Circular Curves Research Articles

Assessing the robustness of the Galactic rotation curve inferred from the Jeans equations using Gaia DR3 and cosmological simulations

Several authors have recently applied Jeans modelling to -based datasets to infer the circular velocity curve for the Milky Way. These works have consistently found evidence for a continuous decline in the rotation curve beyond $ kpc $, which may indicate the existence of a light dark matter (DM) halo. Using a large sample of Gaia DR3 data, we aim to derive the rotation curve of the Milky Way using the Jeans equations, and to quantify the role of systematic effects, both in the data and those inherent to the Jeans methodology under the assumptions of axisymmetry and time independence. We used data from the Gaia DR3 radial velocity spectrometer sample, supplemented with distances inferred through Bayesian frameworks, to determine the radial variation of the second moments of the velocity distribution for stars close to the Galactic plane. We used these profiles to determine the rotation curve using the Jeans equations under the assumption of axisymmetry and explored how they vary with azimuth and position above and below the plane of the Galactic disc. We applied the same methodology to an N-body simulation of a Milky Way-like galaxy impacted by a satellite akin the Sagittarius dwarf, and to the Auriga suite of cosmological simulations. The circular velocity curve we infer for the Milky Way is consistent with previous findings out to $ 15$ kpc, where our statistics are robust. Due to the larger number of stars in our sample, we are able to reveal evidence of disequilibrium and deviations from axisymmetry closer in. For example, we find that the second moment of $V_R$ flattens out at $R kpc, and that the second moment of $V_ is different above and below the plane for $R kpc. Our exploration of the simulations indicates that these features are typical of galaxies that have been perturbed by external satellites. From the simulations, we also estimate that the difference between the true circular velocity curve and that inferred from Jeans equations can be as high as $15<!PCT!>$, but that it is likely of the order of $10<!PCT!>$ for the Milky Way. This is higher than the systematic uncertainties associated with the observations or those linked to most modelling assumptions when using the Jeans equations. However, if the density of the tracer population were truncated at large radii instead of being exponential as often assumed, this could lead to the erroneous conclusion of a steeply declining rotation curve. We find that steady-state axisymmetric Jeans modelling becomes less robust at large radii, indicating that particular caution must be exercised when interpreting the rotation curve inferred in those regions. A more careful and sophisticated approach may be necessary for precision measurements of the DM content of our Galaxy.

Indefinitely flat rotation curves from Mpc sized charged cocoons

Abstract Weak lensing exhibits that rotation curves of isolated galaxies remain flat up to Mpc scale (Mistele et al, 2024). Recently we proposed that dark matter is a combination of electrostatic and vacuum energy in standard physics. In this theory, isolated galaxies may be embedded in ``charged cocoons'', spheres with $\pm 1/r^2$ charge density. The related circular rotation curves decay at the Mpc scale. The analytic solution is extended to the early Universe. A peak in the cosmic microwave background spectrum is expected at the arcsec scale. The induced nanometer size of the cocoons at the Big Bang makes the initial state inhomogeneous.

Причины возникновения и развития дефектов рельсов в кривых на участках обращения поездов повышенной массы и длины

Purpose: determine the causes of defects in rails in areas of circulation of trains of increased weight and length through modeling the operation of rails in curved sections of the railway track using digital twins. Methods: t study the influence of various factors on rail wear in curved sections of the track, software systems were used ased on the numerical solution of differential equations for the movement of rolling stock and the operation of the railway track under the train. To determine the stresses in the rails in order to predict the development of contact-fatigue defects, dynamic calculations using the finite element method were used. Results: it was revealed that in order to reduce rail wear in a curved section of the track in sections with predominantly freight traffic, the elevation of the outer rail must be calculated based on the actually realized speeds of freight trains. It has been established that at the moment the influence of the amount of rail inclination on rail wear has not been sufficiently studied. As an analysis of the position of the rails at various inclines has shown, for the curve under consideration it is most advisable to use a 1/30 inclination within the limits of a circular curve and with a 1/20 to 1/30 inclination within the transition curve. To reduce the likelihood of contact-fatigue defects occurring in such areas, it is necessary to provide for the implementation of measures to lubricate the side working edge of the outer rail thread and the rolling surface of the inner rail thread within the entire curve. Practical importance: the research results indicate the need to revise the approach to calculating the elevation of the outer rails in curves with heavy freight train traffic. The possibility of extending the service life of rails by revising the system for planning and implementing work on lubricating and grinding rails in curves in areas where trains of increased mass and length operate

Road Geometric Redesign used AutoCAD 2D A Case Jalan Majalengka-Rajagaluh

Majalengka-Rajagaluh road is a road located in several sub-districts which is a link to the city and also one of the connecting roads to Cirebon City. This design planning starts in Cigasong sub-district and continues to Rajagaluh sub-district with the length of Majalengka-Rajagaluh road is 5.3 kilometers. The geometric design results are visualized in the form of drawings using AutoCAD 2D. The design speed (Vd) was set at 60 km/h with a horizontal curve radius of 358 m, a maximum slope of 4%, and an elevation (e max) of 8%. Based on these design criteria, a spiral curve with a circular curve length (Lc) of 74.996 m was obtained. Furthermore, the results of the vertical alignment calculation of the length (L) of one type of convex curve in PPV were also calculated.

Wheel-rail wear characteristics of a modern tram passing curves with small radius

The wheel-rail wear was predicted for modern trams with independently rotating wheelset running on a groove-shaped rail. The tram vehicle-track coupled dynamics model, considering the wheel-rail multi-point contact, was developed using software UM to evaluate the dynamic responses of the vehicle and track. Hertz contact theory, the FastSim algorithm, and Archard material wear model were used to solve the normal contact stress, tangential contact stress, and wheel-ail wear, respectively. The wheel and rail profiles were updated when the wear depth reached to 0.1 mm. In calculation, the wheel and rail wear was calculated and analyzed separately. The results of groove rail and independently rotating wheelset wear predicted by this model coincided with relevant literature, which proved the effectiveness of this model. The wheel and rail wear characteristics of modern trams passing through curved tracks with small radii and the influence of wheel-rail friction coefficient on wheel and rail wear were calculated and analyzed using this model. The results show that the wheel and rail wear on the circular curve and the rear transition curve is more intense. The wheel wear is the most intense on circular curve while the rail wear is on the rear transition curve. The wear of inner and outer rails and wheels of wheelset one increases with the increase of wheel-rail friction coefficient while the wear of inner and outer wheels of wheelset three have no obvious change. The wear of the inner and outer rails is the most intense at the gauge corner position while is the lightest at the guard rail. The wear of wheelset one is more intense than that of wheelset three and the inner wheel wear is more intense than that of the outer wheel. The present analysis contributes to improve the life of tram wheel and rail and reduce the frequency of wheel-rail maintenance during operation.

Train Trajectory-Following Control Method Using Virtual Sensors.

Trajectory-following control is the basis for the practical application of an articulated virtual rail train transportation system. In this paper, a planar nonlinear dynamics model of an articulated vehicle is derived using the Euler-Lagrange method. A trajectory-following control strategy based on the first following point is proposed, and a feedback linearization control algorithm is designed based on the vehicle dynamics model to achieve the trajectory following of the rear vehicle. Based on the target trajectory formed by the first following point and measured by virtual sensors, a vector analysis method grounded in geometric relationships is proposed to solve in real time for the desired position, velocity, and acceleration of the vehicle. Finally, a MATLAB/SIMPACK dynamics virtual prototype is established to test the vehicle's trajectory-following effectiveness and dynamics performance under lane change and circular curve routes. The results indicate that the control algorithm can achieve trajectory following while maintaining good vehicle dynamics performance. It is robust to variations in vehicle mass, vehicle speed, tire cornering stiffness, and road friction coefficient.

Enhanced measurement and optimization of railway profile parameters for large tamping machine operations

Abstract In the realm of modern railway maintenance, the employment of large tamping machine for the enhancement of track geometry and elasticity, and the minimization of disturbance to the roadbed, has become a key operational approach. However, factors such as repeated load applications, changes in topography and geology, and ongoing maintenance activities have been known to cause significant deviations of the actual track location from its original design. These deviations present challenges, such as increased construction difficulty and workload, during tamping operations predicated on the original design. Moreover, methods based on manual intervention have rendered large machine maintenance operations inefficient. In this paper, an optimisation method for railway profile parameters suitable for large tamping machine operations is proposed. The method integrates the total least squares method and the direct search method, enabling the accurate fitting of slope segments preceding and following the slope change points and the alignment of circular curve segments to determine the optimal curve radius. Consequently, optimised profile parameters for the continuous track section are obtained. Focusing on the Beijing–Guangzhou line, the operational efficacy of the proposed optimisation method is compared with that of the artificial slope method. The results showed that the proposed optimisation method is not only more accurate and efficient but also adheres to the principle of ‘prefer lifting rather than descending’ of the railways. The method further provides a theoretical basis and practical guidance for the optimisation of railway profile, underscoring the potential for improved maintenance efficiency and enhanced safety in train operations.

Design, Fabrication, and Dynamic Analysis of a MEMS Ring Resonator Supported by Twin Circular Curve Beams.

In this paper, we present a compressive study on the design and development of a MEMS ring resonator and its dynamic behavior under electrostatic force when supported by twin circular curve beams. Finite element analysis (FEA)-based modeling techniques are used to simulate and refine the resonator geometry and transduction. In proper FEA or analytical modeling, the explicit description and accurate values of the effective mass and stiffness of the resonator structure are needed. Therefore, here we outlined an analytical model approach to calculate those values using the first principles of kinetic and potential energy analyses. The natural frequencies of the structure were then calculated using those parameters and compared with those that were simulated using the FEA tool ANSYS. Dynamic analysis was performed to calculate the pull-in voltage, shift of resonance frequency, and harmonic analyses of the ring to understand how the ring resonator is affected by the applied voltage. Additional analysis was performed for different orientations of silicon and assessing the frequency response and frequency shifts. The prototype was fabricated using the standard silicon-on-insulator (SOI)-based MEMS fabrication process and the experimental results for resonances showed good agreement with the developed model approach. The model approach presented in this paper can be used to provide valuable insights for the optimization of MEMS resonators for various operating conditions.

The Characteristics of Long-Wave Irregularities in High-Speed Railway Vertical Curves and Method for Mitigation.

Track geometry measurements (TGMs) are a critical methodology for assessing the quality of track regularities and, thus, are essential for ensuring the safety and comfort of high-speed railway (HSR) operations. TGMs also serve as foundational datasets for engineering departments to devise daily maintenance and repair strategies. During routine maintenance, S-shaped long-wave irregularities (SLIs) were found to be present in the vertical direction from track geometry cars (TGCs) at the beginning and end of a vertical curve (VC). In this paper, we conduct a comprehensive analysis and comparison of the characteristics of these SLIs and design a long-wave filter for simulating inertial measurement systems (IMSs). This simulation experiment conclusively demonstrates that SLIs are not attributed to track geometric deformation from the design reference. Instead, imperfections in the longitudinal profile's design are what cause abrupt changes in the vehicle's acceleration, resulting in the measurement output of SLIs. Expanding upon this foundation, an additional investigation concerning the quantitative relationship between SLIs and longitudinal profiles is pursued. Finally, a method that involves the addition of a third-degree parabolic transition curve (TDPTC) or a full-wave sinusoidal transition curve (FSTC) is proposed for a smooth transition between the slope and the circular curve, designed to eliminate the abrupt changes in vertical acceleration and to mitigate SLIs. The correctness and effectiveness of this method are validated through filtering simulation experiments. These experiments indicate that the proposed method not only eliminates abrupt changes in vertical acceleration, but also significantly mitigates SLIs.

RELATIONSHIP BETWEEN TRANSITION CURVES (CLOTHOIDS) AND CIRCULAR CURVES IN ROAD ALIGNMENT

<p style="text-align: justify;"><span lang="EN-GB" style="font-size: 12pt; line-height: 200%; font-family: arial, helvetica, sans-serif;">The transition from a straight line to a circular curve is always abrupt, even if this is not readily noticeable at very large radii or low driving speeds. On the straight section the steering wheel angle is zero, on the arc section the steering wheel angle must have a certain value, as stated above, which is greater the tighter the curve. This in turn would mean that you would have to turn the steering wheel jerkily at the transition between the straight section and the circular curve section. Otherwise you would go off track. Even in the case of large radii without transition curves, the lines of a road appear inelastic and can satisfy neither aesthetically nor driving psychologically down to the last detail. In perspective foreshortening - how the road is seen by the driver - sudden kinks appear despite the large curve radii.</span></p>

Exact Mathematical Solution for Maximum Transient Offtracking Calculation of a Single-Unit Vehicle Negotiating Circular Curves

The low-speed turning maneuverability of vehicles is closely related to a well-known offtracking phenomenon which occurs when the rear wheels of a turning vehicle deviate towards the inside of a horizontal curve. Although numerous mathematical models and computer programs for vehicle swept path analysis have been developed in the past, only a few of them can calculate the maximum transient offtracking of a turning vehicle, yet with limited accuracy. The authors were motivated by this fact to find a new mathematical solution for maximum transient offtracking calculation of a single-unit vehicle when negotiating circular curves. In the first stage, a transcendental equation defining vehicle maximum transient offtracking position is derived and numerically solved by Python 3.10.12. In the second stage, the polynomial regression model predicting accurate numerical solutions of the transcendental equation with the desired level of accuracy was developed and tested. The new calculation method is simple enough to simply take the vehicle datum length, circular curve radii, and turn angle, while instantly producing the maximum transient offtracking value, without the need to draw any of the vehicle movement trajectories.

Indefinitely Flat Circular Velocities and the Baryonic Tully–Fisher Relation from Weak Lensing

We use a new deprojection formula to infer the gravitational potential around isolated galaxies from weak gravitational lensing. The results imply circular velocity curves that remain flat for hundreds of kiloparsecs, greatly extending the classic result from 21 cm observations. Indeed, there is no clear hint of a decline out to 1 Mpc, well beyond the expected virial radii of dark matter halos. Binning the data by mass reveals a correlation with the flat circular speed that closely agrees with the baryonic Tully–Fisher relation known from kinematic data. These results apply to both early- and late-type galaxies, indicating a common universal behavior.

ОБОСНОВАНИЕ КОНСТРУКЦИИ КРЫТОГО ГРУЗОВОГО ВАГОНА С УВЕЛИЧЕННЫМ ОБЪЕМОМ ГРУЗОВОГО ПОМЕЩЕНИЯ

The market of covered freight cars, as well as existing designs of this car type of domestic and foreign production is analyzed. Promising trends of making innovative designs of freight cars for the transportation of piece and container goods are found out. The original design of a covered freight car with an increased body space due to the use of the space between trucks is proposed. To reduce the complexity of loading and unloading operations, sliding sections of the side walls and roof are provided in the car design. To confirm the compliance of the proposed design with the requirements of regulatory and technical documents, the car was entered into the dimension, checking for automatic coupling at the junction of a straight line and a curve, passage in the coupling of an s-shaped curve and coupling of a straight line and a curve, and a single car along a circular curve of a small radius, as well as passing without self-decoupling of the hump of the sorting slide, the ramp exit of the train ferry. A safety assessment is carried out with regard to rolling the wheel onto the rail and overturning the car in curves. The car dynamic characteristics are found out by mathematical modeling methods. The assessment of the strength of the body load-bearing structure, lifting mechanisms of the floor sections, sliding sections of the roof and side walls is performed using the finite element method implemented in the environment of a specialized software package. The results obtained as a result of calculations and computer modeling confirmed the operability and safety of the proposed design of a covered freight car with an increased loading space.

Wavelet analysis on a generalized helix space curves and its examples

In this paper, wavelet transform on a generalized helix space curves are investigated, including of local continuous wavelet transform at some point and discrete wavelet transform on a class of helix curves. Firstly, a class of helix space curves are introduced and the parameter equations are given. Then the dilation operator and translation on the function ψ(ξ0)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi^{{(\\xi_{{0}} )}}$$\\end{document} is properly defined by the local projection at some point from a space curve on the unit sphere onto its tangent line. The local continuous wavelet transform and its reconstruction formula are deduced at some point of a space curve on the unit sphere. On the other hand, According to the discretization of length-preserving projection, discrete wavelet transform is lifted onto a helix space curve, such as a circular helix curve. Based on length-preserving projection, the some properties are discussed, such as two-scale sequences of scaling function and wavelet, orthogonality, decomposition formula and so on. Finally, two examples are given for our discussion. One example is illustrating the application of local continuous wavelet transform at some point of a space curve. The result shows the signal at some point of a space curve can be reconstructed by local continuous wavelet method. The norm of the error is 0.3783 between original signal and reconstructed signal in this example. The other numerical example is given for decomposing and reconstructing with the signal on a circular helix curve. The result shows the signal on a helix space curve can be decomposed and reconstructed by the length-preserving projection. The norm of the error is 8.0741 × 10−11 between original signal and reconstructed signal. The figures are shown for the simulation results.

Comparative study on the causes of rail corrugations in long steep-grade sections under traction and braking conditions

There are significant differences in rail corrugations between the uphill and downhill sections in long steep-grade sections. Comprehensive field investigations and numerical simulations are conducted to investigate rail corrugations under traction and braking conditions. Firstly, field investigations of rail corrugations in long steep-grade sections are carried out. Secondly, the dynamic models of the vehicle-track system under uphill traction and downhill braking conditions are constructed, and the dynamic characteristics of the vehicle-track system are explored. Then, the finite element models of wheel-rail-traction/brake systems are constructed, and the friction self-excited vibration characteristics of the wheel-rail system are studied by the complex eigenvalue method. Finally, the influences of key parameters of traction and brake friction pairs on rail corrugation are studied, and suppression methods of rail corrugations are proposed. The results show that (1) rail corrugation more easily occurs on the transition positions of the easement curve and circular curve, with slope changing. (2) Under the traction and braking conditions, rail corrugations are induced by the friction self-excited vibration of the wheel-rail-traction/brake system. (3) Reducing the traction speed or increasing the gear mesh stiffness, reducing the brake friction coefficient or the brake force can suppress the rail corrugation.

Asymmetric Drift Map of the Milky Way Disk Populations between 8 -16 kpc with LAMOST and Gaia datasets

The application of asymmetric drift (AD) tomography across different populations provides valuable insights into the kinematics, dynamics, and rotation curves of the Galactic disk. By leveraging common stars identified in both the LAMOST and Gaia surveys, alongside Gaia DR3’s circular velocity curve, we conducted a qualitative exploration of asymmetric drift distributions within the Galactic disk spanning distances from 8 to 16 kpc. In the R-Z plane, we observed that the asymmetric drift is minimal near the mid-plane of the Galactic disk and gradually increases with vertical distance, resulting in a distinctive “horn” shape. Additionally, our analysis revealed that populations with higher [ α/Fe] ratios exhibit greater asymmetric drift compared to those with lower [ α/Fe] ratios. Specifically, we found the asymmetric drift around the solar location to be approximately 6 km s −1, with a median value of 16 km s −1 across the entire sample. Notably, the median asymmetric drift in the northern region of the Galactic disk (20 km s −1) surpasses that in the southern region (13 km s −1), with errors remaining within 2 km s −1. Furthermore, our investigation into mono-age stellar populations unveiled that older stellar populations tend to exhibit larger asymmetric drift and velocity dispersion, aligning closely with predictions from previous numerical models. Finally, based on chemical compositions, we observed that the median asymmetric drift of the thick disk significantly exceeds that of the thin disk and found that star formation within the thick disk primarily occurred 8-10 billion years ago, whereas the thin disk’s predominant star formation period spanned 6-8 billion years ago.

A low loss silicon waveguide bend based on width and curvature variations

A simple, low loss and compact 90° SOI waveguide bend constructed by using an inner circular curve and an outer Euler-circular curve was proposed, optimal designed and fabricated. By adopting this simple structure, the width and curvature of the waveguide bend can be varied simultaneously, which can effectively suppress both the mode mismatch loss and the radiation loss. Three-dimensional finite difference time domain simulation results indicate a very low excess loss of about 0.0056 dB can be achieved for equivalent bending radius of 2 μm. By using the cut-back method, a low loss of about 0.0175 dB at 1550 nm was measured, which is less than one quarter of the traditional circular bend. In addition, the wavelength dependence for the proposed SOI waveguide bend was investigated and 0.0088 dB–0.0247 dB was measured in the wavelength range of 1480∼1580 nm.

Experimental study on impact icing of the superhydrophobic surfaces with cruciferous bionic structure

Superhydrophobic surfaces have been extensively utilized due to their high hydrophobicity and anti-icing properties. Inspired by the shape of a cross flower, research has utilized circular arc curves and Bessel curves to design a cross flower structure model. Using 3D modeling software for modeling and 3D printing technology to prepare biomimetic microstructures in structural design. The structural shape of the microstructure before and after spray coating was detected using ultra depth of field and laser confocal microscopy. Using Ultra-Ever Dry as a low surface energy substance to alter the wettability of microstructure surfaces. Through surface wettability tests, droplet freezing, and droplet impact tests, the cross shaped biomimetic structure designed by the Bessel curve has a maximum droplet freezing time of 4193 s and a minimum droplet impact time of 9.81 ms. The experimental results indicate that the cross shaped biomimetic structure has good hydrophobicity and broad application prospects.

Radial and azimuthal gradients of the moving groups in Gaia DR3: The slow and fast bar degeneracy problem

The structure and dynamics of the central bar of the Milky Way (MW) are still under debate whilst being fundamental ingredients for the evolution of our Galaxy. The recent Gaia DR3 offers an unprecedented detailed view of the 6D phase space of the MW, allowing for a better understanding of the complex imprints of the bar on the phase space. We aim to identify and characterise the dynamical moving groups across the MW disc, and use their large-scale distribution to help constrain the properties of the Galactic bar. We used 1D wavelet transforms of the azimuthal velocity ($V_ distribution in bins of radial velocity to robustly detect the kinematic substructure in the Gaia DR3 catalogue. We then connected these structures across the disc to measure the azimuthal (phi ) and radial ($R$) gradients of $V_ of the moving groups. We simulated thousands of perturbed distribution functions using backward integration, sweeping a large portion of parameter space of feasible Galaxy models that include a bar, in order to compare them with the data and to explore and quantify the degeneracies. The radial gradient of the Hercules moving group ($ V_ R$ = 28.1pm 2.8 $) cannot be reproduced by our simple models of the Galaxy that show much larger slopes both for a fast and a slow bar. This suggests the need for more complex dynamics (e.g. a different bar potential, spiral arms, a slowing bar, a complex circular velocity curve, external perturbations, etc.). We measured an azimuthal gradient for Hercules of $ V_ = -0.63pm $deg$^ $ and find that it is compatible with both the slow and fast bar models. Our analysis points out that in using this type of analysis, at least two moving groups are needed to start breaking the degeneracies. We conclude that it is not sufficient for a model to replicate the local velocity distribution; it must also capture its larger-scale variations. The accurate quantification of the gradients, especially in the azimuthal direction, will be key for the understanding of the dynamics governing the disc.

Multi-gait snake robot for inspecting inner wall of a pipeline

In the field of pipeline inner wall inspection, the snake robot demonstrates significant advantages over other inspection methods. While a simple traveling wave or meandering motion will suffice for inspecting the inner wall of small-diameter pipes, comprehensively and meticulously inspecting the inner wall of large-diameter pipes requires the snake robot to adopt a helical gait that closely adheres to the inner wall. Our review of existing literature indicates that most research and development on the helical gait of snake robots has focused on the outer surface of cylinders, with very few studies dedicated to developing a helical gait specifically for the inspection of the inner wall of pipes. Therefore, in this study, we propose a helical gait that is suitable for the inner wall of pipes and meets the requirements of gas pipeline engineering. The helical gait is designed using the backbone curve method. First, we create a mathematical model for a circular helix curve with constant curvature and torsion, ensuring it is applicable to a snake robot prototype in a laboratory environment. Subsequently, we calculate the joint angles required for two conical spiral curves with variable curvature and torsion, establish a new model, and define the physical significance of the specific parameters. To ensure the feasibility of the proposed gait, we conduct experiments involving meandering and traveling wave motions to verify the communication and control between the host computer and the snake robot. Building upon this foundation, we further validate the mathematical model of the complex helical motion gait through simulation experiments. Our findings provide a theoretical basis for realizing helical movement with a real snake robot.