Assessment of International GNSS Service Global Ionosphere Map products over China region based on measurements from the Crustal Movement Observation Network of China

The global ionosphere maps(GIM)provided by the International GNSS Service(IGS)are extensively utilized for ionospheric morphology monitoring,scientific research,and practical application.Assessing the credibility of GIM products in data-sparse regions is of paramount importance.In this study,measurements from the Crustal Movement Observation Network of China(CMONOC)are leveraged to evaluate the suitability of IGS-GIM products over China region in 2013-2014.The indices of mean error(ME),root mean square error(RMSE),and normalized RMSE(NRMSE)are then utilized to quantify the accuracy of IGS-GIM products.Results revealed distinct local time and latitudinal dependencies in IGS-GIM errors,with substantially high errors at nighttime(NRMSE:39%)and above 40°latitude(NRMSE:49%).Seasonal differences also emerged,with larger equinoctial deviations(NRMSE:33.5%)compared with summer(20%).A preliminary analysis implied that the irregular assimilation of sparse IGS observations,compounded by China’s distinct geomagnetic topology,may manifest as error variations.These results suggest that modeling based solely on IGS-GIM observations engenders inadequate representations across China and that a thorough examination would proffer the necessary foundation for advancing regional total electron content(TEC)constructions.

Photoinduced Floquet higher-order Weyl semimetal in C_(6) symmetric Dirac semimetals

Topological Dirac semimetals are a parent state from which other exotic topological phases of matter, such as Weyl semimetals and topological insulators, can emerge. In this study, we investigate a Dirac semimetal possessing sixfold rotational symmetry and hosting higher-order topological hinge Fermi arc states, which is irradiated by circularly polarized light. Our findings reveal that circularly polarized light splits each Dirac node into a pair of Weyl nodes due to the breaking of time-reversal symmetry, resulting in the realization of the Weyl semimetal phase. This Weyl semimetal phase exhibits rich boundary states, including two-dimensional surface Fermi arc states and hinge Fermi arc states confined to six hinges.Furthermore, by adjusting the incident direction of the circularly polarized light, we can control the degree of tilt of the resulting Weyl cones, enabling the realization of different types of Weyl semimetals.

The anisotropy of suprathermal electrons in the Martian ionosphere

Suprathermal electrons are an important population of the Martian ionosphere, either produced by photoionization of atmospheric neutrals or supplied from the Solar Wind (SW). This study is dedicated to an in-depth investigation of the pitch angle distribution of suprathermal electrons at two representative energies, 19−55 eV and 124−356 eV, using the extensive measurements made by the Solar Wind Electron Analyzer on board the Mars Atmosphere and Volatile Evolution. Throughout the study, we focus on the overall degree of anisotropy, defined as the standard deviation of suprathermal electron intensity among different directions which is normalized by the mean omni-directional intensity. The available data reveal the following characteristics: (1) In general, low energy electrons are more isotropic than high energy electrons, and dayside electrons are more isotropic than nightside electrons;(2) On the dayside, the anisotropy increases with increasing altitude at low energies but remains roughly constant at high energies, whereas on the nightside, the anisotropy decreases with increasing altitude at all energies;(3) Electrons tend to be more isotropic in strongly magnetized regions than in weakly magnetized regions, especially on the nightside. These observations indicate that the anisotropy is a useful diagnostic of suprathermal electron transport, for which the conversion between the parallel and perpendicular momenta as required by the conservation of the first adiabatic invariant, along with the atmospheric absorption at low altitudes, are two crucial factors modulating the observed variation of the anisotropy. Our analysis also highlights the different roles on the observed anisotropy exerted by suprathermal electrons of different origins.

Pipeline thickness estimation using the dispersion of higher-order SH guided waves

Thickness measurement plays an important role in the monitoring of pipeline corrosion damage. However, the requirement for prior knowledge of the shear wave velocity in the pipeline material for popular ultrasonic thickness measurement limits its widespread application. This paper proposes a method that utilizes cylindrical shear horizontal(SH) guided waves to estimate pipeline thickness without prior knowledge of shear wave velocity. The inversion formulas are derived from the dispersion of higher-order modes with the high-frequency approximation. The waveform of the example problems is simulated using the real-axis integral method. The data points on the dispersion curves are processed in the frequency domain using the wave-number method. These extracted data are then substituted into the derived formulas. The results verify that employing higher-order SH guided waves for the evaluation of thickness and shear wave velocity yields less than1% error. This method can be applied to both metallic and non-metallic pipelines, thus opening new possibilities for health monitoring of pipeline structures.

Higher-order expansions of powered extremes of logarithmic general error distribution

In this paper,Let M_(n)denote the maximum of logarithmic general error distribution with parameter v≥1.Higher-order expansions for distributions of powered extremes M_(n)^(p)are derived under an optimal choice of normalizing constants.It is shown that M_(n)^(p),when v=1,converges to the Frechet extreme value distribution at the rate of 1/n,and if v>1 then M_(n)^(p)converges to the Gumbel extreme value distribution at the rate of(loglogn)^(2)=(log n)^(1-1/v).

Opinion consensus incorporating higher-order interactions in individual-collective networks

In the current information society, the dissemination mechanisms and evolution laws of individual or collective opinions and their behaviors are the research hot topics in the field of opinion dynamics. First, in this paper, a two-layer network consisting of an individual-opinion layer and a collective-opinion layer is constructed, and a dissemination model of opinions incorporating higher-order interactions(i.e. OIHOI dissemination model) is proposed. Furthermore, the dynamic equations of opinion dissemination for both individuals and groups are presented. Using Lyapunov's first method,two equilibrium points, including the negative consensus point and positive consensus point, and the dynamic equations obtained for opinion dissemination, are analyzed theoretically. In addition, for individual opinions and collective opinions,some conditions for reaching negative consensus and positive consensus as well as the theoretical expression for the dissemination threshold are put forward. Numerical simulations are carried to verify the feasibility and effectiveness of the proposed theoretical results, as well as the influence of the intra-structure, inter-connections, and higher-order interactions on the dissemination and evolution of individual opinions. The main results are as follows.(i) When the intra-structure of the collective-opinion layer meets certain characteristics, then a negative or positive consensus is easier to reach for individuals.(ii) Both negative consensus and positive consensus perform best in mixed type of inter-connections in the two-layer network.(iii) Higher-order interactions can quickly eliminate differences in individual opinions, thereby enabling individuals to reach consensus faster.

The nature of electron density enhancement over a wide altitude range during ionosphere heating experiments at EISCAT

During the course of ionospheric heating experiments, researchers at the European Incoherent Scatter Scientific Association (EISCAT) observed an apparent electron density enhancement. The enhancement extended over a wide range of altitudes, above the reflection altitude of the high-frequency pump wave. However, whether this enhancement actually corresponds to a true enhancement in electron density remains an open question. When the dispersion relation of ion acoustic waves is followed, the frequency ratio of the enhanced ion line to the background ion line suggests that the profile of the effective ion mass may have remained unchanged. Furthermore, the solar radio flux and ion drift velocity indicate no significant changes in the ion species and their densities. In conclusion, the electron density enhancement observed at EISCAT should not, in fact, be considered a true enhancement.

Time-Domain Higher-Order Boundary Element Method for Simulating High Forward-Speed Ship Motions in Waves

The hydrodynamic performance of a high forward-speed ship in obliquely propagating waves is numerically examined to assess both free motions and wave field in comparison with a low forward-speed ship.This numerical model is based on the time-domain potential flow theory and higher-order boundary element method,where an analytical expression is completely expanded to determine the base-unsteady coupling flow imposed on the moving condition of the ship.The ship in the numerical model may possess different advancing speeds,i.e.stationary,low speed,and high speed.The role of the water depth,wave height,wave period,and incident wave angle is analyzed by means of the accurate numerical model.It is found that the resonant motions of the high forward-speed ship are triggered by comparison with the stationary one.More specifically,a higher forward speed generates a V-shaped wave region with a larger elevation,which induces stronger resonant motions corresponding to larger wave periods.The shoaling effect is adverse to the motion of the low-speed ship,but is beneficial to the resonant motion of the high-speed ship.When waves obliquely propagate toward the ship,the V-shaped wave region would be broken due to the coupling effect between roll and pitch motions.It is also demonstrated that the maximum heave motion occurs in beam seas for stationary cases but occurs in head waves for high speeds.However,the variation of the pitch motion with period is hardly affected by wave incident angles.

A Study of a Moral Dilemma Stories Teaching Model Focusing on the Development of Higher-Order Thinking --"Synthetic polymers" as an example

Cultivating students'higher-order thinking is one of the important goals of modern education,and innovative teaching model is an effective way to achieve this goal.Aiming at the inadequacy of the existing moral dilemma stories approach in the transformation of knowledge and behavior,this research constructs a new Project Based Learning-Ethical Dilemma Stories(PBL-EDS)Teaching Model applicable to China's secondary education stage based on the innovative features of the moral dilemma stories approach on the core competencies,taking the chemistry subject as an example to carry out practice,and puts forward suggestions for the implementation of the teaching model.Chemistry as an example to carry out the practice,and suggestions are made for the implementation of the teaching model.

Influence of higher-order ionospheric delay correction on GPS precise orbit determination and precise positioning

At present, Global Navigation Satellite Systems（GNSS） users usually eliminate the influence of ionospheric delay of the first order items by dual-frequency ionosphere-free combination. But there is still residual ionospheric delay error of higher order term. The influence of the higher-order ionospheric corrections on both GPS precision orbit determination and static Precise Point Positioning（PPP） are studied in this paper. The influence of higher-order corrections on GPS precision orbit determination, GPS observations and static PPP are analyzed by neglecting or considering the higher-order ionospheric corrections by using a globally distributed network which is composed of International GNSS Service（IGS） tracking stations. Numerical experimental results show that, the root mean square（RMS） in three dimensions of satellite orbit is 36.6 mme35.5 mm. The maximal second-order ionospheric correction is 9 cm, and the maximal third-order ionospheric correction is 1 cm. Higher-order corrections are influenced by latitude and station distribution. PPP is within 3 mm in the directions of east and up. Furthermore, the impact is mainly visible in the direction of north, showing a southward migration trend, especially at the lower latitudes where the influence value is likely to be bigger than 3 mm.

Automatic recognition of tweek atmospherics and plasma diagnostics in the lower ionosphere with the machine learning method

Tweek atmospherics are extremely low frequency and very low frequency pulse signals with frequency dispersion characteristics that originate from lightning discharges and that propagate in the Earth–ionosphere waveguide over long distances.In this study,we developed an automatic method to recognize tweek atmospherics and diagnose the lower ionosphere based on the machine learning method.The differences(automatic−manual)in each ionosphere parameter between the automatic method and the manual method were−0.07±2.73 km,0.03±0.92 cm^(−3),and 91±1,068 km for the ionospheric reflection height(h),equivalent electron densities at reflection heights(Ne),and propagation distance(d),respectively.Moreover,the automatic method is capable of recognizing higher harmonic tweek sferics.The evaluation results of the model suggest that the automatic method is a powerful tool for investigating the long-term variations in the lower ionosphere.

Progress of Geodesy Related Ionosphere from Chinese Scientists in the Period of 2019—2023

The ionosphere is the ionized part of the upper atmosphere of the Earth,which plays an important role in atmospheric electricity and forms the inner edge of the magnetosphere.It influences radio propagation significantly,such as the Global Navigation Satellite System(GNSS).Meanwhile,the GNSS is also an essential technique for sensing the variation of ionosphere.During the years of 2019—2023,a large number of Chinese geodesy scientists devoted much efforts to the geodesy related ionosphere.Due to the very limited length,the achievements are carried out from the following six aspects,including:①The ionospheric correction models for BDS and BDSBAS;②Real-time global ionospheric monitoring and modeling;③The ionospheric 2D and 3D modeling based on GNSS and LEO satellites;④The ionospheric prediction based on artificial intelligence;⑤The monitoring and mitigation of ionospheric disturbances for GNSS users;⑥The ionospheric related data products and classical applications.

Assessment of corrected time-step method for nominal ionospheric gradient calculation: A comparative analysis with spatial approaches

The effect of ionospheric delay on the ground-based augmentation system under normal conditions can be mitigated by determining the value of the nominal ionospheric gradient(σvig).The nominal ionospheric gradient is generally obtained from Continuously Operating Reference Stations data by using the spatial single-difference method(mixed-pair,station-pair,or satellite-pair)or the temporal single-difference method(time-step).The time-step method uses only a single receiver,but it still contains ionospheric temporal variations.We introduce a corrected time-step method using a fixed-ionospheric pierce point from the geostationary equatorial orbit satellite and test it through simulations based on the global ionospheric model.We also investigate the effect of satellite paths on the corrected time-step method in the region of the equator,which tends to be in a more north–south direction and to have less coverage for the east–west ionospheric gradient.This study also addresses the limitations of temporal variation correction coverage and recommends using only the correction from self-observations.All processes are developed under simulations because observational data are still difficult to obtain.Our findings demonstrate that the corrected time-step method yieldsσvig values consistent with other approaches.

Assessment of the performance of the TOPGNSS and ANN-MB antennas for ionospheric measurements using low-cost u-blox GNSS receivers

Low-cost GNSS receivers have recently been gaining reliability as good candidates for ionospheric studies. In line with these gains are genuine concerns about improving the performance of these receivers. In this work, we present a comprehensive investigation of the performances of two antennas(the u-blox ANN-MB and the TOPGNSS TOP-106) used on a low-cost GNSS receiver known as the u-blox ZED-F9P. The two antennas were installed on two identical and co-located u-blox receivers. Data used from both receivers cover the period from January to June 2022. Results from the study indicate that the signal strengths are dominantly greater for the receiver with the TOPGNSS antenna than for the receiver with the ANN-MB antenna, implying that the TOPGNSS antenna is better than the ANN-MB antenna in terms of providing greater signal strengths. Summarily, the TOPGNSS antenna also performed better in minimizing the occurrence of cycle slips on phase TEC measurements. There are no conspicuous differences between the variances(computed as 5-min standard deviations) of phase TEC measurements for the two antennas, except for a period around May-June when the TOPGNSS gave a better performance in terms of minimizing the variances in phase TEC. Remarkably, the ANN-MB antenna gave a better performance than the TOPGNSS antenna in terms of minimizing the variances in pseudorange TEC for some satellite observations. For precise horizontal(North and East) positioning, the receiver with the TOPGNSS antenna gave better results, while the receiver with the ANN-MB antenna gave better vertical(Up) positioning. The errors for the receivers of both antennas are typically within about 5 m(the monthly mean was usually smaller than 1 m) in the horizontal direction and within about 10 m(the monthly mean was usually smaller than 4 m) in the vertical direction.

Longitudinal dependence of the forecast accuracy of the ionospheric total electron content in the equatorial zone

The longitudinal dependence of the behavior of ionospheric parameters has been the subject of a number of works where significant variations are discovered.This also applies to the prediction of the ionospheric total electron content(TEC),which neural network methods have recently been widely used.However,the results are mainly presented for a limited set of meridians.This paper examines the longitudinal dependence of the TEC forecast accuracy in the equatorial zone.In this case,the methods are used that provided the best accuracy on three meridians:European(30°E),Southeastern(110°E)and American(75°W).Results for the stations considered are analyzed as a function of longitude using the Jet Propulsion Laboratory Global Ionosphere Map(JPL GIM)for 2015.These results are for 2 h ahead and 24 h ahead forecast.It was found that in this case,based on the metric values,three groups of architectures can be distinguished.The first group included long short-term memory(LSTM),gated recurrent unit(GRU),and temporal convolutional networks(TCN)models as a part of unidirectional deep learning models;the second group is based on the recurrent models from the first group,which were supplemented with a bidirectional algorithm,increasing the TEC forecasting accuracy by 2-3 times.The third group,which includes the bidirectional TCN architecture(BiTCN),provided the highest accuracy.For this architecture,according to data obtained for 9 equatorial stations,practical independence of the TEC prediction accuracy from longitude was observed under the following metrics(Mean Absolute Error MAE,Root Mean Square Error RMSE,Mean Absolute Percentage Error MAPE):MAE(2 h)is 0.2 TECU approximately;MAE(24 h)is 0.4 TECU approximately;RMSE(2 h)is less than 0.5 TECU except Niue station(RMSE(2 h)is 1 TECU approximately);RMSE(24 h)is in the range of 1.0-1.7 TECU;MAPE(2 h)<1%except Darwin station,MAPE(24 h)<2%.This result was confirmed by data from additional 5 stations that formed latitudinal chains in the equatorial part of the three meridians.The complete correspondence of the observational and predicted TEC values is illustrated using several stations for disturbed conditions on December 19-22,2015,which included the strongest magnetic storm in the second half of the year(min Dst=-155 nT).

Statistical Characteristics of the Temporal Spectrum of Scattered Radiation in the Equatorial Ionosphere

On the basis of the solution of the space-time characteristic system by the method of geometric optics using symbolic calculations,analytical and numerical simulation of the propagation of the ordinary and extraordinary radio waves in the conducting equatorial ionospheric plasma was made considering the anisotropy of plasma irregularities and non-stationary nature of propagation medium.Broadening of the spectrum and the displacement of its maximum contain velocity of a turbulent plasma flow and parameters characterizing anisotropic plasmonic structures.Statistical moments of both radio waves do not depend on the absorption sign and are valid for both active and absorptive random media.Temporal pulsations and conductivity of a turbulent ionospheric plasma have an influence on the evaluation of the spectrum-varying propagation distances travelling by these waves.The new double-humped effect in the temporal spectrum has been revealed for the ordinary wave varying anisotropy coefficient and dip angle of stretched plasmonic structures.From a theoretical point of view,the algorithms developed in this work allow effective modelling of the propagation of both radio signals in the equatorial conductive ionospheric plasma,considering the external magnetic field,inhomogeneities of electron density in-homogeneities,as well as non-stationary.

Study of the effects on GPS coordinate time series caused by higher-order ionospheric corrections calculated using the DIPOLE model

As one of the main error sources in high-precision Global Positioning System （GPS） data processing, higher-order ionospheric （HOI） delays cause significant effects on coordinate time series that cannot be ignored in analyses of long time series. Typically two geomagnetic models, DIPOLE model and Inter- national Geomagnetic Reference Field （IGRF） model, are used for calculating HOI corrections. This paper investigates the effects of HOI correction caused by the DIPOLE model on coordinate time series. GPS data from 104 globally distributed International GNSS Service （IGS） stations spanning from January, 1999 to December, 2003 were reprocessed following up-to-date processing strategies utilizing GAMIT and GLOBK software. Two coordinate time series solutions before and after applying HOI corrections using the DIPOLE model were derived for studying the effects in terms of seasonal variations and noise amplitudes. The results show that after applying the HOI corrections calculated with DIPOLE, the noise amplitudes of the coordinate time series increased, especially in the north and east directions, and the increased amplitudes of the flicker noise were larger than those of the white noise. Furthermore, spurious periodic signals that were probably introduced by the HOI corrections from the DIPOLE model were also found. Moreover, an apparent increase was confirmed for the power spectra of most of the stations, especially in the north direction, and the amplitudes of both the annual and semi-annual signals also increased in the north and east directions. It can be inferred that the quality of the external data sources such as the geomagnetic model might be the key factors that lead to the above results. The results also suggest that we should be very careful when the DIPOLE model is used for HOI corrections.

APPLICATIONS OF HIGHER-ORDER UPWIND SCHEME FOR PROJECTILES IN TRANSONIC FLOW

针对弹丸跨音速粘性绕流流场进行了数值仿真研究，并与实验进行了对比。数值仿真的控制方程为雷诺平均的Navier-Stokes方程，湍流模型采用Baldwin-Lomax模型，应用了四阶的MUSCL TVD格式。结果表明，该方法可以取得高清晰度的流场结构。

The earthquake-related disturbances in ionosphere and project of the first China seismo-electromagnetic satellite

Based on the case studies and statistical analysis of earthquake-related ionospheric disturbances mainly from DEMETER satellite, ground-based GPS and ionosounding data, this paper summarizes the statisw tical characteristics of earthquake-related ionospheric disturbances, including electromagnetic emissions, plasma perturbations and variation of energetic particle flux. According to the main results done by Chinese scientists, fusing with the existed study from global researches, seismo-ionospheric disturbances usually occurred a few days or hours before earthquake occurrence. Paralleling to these case studies, lithosphere-atmosphere-ionosphere （LAI） coupling mechanisms are checked and optimized. A thermo-electric model was proposed to explain the seismo-electromagnetic effects before earthquakes. A propagation model was put forward to explain the electromagnetic waves into the ionosphere. According to the requirement of earthquake prediction research, China seismo-electromagnetic satellite, the first space-based platform of Chinese earthquake stereoscopic observation system, is proposed and planned to launch at about the end of 2014. It focuses on checking the LAI model and distinguishing earthquake-related ionospheric disturbance. The preliminary design for the satellite will adopt CAST-2000 platform with eight payloads onboard. It is believed that the satellite will work together with the ground monitoring network to improve the capability to capture seismo-electromagnetic information, which is beneficial for earthquake monitoring and prediction researches.

Penetration characteristics of VLF wave from atmosphere into lower ionosphere

The factors affecting the reflection and transmission coefficient of the ionosphere have been analyzed.These factors include wave frequency,incident angle,geomagnetic inclination,electron density and collision frequency in the ionosphere.The ionosphere refractive index is also analyzed.The ionosphere above 70 km is considered to be homogeneous and anisotropic,and the reflection and transmission coefficient matrix is calculated using matrix method.Simultaneously the Booker quartic equation is solved to get the refractive index in the ionosphere.The results show that when the wave frequency is higher,it is easier to penetrate into the ionosphere from its bottom boundary and the propagation attenuation in the ionosphere is smaller.TE（traverse electric） wave and TM（traverse magnetic） wave can both penetrate into the ionosphere with a small incident angle,while TE wave can hardly transmit into the ionosphere when the incident angle is large.The transmission coefficient decreases as the geomagnetic inclination increases.TE and TM wave cannot penetrate into the ionosphere at magnetic equator.When the electron collision frequency is higher,it is easier for VLF wave to penetrate into the ionosphere and the attenuation of ordinary wave is weaker,which may be caused by the energy transportation between the waves and the particles.The ordinary（O） wave experiences severer attenuation than extraordinary（X） wave,and X wave is a penetration mode whereas O wave is a non-penetration mode in the ionosphere.All the results indicate that VLF wave with higher frequency is easier to penetrate into the ionosphere and to be recorded by the satellites at high latitude.It is hard for ULF and the lower frequency VLF wave to transmit into the ionosphere directly for the severe reflection and attenuation.It may transmit into the ionosphere with a small incident angle due to the nonlinear effect,for example,the interaction between the waves and the particles or cross modulation,and then propagate along the whistle duct with small attenuation.This work may be a preliminary theoretical exploration for the future calculation on the response of ground based VLF artificial transmitter in the ionosphere and further study on the seismic ionosphere coupling model.