Geometric Relationship Research Articles

Effects of multiple relaxation times in the annular flow of pulsatile electro-osmotic flow of a complex biological fluid: blood with low and high cholesterol

This study investigates the electro-osmotic flow of a biological fluid (blood with varying cholesterol levels) in annular flow to simulate a first approximation to arterial occlusion. The fluid´s rheology is characterized by a multi-modal convected Maxwell model equation. The charge density follows the Boltzmann distribution, governing the electrical field. Mathematically, this scenario can be modeled by the Poisson–Boltzmann partial differential equation. Assuming a small zeta potential (less than 25 mV) using the Debye–Huckel approximation and considering a pulsatile electrical field, analytical solutions are derived using the Fourier transform formalism. These solutions, expressed in terms of the modified Bessel function, provide transfer functions for axial velocity and volumetric flow as functions of material parameters represented by characteristic dimensionless numbers. This study further analyzes thermal, electric, inertial, viscoelastic, and various interactions within the plasma, hematocrit, hematocrit–cholesterol, and cholesterol–cholesterol as well as weight concentration through numerical simulations. Finally, the flow and rheology predictions are validated using experimental data on human blood with varying cholesterol levels. The obtained transfer functions reveal that the electric–thermal–viscoelastic effects and the multiple geometric relationships contribute to the dynamic response of the interactions between the input electrical field and output volumetric flow and shear stress functions, leading to and evolution of resonance curves. It is noteworthy that electro-osmotic flow in blood with pathologies associated with low and high cholesterol has been scarcely reported in the literature on rheology. Thus, this work represents a significant contribution to the field.

NLOS visible light positioning and communication based on LoRa modulation

With the rapid development of the Internet of Things, location-based services are becoming increasingly important, especially in indoor environments. Visible light positioning (VLP) has garnered widespread attention due to its high accuracy, low cost, and immunity to the radio frequency electromagnetic interference. However, traditional VLP relies on line-of-sight paths, making it impractical in complex and dynamic indoor environments. In this paper, we propose a non-line-of-sight (NLOS) visible light positioning and communication system based on LoRa modulation to address the issue of link obstruction. LoRa is employed to recover position information transmitted from light emitting diodes (LEDs) over NLOS links, enabling reliable communication under weak lighting conditions. We establish a geometric relationship between the LED and the virtual image of the photodetector (PD). Leveraging the NLOS channel model, we derive the relationship between the received signal strength and the distance from LEDs to the virtual image of the PD. Through this relationship, the trilateration method is applied to calculate the position of the receiver. Based on experimental results, the proposed system achieves 90th percentile localization accuracy of less than 25 and 35 cm for the PD heights of 60 and 80 cm, respectively.

Effect of heat treatments on inhomogeneous deformation of the melt-pool structure of Al–Si alloy manufactured via laser powder bed fusion

Laser powder bed fusion (L-PBF) is an additive manufacturing technology widely applied to the manufacture of metallic parts. The L-PBF processed aluminum-silicon (Al–Si) cast-type alloy components exhibit an anisotropic tensile ductility. In this study, we investigated the influence of heat treatments on the microstructural features of an Al–12%Si binary alloy fabricated via L-PBF and the associated inhomogeneous deformation of its melt-pool structure, which contributes to the resulting anisotropic tensile ductility. The mechanical inhomogeneity of the melt-pool structure and the change induced by annealing at various temperatures (300 and 530 °C) were characterized using microscale digital-image correlation analyses of scanning electron microscopy images obtained in situ during tensile deformation and nanoindentation hardness mapping. In the specimen fabricated via L-PBF, the high strain was concentrated at the locally coarsened microstructure (the soft region) along the boundaries of the melt pools rather than at the refined solidification microstructure (the hard region) within the melt pools. The localized strain varied depending on the geometrical relation between the orientation of the melt-pool boundary and the tensile direction, thus contributing to the anisotropic tensile ductility. This tendency appeared less pronounced in the specimen annealed at 300 °C, which exhibited a slightly homogenized melt-pool structure. The reduced strain localization is associated with a reduced difference in local strength between the melt-pool boundary (soft region) and the melt-pool interior (hard region). The slight homogenization of the melt-pool structure emphasized the effect of grain morphologies in the α-Al matrix on the inhomogeneous deformation within melt pools. In the specimen annealed at 530 °C, which exhibited a homogenized α-Al/Si two-phase microstructure, the uniformly distributed Si phase would be responsible for the homogenous deformation, resulting in an isotropic tensile ductility. This study advances our understanding of the correlation between the melt-pool structure and the deformation behavior of Al–Si alloys processed using L-PBF, which provides new insights for controlling the ductility by post-processing.

UPDs estimation and ambiguity resolution performance evaluation of LEO navigation system

Low-Earth orbit (LEO) satellites have fast motion and thus provide rapid geometric change relation to the ground stations in a short period of time, which are expected to improve the positioning performance. In this study, a LEO constellation of 160 LEO satellites was simulated and simulated LEO observation data at global, European, and American stations were used to estimate the uncalibrated phase delays (UPDs) and achieve static and kinematic precise point positioning (PPP) ambiguity resolution (AR). The quality of the estimated UPD products were evaluated. More than 89 % and 96 % of the wide- and narrow-lane UPDs had a posteriori residual of less than 0.15 and 0.25 cycles, respectively. In static PPP, all ambiguity fixing rates were larger than 63 %. Compared with float solutions, the average convergence time of the fix solutions at the global, European and American stations was accelerated by 8 %, 6 % and 7 %, respectively; the average root-mean-square errors (RMSEs) in the east, north, and up components at the global, European and American stations were decreased by (22 %, 20 %, 15 %), (36 %, 34 %, 28 %) and (44 %, 31 %, 29 %), respectively. In kinematic PPP, all ambiguity fixing rates were larger than 40 %. Compared with float solutions, the average convergence time of the fix solutions at the global, European and American stations was accelerated by 4 %, 19 % and 14 %, respectively; the average RMSEs in the east, north, and up components at the global, European and American stations were decreased by (10 %, 10 %, 7 %), (27 %, 22 %, 11 %) and (32 %, 20 %, 10 %), respectively. In both static and kinematic PPP, AR accelerated the convergence time and improved the positioning accuracy.

Monocular Vision Guidance for Unmanned Surface Vehicle Recovery

The positioning error of the GPS method at close distances is relatively large, rendering it incapable of accurately guiding unmanned surface vehicles (USVs) back to the mother ship. Therefore, this study proposes a near-distance recovery method for USVs based on monocular vision. By deploying a monocular camera on the USV to identify artificial markers on the mother ship and subsequently leveraging the geometric relationships among these markers, precise distance and angle information can be extracted. This enables effective guidance for the USVs to return to the mother ship. The experimental results validate the effectiveness of this approach, with positioning distance errors of less than 40 mm within a 10 m range and positioning angle errors of less than 5 degrees within a range of ±60 degrees.

Research on the Reconstruction Method of Old Houses in Mindong, Republic of China, Based on a Wearable Mobile Scanning System

To address the complex structures of historical buildings in Mindong, lack of historical reference materials, and heavy workload of traditional surveying and mapping methods in the field, a 3D reconstruction method of historical building based on a wearable mobile scanning system for data acquisition was studied. First, a wearable mobile scanning system is used to scan historical buildings in three dimensions. The data are fused to obtain high-precision three-dimensional point cloud data of historical buildings. Second, based on the processed point cloud, a 2D map of historical buildings is accurately drawn using point cloud slicing. Finally, three-dimensional reconstruction of historical buildings is realized using a 2D atlas of historical buildings and modern modeling technology. The accuracy of the three-dimensional reconstruction model was analyzed using a fitting algorithm and structural geometric relationship to verify the effectiveness and accuracy of the method. An old house in Mindong, Republic of China, was taken as the research object. Experimental analysis revealed that (1) a wearable mobile scanning system is suitable for high-quality point cloud data acquisition of buildings with complex geometric features, solving the problems of low efficiency and poor coverage of traditional surveying and mapping results; and (2) the method realizes 2D results rendering and 3D reconstruction of historical buildings based on the wearable mobile scanning system data with good accuracy, providing a reference for the protection and repair of historical buildings and health assessment.

A Target Localization Algorithm for a Single-Frequency Doppler Radar Based on an Improved Subtractive Average Optimizer

A doppler radar holds promising prospects in the field of indoor target localization. However, traditional Doppler radar systems suffer from high power consumption, large size, and noticeable radio frequency interference issues when transmitting carriers of different frequencies. Therefore, an ISABO-based (improved subtraction-average-based optimizer) target localization algorithm for a single-frequency Doppler radar is proposed in this paper. Firstly, a mathematical model for target localization is established according to the spatial geometric relationships during the target movement and the Doppler frequency-shift information in the single-frequency echo signal. Then, the optimization function is constructed with the target motion error as the optimization goal. Finally, an improved subtraction-average-based optimizer algorithm is proposed to solve the optimal parameters and realize the target positioning. The experimental results show that the proposed method can achieve centimeter-level localization accuracy with a cost-effective system structure.

Exploration of mathematical concepts in Batik Truntum Surakarta

This research investigates the mathematical concepts embedded within Batik Truntum motifs, including geometry, analysis, arithmetic, and algebra. Employing a qualitative methodology with an ethnographic approach, the study addresses four critical questions: "Where should I begin the search?", "How do I locate the concepts?", "How do I identify significant findings?", and "How do I comprehend these findings?". Through addressing these questions, the researcher successfully analyzed the mathematical concepts inherent in Batik Truntum. Of the four primary mathematical concepts, only geometry was substantiated by experts, encompassing sub-concepts such as geometric transformations, line relationships, and planar geometry. Specifically, transformation geometry includes translation and reflection, while the study of line relationships involves line alignment, and planar geometry covers the topic of circles. This research aims to ensure that the millennial generation remains connected to batik as a vital part of Indonesia's cultural heritage, preventing cultural erosion amidst technological advancements through the intricate and exploratory study of mathematics.

Head pose estimation with particle swarm optimization‐based contrastive learning and multimodal entangled GCN

AbstractHead pose estimation is an especially challenging task due to the complexity nonlinear mapping from 2D feature space to 3D pose space. To address the above issue, this paper presents a novel and efficient head pose estimation framework based on particle swarm optimized contrastive learning and multimodal entangled graph convolution network. Firstly, a new network, the region and difference‐aware feature pyramid network (RD‐FPN), is proposed for 2D keypoints detection to alleviate the background interference and enhance the feature expressiveness. Then, particle swarm optimized contrastive learning is constructed to alternatively match 2D and 3D keypoints, which takes the multimodal keypoints matching accuracy as the optimization objective, while considering the similarity of cross‐modal positive and negative sample pairs from contrastive learning as a local contrastive constraint. Finally, multimodal entangled graph convolution network is designed to enhance the ability of establishing geometric relationships between keypoints and head pose angles based on second‐order bilinear attention, in which point‐edge attention is introduced to improve the representation of geometric features between multimodal keypoints. Compared with other methods, the average error of our method is reduced by 8.23%, indicating the accuracy, generalization, and efficiency of our method on the 300W‐LP, AFLW2000, BIWI datasets.

Study on formation of exit edge defects in the milling process by using the combined theory of the energy conservation and orthogonal cutting mechanism

1 In the milling process, due to machining materials and process parameters, the material at the edge of the part may break due to shear forces instead of cutting properly, resulting in the irregular pit (defect) at the exit edge. This seriously affects the surface quality of the workpiece. It is vital to understand the forming mechanism of the exit edge defect (EED) before one tries to eliminate or reduce the size of the EED and furthermore to improve the machining accuracy. Therefore, focusing on the milling process at exit edge of a workpiece, this paper presents a novel theoretical model to study the forming principle of the EED and predict the corresponding size. First, the forming process of the EED is separated into two stages. The beginnings of them are symbolized by the initial- and the fracture-negative shear planes. Then, the initial-negative shear plane which is defined by the initial negative shear angle is found. Furthermore, the location of the fracture-negative shear plane is defined using the fracture negative shear angle to study the EED. For the next step, the concentration force of Flamant-Boussinesq problem combined with the yield strength of the material is introduced to obtain the initial negative shear angle. Additionally, using the energy conservation theory, the negative fracture shear angle is calculated. Based on these, the mechanism of the EED is illustrated. Besides, the size (including length and depth) of the EED is predicted based on the geometric relationship between the initial and the fracture negative shear angle. Finally, the correctness of the theoretical model is verified by simulation and experiments. This study provides a promising step to reducing/eliminating the hazards of edge defects.

A Deep Learning-Based Ultrasonic Diffraction Data Analysis Method for Accurate Automatic Crack Sizing

The purpose of this paper is to automate the interpretation of data during ultrasonic diffraction using a non-destructive testing (NDT) technique to accurately size defects for assisting in decision-making. A convolutional neural network (CNN) architecture was developed to automatically measure the length of the defect. Using the architecture, the population of A-scan signals in the scanning path was classified. The defect region was extracted and its size in the scanning direction was obtained by the connected region solution algorithm based on the classification results. The arrival time of diffraction waves was accurately identified by the intelligent denoising framework proposed, combined with Hilbert transform, and then the height of defects was calculated by corresponding geometric relations. The estimation results demonstrate that the measurement method can be considered as a useful technique for crack sizing in industrial structures, even in the case of complex noise.

Study on Calculation Method of Bending Performance of Concrete Sandwich Composite Slab.

In order to explore the flexural behavior of a concrete sandwich panel under concentrated boundary conditions, based on Kirachhoff's elastic thin plate theory in this paper, the geometric deformation, physical conditions, and equilibrium relationship of a sandwich panel are deduced by constructing the layered analysis model of the sandwich panel, the basic differential equation of the flexural deformation of the concrete sandwich thin plate is obtained, and the mathematical expression of the internal force and displacement under the boundary condition of concentrated support is given. Combined with an engineering example, the proposed calculation method is verified. The results show that, in the arrangement of reliable connectors for concrete sandwich panels, the concrete wythes bear the load while the contribution of the core layer to the bending capacity of the structure can be ignored. When subjected to a laterally distributed load, the sandwich panel mainly experiences out-of-plane bending deformation, and the bending normal stress in the concrete panel layer shows a linear non-uniform distribution along the thickness direction of the panel. The bending deformation performance and bearing efficiency of a concrete sandwich slab with the change in concentrated support position have significant effects, and the load transfer efficiency can be improved by optimizing the arrangement of supports. Except for small local areas near the supports, the bending stress distribution and deformation behavior of the concrete sandwich panel can be accurately analyzed by the calculation method established in this paper.

Non-interference slow tool servo turning method for complex surfaces with large undulation changes

Complex curved surface parts are integral to the mechanical industry, demanding precise machining techniques. Multi-axis slow tool servo turning has emerged as an efficient method due to its high precision and quality. However, the challenge of severe tool flank interference arises, especially on surfaces with large undulation changes. Conventional methods, such as increasing tool clearance angles or adding extra tool axes, detrimentally affect machining precision and stability. To address this, a non-interference toolpath planning method is proposed for complex surfaces with large undulation changes. The approach begins with establishing geometric models of the single-point diamond turning tool and typical complex surfaces, followed by analyzing the mechanism and evolution of tool flank interference. By considering geometric parameters and vector relationships, the practical tool clearance angles are calculated. And then a criterion for subregion division is introduced and the non-cutting stroke is designed, accounting for the maximal acceleration of machine tool axis. Multi-pass toolpaths are generated to navigate different subregions while avoiding interference by transforming spindle rotation direction. Furthermore, a method is proposed to optimize toolpath stitching in practical machining regions, ensuring continuous and smooth transitions while maintaining machining precision and surface quality. Experimental validation, conducted on a hyperbolic paraboloid surface with large undulation changes, demonstrates a significant reduction in surface roughness (Sa) from 380.503 nm to 75.664 nm—a reduction of 80.115 %. The proposed method not only enhances machining precision and surface quality but also extends tool life and improves working conditions. This research offers vital guidance for non-interference toolpath planning in engineering practice.

Tangent lines that neither touch nor cross the curves at the points of tangency

Several studies on student's understanding of the concept of the tangent line agree that the difficulties students have when dealing with lines tangent to curves at inflection points or tangent lines that have more than one point in common with the curve are due to a misconception of tangency that is limited to the geometric relationship between line and circle. Here, we report difficulties Mexican high school students had when working on tangent lines in situations like those mentioned before. For our research, we designed Activities mostly carried out with dynamic geometry. Using the zoom-in provided by the software helped strengthen the student's mental image of the local geometric relationship between a curve and a line tangent. Several of the curves we designed for the investigation surprised the students when they zoomed in on the point of tangency. From the point of view of the tangency relation that is intuitively obtained from tangents to the circle or curves at inflection points, in several curves that we presented, the tangent lines neither touch nor cross the curves at the points of tangency. These are cases of curves and tangents that would be worth analyzing in Differential Calculus courses.

Post-buckling behavior of variable-arc-length elastica pipe conveying fluid including effects of self-weight and pressure variation

This paper investigated the post-buckling behaviors of a variable-arc-length (VAL) elastica pipe caused by internal transporting fluid motion, accounting for the effects of the self-weight and variation of internal fluid pressure. Both weak-form and strong-form formulations of the VAL elastica pipe were developed. The weak-form formulation was derived by the virtual work principle, and later solved using the nonlinear finite element method (FEM). The strong-form formulation was derived using equilibrium of the force and moment equations, the geometrical relationship of the differential pipe segment, and the energy conservation of the transported fluid. Because of the large displacement analysis, the variation in the internal pressure inside the pipe was considered, which was taken into account by energy conservation based on the Bernoulli principle. Then, the set of nonlinear governing first-order differential equations, corresponding to the two-point boundary value problem, was conveniently solved using the shooting optimization method (SOM). The numerical results obtained from the presented FEM and SOM analyses independently verified each other, with good agreement between these two methods. The parametric study considered the effects of gravity load (pipe and fluid self-weights) and internal fluid pressure on the post-buckling characteristics of the VAL pipe. The numerical results showed that without the pipe and internal fluid weights, the transporting fluid exerted an axial compressive force on the pipe, causing post-buckling phenomena. Beyond the critical state, the support rotation and the length of the VAL pipe increased as the internal fluid velocity decreased. Finally, by including the effect of self-weight, the mode exchange of the odd buckling modes (1st and 3rd modes) was found from the load-displacement path.

Integrated attitude—orbit control of solar sail with single-axis gimbal mechanism

A new attitude control method for solar sails is proposed using a single-axis gimbal mechanism and three-axis reaction wheels. The gimbal angle is varied to change the geometrical relationship between the force due to solar radiation pressure (SRP) and the center of mass of the spacecraft, such that the disturbance torque is minimized during attitude maintenance for orbit control. Attitude maneuver and maintenance are performed by the reaction wheels based on the quaternion feedback control method. Even if angular momentum accumulates on the reaction wheels due to modelling error, it can also be unloaded by using the gimbal to produce suitable torque due to SRP. In this study, we analyzed the attitude motion under the reaction wheel control by linearizing the equations of motion around the equilibrium point. Further, we newly derived the propellent-free unloading method based on the analytical formulation. Finally, we constructed the integrated attitude-orbit control method, and its validity was verified in integrated attitude-orbit control simulations.

Diastolic Filling in Patients After Heart Transplantation Is Impaired Due to an Altered Geometrical Relationship Between the Left Atrium and Ventricle.

The geometrical relationship between atrial and ventricular short-axis cross-sectional area determines the hydraulic forces acting on intracardiac blood. This is important for diastolic filling. In patients undergoing heart transplantation (HTx), the left atrium is often enlarged as a result of the standard surgical technique. We hypothesized that diastolic filling in HTx patients is affected by the surgery altering the geometrical relationship between atrium and ventricle. This retrospective, cross-sectional study included 25 HTx patients (median age, 52 [range, 25-70] years), 15 patients with heart failure with reduced ejection fraction (median age, 63 [range, 52-75] years), 15 patients with heart failure with preserved ejection fraction (median age, 74 [range, 56-82] years), and 15 healthy controls (median age, 64 [range, 58-67] years) who underwent cardiac magnetic resonance imaging. Left ventricular, atrial, and total heart volumes (THV) were obtained. Atrioventricular area difference at end diastole and end systole was calculated as the largest ventricular short-axis area minus the largest atrial short-axis area. Left atrial minimum volume normalized for THV (LAmin/THV) was larger in HTx patients (median, 0.13 [range, 0.07-0.19]) compared with controls (median, 0.05 [range, 0.03-0.08], P <0.001), whereas left ventricular volume normalized for THV (left ventricular end-diastolic volume/THV) was similar between HTx and controls (median, 0.19 [range, 0.12-0.24] and median, 0.22 [range, 0.20-0.25], respectively). At end diastole, when atrioventricular area difference reached its largest positive value in controls, 11 HTx patients (44%) had a negative atrioventricular area difference, indicating impaired diastolic filling. Diastolic filling is impaired in HTx patients due to an altered geometrical relationship between the left atrium and ventricle. When performing cardiac transplantation, a surgical technique that creates a smaller left atrium may improve diastolic filling by aiding hydraulic forces.

Design and analysis of a solid surface deployable antenna mechanism based on flasher rigid origami

This study proposes a mechanism for solid surface deployable antennas based on flasher rigid origami. The mechanism scheme design and degree-of-freedom analysis were conducted utilizing a Kirigami release constraint strategy. Subsequently, a spatial geometric model of the key points was established incorporating the folding and unfolding characteristics and geometric relationships within the mechanism. Furthermore, a comprehensive 3D model of the antenna was developed by determining the hinge locations, geometric parameters, and driving mechanism, followed by a kinematic simulation analysis. Finally, a prototype was constructed, and a microgravity deployment experiment was conducted to verify the feasibility of the mechanism.

Study on driving safety of vehicle-bridge interaction system based on ultra-high-dimensional point-selected extremum methods

ABSTRACT The driving safety indexes involve the geometric nonlinear contact relationship of the wheel and rail and the high-frequency vibration of the wheel-set. The calculation of their probability characteristic parameters requires very precise selection of random excitation samples. Track irregularity is an essential external excitation force in the vehicle-bridge interaction system (VBIS). Besides, many random phase angles must be considered when using the harmonic superposition method to simulate VBIS, leading to the ultra-high-dimensional random variables problem. Thus, this paper proposes a square power point method and a pseudo-random sequence (Sobol sequence) based on a number theoretic approach to model ultra-high dimensional random variables accurately. This strategy reduces the deviation between the representative track irregularity samples (TIS) and can be applied to fields of strongly nonlinear and high-frequency vibration. Then, by increasing the number of representative TIS, the deviation between response samples caused by non-linear factors can be significantly reduced. Finally, this paper proposes a threshold method for driving safety indexes that determines the service life of bridges, which can quickly obtain the threshold of its extreme value distribution through the cumulative distribution function, and establish the relationship between the threshold and the number of trains travelled. The above theories are verified by calculation examples, and some engineering suggestions are obtained.

Diastology of the Transplanted Heart: Is the Geometrical Relationship of the Left Atrium the Missing Link?

Diastology of the Transplanted Heart: Is the Geometrical Relationship of the Left Atrium the Missing Link?