Minimum Angular Distance Research Articles

Low-Earth-Orbit Mega-Constellation Low-Redundancy Design: Rapid Performance Analysis and Adaptive Configuration Layering

Megaconstellations, which offer convenient communication and navigation services, are at the forefront of satellite application advancements. However, traditional constellations with a single uniform configuration fail to meet the various demands in different regions, thus leading to low utilization. In addition, satellite safety becomes a key consideration that megaconstellations cannot ignore. To address the aforementioned problems, this study proposes an adaptive method for designing layered megaconstellations under the assumptions of circular orbits, uniform distribution in each plane, and a pregiven altitude. Two novel methods are developed for evaluating the coverage performance and satellite safety. First, the longitude-coverage-ratio model is proposed based on the street of coverage theory, enhancing the constellation design for latitude-specific coverage needs. Next, a rapid method is derived for calculating the minimum angular distance between planes. Then, the study investigates the models to be used in subconstellation design techniques for assembling multilayer hybrid megaconstellations. Several hybrid megaconstellations are designed, demonstrating the applicability of the methodology for both nonuniform and global uniform coverage requirements. The results show that this method offers reduced redundancy and a lower number of satellites compared to a single Walker. The examples also suggest that low-Earth-orbit hybrid constellations can achieve global uniform coverage when reaching sufficient coverage folds.

Three-dimensional inversion of corona structure and simulation of solar wind parameters based on the photospheric magnetic field deduced from the Global Oscillation Network Group

In this research, the Potential Field Source Surface–Wang–Sheeley–Arge (PFSS–WSA) solar wind model is used. This model consists of the Potential Field Source Surface (PFSS) coronal magnetic field extrapolation module and the Wang–Sheeley–Arge (WSA) solar wind velocity module. PFSS is implemented by the POT3D package deployed on Tianhe 1A supercomputer system. In order to obtain the three–dimensional (3D) distribution of the coronal magnetic field at different source surface radii (Rss), the model utilizes the Global Oscillation Network Group (GONG) photospheric magnetic field profiles for two Carrington rotations (CRs), CR2069 (in 2008) and CR2217 (in 2019), as the input data, with the source surface at Rss = 2Rs, Rss = 2.5Rs and Rss = 3Rs, respectively. Then the solar wind velocity, the coronal magnetic field expansion factor, and the minimum angular distance of the open magnetic field lines from the coronal hole boundary are estimated within the WSA module. The simulated solar wind speed is compared with the value for the corona extrapolated from the data observed near 1 AU, through the calculations of the mean square error (MSE), root mean square error (RMSE) and correlation coefficient (CC). Here we extrapolate the solar wind velocity at 1 AU back to the source surface via the Parker spiral. By comparing the evaluation metrics of the three source surface heights, we concluded that the solar source surface should be properly decreased with respect to Rss = 2.5Rs during the low solar activity phase of solar cycle 23.

A Modeling Approach for Predicting the Resolution Capability in Terrestrial Laser Scanning

The minimum size of objects or geometrical features that can be distinguished within a laser scanning point cloud is called the resolution capability (RC). Herein, we develop a simple analytical expression for predicting the RC in angular direction for phase-based laser scanners. We start from a numerical approximation of the mixed-pixel bias which occurs when the laser beam simultaneously hits surfaces at grossly different distances. In correspondence with previous literature, we view the RC as the minimum angular distance between points on the foreground and points on the background which are not (severely) affected by a mixed-pixel bias. We use an elliptical Gaussian beam for quantifying the effect. We show that the surface reflectivities and the distance step between foreground and background have generally little impact. Subsequently, we derive an approximation of the RC and extend it to include the selected scanning resolution, that is, angular increment. We verify our model by comparison to the resolution capabilities empirically determined by others. Our model requires parameters that can be taken from the data sheet of the scanner or approximated using a simple experiment. We describe this experiment herein and provide the required software on GitHub. Our approach is thus easily accessible, enables the prediction of the resolution capability with little effort and supports assessing the suitability of a specific scanner or of specific scanning parameters for a given application.

Efficient search of optimal Flower Constellations

We derive an analytical closed expression to compute the minimum distance (quantified by the angle of separation measured from the center of the Earth) between any two satellites located at the same altitude and in circular orbits. We also exploit several properties of Flower Constellations (FCs) that, combined with our formula for the distance, give an efficient method to compute the minimum angular distance between satellites, for all possible FCs with up to a given number of satellites.

The structure of the co-orbital stable regions as a function of the mass ratio

ABSTRACT Although the search for extrasolar co-orbital bodies has not had success so far, it is believed that they must be as common as they are in the Solar system. Co-orbital systems have been widely studied, and there are several works on stability and even on formation. However, for the size and location of the stable regions, authors usually describe their results but do not provide a way to find them without numerical simulations, and, in most cases, the mass ratio value range is small. In this work, we study the structure of co-orbital stable regions for a wide range of mass ratio systems and build empirical equations to describe them. It allows estimating the size and location of co-orbital stable regions from a few system parameters. Thousands of massless particles were distributed in the co-orbital region of a massive secondary body and numerically simulated for a wide range of mass ratios (μ) adopting the planar circular restricted three-body problem. The results show that the upper limit of horseshoe regions is between 9.539 × 10−4 < μ < 1.192 × 10−3, which corresponds to a minimum angular distance from the secondary body to the separatrix of between 27.239º and 27.802º. We also found that the limit to existence of stability in the co-orbital region is about μ = 2.3313 × 10−2, much smaller than the value predicted by the linear theory. Polynomial functions to describe the stable region parameters were found, and they represent estimates of the angular and radial widths of the co-orbital stable regions for any system with 9.547 × 10−5 ≤ μ ≤ 2.331 × 10−2.

Psychoacoustic Optimization of the Spacing of Propellers, Helicopter Rotors, and Axial Fans

The paper deals with the minimization of the subjective annoyance (that is, of the quality of the received sound rather than of its acoustic power) due to tonal noise generated by subsonic low-solidity axial-flow rotors. The employed method is based on the uneven spacing of the blades, is typically applied to open or nearly open rotors, and is based on acoustic interference. Thus, linear propagation of the acoustic waves is a prerequisite for its application. An optimization problem is formulated for which the objective function is derived from a psychoacoustic metric, the decision variables are the blades angular positions, the sound pressure level spectrum generated by a single blade is a parameter, and the constraints are the rotor balancing and the minimum angular distance between adjacent blades. A further intuitive criterion, based on lowering the highest peaks, is also considered. The solution of the problem is critical due to the presence of a very large number of minima in the objective function, which prevents employment of the most common optimization algorithms. Thus, a method based on the simulated annealing is modified and adapted to the present problem. The application to a number of test cases and the analysis of the results show that the method is effective in finding the optimal solution and is computationally affordable.

A modified particle swarm optimization algorithm and its application to the multiobjective FET modeling problem

This paper introduces a modified particle swarm algorithm to handle multiobjective optimization problems. In multiobjective PSO algorithms, the determination of Pareto optimal solutions depends directly on the strategy of assigning a best local guide to each particle. In this work, the PSO algorithm is modified to assign a best local guide to each particle by using minimum angular distance information. This algorithm is implemented to determine field-effect transistor (FET) model elements subject to the Pareto domination between the scattering parameters and operation bandwidth. Furthermore, the results are compared with those obtained by the nondominated sorting genetic algorithm-II. FET models are also built for the 3 points sampled from the different locations of the Pareto front, and a discussion is presented for the Pareto relation between the scattering parameter performances and the operation bandwidth for each model.

Improvement to the global distribution of coronal plasma and magnetic field on the source surface using expansion factor fs and angular distance θb

In this paper, we have developed an improved model to build a self-consistent global structure on the source surface of 2.5 Rs covering four different phases of solar activity. This model involves the topological effect of the magnetic field expansion factor fs and the minimum angular distance θb(at the photosphere) between an open field foot point and its nearest coronal hole boundary. The purpose of this effect is to separate the open field area and the close field area more effectively. The model uses as input for 136 Carrington Rotations (CRs) covering four different phases of solar activity: (1) an empirical model of the magnetic field topology on the source surface using Line-of-sight (los) photospheric field (Blos) measurements by Wilcox Solar Observatory (WSO); and (2) an empirically derived global coronal density distribution using K coronal polarized brightness (pB) by MKIII in High Altitude Observator (HAO). The solar wind speed on the source surface is specified by the function of both fs and θb, which are obtained by the magnetic field data. Then the coronal mass outputs are analyzed and the self-consistent global distribution on the source surface is numerically studied for the four different phases. Finally, the model estimates the solar wind speed at 1AU as a simple function of the speed on the source surface. Our numerical results indicate reasonable semi-quantitative agreement with observations at different phases of solar activity.

A novel multi-planar radiography method for three dimensional pose reconstruction of the patellofemoral and tibiofemoral joints after arthroplasty

Determining the 3D pose of the patella after total knee arthroplasty is challenging. The commonly used single-plane fluoroscopy is prone to large errors in the clinically relevant mediolateral direction. A conventional fixed bi-planar setup is limited in the minimum angular distance between the imaging planes necessary for visualizing the patellar component, and requires a highly flexible setup to adjust for the subject-specific geometries. As an alternative solution, this study investigated the use of a novel multi-planar imaging setup that consists of a C-arm tracked by an external optoelectric tracking system, to acquire calibrated radiographs from multiple orientations. To determine the accuracies, a knee prosthesis was implanted on artificial bones and imaged in simulated ‘Supine’ and ‘Weightbearing’ configurations. The results were compared with measures from a coordinate measuring machine as the ground-truth reference. The weightbearing configuration was the preferred imaging direction with RMS errors of 0.48mm and 1.32° for mediolateral shift and tilt of the patella, respectively, the two most clinically relevant measures. The ‘imaging accuracies’ of the system, defined as the accuracies in 3D reconstruction of a cylindrical ball bearing phantom (so as to avoid the influence of the shape and orientation of the imaging object), showed an order of magnitude (11.5 times) reduction in the out-of-plane RMS errors in comparison to single-plane fluoroscopy. With this new method, complete 3D pose of the patellofemoral and tibiofemoral joints during quasi-static activities can be determined with a many-fold (up to 8 times) (3.4mm) improvement in the out-of-plane accuracies compared to a conventional single-plane fluoroscopy setup.

THREE-DIMENSIONAL SOLARWINDMODELING FROM THE SUN TO EARTH BY A SIP-CESE MHD MODEL WITH A SIX-COMPONENT GRID

The objective of this paper is to explore the application of a six-component overset grid to solar wind simulation with a three-dimensional (3D) Solar-InterPlanetary Conservation Element/Solution Element MHD model. The essential focus of our numerical model is devoted to dealing with: (1) the singularity and mesh convergence near the poles via the use of the six-component grid system, (2) the ∇ · B constraint error via an easy-to-use cleaning procedure by a fast multigrid Poisson solver, (3) the Courant-Friedrichs-Levy number disparity via the Courant-number insensitive method, (4) the time integration by multiple time stepping, and (5) the time-dependent boundary condition at the subsonic region by limiting the mass flux escaping through the solar surface. In order to produce fast and slow plasma streams of the solar wind, we include the volumetric heating source terms and momentum addition by involving the topological effect of the magnetic field expansion factor fS and the minimum angular distance θ b (at the photosphere) between an open field foot point and its nearest coronal hole boundary. These considerations can help us easily code the existing program, conveniently carry out the parallel implementation, efficiently shorten the computation time, greatly enhance the accuracy of the numerical solution, and reasonably produce the structured solar wind. The numerical study for the 3D steady-state background solar wind during Carrington rotation 1911 from the Sun to Earth is chosen to show the above-mentioned merits. Our numerical results have demonstrated overall good agreements in the solar corona with the Large Angle and Spectrometric Coronagraph on board the Solar and Heliospheric Observatory satellite and at 1 AU with WIND observations.

On the Algorithms Used to Compute the Standard Deviation of Wind Direction

Abstract The standard deviation of wind direction is a very important quantity in meteorology because in addition to being used to determine the dry deposition rate and the atmospheric stability class, it is also employed in the determination of the rate of horizontal diffusion, which in turn determines transport and dispersion of air pollutants. However, the computation of this quantity is rendered difficult by the fact that the horizontal wind direction is a circular variable having a discontinuity at 2π radians, beyond which the wind direction starts again from zero, thus preventing angular subtraction from being a straightforward procedure. In view of such a limitation, this work is meant to provide new mathematical expressions that simplify both the computational and analytical work involved in handling the standard deviation of wind direction. This is achieved by deriving a number of Fourier series and Taylor expansions that can represent the minimum angular distance and its powers. Using these expressions, the relation between two algorithms commonly used to determine the standard deviation of wind direction is analyzed. Furthermore, given that these trigonometric expansions effectively reduce the mathematical complexity involved when dealing with circular statistics, their potential application to solve other problems is discussed.

Multi-symmetric close packings of equal spheres on the spherical surface

An analysis is presented for the Tammes problem: how must n points be distributed on the surface of a sphere in order that the minimum angular distance between any two of the points be a maximum? With the analogy of the capsid structure of small 'spherical' viruses, locally extremal arrangements are constructed in tetrahedral, octahedral and icosahedral symmetry. Thirty arrangements defined by four packing sequences are investigated. By the applied construction process, novel locally extremal configurations for n = 78, 96, 108, 144, 150, 192, 198, 270, 360, 372, 480, 492 and improvable configurations for n = 114, 282 are obtained. A table is given of the investigated arrangements; most of them are putative solutions of the Tammes problem.