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We report on a new international community coding project to provide shared scientific computer code that performs common calculations to aid in planning scientific observations, modeling, and data analysis. We have developed code which calculates Jupiter’s internal and external magnetic fields. All magnetic field model code is provided in four programming languages (C++, IDL, MATLAB and Python). The code is freely available on GitHub. For Jupiter’s internal magnetic field, we present a number of spherical harmonic internal magnetic field models. These include JRM33, the latest Jupiter internal magnetic field model (Connerney et al. in J. Geophys. Res., Planets 127(2):e07055, 2022 ), as well as older jovian models (e.g. JRM09 (Connerney et al. in Geophys. Res. Lett. 45(6):2590–2596, 2018 ), O6 (Connerney in Planetary Radio Emissions III, pp. 13–33, 1992 ), VIP4 (Connerney et al. in J. Geophys. Res. 103(A6):11,929–11,940, 1998 ) and VIPAL (Hess et al. in J. Geophys. Res. Space Phys. 116(A5):A05217, 2011 )). The internal magnetic field code can be easily modified for other planets by simply inputting another spherical harmonic magnetic field model. We have also developed code to calculate the magnetic field perturbations due to the azimuthal and radial currents flowing externally around Jupiter in the jovian magnetodisc according to the model of Connerney et al. (J. Geophys. Res. 86(A10):8370–8384, 1981 ; J. Geophys. Res. Space Phys. 125(10):e28138, 2020 ). The internal and external magnetic field codes can be combined to model the magnetic field in Jupiter’s magnetosphere. Finally, we provide field-line tracing software (C++ and a Python wrapper for C++) that utilizes the internal and external magnetic field models. The software can be used to trace along field lines from any position in the jovian magnetosphere to, for example, the ionosphere or an equator, and can also be utilized at different planets.

Recent fully non-linear simulations of ultracompact spherically symmetric boson stars have presented evidence for their long-term stability. All observed dynamics could be mainly attributed to the fundamental radial mode. In this work, we additionally decompose some of the data in spherical harmonics, providing a first step towards the characterization of non-spherical modes present.

Particle shape in granular materials exhibits both polydisperse and multi-level characteristics, which are intrinsically linked to the mechanical behaviours of granular materials. This study develops a particle generation framework to achieve independent control of polydisperse distributions of roundness (second level of particle shape) and roughness (third level) while preserving form (first level) distributions. In this framework, a spherical harmonic amplitude-stretching (SH amplitude-stretching) technique is proposed to precisely control the form distributions. Two decisive factors for particle roundness and roughness are introduced, and two control coefficients are designed to determine their distributions. The applicability of the proposed framework is verified by employing the generated granular assemblies with varying distributions of particle roundness and roughness into DEM simulations for granular packing and repose angle tests. The simulation results demonstrate the independent effects of polydisperse distributions of particle roundness and roughness on packing density and repose angle, providing evidence of the effectiveness of the proposed framework.

Mammals flex, extend, and rotate their spines as they perform behaviors critical for survival, such as foraging, consuming prey, locomoting, and interacting with conspecifics or predators. The atlas–axis complex is a mammalian innovation that allows precise head movements during these behaviors. Although morphological variation in other vertebral regions has been linked to ecological differences in mammals, less is known about morphological specialization in the cervical vertebrae, which are developmentally constrained in number but highly variable in size and shape. Here, we present the first phylogenetic comparative study of the atlas–axis complex across mammals. We used spherical harmonics to quantify 3D shape variation of the atlas and axis across a diverse sample of species, and performed phylogenetic analyses to investigate if vertebral shape is associated with body size, locomotion, and diet. We found that differences in atlas and axis shape are partly explained by phylogeny, and that mammalian subclades differ in morphological disparity. Atlas and axis shape diversity is associated with differences in body size and locomotion; large terrestrial mammals have craniocaudally elongated vertebrae, whereas smaller mammals and aquatic mammals have more compressed vertebrae. These results provide a foundation for investigating functional hypotheses underlying the evolution of neck morphologies across mammals.

It is of great significance to obtain the electromagnetic field radiated by an antenna or scattered by an object over a frequency band. But this data often occupies so large a memory that cannot be applied readily. This paper proposes to compress the field based on the spherical harmonic transformation (SHT) and rational interpolation. First, the tangential electric field over a sphere surrounding the antenna is obtained by simulation or measurement. Then, this field is converted into the spherical harmonic coefficients, which are sparse discrete spectra. Finally, these coefficients are interpolated over the whole frequency band with only a few sampling points. Numerical examples show that the proposed algorithm can compress the data of the near field of a rectangular waveguide antenna by about 17278 times, and those of the far field scattered from an UAV by about 103 times.

The evolution of solar magnetic fields is significant for understanding and predicting solar activities. And our knowledge of solar magnetic fields largely depends on the photospheric magnetic field. In this paper, based on the spherical harmonic expansion of the photospheric magnetic field observed by Wilcox Solar Observatory, we analyze the time series of spherical harmonic coefficients and predict Sunspot Number as well as synoptic maps for Solar Cycle 25. We find that solar maximum years have complex short-period disturbances, and the time series of coefficient g 7 0 is nearly in-phase with Sunspot Number, which may be related to solar meridional circulation. Utilizing Long Short-Term Memory networks (LSTM), our prediction suggests that the maximum of Solar Cycle 25 is likely to occur in June 2024 with an error of 8 months, the peak sunspot number may be 166.9±22.6, and the next solar minimum may occur around January 2031. By incorporating Empirical Mode Decomposition, we enhance our forecast of synoptic maps truncated to Order 5, validating their relative reliability. This prediction not only addresses a gap in forecasting the global distribution of the solar magnetic field but also holds potential reference value for forthcoming solar observation plans.

Space-based optical imaging detection serves as a crucial means for acquiring characteristic information of space objects, with the quality and resolution of images directly influencing the accuracy of subsequent missions. Addressing the scarcity of datasets in space-based optical imaging, this study introduces a method that combines an improved Phong model and higher-order spherical harmonics (HOSH) for the optical imaging computation of space objects. Utilizing HOSH to fit the light field distribution, this approach comprehensively considers direct sunlight, earthshine, reflected light from other extremely distant celestial bodies, and multiple scattering from object surfaces. Through spectral reflectance experiments, an improved Phong model is developed to calculate the optical scattering characteristics of space objects and to retrieve common material properties such as metallicity, roughness, index of refraction (IOR), and Alpha for four types of satellite surfaces. Additionally, this study designs two sampling methods: a random sampling based on the spherical Fibonacci function (RSSF) and a sequential frame sampling based on predefined trajectories (SSPT). Through numerical analysis of the geometric and radiative rendering pipeline, this method simulates multiple scenarios under both high-resolution and wide-field-of-view operational modes across a range of relative distances. Simulation results validate the effectiveness of the proposed approach, with average rendering speeds of 2.86 s per frame and 1.67 s per frame for the two methods, respectively, demonstrating the capability for real-time rapid imaging while maintaining low computational resource consumption. The data simulation process spans six distinct relative distance intervals, ensuring that multi-scale images retain substantial textural features and are accompanied by attitude labels, thereby providing robust support for algorithms aimed at space object attitude estimation, and 3D reconstruction.

Accurate corrections for ionospheric total electron content (TEC) and early warning information are crucial for global navigation satellite system (GNSS) applications under the influence of space weather. In this study, we propose to use a new machine learning model—the Prophet model, to predict the global ionospheric TEC by establishing a short-term ionospheric prediction model. We use 15th-order spherical harmonic coefficients provided by the Center for Orbit Determination in Europe (CODE) as the training data set. Historical spherical harmonic coefficient data from 7 days, 15 days, and 30 days are used as the training set to model and predict 256 spherical harmonic coefficients. We use the predicted coefficients to generate a global ionospheric TEC forecast map based on the spherical harmonic function model and select a year with low solar activity (63.4 < F10.7 < 81.8) and a year with the high solar activity (79.5 < F10.7 < 255.0) to carry out a sliding 2-day forecast experiment. Meanwhile, we verify the model performance by comparing the forecasting results with the CODE forecast product (COPG) and final product (CODG). The results show that we obtain the best predictions by using 15 days of historical data as the training set. Compared with the results of CODE’S 1-Day (C1PG) and CODE’S 2-Day (C2PG). The number of days with RMSE better than COPG on the first and second day of the low-solar-activity year is 151 and 158 days, respectively. This statistic for high-solar-activity year is 183 days and 135 days.

Accurate direction of arrival (DOA) estimation is critical for many audio signal processing tasks in microphone array applications. However, real-world environments pose considerable challenges to DOA estimation algorithms due to noise and reverberation. Therefore, we propose a robust DOA estimation framework. First, the signal power at the zeroth-degree zeroth-order in spherical harmonic domain is used to identify reliable time–frequency bins which represent an omnidirectional field with no variation in the source directions. Two masks are generated by a proportional threshold and a deep neural network, respectively. They are combined with the spherical harmonic features, resulting in two enhanced complex features. Then, we design a new cross-branch fused multi-stream network (CMnet) to exploit the interaction structure between branches, which greatly digs into the specificity and complementarity of real and imaginary parts of the enhanced complex features. Experimental evaluations on simulated data set and LOCATA data set show that our methods have better DOA estimation performance compared with the existing methods, especially in challenging environments, and they are also applicable to real-world scenarios.

Particle morphology is of great significance to the grain- and macro-scale behaviors of granular soils. Most existing traditional morphology descriptors have three perennial limitations, i.e., dissensus of definition, inter-scale effect, and surface roughness heterogeneity, which limit the accurate representation of particle morphology. The inter-scale effect refers to the inaccurate representation of the morphological features at the target relative length scale (RLS, i.e., length scale with respective to particle size) caused by the inclusion of additional morphological details existing at other RLS. To effectively eliminate the inter-scale effect and reflect surface roughness heterogeneity, a novel spherical harmonic-based multi-scale morphology descriptor Rinc is proposed to depict the incremental morphology variation (IMV) at different RLS. The following conclusions were drawn: (1) the IMV at each RLS decreases with decreasing RLS while the corresponding particle surface is, in general, getting rougher; (2) artificial neural network (ANN)-based mean impact values (MIVs) of Rinc at different RLS are calculated and the results prove the effective elimination of inter-scale effects by using Rinc; (3) Rinc shows a positive correlation with the rate of increase of surface area RSA at all RLS; (4) Rinc can be utilized to quantify the irregularity and roughness; (5) the surface morphology of a given particle shows different morphology variation in different sections, as well as different variation trends at different RLS. With the capability of eliminating the existing limitations of traditional morphology descriptors, the novel multi-scale descriptor proposed in this paper is very suitable for acting as a morphological gene to represent the multi-scale feature of particle morphology.