Average Distance Research Articles

Optimization of three-dimensional esophageal tumor ablation by simultaneous functioning of multiple electrodes.

Radiofrequency ablation is a widely accepted minimal-invasive and effective local treatment for tumors. However, its current application in esophageal cancer treatment is limited to targeting thin and superficial lesions, such as Barrett's Esophagus. This study proposes an optimization method using multiple electrodes simultaneously to regulate the temperature field and achieve conformal ablation of tumors. A particle swarm optimization algorithm, coupled with a three-dimensional thermal ablation model, was developed to optimize the status of the functioning electrodes, the optimal voltage (Vopt), and treatment duration (ttre) for targeted esophageal tumors. This approach takes into account both the electrical and thermal interactions of the electrodes. The results indicate that for esophageal cancers at various stages, with thickness (c) ranging from 4.5mm to 10.0mm, major axis (a) ranging from 7.3mm to 27.3mm, and minor axis (b) equaling 7.3mm or 27.3mm, as well as non-symmetrical geometries, complete tumor coverage (over 99.5%) close to conformal can be achieved. This method illustrates possible precise conformal ablation of esophageal cancers and it may also be used for conformal treatments of other intraluminal lesions.

Complexity and weak integration promote the diversity of reef fish oral jaws

Major trade-offs often manifest as axes of diversity in organismal functional systems. Overarching trade-offs may result in high trait integration and restrict the trajectory of diversification to be along a single axis. Here, we explore the diversification of the feeding mechanism in coral reef fishes to establish the role of trade-offs and complexity in a spectacular ecological radiation. We show that the primary axis of variation in the measured musculo-skeletal traits is aligned with a trade-off between mobility and force transmission, spanning species that capture prey with suction and those that bite attached prey. We found weak or no covariation between about half the traits, reflecting deviations from the trade-off axis. The dramatic trophic range found among reef fishes occurs along the primary trade-off axis, with numerous departures that use a mosaic of trait combinations to adapt the feeding mechanism to diverse challenges. We suggest that morphological evolution both along and independent of a major axis of variation is a widespread mechanism of diversification in complex systems where a global trade-off shapes major patterns of diversity. Significant additional diversity emerges as systems use weak integration and complexity to assemble functional units with many trait combinations that meet varying ecological demands.

Precipitation in the mountains of Central Asia: isotopic composition and source regions

Abstract. Over 900 event-based precipitation samples were collected in 2019–2021 in the Tien Shan and its foothills and analysed using cavity ring-down spectroscopy. δD and δ18O values were highest in summer and lowest in winter, and annual cycles of deuterium excess (d-excess) varied between sites, reflecting local conditions. The δ18O and δD values increased from north to south in all seasons except autumn, and latitude was a statistically significant predictor of δ18O and δD in the overall data set, along with elevation in winter and elevation and longitude in autumn. Elevation was a significant predictor of d-excess in all seasons, and local air temperature was a more important control over δ18O and δD than precipitation depth. Local meteoric water lines were derived using seven regression methods applied to non-weighted and weighted precipitation. Non-weighted ordinary least squares regression and reduced major axis regression methods are recommended overall, except for summer when the precipitation-weighted least squares regression should be used, particularly in the south. Atmospheric back-trajectory and mixing-model analyses were applied in combination to identify air mass source regions and their relative contribution to precipitation. Recycled moisture from irrigated land in the Amu Darya and Syr Darya basins and from the study catchments accounted for 29 %–71 % of precipitation, depending on the site and season. In the Chon Kyzyl-Suu catchment, local re-evaporation from Issyk-Kul accounted for up to 85 % of precipitation. These findings highlight the importance of moisture from terrestrial sources, especially irrigated land, for the formation of precipitation in the Tien Shan.

Dynamics of Binary Planets within Star Clusters

We develop analytical tools and perform three-body simulations to investigate the orbital evolution and dynamical stability of binary planets within star clusters. Our analytical results show that the orbital stability of a planetary-mass binary against passing stars is mainly related to its orbital period. Critical flybys, defined as stellar encounters with energy kicks comparable to the binary binding energy, can efficiently produce a wide range of semimajor axes (a) and eccentricities (e) from a dominant population of primordially tight Jupiter-mass binary objects (JuMBOs). The critical flyby criterion we derived offers an improvement over the commonly used tidal radius criterion, particularly in high-speed stellar encounters. Applying our results to the recently discovered JuMBOs by the James Webb Space Telescope (JWST), our simulations suggest that to match the observed ∼9% wide binary fraction, an initial semimajor axis of a 0 ∼ 10–20 au and a density-weighted residence time of χ ≳ 104 Myr pc−3 are favored. These results imply that the JWST JuMBOs probably formed as tight binaries near the cluster core.

AGN feeding along a one-armed spiral in NGC 4593

Context. We investigate active galactic nuclei (AGN) feeding through the molecular gas (CO(2−1) emission) properties of the local Seyfert 1 galaxy NGC 4593, using Atacama Large Millimeter Array (ALMA) observations and other multi-wavelength data. Aims. Our study aims to understand the interplay between the AGN and the interstellar medium (ISM) in this galaxy, examining the role of the AGN in steering gas dynamics within its host galaxy, evaluating the energy injected into the ISM, and determining whether gas is inflowing or outflowing from the galaxy. Methods. After reducing the ALMA CO(2−1) images, we employed two models, 3D-BAROLO and DISCFIT, to construct a disc model and fit its emission to the ALMA data. Additionally, we used photometric data to build a spectral energy distribution (SED) and apply the CIGALE code to derive key physical properties of the AGN and its host. Results. Our analysis reveals a complex interplay within NGC 4593, including a clear rotational pattern, the influence of a non-axisymmetric bar potential, and a central molecular zone (CMZ)-like ring. We observe an outflow of CO(2−1) gas along the minor axis, at a distance of ∼220 pc from the nucleus. The total molecular gas mass is estimated to be 1 − 5 × 108 M⊙, with non-circular motions contributing 10%. Our SED analysis indicates an AGN fraction of 0.88 and a star formation rate (SFR) of 0.42 M⊙ yr−1. Conclusions. These findings highlight the complex dynamics in the centre of NGC 4593, which are significantly influenced by the presence of the AGN. The overall physical properties of this system suggest that the AGN has a substantial impact on the evolution of NGC 4593.

The eyestalk photophore of Northern krill Meganyctiphanes norvegica (M. Sars) (Euphausiacea) re-investigated: Innervation by specialized ommatidia of the compound eye

Members of the Euphausiacea (“krill”) generate bioluminescence using light organs, the so-called photophores, including one pair associated with the eyestalks, two pairs on the thoracic segments, and four unpaired photophores on the pleon. The photophores generate light via a luciferin–luciferase type of biochemical reaction in light-emitting cells comprised in a photophore compartment called “lantern”. The behavioral significance of bioluminescence in krill is discussed controversially, and possible functions include a defensive function, camouflage by counter-shading, and intra-specific communication. Light production of all krill photophores is controlled by hormonal and neuronal pathways but our knowledge about the nature of these pathways is still rudimentary. Here, we provide a detailed description of the eyestalk photophore's histology in Northern krill Meganyctiphanes norvegica, and used immunohistochemistry combined with confocal laser-scan microscopy to explore this organ's serotonergic innervation. Furthermore, we provide evidence that the photophore is innervated by a distinct photophore nerve that originates from a specialized cluster of ca. 30 highly modified ommatidia at the dorsal rim of the compound eye that are optically isolated from the other ommatidia. Our findings suggest the compound eye – photophore link as a major anatomical axis to adjust the photophore activity.

Binary Disruption and Ejected Stars from Hierarchical Star Cluster Assembly

We simulate mergers between star clusters embedded within their natal giant molecular cloud. We extract initial conditions from cloud-scale simulations of cluster formation and introduce different prescriptions for primordial binaries. We find that simulations that do not include primordial binaries result in a larger fraction of unbound stars than simulations that include a prescription for binaries based on observations. We also find a preferred direction of motion for stars that become unbound during the merger. Subcluster mergers within realistic gas environments promote binary disruption, while mergers between idealized, gas-rich spherical clusters do not produce the same disruption. Binary systems with smaller semimajor axes are disrupted in simulations of subcluster mergers within their natal environment compared to simulations that do not include the realistic gas environment. We conclude that binary disruption and the production of an anisotropic distribution of unbound stars are the natural consequences of subcluster mergers during star cluster assembly.

Anisotropic Specular Image‐Based Lighting Based on BRDF Major Axis Sampling

AbstractAnisotropic specular appearances are ubiquitous in the environment: brushed stainless steel pans, kettles, elevator walls, fur, or scratched plastics. Real‐time rendering of these materials with image‐based lighting is challenging due to the complex shape of the bidirectional reflectance distribution function (BRDF). We propose an anisotropic specular image‐based lighting method that can serve as a drop‐in replacement for the standard bent normal technique [Rev11]. Our method yields more realistic results with a 50% increase in computation time of the previous technique, using the same high dynamic range (HDR) preintegrated environment image. We use several environment samples positioned along the major axis of the specular microfacet BRDF. We derive an analytic formula to determine the two closest and two farthest points from the reflected direction on an approximation of the BRDF confidence region boundary. The two farthest points define the BRDF major axis, while the two closest points are used to approximate the BRDF width. The environment level of detail is derived from the BRDF width and the distance between the samples. We extensively compare our method with the bent normal technique and the ground truth using the GGX specular BRDF.

Empirical Stability Criteria for 3D Hierarchical Triple Systems. I. Circumbinary Planets

In this work we revisit the problem of the dynamical stability of hierarchical triple systems with applications to circumbinary planetary orbits. We derive critical semimajor axes based on simulating and analyzing the dynamical behavior of 3 × 108 binary star–planet configurations. For the first time, three-dimensional and eccentric planetary orbits are considered. We explore systems with a variety of binary and planetary mass ratios, binary and planetary eccentricities from 0 to 0.9, and orbital mutual inclinations ranging from 0° to 180°. Planetary masses range between the size of Mercury and the lower fusion boundary (approximately 13 Jupiter masses). The stability of each system is monitored over 106 planetary orbital periods. We provide empirical expressions in the form of multidimensional, parameterized fits for two borders that separate dynamically stable, unstable, and mixed zones. In addition, we offer a machine learning model trained on our data set as an alternative tool for predicting the stability of circumbinary planets. Both the empirical fits and the machine learning model are tested for their predictive capabilities against randomly generated circumbinary systems with very good results. The empirical formulae are also applied to the Kepler and TESS circumbinary systems, confirming that many planets orbit their host stars close to the stability limit of those systems. Finally, we present a REST application programming interface with a web-based application for convenient access to our simulation data set.

Post-Fire Stability Bearing Capacity of I-Shaped Aluminum Alloy Members Under Axial Compression

Compared to steel structures, aluminum alloy structures are more susceptible to fire damage. Accurately evaluating the residual bearing capacity of fire-damaged aluminum alloy members is crucial for effective post-disaster management. Therefore, this paper investigates the post-fire bearing capacity of I-shaped aluminum alloy members under axial compression. First, a post-fire test on 16 I-shaped aluminum alloy members under axial compression was carried out. The test results indicate that all specimens fail by the minor axis flexural buckling, and the bearing capacity of the specimens decreases with the increase of the slenderness ratio. Moreover, a trilinear relationship is found between bearing capacity and post-fire temperatures. Second, finite element (FE) models are established using ABAQUS and validated against the test results. Subsequently, numerical analysis is carried out, considering various aluminum alloy brands, post-fire temperatures, slenderness ratios, initial geometrical imperfections, and cross-section dimensions. Through the statistical regression technology and the introduction of strength and stability-bearing capacity reduction coefficients, the formulae for estimating the post-fire stability-bearing capacity of I-shaped aluminum alloy members under axial compression are derived. Finally, the proposed formulae are verified to be accurate through error analysis.

3D modelling-based left atrium geometry analysis to predict atrial fibrillation in patients with cryptogenic stroke

Abstract Introduction Atrial fibrillation (AF) is a high prevalence condition associated with high morbidity and mortality. Its early diagnosis allows to initiate several prophylactic treatments that have proved to improve its prognosis. 3D modeling techniques allow to design accurate representations of cardiac cavities from diverse source images. Purpose We evaluated the association between new geometrical measurements obtained by 3D echocardiographic models of the left atrium (LA) and the presence of underlying paroxysmal AF in patients with cryptogenic stroke (CS). Methods 3D LA volumes from a sample of consecutive patients aged ≥60 years old and admitted to our Stroke Unit with the diagnosis of CS from April 2019 to November 2020 were analyzed. 15 days ECG monitoring was performed after discharge to detect underlying paroxysmal AF. All 3D echo volumes were analyzed by a 3D modeling open-source application. From this analysis several LA geometry parameters were obtained: sphericity, elongation, flatness, major axis length, minor axis length, maximum 2D diameter (max2Ddiam) and surface-volume ratio (S/V). Functional atrial parameters (3D left atrial ejection fraction, LAEF) were also determined. Results 36 patients were analyzed. Mean age was 78 ± 7 years old. 19% were diabetic, 58% had high blood pressure and 14% of patients had history of ischemic cardiomyopathy. Mean body-mass index was 26. These baseline characteristics were equally distributed between groups. Baseline proBNP was significantly higher in patients developing atrial fibrillation (949 vs 275 pg/mL; p= 0,014.). Maximum 2D diameter (max2Ddiam) and Surface-volume ratio (S/V) were the best predictors of AF (AUC of ROC curves: 0.69; 0.49 – 0.88 and 0.63; 0.42 – 0.84, respectively). An optimal cut-off point of 39 mm was selected for max2Ddiam and of 0.20 for S/V. These values were included in a multivariate model adjusted by baseline proBNP. A Max2Ddiam <39 mm and a S/V ≥0.20 were both significantly associated with the presence of paroxysmal AF (OR 6.96; p= 0.048 and OR 12.22; p = 0.043, respectively). Conclusions New geometrical atrial parameters can be obtained from echo 3D models and might be able to predict AF in patients with CS. Further analysis and larger samples are required to better understand these findings.TableFigure

Predictive factors for recurrent tricuspid regurgitation after tricuspid annuloplasty: 3D echocardiography study

Abstract Introduction There is growing concern about the recurrence of tricuspid regurgitation (TR) after tricuspid annuloplasty (TA) in individuals with functional tricuspid regurgitation (FTR). While TA is effective in treating FTR, a comprehensive understanding of the echocardiographic factors influencing TR recurrence is crucial. Aim This study aims to employ multivariate regression analysis to investigate the prognostic significance of tricuspid valve (TV) geometry and echocardiographic parameters associated with both RV geometry and function. The focus is on comprehending these relationships in the context of recurrent TR subsequent to TA. Methods This prospective observational cohort study aimed to explore factors contributing to recurrent tricuspid regurgitation (TR) after tricuspid annuloplasty (TA). The focus was on patients with moderate or severe functional TR due to left heart valvular disease, particularly severe mitral regurgitation, excluding those with ischemic heart disease. The cohort included 66 individuals undergoing preoperative assessments with 2D and 3D echocardiography, quantifying RV and right atrial (RA) geometry, functional, and tricuspid valve (TV) parameters. TR severity followed ESC guidelines. Patients were categorized into effective TA (50 patients) and recurrent TR (16 patients) groups, defined by mild-moderate TR and significant moderate-severe TR one year post-surgery, respectively. SPSS software facilitated statistical analysis, with adjusted logistic regression considering parameters such as age and gender. Results Among the patients (54% male, mean age 68±9 years), no significant differences were found in gender, left ventricular and atrial parameters, or preoperative TV orifice area between groups (recurrent TR vs. effective TA: 38 [33] mm2 vs. 29 [15] mm2, p=0.117). Univariate logistic regression analysis identified Septal-Lateral Systolic TA Diameter (OR 1.62), Septal-Lateral Diastolic TA Diameter (OR 1.99), and Major Axis Diastolic TA Diameter (OR 1.59) as key predictors. For diagnostic efficacy, ROC analysis revealed Major Axis Diastolic TA Diameter (AUC 0.848; cut-off 52.5 mm), TV Leaflet Tenting Volume (AUC 0.778; cut-off 5.1 ml), and RV Basal Diameter (AUC 0.763; cut-off 47.5 mm) as the most predictive parameters. The combined use of predefined RV basal diameter and Major Axis Diastolic TA Diameter showed the highest odds ratio for recurrent TR. Conclusion Key predictors, including Septal-Lateral Systolic and Diastolic TA Diameters, and Major Axis Diastolic TA Diameter, were identified, emphasizing their significance in understanding TR recurrence after tricuspid annuloplasty. The combination of predefined RV basal diameter and Major Axis Diastolic TA Diameter showed the highest odds ratio for recurrent TR, offering valuable insights for clinical assessment and preventive strategies.

Lyman Limit System with O vi in the Circumgalactic Environment of a Pair of Galaxies

We report on the analysis of a multiphase Lyman limit system (LLS) at z = 0.39047 identified toward the background quasar FBQS J0209–0438. The O VI doublet lines associated with this absorber have a different profile from the low-ionization metals and H i. Ly α has a very broad H i (b ≈ 150 km s−1) component well-aligned with one of the O VI components. The Doppler b-parameters for the broad H i and O VI indicate gas with T = (0.8 − 2.0) × 106 K and a total hydrogen column density that is an order of magnitude larger than the cooler phase of gas responsible for the LLS. Observations by the Very Large Telescope MUSE show two moderately star-forming galaxies within ρ ≲ 105 kpc and ∣Δv∣ ≲ 130 km s−1 of the absorber, one of them a dwarf galaxy (M * ≈ 106 M ⊙) overlapping with the quasar point-spread function, and the other a larger galaxy (R 1/2 ≈ 4 kpc) with M * ≈ 3 × 1010 M ⊙ and M h ≈ 7 × 1011 M ⊙, and the dwarf galaxy within its virial radius. Although the absorption is aligned with the extended major axis of the larger galaxy, the line-of-sight velocity of the absorbing gas is inconsistent with corotating accretion. The metallicity inferred for the LLS is lower than the gas phase [O/H] of the two galaxies. The mixture of cool and warm/hot gas phases for the absorbing gas and its proximity and orientation to the galaxy pair points to the LLS being a high-velocity gas in the combined halo environment of both galaxies.

An Edge-on Regular Disk Galaxy at z = 5.289

While rotation-supported gas disks are known to exist as early as at z ≈ 7, it is still a general belief that stellar disks form late in the Universe. This picture is now being challenged by the observations from the James Webb Space Telescope (JWST), which have revealed a large number of disk-like galaxies that could be at z > 3, with some being candidates at z > 7. As an early formation of stellar disks will greatly impact our theory of galaxy formation and evolution, it is important to determine when such systems first emerged. Here we present D-CEERS-RUBIES-z5289 at z = 5.289 ± 0.001, the second confirmed stellar disk at z > 5, discovered using the archival JWST NIRCam imaging and NIRSpec spectroscopic data. This galaxy has a highly regular edge-on disk morphology, extends to ∼6.2 kpc along its major axis, and has an effective radius of ∼1.3–1.4 kpc. Such a large stellar disk is yet to be produced in numerical simulations. By analyzing its 10-band spectral energy distribution using four different tools, we find that it has a high stellar mass of 109.5–10.0 M ⊙. Its age is in the range of 330–510 Myr, and it has a mild star formation rate of 10–30 M ⊙ yr−1. While the current spectroscopic data do not allow the derivation of its rotation curve, the width of its Hα line from the partial slit coverage on one side of the disk reaches ∼345 km s−1, which suggests that it could have a significant contribution from rotation.

Investigation of ablation threshold and microchannel fabrication on stainless steel using ultrafast laser

ABSTRACT Ultrafast laser processing is a highly versatile tool for creating microscale structures in many materials. The ablation and micromachining characteristics of AISI 304 stainless steel were examined using a femtosecond-pulsed laser. Parameters such as power, scanning speed, transverse overlap, scanning strategies, and shielding gases were systematically varied. The ablation threshold fluence for SS 304 was calculated as 0.16 J/cm2. Two ablation regimes were observed: the gentle regime, where smooth crater walls were formed under low pulse energy (below 20 µJ), and the strong regime, characterized by rough walls created under high pulse energy (above 20 µJ). The optimal parameters for fabricating microchannels on SS 304 surfaces comprised a laser power of 100 mW, a scanning speed of 30 mm/s, a line-to-line distance of 5 µm, and a parallel scan strategy along the major axis. This study provides a practical approach for enhancing the microchannel fabrication process on stainless steel.

Revisiting the Period Change and Frequency Analysis of a Variable Star SZ Lyncis

This study aims to investigate the period change of the variable star SZ Lyncis. The observations were conducted at the Regional Observatory for the Public, Nakhon Ratchasima (ROP-NMA), operated by the National Astronomical Research Institute of Thailand (NARIT), on January 8th-9th and February 19th-20th 2024. The data was acquired using the CCD camera with a B-filter mount on the 0.7-m reflecting telescope. We report the period change of 1.37(±0.08)´10-12 day cycle-1. Analysis of the O-C diagram revealed the presence of a binary companion with a semi-amplitude of 0.0052(±0.0002) days, the projected semi-major axis of 0.90(±0.04) AU, the eccentricity of 0.25(±0.09), and the orbital period of 1184.1(±1.5) days and the mass function of 0.07(±0.01) M⨀. We also identified the time-series light curve data using the Discrete Fourier transform (DFT) in the Period04 package and obtained results of four frequencies. The main frequency of 8.29630(±0.00002) cycle day-1 corresponds to a period of 0.1205357(±0.0000003) days. These results contribute to our understanding of the pulsation properties of SZ Lyncis and its binary system.

Estimating the Orbital Parameters of a Nanosatellite When Measuring the Total Electron Content in the Ionosphere Based on the Retransmission of GPS Navigation Signals

A method for estimating the orbital parameters of a nanosatellite-relay, implemented by measuring the total electron content in the ionosphere based on relaying GPS navigation signals at frequencies of 150/400 MHz, is substantiated. The method involves estimating the Cartesian coordinates of the nanosatellite-relay based on the results of measurements of the total ranges “navigation satellite – nanosatellite relay – ground receiving point”, obtaining estimates of the orbital plane inclination angle and the longitude of the ascending node using the least squares method, and estimating the remaining orbital parameters using the maximum likelihood method. Simulation results and accuracy characteristics of the proposed method are presented. It is shown that for a typical signal-to-noise ratio in the equipment of the receiving point and an observation time of the nanosatellite-relay of 600–800 s, the mean square errors in estimating the orbital parameters of the nanosatellite-relay are: for angular quantities – fractions of arc seconds, the semi-major axis of the ellipse – 4–5 m, eccentricity – 2–3 ppm.

The disc origin of the Milky Way bulg. The high velocity dispersion of metal-rich stars at low latitudes

Previous studies of the chemo-kinematic properties of stars in the Galactic bulge have revealed a puzzling trend. Along the bulge minor axis, and close to the Galactic plane, metal-rich stars display a higher line-of-sight velocity dispersion compared to metal-poor stars, while at higher latitudes metal-rich stars have lower velocity dispersions than metal-poor stars, similar to what is found in the Galactic disc. In this work, we re-examine this issue, by studying the dependence of line-of-sight velocity dispersions on metallicity and latitude in APOGEE Data Release 17, confirming the results of previous works. We then analyse an $N$-body simulation of a Milky Way-like galaxy, also taking into account observational biases introduced by the APOGEE selection function. We show that the inversion in the line-of-sight velocity dispersion-latitude relation observed in the Galactic bulge -- where the velocity dispersion of metal-rich stars becomes greater than that of metal-poor stars as latitude decreases -- can be reproduced by our model. We show that this inversion is a natural consequence of a scenario in which the bulge is a boxy or peanut-shaped structure, whose metal-rich and metal-poor stars mainly originate from the thin and thick disc of the Milky Way, respectively. Due to their cold kinematics, metal-rich, thin disc stars are efficiently trapped in the boxy, peanut-shaped bulge, and at low latitudes show a strong barred morphology, which -- given the bar orientation with respect to the Sun-Galactic centre direction -- results in high velocity dispersions that are larger than those attained by the metal-poor populations. Extremely metal-rich stars in the Galactic bulge, which have received renewed attention in the literature, do follow the same trends as those of the metal-rich populations. The line-of-sight velocity-latitude relation observed in the Galactic bulge for metal-poor and metal-rich stars are thus both an effect of the intrinsic nature of the Galactic bulge (i.e. mostly secular) and of the angle at which we observe it from the Sun.

Equilibrium dynamical models in the inner region of the Large Magellanic Cloud based on Gaia DR3 kinematics

The Large Magellanic Cloud (LMC) contains complex dynamics driven by both internal and external processes. The external forces are due to tidal interactions with the Small Magellanic Cloud and the Milky Way, while internally its dynamics mainly depend on the stellar, gas, and dark matter mass distributions. Despite this complexity, simple physical models often provide valuable insights into the primary driving factors. We used Gaia Data Release 3 (DR3) to explore how well equilibrium dynamical models based on the Jeans equations and the Schwarzschild orbit superposition method are able to describe the LMC's five-dimensional phase-space distribution and line-of-sight (LOS) velocity distribution, respectively. In the Schwarzschild model, we incorporated a triaxial bar component for the first time and derived the LMC's bar pattern speed. We fit comprehensive Jeans dynamical models to all Gaia DR3 stars with proper motion and LOS velocity measurements found in the footprint of the VISTA near-infrared survey of the Magellanic System using a discrete maximum likelihood approach. These models are very efficient at discriminating genuine LMC member stars from Milky Way foreground stars and background galaxies. They constrain the shape, orientation, and enclosed mass of the galaxy under the assumption of axisymmetry. We used the Jeans model results as a stepping stone to more complex two-component Schwarzschild models, which include an axisymmetric disc and a co-centric triaxial bar, which we fit to the LMC Gaia DR3 LOS velocity field using a $ minimisation approach. The Jeans models describe the rotation and velocity dispersion of the LMC disc well, and we find an inclination angle of $ circ circ $, line of nodes orientation of $ circ circ $, and an intrinsic thickness of the disc of $q_0^d = b a (minor to major axis ratio). However, bound to axisymmetry, these models fail to properly describe the kinematics in the central region of the galaxy dominated by the LMC bar. We used the derived disc orientation and the Gaia DR3 density image of the LMC to obtain the intrinsic shape of the bar. Using these two components as input to our Schwarzschild models, we performed orbit integration and weighting in a rotating reference frame fixed to the bar, deriving an independent measurement of the LMC bar pattern speed of $ Both the Jeans and Schwarzschild models predict the same enclosed mass distribution within a radius of $6.2$\,kpc of $ Msun.

A novel approach to solving Euler’s nonlinear equations for a 3DOF dynamical motion of a rigid body under gyrostatic and constant torques

This research focuses on approaching a new technique to solve the rotary movement of a three degrees-of-freedom (DOF) semi-symmetric rigid body (RB) affected by a gyrostatic torque (GT) and under the influence of the RB’s constant-fixed torques (RBCFTs). The governing nonlinear differential equations (NDEs) for the RB are derived from the famous Euler’s equations, along with another system to calculate Euler’s angles, which gives an accurate solution for the RB’s position during its motion. In the case of a semi-symmetric body about its minor axis, novel analytical solutions for the RB’s angular velocities are presented in addition to the solutions of Euler’s angles. Our procedure to obtain these solutions arises through decoupling the governing NDEs into two coupled DEs, and the averaged time parameter is used. General solutions of the later DEs are presented in view of series expansions. The impact of the internal and external torques on the body’s motion is graphically simulated, which gives an overview of the periodicity of the derived solution and the effect of various values of these torques on the solution. Moreover, these simulations present other prospects for the body’s stability by analyzing them using the famous Lyapunov function. The importance of this study arises from its wide applications in our lives in many fields, such as mathematics and physics. It also holds immense potential for enhancing mechanical systems, elucidating celestial motion, and enhancing spacecraft efficiency.