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The signals received by very low-frequency/extremely low-frequency nonlinear receivers are frequently affected by intense atmospheric pulse noise stemming from thunderstorms and global lightning activity. Current noise processing algorithms designed for nonlinear channels within these frequency ranges, which are predicated on fractional p-order moment alpha stable distribution criteria (where 0 < p < α < 2, and p and α denote distinct characteristic indices of alpha stable distribution noise), are constrained by their reliance on limited p-order moment statistics. As a result, the performance of low-frequency nonlinear channel receivers experiences significant degradation when confronted with robust pulse noise interference (0 < p < α < 2). To tackle this challenge, the present study introduces a novel variable step robust mixed norm (RMN) adaptive filtering algorithm, designated as SVS-RMN, which is based on the Sigmoid function. Leveraging the nonlinearity of the Sigmoid function and building upon the power function Hammerstein nonlinear channel model, the algorithm aims to enhance the RMN algorithm by deriving new cost functions and adaptive iteration formulas. The performance of the proposed algorithm is evaluated in comparison to conventional RMN algorithms based on fractional low-order moment (FLOM) criteria (0 < p < 2), as well as other algorithms employing variable step sizes and either FLOM or radial basis function (RBF) criteria, across various intensities of pulse noise and mixed signal-to-noise ratios. The experimental results reveal the following: (1) The proposed algorithm effectively mitigates strong pulse noise interference and significantly enhances the tracking performance of the RMN algorithm compared to conventional RMN algorithms based on FLOM criteria. (2) In terms of computational efficiency, simplicity of structure, convergence speed, and stability, the proposed algorithm surpasses other algorithms based on FLOM or RBF criteria.

Recent emerge of dielectric nanoparticle chains featuring subwavelength topological states has opened unprecedented avenues for light. Here, we demonstrate a mechanical analogy of zigzag nanoparticle chain that supports vibrational and rotational localizations in the form of subwavelength topological edge states at extremely low frequency (near zero). We elaborate analytical methodology to thoroughly analyze the wave dynamics in the near zero-frequency (NZF) regime. Due to weak rotational couplings, we find that motion can be efficiently confined on the boundaries of the chains. Interestingly, the vibration-rotation coupled property enables the granular chain for exotic NZF waves with spreading rotation inside the chain but localized vibration on the boundaries. We characterize the propagation properties of elastic waves in the chain, and exhibit the fingerprints of topological edge states on the boundaries. Our study provides the possibilities for vibration control techniques using granular media at extremely low frequency.

We analyzed a large number (77) of low-to-medium-magnitude earthquakes (M3.5–M6.5) that occurred within a period of three years (2020–2022) in the Southern half of Greece in relation to the ELF activity in that region and time period. In most cases, characteristic ELF signals appear up to 20 days before the earthquakes. This observation may add an important new element to the Lithospheric–Atmospheric–Ionospheric scenario, thus contributing to a better prediction of incoming earthquakes. We discuss the role of ELF observations in reliable seismic forecasting. We conclude that the magnitude of an earthquake larger than M4.0 and the distance of the epicenter shorter than 300 km from the recording site is needed for typical pre-seismic signals to be observed. Finally, we remark that a reliable prediction of earthquakes could result from an integrated project of multi-instrumental observations, where all the known variety of precursors would be included, and the whole data set would be analyzed by advanced machine learning methods.

The controlled source extremely low frequency (CSELF) method bears the potential for deep resource exploitation utilizing the skywave. The “Skywave” denotes the electromagnetic wave propagating through the waveguide formed by the Earth and ionosphere. It has a considerable penetration depth into the lithosphere due to its low-frequency band. Previous research on extremely low-frequency electromagnetic fields with the coupled lithosphere, atmosphere, and planar ionosphere models ignored the effect of the Earth’s curvature. Thus, we aimed to present the exact formulas for horizontal electric dipoles (HED) in a spherical “Earth-ionosphere” model. These new formulas consider the Earth’s curvature as a multilayer medium rather than a homogeneous underground. We introduce three techniques: function combination pairs, addition and subtraction terms, and Padé approximants, to handle slow convergence in numerical calculation. In the spherical waveguide, electromagnetic fields are mutually interfered with and produce oscillations, which is different from the planar model. The influence of Earth’s curvature cannot be neglected with the increase in source–receiver distance, though it is negligible within 3000 km. Furthermore, it is worth noting that apparent resistivity ρθφ enters the waveguide area earlier than ρφθ. This method can be used as Green’s function to simulate the electromagnetic field of actual antennas and 3-D models.

Over the last century, abnormal electromagnetic (EM) emissions associated with earthquake (EQ) activities have been widely reported and recorded by ground-based and satellite observations. However, the frequency at which abnormal EM emissions have been detected varies. In addition, whether low Earth orbit (LEO) satellites can detect EM anomalies from EQs remains controversial. In this paper, we take the Yushu earthquake as an example to address these concerns by DEMETER satellite observations and a newly constructed lithosphere-atmosphere-ionosphere model of extremely low frequency (ELF) wave propagation. The results illustrate that the frequency of ELF EM anomalies of the Yushu earthquake is mainly at 200–400 Hz. The observations and simulations illustrate that the power-frequency curve of the ELF EM wave from an underground source has a peak power frequency at 200–400 Hz, which is significantly different from the ELF EM wave radiated from the ground source.

A numerical analysis on field distribution along the Earth’s surface of a line current source submerged in the ground is conducted in this paper to investigate the potential of the extremely low frequency (ELF) technology in the envisioned long-distance communication techniques. The problem is modeled as a submerged horizontal electric dipole (HED) in a two-layered homogeneous half space and solved by the combined numerical methods of the Romberg-Euler method and Gauss-Laguerre method. The model is validated by experimental results with only a maximum 10% error at 9 Hz around 490 m. Meanwhile, the study shows that the ELF signals emitted by a submerged line current source can transmit at least 1 km with a current sensor sensitivity of 0.1 pT. These results indicate the possibility of applying of ELF technology to long-distance communication or the long-distance transmedia detection.

Some previous research showed that average daily exposure to extremely low frequency (ELF) magnetic fields (MF) of more than 0.3 or 0.4 μT could potentially increase risk of childhood leukaemia. To allow calculations of ELF MF around high voltage (HV) power lines (PL) for the whole Slovenia, a new three-dimensional method including precision terrain elevation data was developed to calculate the long-term average ELF MF. Data on population of Slovenian children and adolescents and on cancer patients with leukaemia's aged 0-19 years, brain tumours at age 0-29, and cancer in general at age 0-14 for a 12-year period 2005-2016 was obtained from the Slovenian Cancer Registry. According to the large-scale calculation for the whole country, only 0.5% of children and adolescents under the age of 19 in Slovenia lived in an area near HV PL with ELF MF density greater than 0.1 μT. The risk of cancer for children and adolescents living in areas with higher ELF MF was not significantly different from the risk of their peers. The new method enables relatively fast calculation of the value of low-frequency magnetic fields for arbitrary loads of the power distribution network, as the value of each source for arbitrary load is calculated by scaling the value for nominal load, which also enables significantly faster adjustment of calculated estimates in the power distribution network.

BackgroundData on the effects of extremely low frequency electromagnetic fields (ELF-EMF) on pregnancy outcomes are inconclusive.ObjectiveTo study the relation between maternal cumulative exposure to ELF-EMF during pregnancy and the risk of prematurity or small for gestational age (SGA) in a pooled analysis of two French birth cohorts.MethodsElfe and Epipage2 are both population-based birth cohorts initiated in 2011 and included 18 329 and 8400 births, respectively. Health data and household, mother and child characteristics were obtained from medical records and questionnaires at maternity and during follow-up. A job exposure matrix was used to assess cumulative exposure to ELF-EMF during three periods: (1) until 15 weeks of gestation, (2) until 28 weeks of gestation and (3) until 32 weeks of gestation. Analyses were restricted to single live births in mainland France and to mothers with documented jobs (N=19 894). Adjusted logistic regression models were used.ResultsAccording to the period studied, 3.2%–4% of mothers were classified as highly exposed. Results were heterogeneous. Increased risks of prematurity were found among low exposed mothers for the three periods, and no association was observed among the most exposed (OR1=0.92 (95% CI 0.74 to 1.15); OR2=0.98 (95% CI 0.80 to 1.21); OR3=1.14 (95% CI 0.92 to 1.41)). For SGA, no association was observed with the exception of increased risk among the low exposed mothers in period 2 and the most exposed in period 3 (OR=1.25 (95% CI 1.02 to 1.53)).ConclusionSome heterogeneous associations between ELF-EMF exposure and prematurity and SGA were observed. However, due to heterogeneity (ie, their independence regarding the level of exposure), associations cannot be definitely explained by ELF-EMF exposure.

Delayed fracture healing and fracture non-unions impose an enormous burden on individuals and society. Successful healing requires tight communication between immune cells and bone cells. Macrophages can be found in all healing phases. Due to their high plasticity and long life span, they represent good target cells for modulation. In the past, extremely low frequency pulsed electromagnet fields (ELF-PEMFs) have been shown to exert cell-specific effects depending on the field conditions. Thus, the aim was to identify the specific ELF-PEMFs able to modulate macrophage activity to indirectly promote mesenchymal stem/stromal cell (SCP-1 cells) function. After a blinded screening of 22 different ELF-PEMF, two fields (termed A and B) were further characterized as they diversely affected macrophage function. These two fields have similar fundamental frequencies (51.8 Hz and 52.3 Hz) but are emitted in different groups of pulses or rather send–pause intervals. Macrophages exposed to field A showed a pro-inflammatory function, represented by increased levels of phospho-Stat1 and CD86, the accumulation of ROS, and increased secretion of pro-inflammatory cytokines. In contrast, macrophages exposed to field B showed anti-inflammatory and pro-healing functions, represented by increased levels of Arginase I, increased secretion of anti-inflammatory cytokines, and growth factors are known to induce healing processes. The conditioned medium from macrophages exposed to both ELF-PEMFs favored the migration of SCP-1 cells, but the effect was stronger for field B. Furthermore, the conditioned medium from macrophages exposed to field B, but not to field A, stimulated the expression of extracellular matrix genes in SCP-1 cells, i.e., COL1A1, FN1, and BGN. In summary, our data show that specific ELF-PEMFs may affect immune cell function. Thus, knowing the specific ELF-PEMFs conditions and the underlying mechanisms bears great potential as an adjuvant treatment to modulate immune responses during pathologies, e.g., fracture healing.

The study aimed to determine effect of extremely low frequency (50 Hz) electromagnetic fields (ELF-EMFs) exposure on serum levels of interleukin-17 (IL-17) and transforming growth factor-β (TGF-β) as signature cytokines of Th17 and regulatory T (Treg) cells, respectively. Retinoid-related orphan receptor γT and transcription factor forkhead box P3 (Foxp3) expression levels as lineage defining of Th17 and Treg cells were also assessed in the spleen and thymus. Eighty male rats were separated into 4 exposed groups (1, 100, 500, and 2,000 μT magnetic flux intensities) and a control. All rats were immunized by human serum albumin after 1 month of the exposure and the experiment was continued in the same manner for 1 month more. The results demonstrated that the weight of thymuses was significantly declined at intensity of 2,000 μT. At the preimmunization phase, the serum levels of IL-17 and TGF-β were significantly decreased at intensities of 1 and 100 μT. The expression of Foxp3 was also downregulated at intensities of 1 and 100 μT. In conclusion, low intensities of ELF-EMF may reduce the serum levels of IL-17 and TGF-β and downregulate the expression of Foxp3 in spleen.