Coordinate System Research Articles

Global magnetic field properties in the solar wind interaction of Mercury from MESSENGER measurements

The space environment of Mercury is shaped by its proximity to the Sun and by the relatively weak planetary magnetic field, presenting a unique regime of plasmas and shock conditions. We present the global magnetic properties in Mercury's space environment based on more than 4 years of MESSENGER Magnetometer data. We used 20 Hz magnetic field data to examine the magnetic strength, the field configurations, and the fluctuations. We considered both compressional and transverse modes, with frequencies from 5 mHz to 10 Hz, which cover typical ultra-low frequency waves at Mercury. We identified regions of the solar wind, the magnetosheath, and the magnetosphere during over 4\,000 MESSENGER orbits. The solar wind and magnetosheath data were analysed in the solar wind interplanetary magnetic field (IMF) coordinate system, and the magnetosphere data were analysed in the aberrated Mercury solar magnetospheric coordinate system. Each data point was relocated into normalised space using averaged magnetopause and bow-shock models. The magnetic environments for a quasi-parallel and quasi-perpendicular IMF were compared. Under the typical Parker-spiral IMF, the magnetic environment of Mercury features strong fluctuations that are dominated by the transverse mode and stem from interactions at the bow shock and the magnetopause. When they are subjected to a quasi-perpendicular IMF, the magnetic fluctuations diminish, and the magnetic field strength becomes highly compressed throughout the bow shock, magnetosheath, and magnetosphere. Unlike Earth, Mercury exhibits weaker dawn-dusk asymmetries in magnetic field strength and lacks substantial magnetosheath-generated sources of magnetic fluctuations. The magnetic field draping pattern associated with the IMF cone angle at Mercury also differs from that at Earth. Our comparative analysis highlights the critical role of the solar wind Mach number, the radial IMF component, and the system scale size in shaping planetary space environments.

A simple approach to rotationally invariant machine learning of a vector quantity.

Unlike with the energy, which is a scalar property, machine learning (ML) prediction of vector or tensor properties poses the additional challenge of achieving proper invariance (covariance) with respect to molecular rotation. For the energy gradients needed in molecular dynamics (MD), this symmetry is automatically fulfilled when taking analytic derivative of the energy, which is a scalar invariant (using properly invariant molecular descriptors). However, if the properties cannot be obtained by differentiation, other appropriate methods should be applied to retain the covariance. Several approaches have been suggested to properly treat this issue. For nonadiabatic couplings and polarizabilities, for example, it was possible to construct virtual quantities from which the above tensorial properties are obtained by differentiation and thus guarantee the covariance. Another possible solution is to build the rotational equivariance into the design of a neural network employed in the model. Here, we propose a simpler alternative technique, which does not require construction of auxiliary properties or application of special equivariant ML techniques. We suggest a three-step approach, using the molecular tensor of inertia. In the first step, the molecule is rotated using the eigenvectors of this tensor to its principal axes. In the second step, the ML procedure predicts the vector property relative to this orientation, based on a training set where all vector properties were in this same coordinate system. As the third step, it remains to transform the ML estimate of the vector property back to the original orientation. This rotate-predict-rotate (RPR) procedure should thus guarantee proper covariance of a vector property and is trivially extensible also to tensors such as polarizability. The RPR procedure has an advantage that the accurate models can be trained very fast for thousands of molecular configurations, which might be beneficial where many training sets are required (e.g., in active learning). We have implemented the RPR technique, using the MLatom and Newton-X programs for ML and MD, and performed its assessment on the dipole moment along MD trajectories of 1,2-dichloroethane.

Global point cloud registration network for large transformations

Abstract Three-dimensional registration is an established yet challenging problem that is key in many different applications, such as mapping the environment for autonomous vehicles, or modeling people for avatar creation, among others. Registration refers to the process of mapping multiple data into the same coordinate system by means of matching correspondences and transformation estimation. Novel proposals exploit the benefits of deep learning architectures for this purpose, as they learn the best features for the data, providing better matches and hence results. However, the state of the art is usually focused on cases of relatively small transformations, although in certain applications and in a real and practical environment, large transformations are very common. In this paper, we present ReLaTo (Registration for Large Transformations), an architecture that addresses the cases where large transformations happen while maintaining good performance for local transformations. This proposal uses a novel Softmax pooling layer to find correspondences in a bilateral consensus manner between two point sets, sampling the most confident matches. These matches estimate a coarse and global registration using weighted Singular Value Decomposition (SVD). A target-guided denoising step is applied to both the obtained matches and latent features to estimate the final fine registration considering the local geometry. All these steps are carried out following an end-to-end approach, which has been shown to perform better than 7 state-of-the-art registration methods in two datasets commonly used for this task (ModelNet40 and the Karlsruhe Institute of Technology and Toyota Technological Institute dataset, KITTI), especially in the case of large transformations. Graphic abstract

Identification of Spin Bowling Deliveries with an Advanced Smart Cricket Ball

The type of throw of a spin bowler can be analysed in the laboratory using a motion analysis system. However, there is still no method to determine the type of throw using other means and less effort. To solve this problem, we revised the traditional classification of spin bowling throws and analysed whether spin bowling throws are separate entities or continuous concepts. We used an advanced smart cricket ball with high-speed gyroscopes to record the bowling actions and mathematically transformed the spin axis from the ball coordinate system (BCS) to the global coordinate system (GCS). We developed a visualisation method to map spin bowling throws from the yaw and pitch angles of the ball’s spin axis in the GCS. We compared the data from the smart ball with the data from the motion analysis system and profiled seven spin bowlers using the new method. The results of this study have shown that spin bowling throws are continuous concepts and that all differences between the two spin axis measurement methods were within 95% limits of agreement. The Smart Ball is sufficiently accurate to measure the direction of the ball’s spin axis in the GCS and is therefore well suited for profiling spin bowlers. Hybrid deliveries between sidespin, top/backspin, and swerve maximise the deviations of the ball in flight from the straight flight path in all three planes of the GCS. Hybrid throws between sidespin, top/backspin, and spin maximise the ball’s deviation from the straight trajectory in all three planes of the GCS.

Multi-season evaluation of hurricane analysis and forecast system (HAFS) quantitative precipitation forecasts

Quantitative precipitation forecasts (QPF) from numerical weather prediction models need systematic verification to enable rigorous assessment and informed use, as well as model improvements. The United States (US) National Oceanic and Atmospheric Administration (NOAA) recently made a major update to its regional tropical cyclone modeling capabilities, introducing two new operational configurations of the Hurricane Analysis and Forecast System (HAFS). NOAA performed multi-season retrospective forecasts using the HAFS configurations during the period that the Hurricane Weather and Forecasting (HWRF) model was operational, which was used to assess HAFS performance for key tropical cyclone forecast metrics. However, systematic QPF verification was not an integral part of the initial evaluation. The first systematic QPF evaluation of the operational HAFS version 1 configurations is presented here for the 2021 and 2022 season re-forecasts as well as the first HAFS operational season, 2023. A suite of techniques, tools, and metrics within the enhanced Model Evaluation Tools (METplus) software suite are used. This includes shifting forecasts to mitigate track errors, regridding model and observed fields to a storm relative coordinate system, as well as object oriented verification. The HAFS configurations have better performance than HWRF for equitable threat score (ETS), but larger over forecast biases than HWRF. Storm relative and object oriented verification show the HAFS configurations have larger precipitation areas and less intense precipitation near the TC center as compared to observations and HWRF. HAFS QPF performance decreased for the 2023 season, but the general spatial patterns of the model QPF were very similar to 2021-2022.

Regular F-manifolds with eventual identities

Abstract Given an F-manifold one may construct a dual multiplication (generalizing the idea of an almost-dual Frobenius manifold introduced by Dubrovin) using a so-called eventual identity, the definition of which ensures that the dual object is also an F-manifold. In this paper we solve the equations for an eventual identity for a regular (so non-semi-simple) F-manifold and construct a dual coordinate system in which dual multiplication is preserved. As an application, families of Nijenhuis operators are constructed.

Sea surface temperature error under tropical cyclone in the western North Pacific.

Tropical cyclone forecasting relies on accurate sea surface temperature, yet the errors in available sea surface temperature products remain unclear. Here, I evaluate the sea surface temperature errors under tropical cyclones in the western North Pacific based on surface drifters across eight widely-used datasets, including satellite, atmospheric and oceanic analysis-or-reanalysis products, spanning from 2014 to 2023. The ensemble mean bias and root-mean-squared-error are firstly quantified. Both satellite and oceanic analysis sea surface temperatures exhibit a cold bias, while atmospheric analysis-or-reanalysis sea surface temperature shows a warm bias. Specifically, atmospheric analysis-or-reanalysis products consistently show a warm bias in the right-rear quadrant of the tropical cyclone coordinate system. Regarding root-mean-squared-error, for most products, the right side consistently exhibits higher errors than the left side. SST bias significantly impacts tropical cyclone intensity change as indicated by empirical relationship. These results provide direct insights for operational tropical cyclone forecasting and research.

New Estimates of the Potential Schrödinger Equation

The Schrödinger equation, a fundamental construct in quantum mechanics, plays a pivotal role in understanding the properties and behaviors of quantum systems across various scientific fields, including but not limited to physics, economics, and geophysics. This research paper delves into the exploration of novel invariants associated with the Schrödinger equation, uncovering previously unrecognized symmetries and properties that open new pathways for theoretical and applied scientific exploration. The investigation reveals that the energy of bound states remains invariant under transformations of the coordinate system, highlighting a universal symmetry embedded within the equation. This discovery, coupled with an analysis of the variation in scattering amplitudes’ phase with different coordinate systems, not only enriches the theoretical framework of quantum mechanics but also has significant practical implications across various domains such as fluid dynamics, material science, and medical imaging. Furthermore, by applying the principles of the Poincaré-Riemann-Hilbert boundary-value problem, the study offers a novel approach to estimate potentials within the Schrödinger equation, advancing the three-dimensional inverse problem of quantum scattering theory. This methodological innovation allows for a more profound understanding of the unitary scattering operator, facilitating enhanced modeling of complex systems and phenomena. The implications of these findings extend beyond theoretical physics, offering transformative insights and applications in areas ranging from fluid dynamics, where it aids in refining models for the Navier-Stokes equations, to seismic exploration, tomography, and ultrasound imaging, where it enhances phase selection and interpretation of measurement results. In essence, this research not only contributes to a deeper understanding of the Schrödinger equation’s fundamental properties but also paves the way for interdisciplinary advancements, demonstrating the profound impact of theoretical discoveries on practical applications in diverse scientific and technological domains.

Robust Multimodal Image Matching Based on Radiation Invariant Phase Correlation

Abstract. Due to the influence of nonlinear radiation distortion and geometric deformation, achieving multimodal image matching remains a challenging task. To address these issues, this paper proposes a method called radiation invariant phase correlation (RIPC) to simultaneously estimate the rotation, scale, and displacement changes of multimodal image pairs. Firstly, based on the local structure characteristics of the image itself, we harness the nonlinear invariance of kernel canonical correlation analysis to devise the multimodal local self-correlation (MLSC) descriptor. This descriptor is resilient to nonlinear radiative differences, as well as local rotation and scale variations. Subsequently, we incorporate the log-polar coordinate transformation to capture the overall rotation and scale changes in the image, enabling independent representation of these factors on the Cartesian coordinate system. Finally, drawing upon the continuity of displacement estimation, as well as rotation and scale estimation, we construct a five-dimensional descriptor tailored for phase correlation. Extensive experiments conducted on five open-source datasets demonstrate that our proposed method surpasses state-of-the-art (SOTA) techniques in matching performance. Furthermore, our RIPC method achieves matching accuracy within 2-pixel threshold, which underscores its effectiveness in multimodal remote sensing image matching.

A high-precision two-parameter road roughness grading and identification methodology across multiple frequency intervals

Based on a dual track road shape meter, various road roughness was measured. It was discovered that the road grading method in ISO 8608 assumes a constant waviness value of W = 2 with a one-straight line approximation, but it could not accurately fit and grade the measured road roughness. A high-precision piecewise fitting function for the low-frequency and high-frequency parts of the road roughness power spectral density (PSD) is established. A high-precision two-parameter grade method in multiple frequency bands for road roughness is proposed ( G q( n0), the geometric average of the road roughness index at n0, W, the waviness, is the slope of the road roughness PSD fitting expression in the double logarithmic coordinate system). According to the vehicle driving performance obtained by simulation, the grading method is verified. For Paved and Undulating roads, compared to the road roughness classification method in ISO 8608, the performance simulated based on the grade results of the two parameters grading method are closer to the performance simulated based on the measured road roughness. The grading method proposed in this paper can more accurately fit and classify the measured road roughness. The influence of these parameters at each frequency interval on vehicle driving performance is studied. A two-parameter identification method for road roughness PSD at variable intervals over a large frequency range is proposed. In the double logarithmic coordinate system, this method divides the selected spatial frequency into three sub-intervals along the abscissa, in each sub-interval, the parameters G q( n0) and W are identified separately. This method can provide effective control inputs for the vehicle’s active or semi-active suspension system.

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.

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.

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.

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.