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Search Results (1,318)

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19 pages, 2788 KiB  
Article
Balanced Fertilization Improves Crop Production and Soil Organic Carbon Sequestration in a Wheat–Maize Planting System in the North China Plain
by Huiyu Zhang, Hao Zhai, Ruixin Zan, Yuan Tian, Xiaofei Ma, Hutai Ji and Dingyi Zhang
Plants 2025, 14(6), 838; https://doi.org/10.3390/plants14060838 - 7 Mar 2025
Abstract
Maintaining the long-term viability of a wheat–maize planting system, particularly the synchronous improvement of crop production and soil organic carbon (SOC) sequestration, is crucial for ensuring food security in the North China Plain. A field experiment in which wheat–maize was regarded as an [...] Read more.
Maintaining the long-term viability of a wheat–maize planting system, particularly the synchronous improvement of crop production and soil organic carbon (SOC) sequestration, is crucial for ensuring food security in the North China Plain. A field experiment in which wheat–maize was regarded as an integral fertilization unit was carried out in Shanxi Province, China, adopting a split-plot design with different distribution ratios of phosphorus (P) and potassium (K) fertilizer between wheat and maize seasons in the main plot (A) (a ratio of 3:0, A1; a ratio of 2:1, A2) and different application rates of pure nitrogen (N) during the entire wheat and maize growth period (B) (450 kg·ha−1, B1; 600 kg·ha−1, B2). Moreover, no fertilization was used in the entire wheat and maize growth period for the control (CK). The findings showed that A2B1 treatment led to the highest response, with an average wheat yield of 7.75 t·ha−1 and an average maize yield of 8.40 t·ha−1 over the last 9 years. The highest SOC content (15.13 g·kg−1), storage (34.20 t·ha−1), and sequestration (7.11 t·ha−1) were also observed under the A2B1 treatment. Both enhanced crop yield and SOC sequestration resulted from improvements in cumulative carbon (C) input, soil nutrients, and stoichiometry under the A2B1 treatment. It was confirmed that total N (TN), alkali-hydrolysable N (AN), available P (AP), available K (AK), and the ratios of C:K, N:K, and N:P had positive effects on crop yield through the labile components of SOC and on SOC sequestration through microbial necromass C. To conclude, our findings highlight the urgent need to optimize fertilizer management strategies to improve crop production and SOC sequestration in the North China Plain. Full article
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<p>The yields of wheat (<b>A</b>), maize (<b>B</b>), and cumulative carbon input (<b>C</b>) under different fertilization treatments from 2014 to 2023: the 3:0 distribution ratio of phosphorus (P) and potassium (K) fertilizer between the wheat and maize seasons combined with 450 kg·ha<sup>−1</sup> of pure nitrogen (N) during the entire growth period of wheat and maize (A1B1); the 3:0 distribution ratio of P and K fertilizer between the wheat and maize seasons combined with 600 kg·ha<sup>−1</sup> of pure N during the entire growth period of wheat and maize (A1B2); the 2:1 distribution ratio of P and K fertilizers between the wheat and maize seasons combined with 450 kg·ha<sup>−1</sup> of pure N during the entire growth period of wheat and maize (A2B1); the 2:1 distribution ratio of P and K fertilizers between the wheat and maize seasons combined with 600 kg·ha<sup>−1</sup> of pure N during the entire growth period of wheat and maize (A2B2); no fertilization in the entire growth period of wheat and maize (CK). Different lowercase letters represent significant differences between different treatments based on Duncan’s multiple comparisons at <span class="html-italic">p</span> &lt; 0.05. The upper and lower boundaries of the box plots represent the 75% and 25% quartiles, respectively. The upper and lower edges of the line in the whisker plot represent positive and negative error values, respectively. The black solid circle represents the average value of yield. The red line connects the average values of each treatment. *, **, and ‘ns’ indicate <span class="html-italic">p</span> &lt; 0.05, <span class="html-italic">p</span> &lt; 0.01, and <span class="html-italic">p</span> &gt; 0.05, respectively.</p>
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<p>The contents of soil total N (<b>A</b>), alkali-hydrolysable N (<b>B</b>), total P (<b>C</b>), available P (<b>D</b>), total K (<b>E</b>), and available K (<b>F</b>) under different fertilization treatments. Different lowercase letters represent significant differences between different treatments based on Duncan’s multiple comparisons at <span class="html-italic">p</span> &lt; 0.05. **, ***, and ‘ns’ indicate <span class="html-italic">p</span> &lt; 0.01, <span class="html-italic">p</span> &lt; 0.001, and <span class="html-italic">p</span> &gt; 0.05, respectively.</p>
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<p>The concentrations of soil particulate organic carbon (<b>A</b>), labile organic carbon (<b>B</b>), dissolved organic carbon (<b>C</b>), and microbial biomass carbon (<b>D</b>) under different treatments. Different lowercase letters represent significant differences between different treatments based on Duncan’s multiple comparisons at <span class="html-italic">p</span> &lt; 0.05. *, **, ***, and ‘ns’ indicate <span class="html-italic">p</span> &lt; 0.05, <span class="html-italic">p</span> &lt; 0.01, <span class="html-italic">p</span> &lt; 0.001, and <span class="html-italic">p</span> &gt; 0.05, respectively.</p>
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<p>The contents of soil bacterial necromass C (<b>A</b>), fungal necromass C (<b>B</b>), microbial necromass C (<b>C</b>), and the ratio of fungal necromass C/bacterial necromass C (<b>D</b>) under different fertilization treatments. Different lowercase letters represent significant differences between different treatments based on Duncan’s multiple comparisons at <span class="html-italic">p</span> &lt; 0.05. *, **, ***, and ‘ns’ indicate <span class="html-italic">p</span> &lt; 0.05, <span class="html-italic">p</span> &lt; 0.01, <span class="html-italic">p</span> &lt; 0.001, and <span class="html-italic">p</span> &gt; 0.05, respectively.</p>
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<p>Pearson’s correlation coefficient between soil chemical nutrients, stoichiometry, related parameters of SOC, and annual crop yield. Total N (TN); alkali-hydrolysable N (AN); total P (TP); available P (AP); total K (TK); and available K (AK). * indicates <span class="html-italic">p</span> &lt; 0.05.</p>
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<p>Structural equation (<b>A</b>) and random forest (<b>B</b>,<b>C</b>) models for annual crop yield and SOC sequestration affected by fertilization methods. In the structural equation model, the red and blue lines represent the positive and negative effects, respectively. The width of the line is proportional to the strength of factor loading. The number adjacent to the arrow line is a standardized coefficient that shows the variance explained by the variable. Solid and dotted lines indicate significant and non-significant effects, respectively. *, **, and *** indicate <span class="html-italic">p</span> &lt; 0.05, <span class="html-italic">p</span> &lt; 0.01, and <span class="html-italic">p</span> &lt; 0.001, respectively.</p>
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13 pages, 3116 KiB  
Article
Research on Key Technologies of Quantum-Safe Metro-Optimized Optical Transport Networks
by Wei Zhou, Bingli Guo, Boying Cao and Xiaohui Cheng
Appl. Sci. 2025, 15(5), 2809; https://doi.org/10.3390/app15052809 - 5 Mar 2025
Viewed by 189
Abstract
This research introduces a novel physical-layer encryption technique for metropolitan-optimized optical transport networks (M-OTNs) that integrates real-time optical signal time-domain scrambling/descrambling with decoy-state quantum key distribution (DS-QKD). The method processes real-time optical data from the optical service unit (OSU) using a series of [...] Read more.
This research introduces a novel physical-layer encryption technique for metropolitan-optimized optical transport networks (M-OTNs) that integrates real-time optical signal time-domain scrambling/descrambling with decoy-state quantum key distribution (DS-QKD). The method processes real-time optical data from the optical service unit (OSU) using a series of tunable Fabry–Perot cavities (FPCs), synchronized and updated with a running key. Experimental validation demonstrates secure communication within the optical network’s physical layer during standard OTU2 data transmission (10.709 Gbps), achieving an online transmission distance exceeding 100 km over typical single-mode fiber with a power loss of approximately 1.77 dB. The results indicate that this integrated approach significantly enhances the security of the optical physical layer in M-OTNs. Full article
(This article belongs to the Special Issue Novel Approaches for High Speed Optical Communication)
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<p>OSU-based M-OTN hierarchy.</p>
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<p>OPU frame structure based on payload blocks.</p>
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<p>Allocating OPU PBs to different OSU services.</p>
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<p>System schematic diagram of an OSU combined with DS-QKD.</p>
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<p>Schematic diagram of the time-domain scrambling/descrambling of the OSU optical signal through a TCM.</p>
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<p>Experimental setup for real-time OSU optical signal time scrambling/descrambling and key transmission via DS-QKD.</p>
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<p>Eye diagram of OSU electrical signal.</p>
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<p>Eye diagram of OSU optical signal scrambling and descrambling.</p>
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<p>BER and running key rate performance.</p>
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18 pages, 4125 KiB  
Article
An Improved Second-Order Generalized Integrator Phase-Locked Loop with Frequency Error Compensation
by Zhaoyang Yan, Hanyi Qiao, Zongze Guo, Dongxu Wang and Yidan Feng
Electronics 2025, 14(5), 1018; https://doi.org/10.3390/electronics14051018 - 3 Mar 2025
Viewed by 167
Abstract
In distributed energy grid-connected systems, fast and accurate grid synchronization technology is crucial for system stability. This article proposes an improved phase-locked loop (FECSOGI-PLL) based on frequency error compensation. By introducing an unbiased adaptive frequency compensation mechanism, the SOGI resonant frequency is adjusted [...] Read more.
In distributed energy grid-connected systems, fast and accurate grid synchronization technology is crucial for system stability. This article proposes an improved phase-locked loop (FECSOGI-PLL) based on frequency error compensation. By introducing an unbiased adaptive frequency compensation mechanism, the SOGI resonant frequency is adjusted in real time to accurately track the input signal. A linear time invariant (LTI) model of the FECSOGI-PLL was established in the article, and its wider stability domain was clarified based on the Routh–Hurwitz criterion. The strong robustness of its fast response under non-ideal conditions, such as frequency jumps and amplitude drops, was verified through simulation and experiments. The core innovation of this study lies in the first implementation of unbiased adaptive regulation of the SOGI resonant frequency through the frequency error compensation mechanism, as well as the system design method based on the extended stability domain, providing theoretical support and engineering practice reference for high robustness power grid synchronization technology. Full article
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<p>SOGI-QSG structure diagram.</p>
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<p>The relationship between the Bode plots of <math display="inline"><semantics> <mrow> <msub> <mi>G</mi> <mi>α</mi> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">s</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>G</mi> <mi>β</mi> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">s</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> with the variation of system gain. (<b>a</b>) The Bode plot of <math display="inline"><semantics> <mrow> <msub> <mi>G</mi> <mi>α</mi> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">s</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math>. (<b>b</b>) The Bode plot of <math display="inline"><semantics> <mrow> <msub> <mi>G</mi> <mi>β</mi> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">s</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math>.</p>
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<p>SOGI-PLL structure block diagram.</p>
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<p>Structure block diagram of FECSOGI-PLL.</p>
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<p>Waveform diagram of the feedback SOGI resonant frequency <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>ω</mi> <mo>^</mo> </mover> <mi>s</mi> </msub> </mrow> </semantics></math>.</p>
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<p>LTI model block diagrams of FECSOGI-PLL and SOGI-PLL, where <math display="inline"><semantics> <mrow> <mi>Z</mi> <mo>=</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <mi>k</mi> <msub> <mi>ω</mi> <mi>n</mi> </msub> </mrow> <mn>2</mn> </mfrac> </mstyle> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>P</mi> <mo>=</mo> <msub> <mi>k</mi> <mi>p</mi> </msub> <msub> <mi>V</mi> <mi>n</mi> </msub> <mo>+</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <msub> <mi>k</mi> <mi>i</mi> </msub> <msub> <mi>V</mi> <mi>n</mi> </msub> </mrow> <mi>s</mi> </mfrac> </mstyle> </mrow> </semantics></math>. (<b>a</b>) The LTI model of the FECSOGI-PLL. (<b>b</b>) The LTI model of the SOGI-PLL.</p>
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<p>Comparison of LTI model outputs between the two under the same <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>p</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>i</mi> </msub> </mrow> </semantics></math> conditions. (<b>a</b>) Case 1. (<b>b</b>) Case 2.</p>
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<p>Waveforms of DQ-axis outputs for SOGI-PLL and FECSOGI-PLL under input voltage frequency step changes. (<b>a</b>) DQ-axis output waveforms under input voltage frequency step changes. (<b>b</b>) DQ-axis output waveforms under simultaneous input amplitude and frequency step changes.</p>
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<p>Experiential setup.</p>
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<p>Power grid frequency mutation. (<b>a</b>) Output phase angle of the SOGI-PLL and FECSOGI-PLL. (<b>b</b>) DQ-axis output of the SOGI-PLL and FECSOGI-PLL. (<b>c</b>) Frequency output waveforms of SOGI-PLL, FECSOGI-PLL, APF-PLL, FFSOGI-PLL.</p>
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<p>Simultaneous mutation of power grid frequency and amplitude. (<b>a</b>) Output phase angle of the SOGI-PLL and FECSOGI-PLL. (<b>b</b>) DQ-axis output of the SOGI-PLL and FECSOGI-PLL. (<b>c</b>) Frequency output waveforms of SOGI-PLL, FECSOGI-PLL, APF-PLL, FFSOGI-PLL.</p>
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<p>(<b>a</b>) Frequency output waveforms of SOGI-PLL, FECSOGI-PRL, APF-PLL, and FFSOGI-PRL under small frequency disturbances. (<b>b</b>) Frequency output waveforms of SOGI-PLL, FECSOGI-PLL, APF-PLL, and FFSOGI-PLL under the frequency jump of adding DC bias.</p>
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24 pages, 6487 KiB  
Article
Synchronous Atmospheric Correction of Wide-Swath and Wide-Field Remote Sensing Image from HJ-2A/B Satellite
by Honglian Huang, Yuxuan Wang, Xiao Liu, Rufang Ti, Xiaobing Sun, Zhenhai Liu, Xuefeng Lei, Jun Lin and Lanlan Fan
Remote Sens. 2025, 17(5), 884; https://doi.org/10.3390/rs17050884 - 1 Mar 2025
Viewed by 357
Abstract
The Chinese HuanjingJianzai-2 (HJ-2) A/B satellites are equipped with advanced sensors, including a Multispectral Camera (MSC) and a Polarized Scanning Atmospheric Corrector (PSAC). To address the challenges of atmospheric correction (AC) for the MSC’s wide-swath, wide-field images, this study proposes a pixel-by-pixel method [...] Read more.
The Chinese HuanjingJianzai-2 (HJ-2) A/B satellites are equipped with advanced sensors, including a Multispectral Camera (MSC) and a Polarized Scanning Atmospheric Corrector (PSAC). To address the challenges of atmospheric correction (AC) for the MSC’s wide-swath, wide-field images, this study proposes a pixel-by-pixel method incorporating Bidirectional Reflectance Distribution Function (BRDF) effects. The approach uses synchronous atmospheric parameters from the PSAC, an atmospheric correction lookup table, and a semi-empirical BRDF model to produce surface reflectance (SR) products through radiative, adjacency effect, and BRDF corrections. The corrected images showed significant improvements in clarity and contrast compared to pre-correction images, with minimum increases of 55.91% and 35.63%, respectively. Validation experiments in Dunhuang and Hefei, China, demonstrated high consistency between the corrected SR and ground-truth data, with maximum deviations below 0.03. For surface types not covered by ground measurements, comparisons with Sentinel-2 SR products yielded maximum deviations below 0.04. These results highlight the effectiveness of the proposed method in improving image quality and accuracy, providing reliable data support for applications such as disaster monitoring, water resource management, and crop monitoring. Full article
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<p>Schematic of synchronized detection between PSAC and MSC.</p>
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<p>Atmospheric correction flowchart for wide-swath and wide-field multispectral images.</p>
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<p>Matching results of AOD and CWV for MSC image. (<b>a</b>) Matched AOD distribution. (<b>b</b>) AOD distribution after linear interpolation. (<b>c</b>) Matched CWV distribution. (<b>d</b>) CWV distribution after linear interpolation.</p>
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<p>Comparison of pre- and post-atmospheric correction for HJ-2A satellite multispectral image of Beijing Daxing Airport, China. The red-marked and green-marked areas represent the selected regions for comparison and validation with Sentinel-2 data, as described in <a href="#sec4dot3-remotesensing-17-00884" class="html-sec">Section 4.3</a>. (CCD1, 14 November 2022; AOD = 0.446; CWV = 0.51 g/cm<sup>2</sup>). (<b>a</b>) Before atmospheric correction. (<b>b</b>) After atmospheric correction.</p>
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<p>Comparison of pre- and post-atmospheric correction for an HJ-2B satellite multispectral image of the Indian Plains region. The red-marked and green-marked areas represent the selected regions for comparison and validation with Sentinel-2 data, as described in <a href="#sec4dot3-remotesensing-17-00884" class="html-sec">Section 4.3</a>. (CCD3, 25 November 2022; AOD = 0.208; CWV = 0.96 g/cm<sup>2</sup>). (<b>a</b>) Before atmospheric correction. (<b>b</b>) After atmospheric correction.</p>
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<p>Comparison of pre- and post-atmospheric correction for HJ-2A satellite multispectral image of Xianning City, Hubei Province, China. The red-marked and green-marked areas represent the selected regions for comparison and validation with Sentinel-2 data, as described in <a href="#sec4dot3-remotesensing-17-00884" class="html-sec">Section 4.3</a>. (CCD3, 23 December 2022; AOD = 0.564; CWV = 0.45 g/cm<sup>2</sup>). (<b>a</b>) Before atmospheric correction. (<b>b</b>) After atmospheric correction.</p>
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<p>The contrast, clarity, and their improvements of the multispectral images of Daxing Airport, Beijing, China, before and after atmospheric correction from the HJ-2A satellite. (<b>a</b>) Contrast. (<b>b</b>) Clarity.</p>
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<p>The contrast, clarity, and their improvements of the multispectral images of the Indian Plains region, before and after atmospheric correction from the HJ-2B satellite. (<b>a</b>) Contrast. (<b>b</b>) Clarity.</p>
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<p>The contrast, clarity, and their improvements of the multispectral images of Xian Ning, Hubei Province, China, before and after atmospheric correction from the HJ-2A satellite. (<b>a</b>) Contrast. (<b>b</b>) Clarity.</p>
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<p>Comparison of pre- and post-atmospheric correction for an HJ-2B satellite multispectral image at the Dunhuang site in China. The red-marked area represents the ground measurement region at the Dunhuang site. (<b>a</b>) Before atmospheric correction. (<b>b</b>) After atmospheric correction.</p>
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<p>Comparison of pre- and post-atmospheric correction for HJ-2B satellite multispectral image at Northern high-reflectance site in Dunhuang, China. The red-marked area represents the ground measurement region at the high-reflectance site. (<b>a</b>) Before atmospheric correction. (<b>b</b>) After atmospheric correction.</p>
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<p>Comparison of pre- and post-atmospheric correction for an HJ-2A satellite multispectral image at the suburban area of Hefei, Anhui Province, China. The red-marked and blue-marked areas represent the ground measurement regions for the wheat field and river water, respectively. (<b>a</b>) Before atmospheric correction. (<b>b</b>) After atmospheric correction.</p>
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<p>The reflectance curve from the ground-based synchronized measurements. (<b>a</b>) Dunhuang, Gansu, China. (<b>b</b>) Hefei, Anhui, China.</p>
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<p>Comparison chart of ground-measured reflectance and atmospheric-corrected SR. (<b>a</b>) Dunhuang site (25 January 2021, HJ-2B). (<b>b</b>) High-reflectance site (25 January 2021, HJ-2B). (<b>c</b>) Wheat field (25 March 2021, HJ-2A). (<b>d</b>) River water (25 March 2021, HJ-2A).</p>
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23 pages, 3893 KiB  
Article
Multistable Synaptic Plasticity Induces Memory Effects and Cohabitation of Chimera and Bump States in Leaky Integrate-and-Fire Networks
by Astero Provata, Yannis Almirantis and Wentian Li
Entropy 2025, 27(3), 257; https://doi.org/10.3390/e27030257 - 28 Feb 2025
Viewed by 165
Abstract
Chimera states and bump states are collective synchronization phenomena observed independently (in different parameter regions) in networks of coupled nonlinear oscillators. And while chimera states are characterized by coexistence of coherent and incoherent domains, bump states consist of alternating active and inactive domains. [...] Read more.
Chimera states and bump states are collective synchronization phenomena observed independently (in different parameter regions) in networks of coupled nonlinear oscillators. And while chimera states are characterized by coexistence of coherent and incoherent domains, bump states consist of alternating active and inactive domains. The idea of multistable plasticity in the network connections originates from brain dynamics where the strength of the synapses (axons) connecting the network nodes (neurons) may change dynamically in time; when reaching the steady state the network connections may be found in one of many possible values depending on various factors, such as local connectivity, influence of neighboring cells etc. The sign of the link weights is also a significant factor in the network dynamics: positive weights are characterized as excitatory connections and negative ones as inhibitory. In the present study we consider the simplest case of bistable plasticity, where the link dynamics has only two fixed points. During the system/network integration, the link weights change and as a consequence the network organizes in excitatory or inhibitory domains characterized by different synaptic strengths. We specifically explore the influence of bistable plasticity on collective synchronization states and we numerically demonstrate that the dynamics of the linking may, under special conditions, give rise to co-existence of bump-like and chimera-like states simultaneously in the network. In the case of bump and chimera co-existence, confinement effects appear: the different domains stay localized and do not travel around the network. Memory effects are also reported in the sense that the final spatial arrangement of the coupling strengths reflects some of the local properties of the initial link distribution. For the quantification of the system’s spatial and temporal features, the global and local entropy functions are employed as measures of the network organization, while the average firing rates account for the network evolution and dynamics. In particular, the spatial minima of the local entropy designate the transition points between domains of different synaptic weights in the hybrid states, while the number of minima corresponds to the number of different domains. In addition, the entropy deviations signify the presence of chimera-like or bump-like states in the network. Full article
(This article belongs to the Section Complexity)
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Figure 1

Figure 1
<p>Coupled LIF dynamics with bistable plasticity and negative coupling strengths. Top row: spacetime plots of the potential values <math display="inline"><semantics> <msub> <mi>u</mi> <mi>i</mi> </msub> </semantics></math> starting from three different initial conditions are depicted in panels (<b>a</b>–<b>c</b>). Middle row: (<b>d</b>–<b>f</b>): Corresponding asymptotic coupling strengths <math display="inline"><semantics> <msub> <mi>σ</mi> <mi>i</mi> </msub> </semantics></math> and firing rates <math display="inline"><semantics> <msub> <mi>f</mi> <mi>i</mi> </msub> </semantics></math> for the above three initial conditions. Bottom row: (<b>g</b>) The global entropy evolution with time, <math display="inline"><semantics> <mrow> <mi>H</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> and (<b>h</b>) The local entropy values <math display="inline"><semantics> <msub> <mi>H</mi> <mi>i</mi> </msub> </semantics></math> at the final stages of the simulations. In panels (<b>g</b>,<b>h</b>) the black solid lines correspond to initial condition (<b>a</b>), the red dashed-dotted line to (<b>b</b>) and the green dashed line to (<b>c</b>). The simulations in (<b>a</b>–<b>c</b>) start from different random initial conditions in <math display="inline"><semantics> <msub> <mi>u</mi> <mi>i</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>σ</mi> <mi>i</mi> </msub> </semantics></math>. All other parameter values are identical in the three cases: <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>rest</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>th</mi> </msub> <mo>=</mo> <mn>0.98</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>1024</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mi>l</mi> </msub> <mo>=</mo> <mo>−</mo> <mn>0.7</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mi>c</mi> </msub> <mo>=</mo> <mo>−</mo> <mn>0.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mi>h</mi> </msub> <mo>=</mo> <mo>−</mo> <mn>0.3</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mi>σ</mi> </msub> <mo>=</mo> <mo>−</mo> <mn>1.0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 2
<p>Coupled LIF dynamics with bistable plasticity and positive coupling strengths. Typical potential spacetime profiles <math display="inline"><semantics> <msub> <mi>u</mi> <mi>i</mi> </msub> </semantics></math> for three different initial conditions (<b>a</b>–<b>c</b>) forming bump-like states. For better understanding of the bump-like state complexity, in the second row, panels (<b>d</b>–<b>f</b>) show specific details in restricted time scales between 550–600 TUs of panels (<b>a</b>–<b>c</b>), respectively. Third row: (<b>g</b>–<b>i</b>): Corresponding coupling strengths <math display="inline"><semantics> <msub> <mi>σ</mi> <mi>i</mi> </msub> </semantics></math> and firing rates <math display="inline"><semantics> <msub> <mi>f</mi> <mi>i</mi> </msub> </semantics></math> for the above three initial conditions. Forth row: (<b>j</b>) The global entropy evolution in time, <math display="inline"><semantics> <mrow> <mi>H</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> and (<b>k</b>) The local entropy values <math display="inline"><semantics> <msub> <mi>H</mi> <mi>i</mi> </msub> </semantics></math> at the final stages of of the simulations. In panels (<b>j</b>,<b>k</b>) the black solid lines correspond to initial condition (<b>a</b>), the red dashed-dotted line to (<b>b</b>) and the green dashed line to (<b>c</b>). The simulations in (<b>a</b>–<b>c</b>) start from different random initial conditions in <math display="inline"><semantics> <msub> <mi>u</mi> <mi>i</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>σ</mi> <mi>i</mi> </msub> </semantics></math>. Coupling fixed point values are: <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mi>l</mi> </msub> <mo>=</mo> <mo>+</mo> <mn>0.3</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mi>c</mi> </msub> <mo>=</mo> <mo>+</mo> <mn>0.5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mi>h</mi> </msub> <mo>=</mo> <mo>+</mo> <mn>0.7</mn> </mrow> </semantics></math>. All other parameter values are the same as in <a href="#entropy-27-00257-f001" class="html-fig">Figure 1</a>.</p>
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<p>LIF network with bistable plasticity coupling comprising positive and negative fixed points cause the formation of complex synchronization patterns combining both bump and chimera features. (<b>a</b>) Typical snapshot of the neuron potential <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> (<span class="html-italic">t</span> = 800 TU), (<b>b</b>) spacetime plot, (<b>c</b>) the average firing rate <math display="inline"><semantics> <msub> <mi>f</mi> <mi>i</mi> </msub> </semantics></math> and (<b>d</b>) the distribution of coupling strengths <math display="inline"><semantics> <mi>σ</mi> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> TU (black crosses, homogeneous random initial conditions) and at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>800</mn> </mrow> </semantics></math> TU (red dots). Parameter values are: <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>rest</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>th</mi> </msub> <mo>=</mo> <mn>0.98</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>1024</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>=</mo> <mn>40</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mi>l</mi> </msub> <mo>=</mo> <mo>−</mo> <mn>0.7</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mi>c</mi> </msub> <mo>=</mo> <mn>0.0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mi>h</mi> </msub> <mo>=</mo> <mo>+</mo> <mn>0.7</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mi>σ</mi> </msub> <mo>=</mo> <mo>−</mo> <mn>1.0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math>. Simulations start from random uniform initial conditions in <math display="inline"><semantics> <msub> <mi>u</mi> <mi>i</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>σ</mi> <mi>i</mi> </msub> </semantics></math>.</p>
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<p>Local entropy deviations <math display="inline"><semantics> <msub> <mi>d</mi> <mi>H</mi> </msub> </semantics></math> as a function of the coupling range <span class="html-italic">R</span> for inhibitory coupling. Parameter values are: <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mi>l</mi> </msub> <mo>=</mo> <mo>−</mo> <mn>0.7</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mi>c</mi> </msub> <mo>=</mo> <mo>−</mo> <mn>0.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mi>h</mi> </msub> <mo>=</mo> <mo>−</mo> <mn>0.3</mn> </mrow> </semantics></math>. Other parameters are as in <a href="#entropy-27-00257-f001" class="html-fig">Figure 1</a>. All simulations start from the same random uniform initial conditions both in <math display="inline"><semantics> <msub> <mi>u</mi> <mi>i</mi> </msub> </semantics></math> and in <math display="inline"><semantics> <msub> <mi>σ</mi> <mi>i</mi> </msub> </semantics></math>.</p>
Full article ">Figure 5
<p>Local entropy deviations <math display="inline"><semantics> <msub> <mi>d</mi> <mi>H</mi> </msub> </semantics></math> as a function of the coupling range <span class="html-italic">R</span> for excitatory coupling. Parameter values are: <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mi>l</mi> </msub> <mo>=</mo> <mo>+</mo> <mn>0.2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mi>c</mi> </msub> <mo>=</mo> <mo>+</mo> <mn>0.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mi>h</mi> </msub> <mo>=</mo> <mo>+</mo> <mn>0.8</mn> </mrow> </semantics></math>. Other parameters are as in <a href="#entropy-27-00257-f001" class="html-fig">Figure 1</a>. All simulations start from the same random uniform initial conditions both in <math display="inline"><semantics> <msub> <mi>u</mi> <mi>i</mi> </msub> </semantics></math> and in <math display="inline"><semantics> <msub> <mi>σ</mi> <mi>i</mi> </msub> </semantics></math>.</p>
Full article ">Figure A1
<p>Synchronization patterns of the potential values <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> for inhibitory coupling without link plasticity. Typical spacetime plots for (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mo>−</mo> <mn>0.3</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mo>−</mo> <mn>0.3</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>=</mo> <mn>350</mn> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mo>−</mo> <mn>0.7</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, and (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mo>−</mo> <mn>0.7</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>=</mo> <mn>350</mn> </mrow> </semantics></math>. All other parameter values are as in <a href="#entropy-27-00257-f001" class="html-fig">Figure 1</a> of the main text. Simulations start from the same random initial conditions in <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>=</mo> <mn>0</mn> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p>
Full article ">Figure A2
<p>Synchronization patterns of the potential values <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> for excitatory coupling without link plasticity. Typical spacetime plots for (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mn>0.3</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mn>0.3</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>=</mo> <mn>350</mn> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mn>0.7</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, and (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mn>0.7</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>=</mo> <mn>350</mn> </mrow> </semantics></math>. All other parameter values are as in <a href="#entropy-27-00257-f001" class="html-fig">Figure 1</a> and in <a href="#secAdot1-entropy-27-00257" class="html-sec">Appendix A.1</a>, <a href="#entropy-27-00257-f0A1" class="html-fig">Figure A1</a>. Simulations start from the same random initial conditions in <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>=</mo> <mn>0</mn> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p>
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19 pages, 35731 KiB  
Article
Robust Synchronization Error Estimation Under Multipath Fading in Distributed SAR
by Jihao Xin, Xingdong Liang, Zhiyu Jiang, Hang Li, Yujie Dai, Huan Wang, Yuan Zhang and Xiangxi Bu
Electronics 2025, 14(5), 983; https://doi.org/10.3390/electronics14050983 - 28 Feb 2025
Viewed by 256
Abstract
Unmanned Aerial Vehicle (UAV)-based distributed Synthetic Aperture Radar (SAR) is a current research focus. Phase synchronization is crucial for eliminating the non-coherence of distributed systems. However, as the number of UAVs increases, fast time-varying multipath effects caused by rotors can lead to multipath [...] Read more.
Unmanned Aerial Vehicle (UAV)-based distributed Synthetic Aperture Radar (SAR) is a current research focus. Phase synchronization is crucial for eliminating the non-coherence of distributed systems. However, as the number of UAVs increases, fast time-varying multipath effects caused by rotors can lead to multipath fading. This degrades the signal-to-noise ratio (SNR) of the synchronization link and distorts the synchronization waveform. It further breaks the reciprocity of the dual one-way synchronization link, ultimately degrading phase synchronization accuracy. We propose a robust method for spike detection and error propagation to improve phase synchronization precision. Using the Hampel filter, we detect pulse peak position jitter and remove observations from anomalous links. We then use data fusion based on minimum variance to recover synchronization errors in these links, leveraging the redundancy in synchronization phase matrices. The effectiveness of the proposed method is confirmed through flight test data from a four-UAV distributed TomoSAR experiment. Compared to the maximum-peak detection method, the phase accuracy is improved from 12.84 deg to 0.61 deg. This method supports the application of distributed SAR. Full article
(This article belongs to the Special Issue New Challenges in Remote Sensing Image Processing)
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Figure 1

Figure 1
<p>The TDMA synchronization scheme applied for the distributed SAR imaging.</p>
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<p>The general shape of the Allan variance. (<b>a</b>) The Modified Allan variance (<math display="inline"><semantics> <mrow> <mi>M</mi> <mi>o</mi> <mi>d</mi> <msubsup> <mrow> <mi>σ</mi> </mrow> <mrow> <mi>φ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msubsup> <mfenced separators="|"> <mrow> <mi>τ</mi> </mrow> </mfenced> </mrow> </semantics></math>) of an oscillator. (<b>b</b>) The Allan variance (<math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>σ</mi> </mrow> <mrow> <mi>φ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msubsup> <mfenced separators="|"> <mrow> <mi>τ</mi> </mrow> </mfenced> </mrow> </semantics></math>) of the synchronization phase, which includes the inherent instability of the oscillator and the measurement error.</p>
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<p>Illustration of multipath in multi-node synchronization links.</p>
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<p>The multipath fading effect after pulse compression. (<b>a</b>) The LOS pulse compression waveform compared with the multipath fading waveform; (<b>b</b>) the residual time and phase errors.</p>
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<p>The Monte Carlo simulation for the different SNRs after pulse compression.</p>
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<p>(<b>a</b>) Optical image; (<b>b</b>) configuration of distributed TomoSAR with 4 UAV SARs.</p>
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<p>Matched filter outputs of sync signals of different UAVs during flight.</p>
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<p>Unprocessed synchronization phase and first-order difference in all links. (<b>a</b>) Link <span class="html-italic">AB</span>; (<b>b</b>) Link <span class="html-italic">AC</span>; (<b>c</b>) Link <span class="html-italic">AD</span>; (<b>d</b>) Link <span class="html-italic">BC</span>; (<b>e</b>) Link <span class="html-italic">BD</span>; (<b>f</b>) Link <span class="html-italic">CD</span>.</p>
Full article ">Figure 8 Cont.
<p>Unprocessed synchronization phase and first-order difference in all links. (<b>a</b>) Link <span class="html-italic">AB</span>; (<b>b</b>) Link <span class="html-italic">AC</span>; (<b>c</b>) Link <span class="html-italic">AD</span>; (<b>d</b>) Link <span class="html-italic">BC</span>; (<b>e</b>) Link <span class="html-italic">BD</span>; (<b>f</b>) Link <span class="html-italic">CD</span>.</p>
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<p>The Modified Allan variances (MVARs) of the synchronization phase for the different links. (<b>a</b>) The MVAR for all the 6 direct links; (<b>b</b>) the MVAR for Link <span class="html-italic">BD</span> from five different paths.</p>
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<p>The 32-times-interpolated pulse compression signal slices from the synchronization links, normalized by each maximum value and centered on the maximum: (<b>a</b>) the link between UAVs <span class="html-italic">A</span> and <span class="html-italic">B</span>; (<b>b</b>) the link between UAVs <span class="html-italic">A</span> and <span class="html-italic">C</span>; (<b>c</b>) the link between UAVs <span class="html-italic">A</span> and <span class="html-italic">D</span>; (<b>d</b>) the link between UAVs <span class="html-italic">B</span> and <span class="html-italic">C</span>; (<b>e</b>) the link between UAVs <span class="html-italic">B</span> and <span class="html-italic">D</span>, where the maximum peaks are misaligned; (<b>f</b>) the link between UAVs <span class="html-italic">C</span> and <span class="html-italic">D</span>.</p>
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<p>The spike detection results. (<b>a</b>) The Hampel filter output of the link <span class="html-italic">BD</span>; (<b>b</b>) the number of effective links, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="bold-italic">R</mi> </mrow> <mrow> <mi mathvariant="bold-italic">n</mi> </mrow> </msub> <mfenced separators="|"> <mrow> <mi>B</mi> <mo>,</mo> <mi>D</mi> </mrow> </mfenced> </mrow> </semantics></math>, calculated by Equation (13).</p>
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<p>The performance of synchronization phase estimations. (<b>a</b>) The synchronization phase estimations and first-order differences (FODs). (<b>b</b>) A statistical histogram of the FODs of the synchronization phase using the max-peak position method and the proposed method.</p>
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<p>The Modified Allan variances of the synchronization phases.</p>
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<p>Imaging results of BiSAR echo from UAVs <span class="html-italic">B</span> and <span class="html-italic">D</span>, with labels “<span class="html-italic">A</span>” and “<span class="html-italic">B</span>” indicating corner reflectors <span class="html-italic">A</span> and scatter <span class="html-italic">B</span>, respectively. (<b>a</b>) SAR image compensated with unprocessed synchronization phase; (<b>b</b>) SAR image compensated with processed synchronization phase.</p>
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<p>Magnified SAR image containing <span class="html-italic">A</span> and <span class="html-italic">B</span> (16× up-sampling): (<b>a</b>) corner reflector <span class="html-italic">A</span> compensated with unprocessed synchronization phase; (<b>b</b>) corner reflector <span class="html-italic">A</span> compensated with processed synchronization phase; (<b>c</b>) scatter <span class="html-italic">B</span> compensated with unprocessed synchronization phase; (<b>d</b>) scatter <span class="html-italic">B</span> compensated with processed synchronization phase.</p>
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32 pages, 1559 KiB  
Review
Time Synchronization Techniques in the Modern Smart Grid: A Comprehensive Survey
by Yu Liu, Biao Sun, Yuru Wu, Yongxin Zhang, Jiahui Yang, Wen Wang, Naga Lakshmi Thotakura, Qian Liu and Yilu Liu
Energies 2025, 18(5), 1163; https://doi.org/10.3390/en18051163 - 27 Feb 2025
Viewed by 206
Abstract
In modern smart grids, accurate and synchronized time signals are essential for effective monitoring, protection, and control. Various time synchronization methods exist, each tailored to specific application needs. Widely adopted solutions, such as GPS, however, are vulnerable to challenges such as signal loss [...] Read more.
In modern smart grids, accurate and synchronized time signals are essential for effective monitoring, protection, and control. Various time synchronization methods exist, each tailored to specific application needs. Widely adopted solutions, such as GPS, however, are vulnerable to challenges such as signal loss and cyber-attacks, underscoring the need for reliable backup or supplementary solutions. This paper examines the timing requirements across different power grid applications and provides a comprehensive review of available time synchronization mechanisms. Through a comparative analysis of timing methods based on accuracy, flexibility, reliability, and security, this study offers insights to guide the selection of optimal solutions for seamless grid integration. Full article
(This article belongs to the Special Issue Energy, Electrical and Power Engineering: 3rd Edition)
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Figure 1
<p>Iridium constellation orbits [<a href="#B51-energies-18-01163" class="html-bibr">51</a>].</p>
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<p>Pulsar beams.</p>
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<p>Derived frequency stability for a range of different frequency sources [<a href="#B59-energies-18-01163" class="html-bibr">59</a>].</p>
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<p>MSP J1939+2134 received waveform and pulse profile.</p>
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<p>Pulses at different frequencies with effect of dispersion.</p>
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<p>Block diagram of pulsar data processing.</p>
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<p>Hierarchy topology of PTP.</p>
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<p>Basic PTP timing message exchange [<a href="#B80-energies-18-01163" class="html-bibr">80</a>].</p>
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<p>The WR network architecture [<a href="#B91-energies-18-01163" class="html-bibr">91</a>].</p>
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<p>WR synchronization and syntonization scheme [<a href="#B93-energies-18-01163" class="html-bibr">93</a>].</p>
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<p>WR time synchronization scheme [<a href="#B91-energies-18-01163" class="html-bibr">91</a>].</p>
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<p>Time synchronization message transportation in 5G-TSN network.</p>
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13 pages, 2523 KiB  
Article
Optimized Configuration of Multi-Source Measurement Devices Based on Distributed Principles
by Yuhao Xu, Jiaqi Zhang, Jing Zhao, Xiaoyu Zhang and Jinming Ge
Energies 2025, 18(5), 1149; https://doi.org/10.3390/en18051149 - 26 Feb 2025
Viewed by 127
Abstract
The increasing uncertainties and model computational complexity of large-scale power system state estimation have led to the emergence of a class of multi-source metrology devices to provide vector data for the grid to improve the observability. Considering the difficult problem of optimizing the [...] Read more.
The increasing uncertainties and model computational complexity of large-scale power system state estimation have led to the emergence of a class of multi-source metrology devices to provide vector data for the grid to improve the observability. Considering the difficult problem of optimizing the configuration of multi-source measurement devices due to the large number of nodes, a distributed optimal configuration framework for multi-source measurement data is proposed. First, based on the concepts of sensitivity and electrical distance, the sensitivity electrical distance is derived and the power system is partitioned using the improved community partitioning principle; considering the problem of partitioning information exchange, synchronized phase measurement units are configured at the boundary nodes. Secondly, within the aforementioned partition, the optimal configuration of feeder terminal units and smart meters is carried out by combining the requirements of zero-injection nodes and viewability. Finally, the proposed method is verified in the IEEE33 node example, and the results show that the proposed method significantly reduces the configuration cost of the equipment on both sides of the system while guaranteeing the system viewability, which is highly feasible and economical. Full article
(This article belongs to the Section F: Electrical Engineering)
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<p>Schematic diagram of IEEE33 node arithmetic example.</p>
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<p>Schematic diagram of IEEE69 nodes.</p>
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<p>IEEE33 node partitioning result map.</p>
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<p>Nodal diagram of PMU installation in the sub-district.</p>
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<p>Nodal diagram of FTU or SM installation in the sub-area.</p>
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<p>IEEE69 node partition result.</p>
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<p>IEEE69 node example: PMU and FTU or SM node installation diagram.</p>
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32 pages, 2442 KiB  
Article
Federated Learning System for Dynamic Radio/MEC Resource Allocation and Slicing Control in Open Radio Access Network
by Mario Martínez-Morfa, Carlos Ruiz de Mendoza, Cristina Cervelló-Pastor and Sebastia Sallent-Ribes
Future Internet 2025, 17(3), 106; https://doi.org/10.3390/fi17030106 - 26 Feb 2025
Viewed by 248
Abstract
The evolution of cellular networks from fifth-generation (5G) architectures to beyond 5G (B5G) and sixth-generation (6G) systems necessitates innovative solutions to overcome the limitations of traditional Radio Access Network (RAN) infrastructures. Existing monolithic and proprietary RAN components restrict adaptability, interoperability, and optimal resource [...] Read more.
The evolution of cellular networks from fifth-generation (5G) architectures to beyond 5G (B5G) and sixth-generation (6G) systems necessitates innovative solutions to overcome the limitations of traditional Radio Access Network (RAN) infrastructures. Existing monolithic and proprietary RAN components restrict adaptability, interoperability, and optimal resource utilization, posing challenges in meeting the stringent requirements of next-generation applications. The Open Radio Access Network (O-RAN) and Multi-Access Edge Computing (MEC) have emerged as transformative paradigms, enabling disaggregation, virtualization, and real-time adaptability—which are key to achieving ultra-low latency, enhanced bandwidth efficiency, and intelligent resource management in future cellular systems. This paper presents a Federated Deep Reinforcement Learning (FDRL) framework for dynamic radio and edge computing resource allocation and slicing management in O-RAN environments. An Integer Linear Programming (ILP) model has also been developed, resulting in the proposed FDRL solution drastically reducing the system response time. On the other hand, unlike centralized Reinforcement Learning (RL) approaches, the proposed FDRL solution leverages Federated Learning (FL) to optimize performance while preserving data privacy and reducing communication overhead. Comparative evaluations against centralized models demonstrate that the federated approach improves learning efficiency and reduces bandwidth consumption. The system has been rigorously tested across multiple scenarios, including multi-client O-RAN environments and loss-of-synchronization conditions, confirming its resilience in distributed deployments. Additionally, a case study simulating realistic traffic profiles validates the proposed framework’s ability to dynamically manage radio and computational resources, ensuring efficient and adaptive O-RAN slicing for diverse and high-mobility scenarios. Full article
(This article belongs to the Special Issue AI and Security in 5G Cooperative Cognitive Radio Networks)
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<p>O-RAN integration scenario in 5G and MEC systems.</p>
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<p>Iterative ILP.</p>
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<p>Bandwidth parts with mixed numerologies.</p>
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<p>Slices admission control algorithm.</p>
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<p>Proposed implementation scenario for the federated stage.</p>
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<p>Federated system scenario (Test 1).</p>
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<p>Reward obtained in Test 1 by Client 1 (<b>a</b>) and Client 2 (<b>b</b>).</p>
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<p>Federated system scenario (Test 2).</p>
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<p>Reward obtained in Test 2 by Client 1 (<b>a</b>), Client 2 (<b>b</b>), and Client 3 (<b>c</b>).</p>
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<p>Federated system scenario (Test 3).</p>
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<p>Reward obtained in Test 3 by Client 1 (<b>a</b>), Client 2 (<b>b</b>), and Client 3 (<b>c</b>).</p>
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<p>Example of a realistic use case implementation scenario.</p>
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<p>FL evaluation results in the use case for Client 1 (<b>a</b>), Client 2 (<b>b</b>), Client 3 (<b>c</b>), and Client 4 (<b>d</b>).</p>
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<p>Results of joint evaluation in the use case.</p>
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<p>Centralized ML vs FL.</p>
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<p>Comparison of training between centralized and federated systems.</p>
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14 pages, 2627 KiB  
Review
Synchronization of Kuromoto Oscillators on Simplicial Complexes: Hysteresis, Cluster Formation and Partial Synchronization
by Samir Sahoo and Neelima Gupte
Entropy 2025, 27(3), 233; https://doi.org/10.3390/e27030233 - 24 Feb 2025
Viewed by 235
Abstract
The analysis of the synchronization of oscillator systems based on simplicial complexes presents some interesting features. The transition to synchronization can be abrupt or smooth depending on the substrate, the frequency distribution of the oscillators and the initial distribution of the phase angles. [...] Read more.
The analysis of the synchronization of oscillator systems based on simplicial complexes presents some interesting features. The transition to synchronization can be abrupt or smooth depending on the substrate, the frequency distribution of the oscillators and the initial distribution of the phase angles. Both partial and complete synchronization can be seen as quantified by the order parameter. The addition of interactions of a higher order than the usual pairwise ones can modify these features further, especially when the interactions tend to have the opposite signs. Cluster synchronization is seen on sparse lattices and depends on the spectral dimension and whether the networks are mixed, sparse or compact. Topological effects and the geometry of shared faces are important and affect the synchronization patterns. We identify and analyze factors, such as frustration, that lead to these effects. We note that these features can be observed in realistic systems such as nanomaterials and the brain connectome. Full article
(This article belongs to the Special Issue Universality Classes of Synchronization Phase Transitions)
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<p>Three typical network structures obtained using the rules of self-assembly described in the text, considering the geometric compatibility and different chemical potentials <math display="inline"><semantics> <mi>ν</mi> </semantics></math>, shown from left to right: <math display="inline"><semantics> <mrow> <mi>ν</mi> <mo>=</mo> </mrow> </semantics></math> 5 (compact), <math display="inline"><semantics> <mrow> <mi>ν</mi> <mo>=</mo> </mrow> </semantics></math> 0 (mixed) and <math display="inline"><semantics> <mrow> <mi>ν</mi> <mo>=</mo> </mrow> </semantics></math>−5 (sparse structure) [<a href="#B21-entropy-27-00233" class="html-bibr">21</a>]. The addition of 5-cliques is stopped when the number of nodes reaches <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>∼</mo> </mrow> </semantics></math> 1000.</p>
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<p>The transition to synchronization and hysteresis behavior shown by networks with <math display="inline"><semantics> <mrow> <mi>ν</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math>, 0, −5 when <math display="inline"><semantics> <mi>ω</mi> </semantics></math> is drawn from a Gaussian distribution with mean frequencies <math display="inline"><semantics> <mrow> <mi mathvariant="normal">Ω</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> </mrow> </semantics></math> 0.01. The parameter <math display="inline"><semantics> <msub> <mi>K</mi> <mn>2</mn> </msub> </semantics></math> is varied along the three columns, namely, <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mn>2</mn> </msub> <mo>=</mo> </mrow> </semantics></math> 0 &amp; 0.2 for the top and bottom horizontal row panels, respectively. The solid triangles (black) and solid circles (magenta) represent the value of order parameter <span class="html-italic">r</span> in the forward and backward sweeps, respectively [<a href="#B21-entropy-27-00233" class="html-bibr">21</a>].</p>
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<p>The hysteresis sweep of the order parameter <span class="html-italic">r</span> is plotted against <math display="inline"><semantics> <msub> <mi>K</mi> <mn>1</mn> </msub> </semantics></math> for the three different networks with <math display="inline"><semantics> <mrow> <mi>ν</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math>, 0 and −5 (along three vertical columns), at <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mn>2</mn> </msub> <mo>=</mo> </mrow> </semantics></math> 0 and <math display="inline"><semantics> <mrow> <mn>0.2</mn> </mrow> </semantics></math> (along two horizontal panels). The solid triangles (black) and solid circles (magenta) represent the value of the order parameter <span class="html-italic">r</span> for the forward and backward sweeps, respectively. The frequency <math display="inline"><semantics> <mi>ω</mi> </semantics></math> is drawn from a Gaussian distribution with a mean of 1 and standard deviation of 0.1 [<a href="#B21-entropy-27-00233" class="html-bibr">21</a>].</p>
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<p>The hysteresis sweep of the order parameter <span class="html-italic">r</span> as a function of the one-simplex coupling strength <math display="inline"><semantics> <msub> <mi>K</mi> <mn>1</mn> </msub> </semantics></math> at different two-simplex coupling strengths <math display="inline"><semantics> <msub> <mi>K</mi> <mn>2</mn> </msub> </semantics></math>; the three vertical columns (from <b>left</b> to <b>right</b>) correspond to the three simplicial complexes seen in <a href="#entropy-27-00233-f001" class="html-fig">Figure 1</a>, grown with the chemical affinities <math display="inline"><semantics> <mrow> <mi>ν</mi> <mo>=</mo> </mrow> </semantics></math>5, 0 &amp; −5, respectively. In each panel, the solid triangles (black) and solid circles (magenta) refer to forward and backward sweeps, respectively. The intrinsic frequencies are <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mi>i</mi> </msub> <mo>=</mo> <mi>ω</mi> <mo>=</mo> </mrow> </semantics></math>1 at all nodes. The phase evolution patterns analyzed in the text correspond to the points indicated by crosses here [<a href="#B21-entropy-27-00233" class="html-bibr">21</a>].</p>
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<p>The phases of elementary nodes <math display="inline"><semantics> <msub> <mi>θ</mi> <mi>i</mi> </msub> </semantics></math> as a function of time, the average phase <math display="inline"><semantics> <mi>θ</mi> </semantics></math> as a function of time and the distribution of phases (in radians) in the final (after 50,000 iterations) states of the simulations are shown along the three vertical panels i.e., from top to bottom, respectively, for different combinations of <math display="inline"><semantics> <msub> <mi>K</mi> <mn>1</mn> </msub> </semantics></math> &amp; <math display="inline"><semantics> <msub> <mi>K</mi> <mn>2</mn> </msub> </semantics></math> when <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> for each node of a network. The vertical panels (<b>a1</b>–<b>c1</b>) and (<b>d1</b>–<b>f1</b>) correspond to the networks with <math display="inline"><semantics> <mrow> <mi>ν</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> and −5, respectively. The (<math display="inline"><semantics> <msub> <mi>K</mi> <mn>1</mn> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>K</mi> <mn>2</mn> </msub> </semantics></math>) combinations along these vertical panels are the following: (<b>a1</b>–<b>a3</b>) (−1, 0)-forward (<b>b1</b>–<b>b3</b>) (1, 0)-forward, (<b>c1</b>–<b>c3</b>) (0, 0.2)-forward, (<b>d1</b>–<b>d3</b>) (−1, 0)-forward, (<b>e1</b>–<b>e3</b>) (−1, 0)-backward, (<b>f1</b>–<b>f3</b>) (−1, 0.2)-backward [<a href="#B21-entropy-27-00233" class="html-bibr">21</a>].</p>
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<p>The hysteresis sweep of order parameter <span class="html-italic">r</span> as a function of <math display="inline"><semantics> <msub> <mi>K</mi> <mn>1</mn> </msub> </semantics></math> at different values of <math display="inline"><semantics> <msub> <mi>K</mi> <mn>2</mn> </msub> </semantics></math>, varying along the columns; the four vertical columns (from <b>left</b> to <b>right</b>) correspond to four simplices sharing a node, link, triangle and a tetrahedron, respectively. In each panel, the solid triangles (black) and solid circles (magenta) refer to forward and backward sweeps, respectively. The intrinsic frequencies <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mi>i</mi> </msub> <mo>=</mo> </mrow> </semantics></math>1 at all nodes. The evolution of phases with time is analyzed at the the points indicated by crosses, stars, and diamonds.</p>
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<p>The to a distinct node. phases of each node <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> vs. <span class="html-italic">t</span> at different <math display="inline"><semantics> <msub> <mi>K</mi> <mn>1</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>K</mi> <mn>2</mn> </msub> </semantics></math> values, marked by crosses in <a href="#entropy-27-00233-f006" class="html-fig">Figure 6</a>.</p>
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<p>The phases of each node <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> vs. <span class="html-italic">t</span> at different <math display="inline"><semantics> <msub> <mi>K</mi> <mn>1</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>K</mi> <mn>2</mn> </msub> </semantics></math> values, marked as stars in <a href="#entropy-27-00233-f006" class="html-fig">Figure 6</a>. Each color corresponds to a distinct node.</p>
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<p>The phases of each node <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> vs. <span class="html-italic">t</span> at different <math display="inline"><semantics> <msub> <mi>K</mi> <mn>1</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>K</mi> <mn>2</mn> </msub> </semantics></math> values, marked as diamonds in <a href="#entropy-27-00233-f006" class="html-fig">Figure 6</a>. Each color corresponds to a distinct node.</p>
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<p>The time evolution of each node <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> vs. <span class="html-italic">t</span> at different <math display="inline"><semantics> <msub> <mi>K</mi> <mn>1</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>K</mi> <mn>2</mn> </msub> </semantics></math> values, as marked by diamonds, stars and crosses in <a href="#entropy-27-00233-f006" class="html-fig">Figure 6</a>.</p>
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15 pages, 1736 KiB  
Article
Mathematical Models of Critical Soft Error in Synchronous and Self-Timed Pipeline
by Igor Sokolov, Yuri Stepchenkov, Yuri Diachenko and Dmitry Khilko
Mathematics 2025, 13(5), 695; https://doi.org/10.3390/math13050695 - 21 Feb 2025
Viewed by 239
Abstract
This paper analyzes the impact of a single soft error on the performance of a synchronous and self-timed pipeline. A nuclear particle running through the integrated circuit body is considered the most probable soft error source. The existing estimates show that self-timed circuits [...] Read more.
This paper analyzes the impact of a single soft error on the performance of a synchronous and self-timed pipeline. A nuclear particle running through the integrated circuit body is considered the most probable soft error source. The existing estimates show that self-timed circuits offer an advantage in terms of single soft error tolerance. The paper proves these estimates on the basis of a comparative probability analysis of a critical fault in two types of pipelines. The mathematical models derived in the paper describe the probability of a critical fault depending on the circuit’s characteristics, its operating discipline, and the soft error parameters. The self-timed pipeline operates in accordance with a two-phase discipline, based on the request–acknowledge interaction within the pipeline’s stages, which provides it with increased immunity to soft errors. Quantitative calculations performed on the basis of the derived mathematical models show that the self-timed pipeline has about 6.1 times better tolerance to a single soft error in comparison to its synchronous counterpart. The obtained results are in good agreement with empirical estimates of the soft error tolerance level of synchronous and self-timed circuits. Full article
(This article belongs to the Special Issue Reliability Estimation and Mathematical Statistics)
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<p>Block diagram of a synchronous pipeline.</p>
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<p>Block diagram of a self-timed pipeline.</p>
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<p>Condition <math display="inline"><semantics> <mrow> <msub> <mi>t</mi> <mi>S</mi> </msub> <mo>+</mo> <msub> <mi>t</mi> <mrow> <mi>D</mi> <mi>S</mi> </mrow> </msub> <mo>&lt;</mo> <msub> <mi>T</mi> <mi>C</mi> </msub> </mrow> </semantics></math> probability calculation.</p>
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<p>Condition <span class="html-italic">T<sub>C</sub></span> &gt; <span class="html-italic">t<sub>S</sub> + t<sub>DS</sub></span> probability calculation (crosshatched region).</p>
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<p>Critical SE probability vs. SE duration distribution function variance <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mrow> <mi>S</mi> <mi>E</mi> </mrow> </msub> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mrow> <mi>S</mi> <mi>E</mi> </mrow> </msub> </mrow> </semantics></math> = 1 ns.</p>
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<p>Critical SE probability vs. SE duration distribution function mathematical expectation <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mrow> <mi>S</mi> <mi>E</mi> </mrow> </msub> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mrow> <mi>S</mi> <mi>E</mi> </mrow> </msub> </mrow> </semantics></math> = 0.4 ns.</p>
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15 pages, 1102 KiB  
Article
Quantum Secure Direct Communication Technology-Enhanced Time-Sensitive Networks
by Shiqi Zhang and Chao Zheng
Entropy 2025, 27(3), 221; https://doi.org/10.3390/e27030221 - 21 Feb 2025
Viewed by 185
Abstract
Quantum information has emerged as a frontier in scientific research and is transitioning to real-world technologies and applications. In this work, we explore the integration of quantum secure direct communication (QSDC) with time-sensitive networking (TSN) for the first time, proposing a novel framework [...] Read more.
Quantum information has emerged as a frontier in scientific research and is transitioning to real-world technologies and applications. In this work, we explore the integration of quantum secure direct communication (QSDC) with time-sensitive networking (TSN) for the first time, proposing a novel framework to address the security and latency challenges of Ethernet-based networks. Because our QSDC-TSN protocol inherits all the advantages from QSDC, it will enhance the security of the classical communications both in the traditional TSN- and QKD-based TSN by the quantum principle and reduce the communication latency by transmitting information directly via quantum channels without using keys. By analyzing the integration of QSDC and TSN in terms of time synchronization, flow control, security mechanisms, and network management, we show how QSDC enhances the real-time performance and security of TSN. These advantages enable our QSDC-TSN to keep the balance between and meet the requirements of both high security and real-time performance in industrial control, in a digital twin of green power and green hydrogen systems in distributed energy networks, etc., showing its potential applications in future quantum-classical-hybrid systems. Full article
(This article belongs to the Special Issue Quantum Information: Working towards Applications)
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<p>TSN architecture and QSDC technology combination diagram.</p>
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<p>Flowchart of comparative experiments for TSN scheme based on QSDC.</p>
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<p>Time synchronization with QSDC diagram.</p>
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<p>An illustration of the flow control and scheduling mechanism combined with QSDC.</p>
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27 pages, 7925 KiB  
Article
A Distributed Collaborative Navigation Strategy Based on Adaptive Extended Kalman Filter Integrated Positioning and Model Predictive Control for Global Navigation Satellite System/Inertial Navigation System Dual-Robot
by Wanqiang Chen, Yunpeng Jing, Shuo Zhao, Lei Yan, Quancheng Liu and Zichang He
Remote Sens. 2025, 17(4), 721; https://doi.org/10.3390/rs17040721 - 19 Feb 2025
Viewed by 210
Abstract
In the field of multi-robot cooperative localization and task planning, traditional filtering algorithms encounter synchronization and consistency issues during multi-source data fusion. These challenges result in cumulative localization errors and inefficient information sharing, which limits the system’s collaborative capabilities and control accuracy. To [...] Read more.
In the field of multi-robot cooperative localization and task planning, traditional filtering algorithms encounter synchronization and consistency issues during multi-source data fusion. These challenges result in cumulative localization errors and inefficient information sharing, which limits the system’s collaborative capabilities and control accuracy. To overcome these limitations, a distributed cooperative navigation strategy is introduced. Initially, a Distributed Adaptive Extended Kalman Filter (DAEKF) is implemented, which adaptively adjusts the noise covariance matrix to effectively manage nonlinearities and multi-source noise conditions. Subsequently, a Distributed Model Predictive Control (DMPC) framework is introduced. This framework predicts and optimizes each robot’s kinematic model, thereby improving the system’s collaborative operations and dynamic decision-making capabilities. Finally, the efficacy of this strategy is confirmed through detailed simulations and robotic experiments. The simulation results for cooperative localization demonstrate that DAEKF outperforms Kalman Filter (KF) and Extended Kalman Filter (EKF) in terms of localization accuracy. In the straight-line path-tracking experiments, DAEKF effectively reduced both lateral and heading errors for both robots. For Robot 1, DAEKF reduced the lateral error Root Mean Squared Error (RMSE) by 68.87%, 27.80%, and 25.76%, compared to No Filtering, KF, and EKF. In heading error, DAEKF reduced the RMSE by 52.29%, 41.89%, and 36.47%. For Robot 2, DAEKF reduced the lateral error RMSE by 51.30%, 22.88%, and 11.60%, compared to No Filtering, KF, and EKF. In heading error, DAEKF reduced the RMSE by 39.55%, 37.15%, and 26.00%. In the curved path-tracking experiments, both robots demonstrated high trajectory conformity while traveling along a predefined path combining straight-line and circular arc segments, with lateral errors in the straight-line segments all below 0.05 m. The strategy proposed in this study significantly enhanced the precision and stability of multi-robot collaborative navigation, demonstrating strong practicality and scalability. Full article
(This article belongs to the Special Issue Satellite Navigation and Signal Processing (Second Edition))
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<p>Schematic diagram of the DAEKF framework for dual-robot systems.</p>
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<p>Schematic diagram of DMPC framework for dual-robot systems.</p>
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<p>Structure and information flow diagram of the dual-robot system.</p>
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<p>RTK–GNSS base station and robotic control hardware configuration. (<b>a</b>) RTK–GNSS base station setup; (<b>b</b>) hardware composition of the experimental robots.</p>
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<p>Analysis of front wheel steering tracking performance and experimental pathways. (<b>a</b>) steering angle tracking for robot 1; (<b>b</b>) steering angle tracking for robot 2.</p>
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<p>Experimental robots in operation and path tracking. (<b>a</b>) Experimental robots in field operation; (<b>b</b>) dual straight-line and curved experimental pathways.</p>
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<p>Simulation-based path tracking performance of robot 1 and robot 2 under different filtering strategies.</p>
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<p>Noise matrix variation during the DAEKF adaptive noise estimation process. (<b>a</b>) Adaptive adjustment of process noise covariance matrix Q; (<b>b</b>) adaptive adjustment of measurement noise covariance matrix R.</p>
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<p>Localization error analysis under different filtering strategies. (<b>a</b>) X-axis error of robot 1; (<b>b</b>) Y-axis error of robot 1; (<b>c</b>) X-axis error of robot 2; (<b>d</b>) Y-axis error of robot 2.</p>
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<p>Localization error comparison of different filtering methods. (<b>a</b>) X-axis error comparison; (<b>b</b>) Y-axis error comparison.</p>
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<p>Experimental path-tracking performance of robot 1 and robot 2 along a subset of the trajectory under different filtering strategies.</p>
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<p>Control performance and coordination of robot 1 and robot 2 during path tracking. (<b>a</b>) Steering angle of robot 1; (<b>b</b>) steering angle of robot 1; (<b>c</b>) offset distance between robot 1 and robot 2; (<b>d</b>) velocity of robot 1 and robot 2.</p>
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<p>Dynamic adjustment of noise in DAEKF filtering. (<b>a</b>) Measurement noise R<sub>d</sub>; (<b>b</b>) process noise Q<sub>d</sub>; (<b>c</b>) measurement noise R<sub>d</sub>; (<b>d</b>) process noise Q<sub>a</sub>.</p>
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<p>Experimental localization performance analysis under different filtering strategies. (<b>a</b>) Lateral error of robot 1; (<b>b</b>) lateral error of robot 2; (<b>c</b>) heading error of robot 1; (<b>d</b>) heading error of robot 2.</p>
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<p>Comparison of lateral and heading errors for robot 1 and robot 2. (<b>a</b>) Lateral error comparison; (<b>b</b>) heading error comparison.</p>
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<p>Comparison of lateral and heading errors for robot 1 and robot 2 across different control methods. (<b>a</b>) Lateral error comparison; (<b>b</b>) heading error comparison.</p>
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<p>Experimental dual-loop path-tracking performance of robot 1 and robot 2. (<b>a</b>) Path tracking of robot 1; (<b>b</b>) path tracking of robot 2; (<b>c</b>) lateral error of robot 1 during path tracking; (<b>d</b>) lateral error of robot 2 during path tracking.</p>
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23 pages, 8148 KiB  
Article
Flexible On-Grid and Off-Grid Control for Electric–Hydrogen Coupling Microgrids
by Zhengyao Wang, Fulin Fan, Hang Zhang, Kai Song, Jinhai Jiang, Chuanyu Sun, Rui Xue, Jingran Zhang and Zhengjian Chen
Energies 2025, 18(4), 985; https://doi.org/10.3390/en18040985 - 18 Feb 2025
Viewed by 270
Abstract
With the widespread integration of renewable energy into distribution networks, energy storage systems are playing an increasingly critical role in maintaining grid stability and sustainability. Hydrogen, as a key zero-carbon energy carrier, offers unique advantages in the transition to low-carbon energy systems. To [...] Read more.
With the widespread integration of renewable energy into distribution networks, energy storage systems are playing an increasingly critical role in maintaining grid stability and sustainability. Hydrogen, as a key zero-carbon energy carrier, offers unique advantages in the transition to low-carbon energy systems. To facilitate the coordination between hydrogen and renewables, this paper proposes a flexible on-grid and off-grid control method for an electric–hydrogen hybrid AC-DC microgrid which integrates photovoltaic panels, battery energy storage, electrolysers, a hydrogen storage tank, and fuel cells. The flexible control method proposed here employs a hierarchical structure. The upper level adopts a power management strategy (PMS) that allocates power to each component based on the states of energy storage. The lower level utilises the master–slave control where master and slave converters are regulated by virtual synchronous generator (VSG) and active and reactive power (PQ) control, respectively. In addition, a pre-synchronisation control strategy which does not rely on traditional phase-locked loops is introduced to enable a smooth transition from the off-grid to on-grid mode. The electric–hydrogen microgrid along with the proposed control method is modelled and tested under various operating modes and scenarios. The simulation results demonstrate that the proposed control method achieves an effective power dispatch within microgrid and maintains microgrid stability in on- and off-grid modes as well as in the transition between the two modes. Full article
(This article belongs to the Section A1: Smart Grids and Microgrids)
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<p>Scheme of an electric–hydrogen coupling AC-DC hybrid microgrid.</p>
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<p>Equivalent model of BESS.</p>
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<p>Flowchart of power management of electric–hydrogen AC-DC microgrid.</p>
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<p>Control block diagram of the electric–hydrogen coupling AC-DC microgrid.</p>
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<p>Vector diagrams of VSG output voltage and grid-side voltage.</p>
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<p>Microgrid dynamics in off-grid mode under Scenario I: (<b>a</b>) active power of PV, BESS, ELs, FCs, and total loads; (<b>b</b>) SOC of BESS and SOHC of HTS; (<b>c</b>) active and reactive power; and (<b>d</b>) frequencies of master and slave converters.</p>
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<p>Microgrid dynamics in on-grid mode under Scenario II: (<b>a</b>) active power of PV, BESS, ELs, FCs, and total loads; (<b>b</b>) SOC of BESS and SOHC of HTS; (<b>c</b>) active and reactive power; and (<b>d</b>) frequencies of master and slave converters.</p>
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<p>Microgrid dynamics in on-grid mode under Scenario III: (<b>a</b>) active power of PV, BESS, ELs, FCs, and total loads; (<b>b</b>) SOC of BESS and SOHC of HTS; (<b>c</b>) active and reactive power; and (<b>d</b>) frequencies of master and slave converters.</p>
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<p>Microgrid dynamics in on-grid mode under Scenario III: (<b>a</b>) active power of PV, BESS, ELs, FCs, and total loads; (<b>b</b>) SOC of BESS and SOHC of HTS; (<b>c</b>) active and reactive power; and (<b>d</b>) frequencies of master and slave converters.</p>
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<p>Microgrid dynamics in on-grid mode under Scenario IV: (<b>a</b>) active power of PV, BESS, ELs, FCs, and total loads; (<b>b</b>) SOC of BESS and SOHC of HTS; (<b>c</b>) active and reactive power; and (<b>d</b>) frequencies of master and slave converters.</p>
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<p>Microgrid dynamics in on-grid mode under Scenario IV: (<b>a</b>) active power of PV, BESS, ELs, FCs, and total loads; (<b>b</b>) SOC of BESS and SOHC of HTS; (<b>c</b>) active and reactive power; and (<b>d</b>) frequencies of master and slave converters.</p>
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<p>Microgrid dynamics in off-grid/on-grid switching under Scenario V: (<b>a</b>) frequencies and (<b>b</b>) active and reactive power of master and slave converters; differences in (<b>c</b>) voltage phase and (<b>d</b>) amplitude between microgrid and upstream grid; and (<b>e</b>) voltage waveforms of grid and microgrid during pre-synchronisation.</p>
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<p>Microgrid dynamics in off-grid/on-grid switching under Scenario VI: (<b>a</b>) frequencies and (<b>b</b>) active and reactive power of master and slave converters; differences in (<b>c</b>) voltage phase and (<b>d</b>) amplitude between microgrid and upstream grid; and (<b>e</b>) voltage waveforms of grid and microgrid during pre-synchronisation.</p>
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<p>Microgrid dynamics in off-grid/on-grid switching under Scenario VI: (<b>a</b>) frequencies and (<b>b</b>) active and reactive power of master and slave converters; differences in (<b>c</b>) voltage phase and (<b>d</b>) amplitude between microgrid and upstream grid; and (<b>e</b>) voltage waveforms of grid and microgrid during pre-synchronisation.</p>
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21 pages, 2935 KiB  
Article
Mathematical Modeling and Electromagnetic Characteristics Analysis of a Six-Phase Distributed Single-Winding BPMSM with 12 Slots and 2 Poles
by Wenshao Bu, Jiangdi Li and Yongfang Lu
Appl. Sci. 2025, 15(4), 2093; https://doi.org/10.3390/app15042093 - 17 Feb 2025
Viewed by 167
Abstract
This work focuses on small bearingless permanent magnet synchronous motors (BPMSMs). In order to enhance its torque control stiffness and improve the stability of its torque and magnetic levitation force dynamic waveforms, a novel six-phase distributed single-winding BPMSM with 12 slots and 2 [...] Read more.
This work focuses on small bearingless permanent magnet synchronous motors (BPMSMs). In order to enhance its torque control stiffness and improve the stability of its torque and magnetic levitation force dynamic waveforms, a novel six-phase distributed single-winding BPMSM with 12 slots and 2 poles (six-phase DSW-12/2-BPMSM) is proposed and researched in this work. First, the structure and working principle of the six-phase DSW-12/2-BPMSM are analyzed. Subsequently, considering the relative permeability of permanent magnets, mathematical models of the inductance matrix, electromagnetic torque and radial magnetic levitation force are established. Then, using the finite element method (FEM), the control characteristics of the electromagnetic torque and magnetic levitation force of the six-phase DSW-12/2-BPMSM are analyzed, and the mathematical model is verified. Finally, FEM simulation analysis and comparisons are conducted with a commonly used six-phase centralized single-winding BPMSM with 6 slots and 2 poles (six-phase CSW-6/2-BPMSM). The research results show that the established mathematical model is effective and accurate compared with the six-phase CSW-6/2-BPMSM. The six-phase DSW-12/2-BPMSM has greater torque control stiffness, its dynamic waveforms of torque and radial magnetic levitation force have higher quality and stability, and the coupling degree between its torque and radial magnetic levitation force is lower. Full article
(This article belongs to the Special Issue Power Electronics and Motor Control)
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<p>Structural diagram of the six-phase DSW-12/2-BPMSM.</p>
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<p>Unfolding diagram of the six-phase DSW-12/2-BPMSM winding.</p>
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<p>Magnetic levitation force generation principal diagram.</p>
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<p>Schematic diagram of rotor eccentricity.</p>
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<p>Distribution of magnetic lines of force after applying levitation current.</p>
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<p>Torque waveform when the torque current changes.</p>
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<p>Curve of torque variation with torque current.</p>
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<p>Dynamic waveform of radial magnetic levitation force with variation in the levitation current.</p>
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<p>Variation curve of radial magnetic levitation force with levitation current.</p>
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<p>Eccentric magnetic pull waveform at static eccentricity.</p>
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<p>Variation curve of eccentric magnetic tension with static eccentric displacement.</p>
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<p>Eccentric magnetic pull waveform during dynamic eccentricity.</p>
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<p>Torque and magnetic levitation force waveforms of the six-phase CSW-6/2-BPMSM used for comparison.</p>
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<p>Magnetic levitation force waveform of the six-phase CSW-6/2-BPMSM under different torque currents.</p>
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<p>Magnetic levitation force waveform of the six-phase DSW-12/2-BPMSM under different torque currents.</p>
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<p>Comparison chart of numerical values after comprehensive processing: (<b>a</b>) steady-state numerical value comparison of torque and magnetic levitation force; (<b>b</b>) numerical comparison of fluctuation rate and coupling rate.</p>
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