Coordinate System Research Articles

A Newly Custom Coordinate System Used for Preoperative Planning of Robotic-assisted Total Knee Arthroplasty

PurposePreoperative planning is critical for total knee arthroplasty (TKA) performed with surgical robots, as it involves establishing a coordinate system to calculate the angle values of the components. This coordinate system serves as a reference during the surgical planning stage. This study aimed to develop a newly custom coordinate system suitable for integration with a surgical robot system. MethodsThe "Skywalker" surgical robot system was used to import computed tomography (CT) images of the entire lower extremities from 50 patients diagnosed with osteoarthritis. Three-dimensional reconstruction was subsequently performed. The TKA component was positioned at a fixed angle using the newly developed custom coordinate system. The angle values of the components, based on the standard CT coordinate system, were then recorded without altering their positioning. These values were analyzed to assess the differences between the two coordinate systems. ResultsThe mean and standard deviation values for the coronal, sagittal, and transverse plane positioning of the femoral component (absolute value of error) were 0.004° ± 0.020°, 0.006° ± 0.024°, and 0.158° ± 0.186°, respectively. Similarly, the mean and standard deviation values for the coronal, sagittal, and transverse plane positioning of the tibial component (absolute value of error) were 0.544° ± 0.452°, 0.042° ± 0.076°, and 0.348° ± 0.445°, respectively. ConclusionThis newly developed custom coordinate system can be employed for preoperative planning in Skywalker surgical robot system-assisted TKA, particularly for patients with significant positional abnormalities in their CT scans.

Periodic orbits of solar sails in the Sun-Earth system

Abstract This paper studies the periodic orbits of solar sails using reflectivity control devices (RCDs) in the circular Sun-Earth system. Significantly, the dynamical equations about the solar sail are given separately in the rotational coordinate system and adjoint coordinate system. Analytical solutions about the periodic orbits of solar sails are given. So as to gain the periodic orbits of solar sails, we discuss the conditions of the attitude angles and reflectivity modulation ratio of solar sails. This paper simulates some periodic orbits of solar sails and analyzes the stability of a periodic orbit of a solar sail by using the Floquet theory. The outcomes show that it is unstable for the periodic orbit of a solar sail. Based on the linear quadratic regulator (LQR), this paper designs a control algorithm to achieve tracking in the target orbit of solar sails.

Ethical mediarhetoric in videogame cybertexts: procedural explication of moral topics in an educational context

Introduction. Education in the field of ethics and practical philosophy is important both within the framework of educational and disciplinary discourse and in terms of personal and social formation of a person, his/her value-behavioral system of coordinates. Video game cybertexts containing moral themes in their narrative and procedural structure can increase interest in the study of theoretical issues of ethics and create a special virtual-simulative space of moral experimentation. Materials and Methods. The theoretical part of the paper is based on the conceptual framework of understanding video games as a procedural cybertext formulated by E. Aarseth and I. Bogost. The operation of the multimodal-semiotic structure of video games is based on the ideas of J. Havreljak and W. Toch. The experimental cluster of work is realized on the principles of Digital Game-Based Learning developed by M. Prensky and a set of pedagogical practices on the use of ICT-based learning. Results. Based on the interpretation of the features of multimodal semiotics of ethically engaged video games, two modes of their distinction are revealed – narrative and gameplay. Narrative represents moral themes through narrative storytelling, and gameplay through gameplay. It has two forms of manifestation and certainty - external-iconic (based on visual reading and ethically binary interpretation of videogame cybertext) and procedural, where at the level of program architectonics the possibilities of choice and realization of simulations of ethical activities are created. The experiment allowed a radical change for the better (from 20% to 73%) in most students' expectations about the educational possibilities of video games in this disciplinary area. The DGBL methodology helped the learners (80%) to experience (80%) the practical dimension of important ethical issues and to conduct a series of moral experiments within the virtual simulations. Most of the students (75%) were able to correctly relate theoretical knowledge from philosophy and ethics to specific video game situations and successfully interpreted them. Conclusion. Given the time-consuming nature of these cybertexts, it is recommended that they be used only as supplementary media to the main course texts. It seems most appropriate to study them as part of an elective to a basic course in ethics or philosophy. This material could also be the basis for the creation of an educational laboratory on practical ethics in a social and humanitarian quantorium.

Modeling of the leader-follower satellite formation for long baseline

Abstract Interferometric Synthetic Aperture Radar (InSAR) represents a crucial component of synthetic aperture radar technologies, with the accuracy of measurements significantly improving as the baseline length increases. In comparison with the traditional Hill-Clohessy-Wiltshire (HCW) equations, the application of curvilinear coordinate systems for modeling satellite formations in circular orbits has demonstrated enhanced precision, especially when the formations span larger distances. However, these improvements were initially limited to circular orbits. Addressing this limitation, this study introduces a novel approach by incorporating elliptical orbits into the model, thereby refining the state transition matrix through the incorporation of eccentricity factors and maintaining the direct correlation with the temporal dynamics of satellite motion in three dimensions. Through rigorous numerical simulations, it has been established that this refined model substantially improves accuracy in leader-follower satellite formations.

Hydrodynamic parameters affecting flow-accelerated corrosion in elbows

Flow-accelerated corrosion (FAC) is a serious degradation mechanism affecting carbon-steel piping in the secondary coolant systems of nuclear power plants. Many researchers have investigated the correlation between wall thinning and hydrodynamic parameters; however, their relationship remains unclear. In this study, the hydrodynamic parameters influencing FAC in elbow sections were investigated for identifying the locations highly susceptible to FAC. Accelerated FAC tests and computational fluid dynamics (CFD) analyses were conducted on a specimen containing elbow sections. The results revealed that the side of the elbow pipe was the most susceptible to FAC because it experienced the most severe wall thinning. The velocity and vorticity vectors obtained from the CFD analysis were decomposed into axial, circumferential, and radial components within a cylindrical coordinate system to evaluate their effects. We found that all velocity and vorticity components contribute to the rate of wall thinning induced by FAC. Therefore, a combination of velocity and vorticity components should be used as hydrodynamic parameters to characterize FAC-induced wall thinning. Specifically, the circumferential velocity and axial vorticity were identified as dominant parameters influencing FAC in the elbows.

Sturm–Liouville problem for a one-dimensional thermoelastic operator in Cartesian, cylindrical, and spherical coordinate systems

The problem of constructing eigenfunctions of a one-dimensional thermoelastic operator in Cartesian, cylindrical, and spherical coordinate systems is considered. The corresponding Sturm–Liouville problem is formulated using Fourier’s separation of variables applied to a coupled system of thermoelasticity equations, assuming that the heat transfer rate is finite. It is shown that the eigenfunctions of the one-dimensional thermoelastic operator are expressed in terms of well-known trigonometric, cylinder, and spherical functions. However, coupled thermoelasticity problems are solved analytically only under certain boundary conditions, whose form is determined by the properties of the eigenfunctions.

A baseline decomposition ultra-short baseline localization algorithm for arbitrary array structures.

With the rapid development of the marine economy, hydroacoustic positioning technology plays an increasingly important role in marine engineering. The ultra-short baseline (USBL) hydroacoustic positioning system has the advantages of small size, simple operation, and flexible use, and has been widely used. Aiming at the existing USBL acoustic positioning algorithm with low positioning accuracy and complex calculation, a baseline decomposition localization algorithm with arbitrary array structure is proposed. The algorithm is based on the theory of coordinate system transformation, establishes positioning observation equations for each baseline in the base array, and adopts the least squares method to obtain positioning results by selecting different combinations of baselines. The systematic errors of different positioning models themselves are simulated, and then the effects of the three parameter errors, namely, time delay, element coordinates, and sound speed, on the positioning results are analyzed, respectively. Finally, the simulation results and sea trial data show that, compared with the existing algorithms, this algorithm not only simplifies the complicated computation process, but also improves the positioning accuracy and robustness, and has a better application effect.

Simulation of a Mesoscale Convective System Using a New Formulation for Advection in a Bin Microphysics: Sensitivity to Advection, Microphysics, and Grid Spacing

Abstract A computationally efficient semi-Lagrangian advection (SLA) scheme designed for microphysical variable advection was implemented into the Weather Research and Forecasting (WRF) Model with spectral bin microphysics (SBM). The primary goal was to reduce the CPU time for advection of the scalar SBM variables and demonstrate its applicability to simulation of a real-data case study in the eta vertical coordinate system. A mesoscale convective system (MCS) in Midlatitude Continental Convective Clouds Experiment (MC3E-0520) was selected for simulations. We compared the SLA and high-order, nonlinear monotonic advection schemes and tested the sensitivity of the simulated radar reflectivity, microphysical, and dynamic properties of the MCS to the choice of microphysical schemes, aerosol concentration, and grid spacing. Simulations using the SLA and monotonic advection schemes were similar, and the differences between them were much smaller than those between the SBM and bulk microphysical schemes tested. Improvement of the grid resolution had a larger impact on the vertical velocity field than did the choice of aerosol concentration. The total computational time in simulations with SLA was about 25% shorter than that with monotonic advection, which resulted from a reduction of more than 50% in computational time required for advection of the microphysical variables. Significance Statement Clouds comprise particles of various sizes and types: aerosols, liquid droplets, ice crystals, hail, and snow. Two major approaches describe the time and spatial evolution of these particle species: solving basic microphysical (bin microphysics) and simplified parameterization (bulk microphysics) equations. Bin microphysics is time-consuming as it operates with size distributions described by multiple mass bins. Among the microphysical processes, the advection of the microphysical variables requires significant CPU time. We tested a new numerical advection scheme that requires several times less computer time than the standard high-order nonlinear schemes being of similar accuracy. Due to the introduced change, the advection of droplet size distributions became less of a factor affecting the total computer time of bin-type schemes. This is an important step toward making the bin approach computationally efficient without losing accuracy. It is shown that the sensitivity of the results to spatial grid spacing and to the choice of microphysical schemes is significant and may be larger than that to variations in the aerosol concentration.

Analytical model of small- and large-amplitude drop oscillation dynamics

The mechanical energy balance over a bulk of fluid that oscillates between prolate and oblate shapes in another immiscible fluid is solved using a general spheroidal coordinate system. The drop shape is described by a unique parameter that may continuously vary over the time, making the implementation of the model rather simple. Potential flow is assumed, and inertial and viscous effects are accounted for in both the inner and outer flow fields. The characteristics of drop oscillation for small and large amplitudes are studied, and the results are compared with theoretical, experimental, and numerical data from the open literature. The rather satisfactory validation of the model over a large variety of operating conditions allows its extension to include other physical phenomenon, like evaporation and its effect on drop oscillation.

Credibility-based multi-sensor fusion for non-Gaussian conversion error mitigation

In a complex environment, a multi-sensor fusion algorithm can compensate for the limitations of a single sensor’s performance. In a distributed fusion algorithm, sensors need to transmit local estimates to a central coordinate system, and the existence of coordinate transformation uncertainty can undermine the performance of data transmission. Therefore, this paper proposes a multi-sensor distributed fusion method based on trustworthiness. Firstly, considering the presence of non-Gaussian conversion errors, a credibility-based multi-sensor fusion framework is constructed. Secondly, to address the difficulty in estimating conversion errors when measurement errors follow a non-Gaussian distribution, an optimization model is constructed based on actual measurement information to estimate the distribution of non-Gaussian conversion errors. Then, in response to the non-linear and non-Gaussian characteristics of the target optimization function, a particle swarm optimization algorithm based on trustworthiness adaptive weights is proposed to estimate the coordinate transformation errors. Finally, given the inconsistency in local estimates due to missing sensor measurements or significant errors in a non-Gaussian complex environment, a maximum correntropy consensus algorithm is proposed to avoid the trustworthiness calculation being affected by the current measurement errors, thereby improving the accuracy of the global estimation.

MCMS submersibles: A safe undersea adventure

Abstract. Maritime Cruises Mini-Submarines (MCMS), a company based in Greece, aims to offer safe and deep-sea exploratory experiences to tourists. This paper discusses the primary challenges involved in ensuring tourist safety, particularly focusing on maintaining security in scenarios of mechanical failures or lost communication with the main vessel. We propose comprehensive safety protocols and technological solutions tailored for deep-sea tourist submersibles. The analysis begins with a detailed study of the forces acting on a submersible, considering both operational modes and the impact of ocean currents, utilizing a rigid-body coordinate system and Eulerian angular coordinate transformations to describe the submersibles motion comprehensively. We derive motion and safety parameters by solving the force differential equations, allowing the host ship to predict the submersibles position accurately. In addressing the recovery of lost submersibles, our approach evaluates power loss scenarios and search efficiency, recommending an optimal combination of hydroacoustic and frequency-hopping communication technologies for reliable, low-loss data transmission. We further enhance search methodologies by integrating motion parameters and ocean current dynamics to pinpoint probable locations, adjusting search strategies dynamically based on real-time data, and employing probabilistic models to optimize resource allocation during search operations. A case study in the Caribbean Sea exemplifies applying these methodologies, incorporating localized flow regimes and cooperative communication strategies among multiple submersibles to improve operational efficiency and safety.

Coordinate-Independent 3-D Ultrasound Principal Stretch and Direction Imaging.

In clinical ultrasound, current 2-D strain imaging faces challenges in quantifying three orthogonal normal strain components. This requires separate image acquisitions based on the pixel-dependent cardiac coordinate system, leading to additional computations and estimation discrepancies due to probe orientation. Most systems lack shear strain information, as displaying all components is challenging to interpret. This paper presents a 3-D high-spatial-resolution, coordinate-independent strain imaging approach based on principal stretch and axis estimation. All strain components are transformed into three principal stretches along three normal principal axes, enabling direct visualization of the primary deformation. We devised an efficient 3-D speckle tracking method with tilt filtering, incorporating randomized searching in a two-pass tracking framework and rotating the phase of the 3-D correlation function for robust filtering. The proposed speckle tracking approach significantly improves estimates of displacement gradients related to the axial displacement component. Non-axial displacement gradient estimates are enhanced using a correlation-weighted least-squares method constrained by tissue incompressibility. Simulated and in vivo canine cardiac datasets were evaluated to estimate Lagrangian strains from end-diastole to end-systole. The proposed speckle tracking method improves displacement estimation by a factor of 4.3 to 10.5 over conventional 1-pass processing. Maximum principal axis/direction imaging enables better detection of local disease regions than conventional strain imaging. Coordinate-independent tracking can identify myocardial abnormalities with high accuracy. This study offers enhanced accuracy and robustness in strain imaging compared to current methods.

A New Perspective on the Homogeneous Coordinate System for Calculating Interatomic Distances and Their Derivatives in Terms of Internal Coordinates (Adv. Theory Simul. 11/2024)

A New Perspective on the Homogeneous Coordinate System for Calculating Interatomic Distances and Their Derivatives in Terms of Internal Coordinates (Adv. Theory Simul. 11/2024)

Distribution of Australian dental practices in relation to residential aged care facilities: A geographic analysis.

Limited access to oral health services contributes to poor oral health in institutionalised older adults. The objective of this study was to map and analyse the distribution of residential age-care facilities (RACFs) in relation to dental practices across Australia. Age-care data were sourced from the Australian Institute of Health and Welfare. The data were categorised according to the Australian Bureau of Statistics remoteness index in each state and territory, defined by a geographic coordinate system. The structure of remoteness area data was integrated into RACF data using a geographic information system. Buffer analysis in QGIS was employed to calculate the buffer distance surrounding RACFs by identifying dental practices relative to a measuring distance. In total, Australia had 2718 RACFs and 7379 dental practices (both private 95.5% and public 4.5%). In all States, more than a third of metropolitan RACFs were within accessible reach of a private practice (ranging from 37% of RACFs in NSW to 55% in WA). However, proximity to public clinics was low, ranging from only 4% (WA) to 9% (QLD). More than one-fifth of metropolitan RACFs in NSW, QLD, WA and ACT (ranging from 20% to 24%) were not within accessible proximity of either a public or private dental clinic/practice. While more than 70% of RACFs in regional and remote Australia are reasonably close to dental practices, areas with inadequate access exist, with the highest percentage recorded in WA (6%). Ensuring an equitable distribution of dental practices relative to RACFs is crucial in bridging the service access gap in underserved areas.

Coupling of two helical circular waveguides.

Coupling between optical waveguides has always been an important topic. By using the finite element method (FEM) based on a helicoidal coordinate system, we present a detailed study of the couplings between two helical coupled circular waveguides, showing several important aspects that were not found in previous studies. Our numerical results show that for the two-fold rotationally symmetric cases, intersections will appear in the effective index curves of the two composite modes with increasing twist rate, and we have found that this is related to the different increases of the composite modes in the helical path and the emergence of high-order harmonics. Further, for the one-fold rotationally symmetric structures formed by the two waveguides with the same radical but different azimuthal positions, as the twist rate increases, we observe the emerging asymmetric modal distributions of the composite modes, indicating that couplings between the two waveguides are no longer equivalent.

Automated Posterior Scleral Topography Assessment for Enhanced Staphyloma Visualization and Quantification With Improved Maculopathy Correlation.

To quantitatively characterize the posterior morphology of high myopia eyes with posterior staphyloma. Surface points of the eyeball were automatically extracted from magnetic resonance imaging scans using deep learning. Subsequently, the topography of posterior staphylomas was constructed to facilitate accurate visualization and quantification of their location and severity. In the three-dimensional Cartesian coordinate system established with surface points, measurements of distances (D) from each point to the hypothetical pre-elongation eye center within the eyeball and local curvatures (C) at each point on the posterior sclera were computed. Using this data, specific parameters were formulated. The concordance of these parameters with traditional staphyloma classification methods and their association with myopic traction maculopathy (MTM) grades based on the ATN classifications were investigated. The study included 102 eyes from 52 participants. The measured parameters, particularly the variance of distance (Dvar) and the maximum value of the curvature and distance product (C · Dmax), demonstrated efficacy in differentiating various types of posterior staphyloma and exhibited strong correlations with the grades of MTM. The automated generation of the posterior scleral topography facilitated visualization and quantification of staphyloma location and severity. Simple geometric parameters can quantify staphyloma shape and correlate well with retinal complications. Future works on expanding these measures to more imaging modalities could improve their clinical use and deepen insights into the link between posterior staphyloma and related retinal diseases. This work has the potential to be translated into clinical practice, allowing for the accurate assessment of staphyloma severity and ultimately improving disease management.

Global Ionospheric Response During Extreme Geomagnetic Storm in May 2024

The main idea of the present study is to investigate in detail the time evolution of the spatial inhomogeneities connected with the ionospheric response to the geomagnetic storm registered in the period of 10–11 May 2024. The obtained ionospheric anomalies represented by the relative deviations of the global Total Electron Content (TEC) data have been utilized in the analysis. The used global TEC data have been converted to a coordinate system with a modip latitude and geographical longitude. In addition to the maps illustrating the global spatial distribution of the geomagnetically forced ionospheric anomalies, a presentation of the observed longitudinal structures by sinusoidal approximation has also been used. The resulting positive and negative responses have been studied depending on the magnetic latitude, local times and the behavior of the geomagnetic activity parameters during the considered event. The interpretation takes into account the known mechanisms for the effect of the geomagnetic storm on the electron density. A special attention is focused on the differences in the two hemispheres at high and mid latitudes, where a simultaneous direct impact of the particle precipitation and the change in the temperature regime of the neutral atmosphere has been assumed. The low-latitude response as a result of the Equatorial Ionization Anomaly (EIA) associated with Disturbed Dynamo Electric Fields (DDEFs) and its relationship with local time has also been considered.

Magnetosheath Plasma Flow and Its Response to IMF and Geodipole Tilt as Obtained From the Data‐Based Modeling

AbstractLarge‐scale patterns of the steady‐state magnetosheath plasma flow and their dependence on the interplanetary magnetic field (IMF) have been reconstructed for the first time on the basis of large multi‐year multi‐mission pool of spacecraft observations, concurrent interplanetary data, and an empirical high‐resolution model. The flow model architecture builds upon a recently developed magnetosheath magnetic field representation by flexible expansions of its toroidal and poloidal components in a coordinate system, naturally conformed with the magnetopause and bow shock shapes. The model includes two physics‐based flow symmetry modes: the first one treats the magnetosphere as an axisymmetric unmagnetized obstacle, whereas the second mode takes into account the geodipole tilt, an important factor in the reconnection effects. The spacecraft data pool includes 1‐min average data by Themis (2007–2024), Cluster (2001–2022), and MMS‐1 (2015–2024) missions, as well as OMNI interplanetary data. The model drivers include the solar wind particle flux, IMF components, and the geodipole tilt angle. The model calculations faithfully reproduce the average plasma flow geometry and substantial effects have been found of the IMF orientation and magnitude, a principal factor that defines electromagnetic forces inside the magnetosheath. A strong dependence of the magnetosheath flow patterns on the Earth's dipole tilt indicates an important contribution of reconnection effects at the magnetopause to the solar wind particle transport around the dayside magnetosphere.

PZS‐Net: Incorporating of Frame Sequence and Multi‐Scale Priors for Prostate Zonal Segmentation in Transrectal Ultrasound

Transrectal ultrasound (TRUS) videos offer valuable histopathologic information about the prostate. Accurate prostate zonal segmentation in TRUS videos is vital for diagnosing prostate cancer and guiding surgery. However, TRUS videos are manually recorded by urologists, resulting in no standardized coordinate system, which limits direct prostate zonal segmentation in these videos. To overcome the limitation, a novel Prostate Zonal Segmentation Network (PZS‐Net), based on U‐Net, which learns critical cross‐frame information and multi‐scale features from sequential frames, is proposed. First, a sequential frame cross‐attention (SFCA) module is designed to capture remote information from sequential frames to enhance the feature representation of the current frame. The SFCA module is embedded at each skip connection layer to extract crucial cross‐frame information. Then, a multi‐scale fusion (MSF) module that utilizes three parallel branches with different atrous convolutions is designed. The MSF module is placed at the bottleneck layer to dynamically fuse multi‐scale context information from high‐level features. Extensive experiments on TRUS image datasets show that the PZS‐Net achieves higher accuracy in both the transitional zone (dice coefficient [Dice]: 68.90% ± 1.73%, mean intersection over union [mIoU]: 59.19% ± 2.09%, 95% Hausdorff distance [HD95]: 5.02 ± 0.83 mm) and the peripheral zone (Dice: 63.99% ± 3.16%, mIoU: 54.60% ± 3.35%, HD95: 5.28 ± 1.12 mm) and demonstrates the effectiveness and competitiveness of its key components via comprehensive ablation studies.

Nonlinear evolution of vortical disturbances entrained in the entrance region of a circular pipe

The nonlinear evolution of free-stream vortical disturbances entrained in the entrance region of a circular pipe is investigated using asymptotic and numerical methods. Attention is focused on the low-frequency disturbances that induce streamwise elongated structures. A pair of vortical modes with opposite azimuthal wavenumbers is used to model the free-stream disturbances. Their amplitude is assumed to be intense enough for nonlinear interactions to occur inside the pipe. The formation and evolution of the perturbation flow are described by the nonlinear unsteady boundary-region equations in the cylindrical coordinate system, derived and solved herein for the first time. Matched asymptotic expansions are employed to construct appropriate initial conditions and the initial–boundary value problem is solved numerically by a marching procedure in the streamwise direction. Numerical results show the stabilising effect of nonlinearity on the intense algebraic growth of the disturbances and an increase of the wall-shear stress due to the nonlinear interactions. A parametric study is carried out to evince the effect of the Reynolds number, the streamwise and azimuthal wavelengths, and the radial length scale of the inlet disturbance on the nonlinear flow evolution. Elongated pipe-entrance nonlinear structures (EPENS) occupying the whole pipe cross-section are discovered. EPENS with $h$ -fold rotational symmetry comprise $h$ high-speed streaks positioned near the wall, and $h$ low-speed streaks centred around the pipe core. These distinct structures display a striking resemblance to nonlinear travelling waves found numerically and observed experimentally in fully developed pipe flow. Good agreement of our mean-flow and root mean square data with experimental measurements is obtained.