Local Coordinate System Research Articles

Grad B Drifts of Heavy Ions Solar Energetic Particles at Solar Corona Region

The objective of this research study the Grad B drifts velocity of the heavy ion of the solar wind (C+4, C+5 (at corona region with distance (1 to 15) * 6.69*108m for two varied angles (Ɵ= 90ᵒ, 180ᵒ). It has been studied, that grad B drifts velocity, in the model of Parker spiral. within single particle dynamics model, in a spherical coordinate system (local coordinate system with an axis aligned with the magnetic field). This work result shown that, azimuthal grad B drift velocity, V∇Bφ` takes maximum value at polar zone for (C+4, C+5) for both velocities of solar wind. Also, there is no azimuthal grad B drifts V∇Bφ` at equators zone. And as for colatitude grad B drift velocity, V∇Bθ` takes high value at most of regions and the highest value at polar zone for fast and slow solar winds. And noting that the slow solar winds have higher values than fast solar wind at the equator region.

A High-Precision Inverse Finite Element Method for Shape Sensing and Structural Health Monitoring

In the contemporary era, the further exploitation of deep-sea resources has led to a significant expansion of the role of ships in numerous domains, such as in oil and gas extraction. However, the harsh marine environments to which ships are frequently subjected can result in structural failures. In order to ensure the safety of the crew and the ship, and to reduce the costs associated with such failures, it is imperative to utilise a structural health monitoring (SHM) system to monitor the ship in real time. Displacement reconstruction is one of the main objectives of SHM, and the inverse finite element method (iFEM) is a powerful SHM method for the full-field displacement reconstruction of plate and shell structures. However, existing inverse shell elements applied to curved shell structures with irregular geometry or large curvature may result in element distortion. This paper proposes a high-precision iFEM for curved shell structures that does not alter the displacement mode of the element or increase the mesh and node quantities. In reality, it just modifies the methods of calculation. This method is based on the establishment of a local coordinate system on the Gaussian integration point and the subsequent alteration of the stiffness integration. The results of numerical examples demonstrate that the high-precision iFEM is capable of effectively reducing the displacement difference resulting from inverse finite element method reconstruction. Furthermore, it performs well in practical engineering applications.

Segmental vertebral three-dimensional motion in patients with L4 isthmic spondylolisthesis under weight-bearing conditions

ObjectiveTo investigate in vivo 6-degree-of-freedom (DOF) vertebral motion in patients with isthmic spondylolisthesis (IS) during various functional weight-bearing activities.MethodsFifteen asymptomatic volunteers (mean age 54.8 years) and fourteen patients with IS at L4-5 (mean age 53.4 years) were recruited. The positions of the vertebrae (L4-L5) in the supine, standing, flexion–extension, left–right twisting and left–right bending positions were determined using previously described CT-based models and dual fluoroscopic imaging techniques. Local coordinate systems were established at the center of the anterior vertebra of L4 isthmic spondylolisthesis (AIS), the posterior lamina of L4 isthmic spondylolisthesis (PIS) and the center of the L5 vertebra to obtain the 6DOF range of motion (ROM) at L4-L5 and the range of motion (ROM) between the AIS and the PIS.ResultsThe translation along the anteroposterior axis at L4-L5 during flexion–extension, left–right bending and left–right twisting was significantly greater than that of the healthy participants. However, the translation along the mediolateral axis at L4-L5 presented paradoxical motion under different positions: the ROM increased in the supine-standing and flexion–extension positions but decreased in the left–right bending and left–right twisting positions. The separation along the anteroposterior axis during flexion was significantly greater than that during standing, on average, reaching more than 1 mm. The separation along the mediolateral axis during standing, flexion and extension was significantly greater than that in the supine position.ConclusionsThis study revealed the occurrence of displacement between the AIS and PIS, primarily in the form of separation during flexion. Symptomatic patients with isthmic spondylolisthesis exhibit intervertebral instability, which might be underestimated by flexion–extension radiographs.

Effects of Analog Modeling Materials on Topographic Photogrammetry (SfM) Reconstructions

AbstractAccurate topographic data are essential for quantitative structural analysis, both in natural settings and in the laboratory. The selection of modeling materials (with appropriate rheological properties) is known to be fundamental for the success of scaled physical analog experiments. However, the optical properties of analog materials and their impact on the reliability and precision of high‐resolution topographic reconstructions have not (to our knowledge) previously been assessed. Here we evaluate the effects of material composition, color, and grain size on Structure‐from‐Motion (SfM) photogrammetry reconstruction efficacy for deformed and undeformed model configurations in the laboratory. Image collections for photogrammetry are acquired from multiple camera positions with a handheld digital camera, and reconstructions are registered using ground control points in a local coordinate system. Static experiments show that low reflectivity granular materials (e.g., silica sand, volcanic ash, pumice, and Al2O3) yield relatively reliable photogrammetry data for a wide range of grain sizes (44–2,400 μm) but larger grain sizes (≥250 μm) provide more robust results. Reflective materials (e.g., glass beads, wet clay) yield less reliable point‐clouds but the addition of low‐reflectivity granular materials (e.g., Al2O3 grains) on the surface of wet clay improves reconstruction results, with higher grain densities typically yielding lower point‐cloud residuals. SfM‐photogrammetry reconstruction of deformed clay analog models tends to improve at higher extension magnitudes because of fault and associated texture development on model surfaces. We anticipate that our results will help practitioners to improve the precision and reliability of photogrammetric data acquired in the analog modeling laboratory.

Geometric descriptors for beta turns.

Beta turns, in which the protein backbone abruptly changes direction over four amino acid residues, are the most common type of protein secondary structure after alpha helices and beta sheets and play key structural and functional roles. Previous work has produced classification systems for turn geometry at multiple levels of precision, but these operate in backbone dihedral-angle (Ramachandran) space, and the absence of a local Euclidean-space coordinate system and structural alignment for turns, or of any systematic Euclidean-space characterization of turn backbone shape, presents challenges for the visualization, comparison and analysis of the wide range of turn conformations and the design of turns and the structures that incorporate them. This work derives a turn-local coordinate system that implicitly aligns turns, together with a set of geometric descriptors that characterize the bulk BB shapes of turns and describe modes of structural variation not explicitly captured by existing systems. These modes are shown to be meaningful by the demonstration of clear relationships between descriptor values and the electrostatic energy of the beta-turn H-bond, the overrepresentations of key side-chain motifs, and the structural contexts of turns. Geometric turn descriptors complement Ramachandran-space classifications, and they can be used to select turn structures for compatibility with particular side-chain interactions or contexts. Potential applications include protein design and other tasks in which an enhanced Euclidean-space characterization of turns may improve understanding or performance. The web-based tools ExploreTurns, MapTurns, and ProfileTurn, available at www.betaturn.com, incorporate turn-local coordinates and turn descriptors and demonstrate their utility.

Méary's angle decoded: 3D analysis of first ray plantarflexion deformity in Charcot-marie-tooth disease

BackgroundThe typical cavovarus deformity seen in patients with Charcot-Marie-Tooth (CMT) involves plantarflexion of the first ray. The exact apex of the deformity has never been proven, although it is presumed to be within the medial cuneiform. The aim of this study was to utilize weight-bearing computed tomography (WBCT) to localize and quantify first ray plantarflexion deformity in CMT patients. MethodsWBCTs of 16 CMT patients with lateral Méary’s angle > 20 degrees were compared to controls utilizing semi-automated analysis software. A local coordinate system based on the first metatarsal was used to avoid bias of proximal deformity. The tarsometatarsal angle was subdivided into components (cuneiform-cuneiform joint normal, tarsometatarsal joint and metatarsal-metatarsal joint normal) and compared between CMT and controls. CMT patient’s first, second and third rays were also compared. Means were compared with a 2-sample t test (p < .05). ResultsCMT patients had significantly more plantarflexion of the first ray than controls (16.4 versus 8.8 degrees respectively(p < 0.001)). The largest difference of was found at the medial cuneiform with 20.6 degrees of plantarflexion in CMT patients versus 14.8 degrees in controls (p < .0001). There was also approximately 2 degrees of plantarflexion at the TMT joint (p < .001). ConclusionsPlantarflexion deformity in CMT patients is primarily an osseous deformity at the level of the medial cuneiform with a lesser contribution from the tarsometatarsal joint. Level of evidenceIII Retrospective comparative study

A novel isogeometric coupling approach for assembled thin-walled structures

In the aerospace field, there are numerous assembled thin-walled structures with complex geometric continuity conditions. This makes isogeometric analysis (IGA) inevitably meet multi-patch issues. In previous work on 5-DOFs shell, when encountering G0 continuity or kinks, the approach often involved converting two local coordinate system rotations into three global coordinate system rotations to achieve multi-patch coupling. This often introduces additional DOFs and may destabilize the stiffness matrix. In this study, inspired by the concept of solid coupling, a new shell coupling approach is proposed, developing a 5-DOFs shell coupling framework suitable for different geometric continuities, providing a more efficient and simpler framework. When calculating the coupling stiffness matrix, there is no need for prior classification of the control points. Within this framework, the Nitsche, Penalty, and Mortar methods based on IGA are implemented. To demonstrate the effectiveness of the proposed framework in static and linear buckling analyzes, four different numerical examples were constructed, including G1, G0 continuity, and kinks. Under different continuity conditions, the results are sensitive to the parameter selection of the Nitsche and Penalty methods. Appropriate parameter selection can lead to better results for them. Compared to others, the Mortar method avoids this problem, making it easier to apply in engineering. The core codes are publicly available at https://github.com/tasteofbbq/ICA4ATWS.

Конечно-элементное моделирование нелинейных задач упругости в абсолютных узловых координатах на неструктурированных шестигранных сетках

We consider a finite element approach to solving the problem of elasticity theory in terms of absolute nodal coordinate formulation (ANCF), in which large body displacements are described in a global reference frame without using any local coordinate system. The main feature of the method is the absence of gyroscopic effects and, as a result, constancy of the mass matrix and the vector of the generalized force of gravity. In contrast to the traditional ANCF approach, the sets of nodal degrees of freedom of the finite element are formed only on the basis of absolute coordinates of nodes, which allows us to solve the problem using, in particular, unstructured hexahedral meshes. To construct the stiffness matrix, we apply a second-order automatic differentiation algorithm, which ensures its symmetrical form (Hessian matrix) and is analytically accurate in calculating the derivative. This approach also makes it possible to carry out calculations for models of hyperelastic materials without the corresponding Piola-Kirchhoff tensor. It has been shown that within the framework of discretization of the equation of motion, along with the well-known Newmark numerical integration scheme, it is possible to use the HTT-α scheme, which is unconditionally stable, second-order accurate and dissipative for high frequencies. We present several examples of solving static and dynamic elasticity problems for compressible and incompressible models of hyperelastic materials, in which the functions of internal energy density of the body are specified in terms of the deformation gradient.

Theoretical and experimental investigation into detection of early-stage propagation of double cracks with distributed fiber optic sensor

A strain transfer model is developed to describe the transfer of crack opening displacement (COD) of double cracks in a structural substrate to the distributed fiber optic sensor (DFOS). Global and local coordinate systems are set up to aid in the deduction of the transfer of CODs of the double cracks to the DFOS. The analytical model of strain transfer is first derived in the local coordinate system and then is transformed into the global coordinate system. Analytical results show that the DFOS fiber strain induced by CODs of the double cracks in the structural substrate is affected by both the spacing and the CODs of the double cracks, and the strain peak is suppressed as the crack spacing is less than the characteristic length which is defined as the range of influence of the COD of the individual crack. The influences of the material properties of the DFOS, the fiber coating, the bonding adhesive, and the DFOS-fiber coating interfacial stiffness are discussed. The developed model is also experimentally validated by monitoring CODs of double cracks in aluminum alloy plates with optical frequency domain reflectometer (OFDR) DFOSs. Experimental results show that the strain distribution measured by the OFDR DFOSs agree well with the analytical results of the developed model. The limitations of the developed model and future work anticipated are then discussed.

High-order compact gas-kinetic scheme in arbitrary Lagrangian-Eulerian formulation

This study proposes an extension of the high-order compact gas-kinetic scheme (CGKS) to compressible flow simulation in an arbitrary Lagrangian-Eulerian (ALE) formulation in unstructured mesh. The ALE method is achieved by subdividing arbitrary mesh into tetrahedrons and integrating flux function in a local coordinate system at the cell interface to ensure geometric conservation law. The scheme incorporates a compact reconstruction with third-order accuracy for updating both cell-averaged conservative flow variables and their gradients. HWENO-type nonlinear reconstruction and gradient compression factors are adopted to improve the accuracy and robustness of the scheme. A multi-stage multi-derivative (MSMD) time-stepping method is also implemented to achieve high-order time accuracy with fewer middle stages. The scheme is used to study problems involving moving boundaries. The numerical experiments demonstrate the effectiveness of the scheme in capturing the accurate solutions of both low-speed smooth flow and highly compressible ones with strong shock waves.

A method for assessing guide layout and error on implant accuracy

Functional and esthetic results require accurate implant placement. We aimed to develop a predictive method for assessing guide layout and error on implant accuracy. A mathematical model for position error analysis was constructed based on triangular mesh data. This model examines the relationship between the spatial shifts of multiple surfaces and the spatial shifts of specific points. It involves encasing these surfaces in a cuboid bounding box and expressing them in a local coordinate system. The influence of positioning surface error and layout of surgical guide were researched with a simulation test. The result shows that error in the implant site position is directly related to the error in the guide locating surface under the same layout. When the guide locating surface layout varies, as the length, width, and height of the minimum cuboid envelope increase, the maximum deviation in the implant site position decreases.

Equivariant Line Graph Neural Network for Protein-Ligand Binding Affinity Prediction.

Binding affinity prediction of three-dimensional (3D) protein-ligand complexes is critical for drug repositioning and virtual drug screening. Existing approaches usually transform a 3D protein-ligand complex to a two-dimensional (2D) graph, and then use graph neural networks (GNNs) to predict its binding affinity. However, the node and edge features of the 2D graph are extracted based on invariant local coordinate systems of the 3D complex. As a result, these approaches can not fully learn the global information of the complex, such as the physical symmetry and the topological information of bonds. To address these issues, we propose a novel Equivariant Line Graph Network (ELGN) for binding affinity prediction of 3D protein-ligand complexes. The proposed ELGN firstly adds a super node to the 3D complex, and then builds a line graph based on the 3D complex. After that, ELGN uses a new E(3)-equivariant network layer to pass the messages between nodes and edges based on the global coordinate system of the 3D complex. Experimental results on two real datasets demonstrate the effectiveness of ELGN over several state-of-the-art baselines.

Research on path planning for clear aligner flexible manufacturing

In recent years, clear aligner can enhance individual appearance with dental defects, so it used more and more widely. However, in manufacturing process, there are still some problems, such as low degree of automation and high equipment cost. The problem of coordinate system mismatch between gingival curve point cloud and dental CAD model is faced to. The PCA-ICP registration algorithm is proposed, which includes coarse match algorithm and improve-ICP registration algorithm. The principal component analysis (PCA) based method can roughly find the posture relationship between the two point clouds. Using z-level dynamic hierarchical, the ICP registration can accurately find the posture between these two clouds. The final registration maximum distance error is 0.03 mm, which is smaller than robot machining error. Secondly, the clear aligner machining process is conducted to verify the registration effectiveness. Before machining, the path is generated based on the well registered gingival curve. After full registration, the tool path is calculated by establishing a local coordinate system between the workpiece and the tool to avoid interference. This path is calculated and generated as an executable program for ABB industrial robots. Finally, the robot was used for flexible cutting of clear aligners and was able to extract products, ensuring the effectiveness of the proposed research. This method can effectively solve the limitations of traditional milling path planning under such complex conditions.

Development of a method for solving elliptic differential equations based on a nonlinear compact-polynomial scheme

A numerical method for solving elliptic differential equations (on unstructured computational grids) is described, which is based on a nonlinear compact-polynomial computational scheme. For this purpose, an approximate transition from the elliptic equation to the hyperbolic type of equations was carried out in the work. To find the solution of the hyperbolic version of the diffusion equation, a transition (in the vicinity of the computational cell Ωi) to a local curvilinear coordinate system was performed, a nonlinear compact-polynomial computational scheme was used (the "predictor" stage), and the control volume method was applied (the "corrector" stage). The results of initial testing (on problems of different physical nature) of the proposed numerical method are presented.

Longitudinal failure criterion considering local fiber misplacement for UD composites

A new longitudinal failure criterion for unidirectional fibre reinforced (UD) composites is proposed, incorporating the contribution of local fibre misalignment to fibre failure. The failure function was established based on the quadratic polynomial expansion of stress components in the local coordinate system parallel to the misaligned fibres, with coefficients rationally determined based on the basic strength parameters of UD composites. The local stress components were used to determine the failure status associated with fibre compression, while the tensile load along fibres was assumed to have negligible influence on the development of the fibre misalignment. The predicted failure envelopes agreed well with the experimental data for different stress combinations, particularly in the regimes where the fibre failure was influenced by transverse stresses. This validates the predictive ability of the proposed criteria and highlights the importance of the contribution of matrix-failure-related stresses to the fibre-dominated failure behaviour of fibre reinforced composites.

The Kinematic Models of the SINS and Its Errors on the SE(3) Group in the Earth-Centered Inertial Coordinate System.

In this paper, the kinematic models of the Strapdown Inertial Navigation System (SINS) and its errors on the SE(3) group in the Earth-Centered Inertial frame (ECI) are established. On the one hand, with the ECI frame being regarded as the reference, based on the joint representation of attitude and velocity on the SE(3) group, the dynamic of the local geographic coordinate system (n-frame) and the body coordinate system (b-frame) evolve on the differentiable manifold, respectively, and the high-order expansion of the Baker-Campbell-Haussdorff equation compensates for the non-commutative motion errors stimulated by strong maneuverability. On the other hand, the kinematics of the left- and right-invariant errors of the n-frame and the b-frame on the SE(3) group are separately derived, where the errors of the b-frame completely depend on inertial sensor errors, while the errors of the n-frame rely on position errors and velocity errors. In this way, the errors brought by the inconsistency of the reference coordinate system are tackled, and a novel attitude error definition is introduced to separate and decouple the factors affecting the dynamic of the n-frame errors and the b-frame errors for better attitude estimation. Through a turntable experiment and a car-mounted field experiment, the effectiveness of the proposed kinematic models in estimating attitude has been verified, with a remarkable improvement in yaw angle accuracy in the case of large initial misalignment angles, and the models developed have better robustness compared to the traditional SE(3) group-based model.

Validation of Inertial-Measurement-Unit-Based Ex Vivo Knee Kinematics during a Loaded Squat before and after Reference-Frame-Orientation Optimisation.

Recently, inertial measurement units have been gaining popularity as a potential alternative to optical motion capture systems in the analysis of joint kinematics. In a previous study, the accuracy of knee joint angles calculated from inertial data and an extended Kalman filter and smoother algorithm was tested using ground truth data originating from a joint simulator guided by fluoroscopy-based signals. Although high levels of accuracy were achieved, the experimental setup leveraged multiple iterations of the same movement pattern and an absence of soft tissue artefacts. Here, the algorithm is tested against an optical marker-based system in a more challenging setting, with single iterations of a loaded squat cycle simulated on seven cadaveric specimens on a force-controlled knee rig. Prior to the optimisation of local coordinate systems using the REference FRame Alignment MEthod (REFRAME) to account for the effect of differences in local reference frame orientation, root-mean-square errors between the kinematic signals of the inertial and optical systems were as high as 3.8° ± 3.5° for flexion/extension, 20.4° ± 10.0° for abduction/adduction and 8.6° ± 5.7° for external/internal rotation. After REFRAME implementation, however, average root-mean-square errors decreased to 0.9° ± 0.4° and to 1.5° ± 0.7° for abduction/adduction and for external/internal rotation, respectively, with a slight increase to 4.2° ± 3.6° for flexion/extension. While these results demonstrate promising potential in the approach's ability to estimate knee joint angles during a single loaded squat cycle, they highlight the limiting effects that a reduced number of iterations and the lack of a reliable consistent reference pose inflicts on the sensor fusion algorithm's performance. They similarly stress the importance of adapting underlying assumptions and correctly tuning filter parameters to ensure satisfactory performance. More importantly, our findings emphasise the notable impact that properly aligning reference-frame orientations before comparing joint kinematics can have on results and the conclusions derived from them.

Finding reconnection lines and flux rope axes via local coordinates in global ion-kinetic magnetospheric simulations

Abstract. Magnetic reconnection is a crucially important process for energy conversion in plasma physics, with the substorm cycle of Earth's magnetosphere and solar flares being prime examples. While 2D models have been widely applied to study reconnection, investigating reconnection in 3D is still, in many aspects, an open problem. Finding sites of magnetic reconnection in a 3D setting is not a trivial task, with several approaches, from topological skeletons to Lorentz transformations, having been proposed to tackle the issue. This work presents a complementary method for quasi-2D structures in 3D settings by noting that the magnetic field structures near reconnection lines exhibit 2D features that can be identified in a suitably chosen local coordinate system. We present applications of this method to a hybrid-Vlasov Vlasiator simulation of Earth's magnetosphere, showing the complex magnetic topologies created by reconnection for simulations dominated by quasi-2D reconnection. We also quantify the dimensionalities of magnetic field structures in the simulation to justify the use of such coordinate systems.

A Vision/Inertial Navigation/Global Navigation Satellite Integrated System for Relative and Absolute Localization in Land Vehicles.

This paper presents an enhanced ground vehicle localization method designed to address the challenges associated with state estimation for autonomous vehicles operating in diverse environments. The focus is specifically on the precise localization of position and orientation in both local and global coordinate systems. The proposed approach integrates local estimates generated by existing visual-inertial odometry (VIO) methods into global position information obtained from the Global Navigation Satellite System (GNSS). This integration is achieved through optimizing fusion in a pose graph, ensuring precise local estimation and drift-free global position estimation. Considering the inherent complexities in autonomous driving scenarios, such as the potential failures of a visual-inertial navigation system (VINS) and restrictions on GNSS signals in urban canyons, leading to disruptions in localization outcomes, we introduce an adaptive fusion mechanism. This mechanism allows seamless switching between three modes: utilizing only VINS, using only GNSS, and normal fusion. The effectiveness of the proposed algorithm is demonstrated through rigorous testing in the Carla simulation environment and challenging UrbanNav scenarios. The evaluation includes both qualitative and quantitative analyses, revealing that the method exhibits robustness and accuracy.

Prismatic-element SBPML coupled with SBFEM for 3D infinite transient wave problems

In this paper, an enhanced prismatic-element scaled boundary perfectly matched layer (SBPML) is developed, which is a novel time-domain artificial boundary method for 3D infinite wave problems. The SBPML permits the utilization of an artificial boundary with general geometry and can consider planar physical surfaces and interfaces extending to infinity. Moreover, this enhancement enables the seamless integration with surface meshes of arbitrary polygonal faces (such as triangles, quadrangles, pentagons, heptagons, octagons, etc.) at the truncation boundaries. The interior domain can be modelled by polyhedrons formulated by the scaled boundary finite element method (SBFEM). The geometric shape of the SBPML elements in the proposed method, within the local coordinate system, takes the form of a regular prism with regular polygonal top and bottom faces. Consequently, it is referred to as the Prismatic-element SBPML. Local scaled boundary coordinates based on the polygonal shape function are firstly introduced into the truncated infinite domain to describe its general geometry properties and provide the coupled capabilities with arbitrary polygonal face meshes at the truncation boundaries of numerical models. Then, a complex stretching function from PML is applied to radial direction of the local scaled boundary coordinates to map the physical space onto the complex space, resulting in a SBPML domain. Upon spatial discretization, the proposed method is formulated using a 2nd-order mixed displacement-stress unsplit-field formulation, allowing seamless coupling with FEM and SBFEM originally designed for the interior computational domain. Finally, three benchmark examples of wave propagation problems in unbounded domains and two soil-structure interaction problems of engineering problems are presented to demonstrate the accuracy and robustness of the Prismatic-element SBPML.