the circular hole in a spherical range are sampled using the trinocular constraint principle and fitted with the circular equation. The experimental results show that the proposed algorithm performs well, with an error of approximately 0.04 mm, and improves the measurement accuracy compared with the state-of-the-art algorithms.

The reciprocal linear effect, a new optical effect of the Sagnac type

Abstract The Sagnac effect can be demonstrated with light propagating either along a circular contour or, as done by Wang et al., back and forth along a linear contour. In the linear Sagnac effect, the emitter–receiver device is in motion relative to the contour where light propagates. In the reciprocal linear Sagnac effect (RLSE), the device is stationary and the contour is in motion. When the contour changes direction of motion, some special features of the linear Sagnac effect are not fully reciprocal to the RLSE, which foresees variations of the first order in v ⁄ c v/c in the round-trip time taken by a light signal to cover the contour. The RLSE can be tested with present technology and, if confirmed experimentally, it might have interesting technological applications. Presently, it can be important for testing light-speed invariance, simultaneity, and the relativity principle.

Indices of polarization Möbius strips surrounding lines of circular polarization in nonparaxial optical fields.

Detailed analysis of polarization ellipse strips constructed on small circular contours surrounding a single polarization singularity line of an electromagnetic field is carried out. It is shown that the strips formed by major and minor axes of polarization ellipses are nonorientable Möbius strips with opposite directions of twist. Explicit analytical expressions relating the direction of the strip twist to the orientation of its construction contour and the parameters of the electromagnetic field at the polarization singularity point are found.

Contour integration deficits at high spatial frequencies in children treated for anisometropic amblyopia.

This study was conducted to reexamine the question of whether children treated for anisometropic amblyopia have contour integration deficits. To do so, we used psychophysical methods that require global contour processing while minimizing the influence of low-level deficits: visibility, shape perception, and positional uncertainty. Thirteen children with anisometropic amblyopia (age: 10.1 ± 1.8 years) and thirteen visually normal children (age: 10.8 ± 2.0 years) participated in this study. The stimuli were closed figures made up of Gabor patches either in noise or on a blank field. The contrast thresholds to detect a circular contour on a blank field, as well as the thresholds of aspect ratio and contour element number to discriminate a circular or elliptical contour in noise, were measured at Gabor spatial frequencies of 1.5, 3, and 6 cpd for amblyopic eyes (AEs), fellow eyes (FEs), and normal control eyes. Visual acuities and contrast sensitivity functions for AEs and FEs and the Randot stereoacuity were measured before testing. The AEs showed contrast deficits and degraded shape perception compared to the FEs at higher spatial frequencies (6 cpd). When the influence of abnormal contrast sensitivity and shape perception were minimized, the AEs showed contour integration deficits at spatial frequencies 3 and 6 cpd. These deficits were not related to basic losses in contrast sensitivity and acuity, stereoacuity, and visual crowding. Besides, no significant difference was found between the fellow eyes of the amblyopic children and the normal control eyes in the performance of contour integration. After eliminating or compensating for the low-level deficits, children treated for anisometropic amblyopia still show contour integration deficits, primarily at higher spatial frequencies, which might reflect the deficits in global processing caused by amblyopia. Contour integration deficits are likely independent of spatial vision deficits. Refractive correction and/or occlusion therapies may not be sufficient to fully restore contour integration deficits, which indicates the need for the development of clinical treatments to recover these deficits.

Study of geometrical properties of 96Mo, 98Ru and 100Pd isotones within interacting boson model

The software package for interacting boson model-1 and for the geometrical boson model has been used to calculate energy levels and potential energy surfaces for and by estimating a set of parameters which are used to predict the behavior of even-even and isotones. According to a framework, the interaction is prominent between the two parameters (and). This means that vibrational structures are constant rises with opposite of rotational. Thus, the potential energy surfaces are considered as a pointer of and distortions for even-even and isotones. The behaviors of the potential energy surfaces with minimum β (-0.84356,- 0.39928, and -0.19045) have circular contours centered at this point that indicates a good agreement with the typical axially symmetric limits. The results of the calculated energy levels were in acceptable agreement with the experimental data. There is no pure vibrational property of these isotones which is clearly shown in the behavior of potential energy surfaces.

Optimal design of the forced oscillation frequencies of the minimum surface shell on a circular contour consisting of two inclined ellipses under thermal and power loading

The problem of choosing the optimal design solution is a multi-purpose complex task, the solution of which requires taking into account a wide range of requirements for different stages of implementation. There are several levels of solving optimal design problems. The first level deals with general design models, including the main structural elements, taking into account the physical and geometric features of their behavior. This level can be called the "global" level of optimization. Due to the fact that the automated calculation of structures is impossible without the use of finite element models, and at the next "detailed" level, the parameters that make up this model (coordinates of nodes, physical and geometric properties of individual elements, etc.)&#x0D; The choice of a finite element model for optimal design is directly related to the complexity (the possibility of computer implementation) of the optimal design problem. To reduce the computational procedures associated with solving the problem of numerical analysis, an approach based on the approximation of system parameters (displacements, forces, frequencies, waveforms, etc.) can be used.&#x0D; The problem of forced oscillations for shells of minimal surfaces is solved by the finite element method using the Lagrange's variational principle. The potential and kinetic deformation energies of the shell of a minimal surface are defined in matrix form as the sum of the potential and kinetic energies of each finite element.&#x0D; The optimization algorithm for single-criterion parametric optimization is performed as follows: the objective function is the weight of the shell of the minimum surface on a circular contour consisting of two inclined ellipses, the design variables are the thickness of the shell, and the constraints are represented by the first forced vibration frequency. The results of changing the objective function are a decrease in the weight of the shell by 3050 kg of C240 steel, which is a percentage equivalent of 13.4% without loss of strength and stability of the shell of the minimum surface on a circular contour consisting of two inclined ellipses, which proves the effectiveness of the authors' methodology.

The computation of the average speckle size from the point spread function for triangular apertures

We suggest triangular aperture modeling for the computation of speckle size using the point spread function (PSF) concept. The fast Fourier transform (FFT) algorithm indicates three models of triangular apertures in the point spread function (PSF) computation. We calculated for the first time the average speckle size from the full width at half maximum (FWHM) for the triangular apertures in the PSF. The results are compared with the speckle sizes results obtained from the autocorrelation of speckle images corresponding to the considered models showed an agreement. In the analysis, I consider the 1st model with four equilateral triangular apertures, each of equal sides (b), along the Cartesian coordinates at equal distances from the center (xd). In the 2nd model, I assume 16 triangular apertures in a circular contour. In contrast, in the 3rd model, a sequence of six equilateral triangular black and white (B/W) zones is shown where the central triangle is black. I consider central obstruction to attenuate the low spatial frequency in the PSF. I take a transparent triangular aperture for comparison. Also, the PSF corresponding to the circular aperture is given for comparison. In addition, reconstructed images of apertures from the speckle images are obtained. We considered MATLAB codes for all the computations and plots.

Magnetic properties of pipe-layers of magnetized chain of spheres: a control based on measured magnetic properties of its cores

The use of circular contour sensors on printed circuit boards placed between contacting spheres with radius R in the magnetized chain of balls makes it possible to measure magnetic microflows in the chain along its cores of different radius r c . Thus, it becomes possible to obtain information about the magnetic properties of not only the cores of the chain themselves, but also its pipe quasi-functional layers limited by adjacent sensors. It is the purpose of the work. According to the magnetic flux measured with the help of well-recommended contour sensors (eight: from r c /R from 0.2 to 0.9) at magnetizing fi eld intensity in the range of 10–55 kA/m, magnetic flux is established along seven pipe-layers of relative radius r p /R (from 0.25 to 0.85). The values χ p of their magnetic susceptibility were found, as the r p /R values increase χ p -values decrease according to the inverse power dependence with a power degree equals 2.4. The values of the demagnetizing factor are set and functionally approximated for pipe-layers in relatively short chains of different lengths (with a number of spheres from 2 to 8). The obtained information expands idea about magnetization a chain of granules as the basic element of the granular medium. This information is useful in detailing the characteristics of such heterogeneous media used to solve scientific and practical problems, in particular, to clarify the conditions for building zones that are responsible for the magnetic capture of magnetoactive particles between granules of working elements (matrix type) of polygradient magnetic separators and analyzers.

On the flow of viscoplastic fluids in non-circular tubes

Steady flow of the viscoplastic Bingham and Herschel–Bulkley (H–B)​ fluids in tubes of non-circular cross-section is investigated analytically. The solution methodology is general in scope, does not put any restrictions on the Bingham number and thus allows the mapping of the flow field for high Bingham numbers in straight tubes with non-circular axially-symmetric but otherwise arbitrary cross-sectional contours. The circular tube contour is mapped onto an arbitrary non-circular contour on which the no-slip condition is satisfied via a one-to-one and continuous mapping. Governing equations are solved for the full spectrum of axially symmetrical cross-sectional shapes and a specific example is developed for the viscoplastic H–B fluid flow in a tube with an equilateral triangular cross-section. The shape and the extent of the plug zones centered on the tube axis and the stagnant zones in the corners are predicted for both Bingham and H–B fluids. The effect of the shear rate dependent viscosity of the H–B fluids, leading to either shear-thickening or shear-thinning behavior, on the formation of the plug and stagnation zones is examined.