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We present a measurement of the cosmic-ray spectrum above 100 PeV using the part of the surface detector of the Pierre Auger Observatory that has a spacing of 750 m. An inflection of the spectrum is observed, confirming the presence of the so-called second-knee feature. The spectrum is then combined with that of the 1500 m array to produce a single measurement of the flux, linking this spectral feature with the three additional breaks at the highest energies. The combined spectrum, with an energy scale set calorimetrically via fluorescence telescopes and using a single detector type, results in the most statistically and systematically precise measurement of spectral breaks yet obtained. These measurements are critical for furthering our understanding of the highest energy cosmic rays.

In this study, we analyzed a rare hard, bright X‐ray burst associated with intense natural lightning. Through spectral analysis and source model fitting, we demonstrate that the energy spectrum of the X‐ray source region exhibits significant uncertainty due to the strong dependence on radiation beam geometry, which may appear as a TGF‐like hard spectrum. The X‐ray burst is estimated to produce approximately 1013 to 1014 source photons (>30 keV), which is 1–2 orders of magnitude higher than a typical X‐ray burst and comparable to the brightness of downward TGFs. The hard, bright X‐ray burst challenges the traditional classification boundary between soft/weak X‐rays and hard/strong TGFs, suggesting that both may exist in a continuous spectrum. The generation mechanism for such hard, bright X‐ray bursts may involve Relativistic Runaway Electron Avalanche processes, though likely in an incomplete stage.

Nonlinear energy sink (NES) refers to a typical passive vibration device connected to linear or weakly nonlinear structures for vibration absorption and mitigation. This study investigates the dynamics of 1-dof and 2-dof NES with nonlinear damping and combined stiffness connected to a linear oscillator. For the system of 1-dof NES, a truncation damping and failure frequency are revealed through bifurcation analysis using the complex variable averaging method. The frequency detuning interval for the existence of the strongly modulated response (SMR) is also reported. For the system of 2-dof NES, it is reported in a similar bifurcation analysis that the mass distribution between NES affects the maximum value of saddle-node bifurcation. To obtain the periodic solution of the 2-dof NES system with the consideration of frequency detuning, the incremental harmonic balance method (IHB) and Floquet theory are employed. The corresponding response regime is obtained by Poincare mapping, it shows that the responses of the linear oscillator and 2-dof NES are not always consistent, and 2-dof NES can generate extra SMR than 1-dof NES. Finally, the vibration suppression effect of the proposed NES with nonlinear damping, and combined stiffness is analyzed and verified by the energy spectrum, and it also shows that the 2-dof NES system demonstrates better performance.

ERA5 represents the state of the art for atmospheric reanalyses and is widely used in meteorological and climatological research. In this work, this dataset is evaluated using the wind kinetic energy spectrum. Seasonal climatologies are generated for 30° latitudinal bands in the Northern Hemisphere (periodic domain) and over the North Atlantic area (limited-area domain). The spectra are also assessed to determine the effective resolution of the reanalysis. The results present notable differences between the latitudinal domains, indicating that ERA5 is properly capturing the synoptic conditions. The seasonal variability is adequate too, being winter the most energetic, and summer the least energetic season. The limited area domain results introduce a larger energy density and range. Despite the good results for the synoptic scales, the reanalysis’ spectra are not able to properly reproduce the dissipation rates at mesoscale. This is a source of uncertainties which needs to be taken into account when using the dataset. Finally, a cyclone tropical transition is presented as a case study. The spectrum generated shows a clear difference in energy density at every wavelength, as expected for a highly-energetic status of the atmosphere.

Eleven 40-day long integrations of five different global models with horizontal resolutions of less than 9 km are compared in terms of their global energy spectra. The method of normal-mode function decomposition is used to distinguish between balanced (Rossby wave; RW) and unbalanced (inertia-gravity wave; IGW) circulation. The simulations produce the expected canonical shape of the spectra, but their spectral slopes at mesoscales, and the zonal scale at which RW and IGW spectra intersect differ significantly. The partitioning of total wave energies into RWs an IGWs is most sensitive to the turbulence closure scheme and this partitioning is what determines the spectral crossing scale in the simulations, which differs by a factor of up to two. It implies that care must be taken when using simple spatial filtering to compare gravity wave phenomena in storm-resolving simulations, even when the model horizontal resolutions are similar. In contrast to the energy partitioning between the RWs and IGWs, changes in turbulence closure schemes do not seem to strongly affect spectral slopes, which only exhibit major differences at mesoscales. Despite their minor contribution to the global (horizontal kinetic plus potential available) energy, small scales are important for driving the global mean circulation. Our results support the conclusions of previous studies that the strength of convection is a relevant factor for explaining discrepancies in the energies at small scales. The models studied here produce the major large-scale features of tropical precipitation patterns. However, particularly at large horizontal wavenumbers, the spectra of upper tropospheric vertical velocity, which is a good indicator for the strength of deep convection, differ by factors of three or more in energy. High vertical kinetic energies at small scales are mostly found in those models that do not use any convective parameterisation.

We expand on a recent determination of the first global energy spectrum of the ocean's surface geostrophic circulation (Storer et al., 2022, https://doi.org/10.1038/s41467-022-33031-3) using a coarse‐graining (CG) method. We compare spectra from CG to those from spherical harmonics by treating land in a manner consistent with the boundary conditions. While the two methods yield qualitatively consistent domain‐averaged results, spherical harmonics spectra are too noisy at gyre‐scales (>1,000 km). More importantly, spherical harmonics are inherently global and cannot provide local information connecting scales with currents geographically. CG shows that the extra‐tropics mesoscales (100–500 km) have a root‐mean‐square (rms) velocity of ∼15 cm/s, which increases to ∼30–40 cm/s locally in the Gulf Stream and Kuroshio and to ∼16–28 cm/s in the ACC. There is notable hemispheric asymmetry in mesoscale energy‐per‐area, which is higher in the north due to continental boundaries. We estimate that ≈25%–50% of total geostrophic energy is at scales smaller than 100 km, and is un(der)‐resolved by pre‐SWOT satellite products. Spectra of the time‐mean circulation show that most of its energy (up to 70%) resides in stationary eddies with characteristic scales smaller than (<500 km). This highlights the preponderance of “standing” small‐scale structures in the global ocean due to the temporally coherent forcing by boundaries. By coarse‐graining in space and time, we compute the first spatio‐temporal global spectrum of geostrophic circulation from AVISO and NEMO. These spectra show that every length‐scale evolves over a wide range of time‐scales with a consistent peak at ≈200 km and ≈2–3 weeks. Plain Language Summary Traditionally, “eddies” are identified as time‐varying features relative to a background time‐mean flow. As such, “mean” does not imply large length‐scale. Standing eddies or meanders due to topography have little time‐variation, but can have significant energy at small length‐scales that are unresolved and need to be parameterized in coarse climate simulations. Similarly, “eddy” or “time‐varying” do not imply small length‐scale, such as large‐scale motions from Rossby waves or fluctuations of the Kuroshio. Another common method is Fourier analysis in “representative” ocean boxes that cannot capture the circulation's planetary scales. We overcome these limitations thanks to recent advances: (a) a method for calculating spectra by coarse‐graining, (b) properly defining convolutions on the sphere, which “blur” oceanic flow in a way that preserves its underlying symmetries, opening the door for global “wavelet” analysis and, more generally, spatial coarse‐graining, and (c) FlowSieve: an efficient parallel code. We employ coarse‐graining in space‐time to gain new insights into the global oceanic circulation, including how much energy resides in its different spatial structures and how they vary in time. Key Points Coarse‐graining, which disentangles flow concurrently in scale and space, reveals hemispheric asymmetry in mesoscale energy‐per‐area due to boundaries Coarse‐graining spectra of the time‐mean velocity show that most (up to 70%) of its energy resides in “standing” small‐scale eddies <500 km We estimate that ≈25%–50% of total geostrophic energy is at scales smaller than 100 km, and is un(der)‐resolved by pre‐SWOT satellite products

Fourier spectra are powerful tools to analyze the scale behavior of turbulent flows. While such spectra are mathematically based on regular periodic data, some state‐of‐the‐art ocean and climate models use unstructured triangular meshes. Observational data is often also available only in an unstructured fashion. In this study, scale analysis specifically for the output of models with triangular meshes is discussed and the representable wavenumbers for Fourier analysis are derived. Aside from using different interpolation methods and oversampling prior to the computation of Fourier spectra, we also consider an alternative scale analysis based on the Walsh–Rademacher basis, that is, indicator functions. It does not require interpolation and can be extended to general unstructured meshes. A third approach based on smoothing filters which focus on grid scales is also discussed. We compare these methods in the context of kinetic energy and dissipation power of a turbulent channel flow simulated with the sea ice‐ocean model FESOM2. One simulation uses a classical viscous closure, another a new backscatter closure. The latter is dissipative on small scales, but anti‐dissipative on large scales leading to more realistic flow representation. All three methods clearly highlight the differences between the simulations as concerns the distribution of dissipation power and kinetic energy over scales. However, the analysis based on Fourier transformation is highly sensitive to the interpolation method in case of dissipation power, potentially leading to inaccurate representations of dissipation at different scales. This highlights the necessity to be cautious when choosing a scale analysis method on unstructured grids. Plain Language Summary To better understand the physical processes that drive and define the circulation in our oceans, it is necessary to analyze the temporal and spatial scales on which these processes act. The classical method to investigate the spatial scale behavior is Fourier analysis which splits any given data into waves of different amplitudes and wavelengths. Mathematically this requires data on an equidistantly spaced grid. However, many ocean models apply triangular or other irregular grids for their computations of oceanic flows. In this study, we describe the advantages and disadvantages of applying Fourier analysis for models that use triangular meshes, with prior interpolation of data to regularly spaced rectangular meshes. We also introduce two other methods that can analyze the distribution of kinetic energy and kinetic energy dissipation across scales without interpolation. The results show that one needs to be very careful when choosing a specific scale analysis and, potentially, an interpolation method for triangular grids, especially when it comes to analyzing the process of kinetic energy dissipation. Key Points Three different scale analysis methods for unstructured triangular grids are presented and discussed Fourier spectra after interpolation of fields should be applied with caution especially for dissipation power spectra Scale analysis via indicator functions does not rely on interpolation and can be applied to non‐smooth, unstructured data

We study the transport properties of Dirac fermions in ABC trilayer graphene (ABC-TLG) superlattices. More specifically, we analyze the impact of varying the physical parameters-the number of cells, barrier/well width, and barrier heights-on electron tunneling in the ABC-TLG. In the initial stage, we solved the eigenvalue equation to determine the energy spectrum solutions for the ABC-TLG superlattices. Subsequently, we applied boundary conditions to the eigenspinors and employed the transfer matrix method to calculate transmission probabilities and conductance. For the two-band model, we identified the presence of Klein tunneling, with a notable decrease as the number of cells increased. The introduction of interlayer bias opened a gap as the number of cells increased, accompanied by an asymmetry in scattered transmission. Increasing the barrier/well width and the number of cells resulted in an amplified number of gaps and oscillations in both two-band and six-band cases. We observed a corresponding decrease in conductance as the number of cells increased, coinciding with the occurrence of a gap region. Our study demonstrates that manipulating parameters such as the number of cells, the width of the barrier/well, and the barrier heights provides a means of controlling electron tunneling and the occurrence of gaps in ABC-TLG. Specifically, the interplay between interlayer bias and the number of cells is identified as a crucial factor influencing gap formation and transmission asymmetry.

The FY-3E satellite plasma analyzer marks China’s first detection of the characteristics, occurrence, and development of the typical plasma environment in the dawn–dusk orbit space. It provides data source support for operational space weather alerts and forecasts, helps ensure the in-orbit safety of the satellite, and accumulates space environment detection data for space environment modeling and space physics research. This paper gives a detailed introduction to the detection technology adopted by the FY-3E satellite plasma analyzer. We calibrated its performance through a calibration experiment and then analyzed and compared it with similar instruments in China. It is indicated that the instrument is capable of measuring an ion energy spectrum of 24 eV~32 keV and an electron energy spectrum of 23.7 eV~31.6 keV, its field of view reaches 180° × 90°, and the inversed measurement range of spacecraft absolute potential is better than −30 kV~+30 kV. All these contribute to a notably improved technology for plasma and satellite potential detection of China’s LEO satellites.

Among the coronal mass ejections (CMEs) and solar proton events (SPEs) frequently observed by near-Earth spacecraft, the SPE that occurred on 28 October 2021 stands out as a remarkable research event. This is due to the infrequency of reported ground-level enhancements it induced. The CSES (China seismo-electromagnetic satellite) is equipped with high-energy particle detectors, namely, HEPP and HEPD, capable of measuring protons within an energy range of 2 MeV to 143 MeV. These detectors provide valuable opportunities for studying solar activity. By utilizing the Monte Carlo method to simulate the pile-up effect and accounting for the detector’s dead time, with the assistance of real-time incident counting rates, we successfully corrected the spectra in the 10–50 MeV range. The energy spectrum is important for understanding solar proton events. We used the data from the HEPP (high-energy particle package) and HEPD (high-energy particle detector) to obtain the total event-integrated spectrum, which possessed good continuity. Additionally, we compared the observations from the CSES with those from the NOAA satellite and achieved reasonable agreement. We also searched for ground-based responses to this solar activity in China and discovered Forbush decreases detected by the Yang Ba Jing Muon Telescope experiment. In conclusion, the HEPP and HEPD can effectively combine to study solar activity and obtain a smooth and consistent energy spectrum of protons across a very wide energy range.