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27 pages, 11524 KiB  
Article
GPU Ray Tracing for the Analysis of Light Deflection in Inhomogeneous Refractive Index Fields of Hot Tailored Forming Components
by Pascal Kern, Max Brower-Rabinowitsch, Lennart Hinz, Markus Kästner and Eduard Reithmeier
Sensors 2025, 25(6), 1663; https://doi.org/10.3390/s25061663 (registering DOI) - 7 Mar 2025
Abstract
In hot-forming, integrating in situ quality monitoring is essential for the early detection of thermally induced geometric deviations, especially in the production of hybrid bulk metal parts. Although hybrid components are key to meeting modern technical requirements and saving resources, they exhibit complex [...] Read more.
In hot-forming, integrating in situ quality monitoring is essential for the early detection of thermally induced geometric deviations, especially in the production of hybrid bulk metal parts. Although hybrid components are key to meeting modern technical requirements and saving resources, they exhibit complex shrinkage behavior due to differing thermal expansion coefficients. During forming, these components are exposed to considerable temperature gradients, which result in density fluctuations in the ambient air. These fluctuations create an inhomogeneous refractive index field (IRIF), which significantly affects the accuracy of optical geometry reconstruction systems due to light deflection. This study utilizes existing simulation IRIF data to predict the magnitude and orientation of refractive index fluctuations. A light deflection simulation run on a GPU-accelerated ray tracing framework is used to assess the impact of IRIFs on optical measurements. The results of this simulation are used as a basis for selecting optimized measurement positions, reducing and quantifying uncertainties in surface reconstruction, and, therefore, improving the reliability of quality control in hot-forming applications. Full article
(This article belongs to the Section Optical Sensors)
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Figure 1

Figure 1
<p>A camera records a hot measurement object and is influenced by an inhomogeneous refractive index field.</p>
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<p>Visualization of Snell’s law of refraction.</p>
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<p>Visualization of ray tracing through an inhomogeneous refractive medium.</p>
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<p>General procedure for calculating viewing ray deviations.</p>
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<p>Core ray tracing functions.</p>
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<p>Reduction in edge formations using the Taubin filter: (<b>a</b>) the original and (<b>b</b>) with the applied Taubin filter.</p>
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<p>Illustration of the impact of COMSOL configuration on the simulation results. The color-coded viewing ray displacement on the surface of a cylinder during ray tracing through the IRIF is presented. (<b>a</b>) Configuration B+: normal mesh resolution and high isosurface resolution. (<b>b</b>) Configuration D: extra-fine mesh resolution and normal isosurface resolution.</p>
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<p>The number of viewing rays used in ray tracing exhibits a linear relationship with runtime.</p>
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<p>The number of polygons per boundary layer exhibits an approximately linear relationship with runtime.</p>
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<p>The number of boundary layers used exhibits a linear relationship with runtime and a diminishing trend with respect to the quality metric.</p>
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<p>Smoothing the boundary layers has no impact on runtime. The RMSE relative to the reference increases linearly with the number of smoothing iterations.</p>
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<p>Runtime and RMSE values for different simulation-based mesh configurations.</p>
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<p>Resolutions depending on the angle of incidence with (<b>a</b>) resolutions at <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>inc</mi> </msub> <mo>=</mo> <mn>0</mn> <mo>°</mo> </mrow> </semantics></math>; (<b>b</b>) describes the resolutions at <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>inc</mi> </msub> <mo>=</mo> <mn>45</mn> <mo>°</mo> </mrow> </semantics></math>, and (<b>c</b>) visualizes resolutions for a cylinder.</p>
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<p>Calculation time (<b>a</b>) and measurement object coverage (<b>b</b>) for each camera position.</p>
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<p>(<b>a</b>) Displacements for the surface area of the cylinder head. (<b>b</b>) Displacements for the lateral surface area of the cylinder. (<b>c</b>) Displacements for the total surface area of the cylinder. (<b>d</b>) Angle of incidence.</p>
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<p>Lateral (<b>a</b>) and axial (<b>b</b>) resolutions for each camera position.</p>
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<p>(<b>a</b>) Steel–aluminum hybrid cylinder geometry. (<b>b</b>) Mean displacement for each camera position. (<b>c</b>) Camera position with the highest displacement. (<b>d</b>) Camera position with the lowest displacement.</p>
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<p>(<b>a</b>) Bevel gear geometry. (<b>b</b>) Mean displacement for each camera position. (<b>c</b>) Camera position with the highest displacement. (<b>d</b>) Camera position with the lowest displacement.</p>
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<p>(<b>a</b>) Wishbone geometry. (<b>b</b>) Mean displacement for each camera position. (<b>c</b>) Camera position with the highest displacement. (<b>d</b>) Camera position with the lowest displacement.</p>
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<p>Investigation of a bevel gear tooth based on ray tracing metrics: (<b>a</b>) total mean displacement per camera position; (<b>b</b>) total coverage per camera position; (<b>c</b>) total mean axial resolution per camera position; (<b>d</b>) total mean lateral resolution per camera position; (<b>e</b>) combined metric per camera position; (<b>f</b>) camera position with the lowest displacement value.</p>
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<p>The intersection of boundary layers can lead to ray tracing errors as the boundary layers are sequentially incorporated into the ray tracing process hierarchically.</p>
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<p>Number of polygons (<b>a</b>) and number of ray hits (<b>b</b>) per camera position.</p>
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<p>Distributions of the four metrics for the simulation from <a href="#sensors-25-01663-f020" class="html-fig">Figure 20</a>.</p>
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<p>Normalized distributions of the four metrics for the simulation from <a href="#sensors-25-01663-f020" class="html-fig">Figure 20</a>.</p>
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28 pages, 13595 KiB  
Article
Research on Optimization of Diesel Engine Speed Control Based on UKF-Filtered Data and PSO Fuzzy PID Control
by Jun Fu, Shuo Gu, Lei Wu, Nan Wang, Luchen Lin and Zhenghong Chen
Processes 2025, 13(3), 777; https://doi.org/10.3390/pr13030777 (registering DOI) - 7 Mar 2025
Abstract
With the continuous development of industrial automation, diesel engines play an increasingly important role in various types of construction machinery and power generation equipment. Improving the dynamic and static performance of the speed control system of single-cylinder diesel engines can not only significantly [...] Read more.
With the continuous development of industrial automation, diesel engines play an increasingly important role in various types of construction machinery and power generation equipment. Improving the dynamic and static performance of the speed control system of single-cylinder diesel engines can not only significantly improve the efficiency of the equipment, but also effectively reduce energy consumption and emissions. Particle swarm optimization (PSO) fuzzy PID control algorithms have been widely used in many complex engineering problems due to their powerful global optimization capability and excellent adaptability. Currently, PSO-based fuzzy PID control research mainly integrates hybrid algorithmic strategies to avoid the local optimum problem, and lacks optimization of the dynamic noise suppression of the input error and the rate of change of the error. This makes the algorithm susceptible to the coupling of the system uncertainty and measurement disturbances during the parameter optimization process, leading to performance degradation. For this reason, this study proposes a new framework based on the synergistic optimization of the untraceable Kalman filter (UKF) and PSO fuzzy PID control for the speed control system of a single-cylinder diesel engine. A PSO-optimized fuzzy PID controller is designed by obtaining accurate speed estimation data using the UKF. The PSO is capable of quickly adjusting the fuzzy PID parameters so as to effectively alleviate the nonlinearity and uncertainty problems during the operation of diesel engines. By establishing a Matlab/Simulink simulation model, the diesel engine speed step response experiments (i.e., startup experiments) and load mutation experiments were carried out, and the measurement noise and process noise were imposed. The simulation results show that the optimized diesel engine speed control system is able to reduce the overshoot by 76%, shorten the regulation time by 58%, and improve the noise reduction by 25% compared with the conventional PID control. Compared with the PSO fuzzy PID control algorithm without UKF noise reduction, the optimized scheme reduces the overshoot by 20%, shortens the regulation time by 48%, and improves the noise reduction effect by 23%. The results show that the PSO fuzzy PID control method with integrated UKF has superior control performance in terms of system stability and accuracy. The algorithm significantly improves the responsiveness and stability of diesel engine speed, achieves better control effect in the optimization of diesel engine speed control, and provides a useful reference for the optimization of other diesel engine control systems. In addition, this study establishes the GT-POWER model of a 168 F single-cylinder diesel engine, and compares the cylinder pressure and fuel consumption under four operating conditions through bench tests to ensure the physical reasonableness of the kinetic input parameters and avoid algorithmic optimization on the distorted front-end model. Full article
(This article belongs to the Section Process Control and Monitoring)
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Figure 1
<p>Diesel engine speed control system schematic diagram.</p>
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<p>Diesel engine system schematic diagram.</p>
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<p>Schematic diagram of the overall architecture of the speed control system.</p>
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<p>Diesel engine test bench.</p>
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<p>GT-POWER model of 168 F single cylinder diesel engine.</p>
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<p>Comparison of cylinder pressure under different loads.</p>
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<p>Fuel consumption comparison chart under different loads.</p>
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<p>Schematic diagram of overall technical scheme.</p>
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<p>Schematic diagram of the PSO fuzzy PID controller based on UKF data.</p>
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<p>UKF algorithm flowchart.</p>
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<p>Unscented kalman filtering noise reduction effect diagram.</p>
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<p>Characteristic face of the fuzzy inference system: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <msub> <mrow> <mi>k</mi> </mrow> <mrow> <mi>p</mi> </mrow> </msub> </mrow> </semantics></math> (Proportional term characteristic surface), (<b>b</b>) <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <msub> <mrow> <mi>k</mi> </mrow> <mrow> <mi>i</mi> </mrow> </msub> </mrow> </semantics></math> (Integral term characteristic surface), (<b>c</b>) <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <msub> <mrow> <mi>k</mi> </mrow> <mrow> <mi>d</mi> </mrow> </msub> </mrow> </semantics></math> (Derivative term characteristic surface).</p>
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<p>Particle swarm optimization flowchart.</p>
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<p>Fitness value optimization results.</p>
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<p>Model of fuzzy PID control algorithm optimized by particle swarm optimization based on UKF in Matlab/Simulink (R2022b).</p>
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<p>Model of PID, Fuzzy PID, Fuzzy PID based on data of UKF, and PSO Fuzzy PID based on data of UKF in Matlab/Simulink (R2022b).</p>
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<p>Step response experiment results.</p>
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<p>Load disturbance experiment results.</p>
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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 (registering DOI) - 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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Figure 1
<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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25 pages, 863 KiB  
Review
Chronic Obstructive Pulmonary Disease and Type 2 Diabetes Mellitus: Complex Interactions and Clinical Implications
by Lucreția Anghel, Anamaria Ciubară, Diana Patraș and Alexandru Bogdan Ciubară
J. Clin. Med. 2025, 14(6), 1809; https://doi.org/10.3390/jcm14061809 (registering DOI) - 7 Mar 2025
Abstract
Chronic obstructive pulmonary disease (COPD) and type 2 diabetes mellitus (T2DM) are highly prevalent chronic conditions, frequently coexisting due to their shared pathophysiological mechanisms and risk factors. Epidemiological studies estimate that up to 30% of COPD patients have comorbid T2DM, contributing to worsened [...] Read more.
Chronic obstructive pulmonary disease (COPD) and type 2 diabetes mellitus (T2DM) are highly prevalent chronic conditions, frequently coexisting due to their shared pathophysiological mechanisms and risk factors. Epidemiological studies estimate that up to 30% of COPD patients have comorbid T2DM, contributing to worsened disease progression, more hospitalizations, and higher mortality rates. Systemic inflammation in COPD contributes to insulin resistance by increasing pro-inflammatory cytokines (TNF-α, IL-6, and CRP), which impair glucose metabolism and beta-cell function. Conversely, hyperglycemia in T2DM exacerbates oxidative stress, leading to endothelial dysfunction, reduced lung function, and impaired pulmonary repair mechanisms. A comprehensive narrative review was conducted to evaluate the interplay between COPD and T2DM, examining shared pathophysiological mechanisms, clinical consequences, and management strategies. The co-occurrence of COPD and T2DM accelerates disease development, elevates hospitalization rates, and deteriorates overall prognosis. Pharmacological interactions complicate illness treatment, requiring a multidisciplinary therapy strategy. Recent data underscore the need to integrate palliative care, facilitate shared decision-making, and provide psychological support to enhance patient outcomes. Efficient therapy of COPD-T2DM comorbidity necessitates a customized, interdisciplinary strategy that targets both respiratory and metabolic health. Preliminary prognostic dialogues, palliative care, and holistic lifestyle modifications can improve patient quality of life and clinical results. Full article
(This article belongs to the Section Pulmonology)
20 pages, 2198 KiB  
Article
Optimizing Solar-Integrated Microgrid Design for Sustainable Rural Electrification: Insights from the LEOPARD Project
by Ahmed Rachid, Talha Batuhan Korkut, Jean-Sebastien Cardot, Cheikh M. F. Kébé, Ababacar Ndiaye, Léonide Michael Sinsin and François Xavier Fifatin
Solar 2025, 5(1), 9; https://doi.org/10.3390/solar5010009 (registering DOI) - 7 Mar 2025
Abstract
This paper presents findings from the LEOPARD project, part of the LEAP-RE program, a joint European Union (EU) and African Union initiative to advance renewable energy solutions. The study employs a simulation-based approach to optimize solar-integrated microgrid configurations for rural electrification. The project [...] Read more.
This paper presents findings from the LEOPARD project, part of the LEAP-RE program, a joint European Union (EU) and African Union initiative to advance renewable energy solutions. The study employs a simulation-based approach to optimize solar-integrated microgrid configurations for rural electrification. The project deployed a solar-integrated pilot microgrid at the Songhai agroecological center in Benin to address key challenges, including load profile estimation, energy balancing, and diesel dependency reduction. A hybrid methodology integrating predictive modeling, real-time solar and weather data analysis, and performance simulations was employed, leading to a 65% reduction in diesel reliance and an LCOE of EUR 0.47/kWh. Quality control measures, including compliance with IEC 61215 and IEC 62485-2 standards, ensured system reliability under extreme conditions. Over 150 days, the system consistently supplied energy, preventing 10.16 tons of CO2 emissions. Beyond the Benin pilot, the project conducted feasibility assessments in Senegal to evaluate microgrid replicability across different socio-economic and environmental conditions. These analyses highlight the scalability potential and the economic viability of expanding solar microgrids in rural areas. Additionally, this research explores innovative business models and real-time diagnostics to enhance microgrid sustainability. By providing a replicable framework, it promotes long-term energy access and regional adaptability. With a focus on community involvement and capacity building, this study supports efforts to reduce energy poverty, strengthen European–African collaboration, and advance the global clean energy agenda. Full article
14 pages, 4375 KiB  
Article
Frequency Scanning-Based Dynamic Model Parameter Estimation: Case Study on STATCOM
by Hyeongjun Jo, Juseong Lee and Soobae Kim
Energies 2025, 18(6), 1326; https://doi.org/10.3390/en18061326 (registering DOI) - 7 Mar 2025
Abstract
The integration of power electronic equipment with complex internal structures, which are represented by switching elements or black-box models, is increasing because of the growing penetration of renewable energy into the power grid. The increase in model complexity causes greater computational workload and [...] Read more.
The integration of power electronic equipment with complex internal structures, which are represented by switching elements or black-box models, is increasing because of the growing penetration of renewable energy into the power grid. The increase in model complexity causes greater computational workload and presents challenges for grid stability analysis. To address this issue, this paper proposes a method for estimating the parameters of a simple generic model capable of emulating the dynamic behavior of complex power-electronic models. For the estimation, the frequency scanning method is utilized, involving the injection of various frequency inputs into the complex model. The responses obtained are then utilized in the optimization process as the objective function. The use of frequency scanning is reasonable because it can cover a wide frequency range, thus comprehensively capturing the dynamic properties of the model. The optimization process aims to minimize the difference in responses to frequency scanning between the complicated and simple generic models. The accuracy of the generic model with estimated parameters is verified by Bode plot comparison and time-domain simulations. Simulation results demonstrated that the generic model, optimized via parameter estimation using the frequency scanning method, accurately replicated the response of the reference model, particularly in the low-frequency range. The proposed method allows for the integration of power electronic equipment, which may represent switching-based components or lack internal information, into stability analysis using existing power-system analysis tools. Full article
(This article belongs to the Section F3: Power Electronics)
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Figure 1

Figure 1
<p>Equivalent circuit for frequency scanning with (<b>a</b>) a shunt current source and (<b>b</b>) a series voltage source [<a href="#B15-energies-18-01326" class="html-bibr">15</a>,<a href="#B17-energies-18-01326" class="html-bibr">17</a>].</p>
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<p>Block diagrams of the systems in <a href="#energies-18-01326-f001" class="html-fig">Figure 1</a>: (<b>a</b>) shunt current source injection and (<b>b</b>) series voltage source injection.</p>
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<p>Flowchart for the parameter estimation process.</p>
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<p>Injection voltage signal.</p>
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<p>Block diagram of the CSTCNT.</p>
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<p>Three-bus test system with a STATCOM.</p>
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<p>Thevenin equivalent used for the optimization process in MATLAB/Simulink.</p>
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<p>Comparisons of current magnitude, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="normal">I</mi> </mrow> <mrow> <msub> <mrow> <mi mathvariant="normal">f</mi> </mrow> <mrow> <mi mathvariant="normal">i</mi> </mrow> </msub> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>Comparison of Bode plots for the generic STATCOM models with different parameter sets.</p>
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<p>Pole-zero map of STATCOM (Circles denote zeros; crosses denote poles).</p>
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<p>Time-domain simulation results; (<b>a</b>) Scenario 1, (<b>b</b>) Scenario 2, (<b>c</b>) Scenario 3.</p>
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<p>Comparison of current magnitude, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="bold-italic">I</mi> </mrow> <mrow> <mi mathvariant="bold-italic">f</mi> <mi mathvariant="bold-italic">i</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>Comparison of reactive power outputs of STATCOMs with load reactive power variation.</p>
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<p>Comparison of bus voltage magnitude where the STATCOM is located with load reactive power variation.</p>
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<p>Comparison of the reactive power output of the STATCOM during a three-phase-to-ground fault.</p>
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20 pages, 1038 KiB  
Article
Accelerometer Bias Estimation for Unmanned Aerial Vehicles Using Extended Kalman Filter-Based Vision-Aided Navigation
by Djedjiga Belfadel and David Haessig
Electronics 2025, 14(6), 1074; https://doi.org/10.3390/electronics14061074 (registering DOI) - 7 Mar 2025
Abstract
Accurate estimation of accelerometer biases in Inertial Measurement Units (IMUs) is crucial for reliable Unmanned Aerial Vehicle (UAV) navigation, particularly in GPS-denied environments. Uncompensated biases lead to an unbounded accumulation of position error and increased velocity error, resulting in significant navigation inaccuracies. This [...] Read more.
Accurate estimation of accelerometer biases in Inertial Measurement Units (IMUs) is crucial for reliable Unmanned Aerial Vehicle (UAV) navigation, particularly in GPS-denied environments. Uncompensated biases lead to an unbounded accumulation of position error and increased velocity error, resulting in significant navigation inaccuracies. This paper examines the effects of accelerometer bias on UAV navigation accuracy and introduces a vision-aided navigation system. The proposed system integrates data from an IMU, altimeter, and optical flow sensor (OFS), employing an Extended Kalman Filter (EKF) to estimate both the accelerometer biases and the UAV position and velocity. This approach reduces the accumulation of velocity and positional errors. The efficiency of this approach was validated through simulation experiments involving a UAV navigating in circular and straight-line trajectories. Simulation results show that the proposed approach significantly enhances UAV navigation performance, providing more accurate estimates of both the state and accelerometer biases while reducing error growth through the use of vision aiding from an Optical Flow Sensor. Full article
(This article belongs to the Special Issue Precision Positioning and Navigation Communication Systems)
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<p>Basic block diagram for a strapdown inertial navigation system, courtesy [<a href="#B16-electronics-14-01074" class="html-bibr">16</a>].</p>
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<p>Strapdown inertial navigation with IMU acceleration input corrected for IMU bias.</p>
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<p>System and Simulation Block Diagram.</p>
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<p>Position Errors, Dead-Reckoning, biases not present.</p>
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<p>Velocity Errors, Dead-Reckoning, biases not present.</p>
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<p>Position Errors, Dead-Reckoning, biases present.</p>
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<p>Velocity Errors, Dead-Reckoning, biases present.</p>
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<p>Position Errors, Kalman Est. on, biases not present, bias est. off.</p>
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<p>Velocity Errors, Kalman Est. on, biases not present, bias est. off.</p>
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<p>Position Errors, Kalman est. on, biases present, bias est. off.</p>
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<p>Velocity Errors, Kalman est. on, biases present, bias est. off.</p>
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<p>Position Errors, Kalman est. on, biases present, bias est. on.</p>
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<p>Velocity Errors, Kalman est. on, biases present, bias est. on.</p>
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<p>Bias Estimates during Scheme 4.</p>
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<p>Position Errors, Kalman est. on, biases present, bias est. off.</p>
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<p>Velocity Errors, Kalman est. on, biases present, bias est. off.</p>
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<p>Position Errors, Kalman est. on, biases present, bias est. on.</p>
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<p>Velocity Errors, Kalman est. on, biases present, bias est. on.</p>
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21 pages, 1279 KiB  
Article
Stakeholder and Techno-Economic Assessment of Iceland’s Green Hydrogen Economy
by Nargessadat Emami, Reza Fazeli, Til Seth Tzschockel, Kevin Joseph Dillman and Jukka Heinonen
Energies 2025, 18(6), 1325; https://doi.org/10.3390/en18061325 (registering DOI) - 7 Mar 2025
Abstract
Green hydrogen is a promising energy carrier for the decarbonization of hard-to-abate sectors and supporting renewable energy integration, aligning with carbon neutrality goals like the European Green Deal. Iceland’s abundant renewable energy and decarbonized electricity system position it as a strong candidate for [...] Read more.
Green hydrogen is a promising energy carrier for the decarbonization of hard-to-abate sectors and supporting renewable energy integration, aligning with carbon neutrality goals like the European Green Deal. Iceland’s abundant renewable energy and decarbonized electricity system position it as a strong candidate for green hydrogen production. Despite early initiatives, its hydrogen economy has yet to significantly expand. This study evaluated Iceland’s hydrogen development through stakeholder interviews and a techno-economic analysis of alkaline and PEM electrolyzers. Stakeholders were driven by decarbonization goals, economic opportunities, and energy security but faced technological, economic, and governance challenges. Recommendations include building stakeholder confidence, financial incentives, and creating hydrogen-based chemicals to boost demand. Currently, alkaline electrolyzers are more cost-effective (EUR 1.5–2.8/kg) than PEMs (EUR 2.1–3.6/kg), though the future costs for both could drop below EUR 1.5/kg. Iceland’s low electricity costs and high electrolyzer capacity provide a competitive edge. However, this advantage may shrink as solar and wind costs decline globally, particularly in regions like Australia. This work’s findings emphasize the need for strategic planning to sustain competitiveness and offer transferable insights for other regions introducing hydrogen into ecosystems lacking infrastructure. Full article
(This article belongs to the Special Issue Green Hydrogen Energy Production)
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<p>Stakeholder map of the green hydrogen economy in Iceland.</p>
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<p>Categorization of interviewed stakeholders by their societal sector.</p>
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<p>Categorization of themes discovered in the interviews.</p>
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<p>Development of hydrogen production cost in Iceland using alkaline and PEM electrolyzers.</p>
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<p>Comparison of the levelized cost of hydrogen production in Iceland with global estimates from the IEA, (2021) [<a href="#B11-energies-18-01325" class="html-bibr">11</a>].</p>
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31 pages, 556 KiB  
Article
Modeling of Nonlinear Systems: Method of Optimal Injections
by Anatoli Torokhti and Pablo Soto-Quiros
Math. Comput. Appl. 2025, 30(2), 26; https://doi.org/10.3390/mca30020026 (registering DOI) - 7 Mar 2025
Abstract
In this paper, a nonlinear system is interpreted as an operator transforming random vectors. It is assumed that the operator is unknown and the random vectors are available. It is required to find a model of the system represented by a best [...] Read more.
In this paper, a nonlinear system is interpreted as an operator transforming random vectors. It is assumed that the operator is unknown and the random vectors are available. It is required to find a model of the system represented by a best constructive operator approximation. While the theory of operator approximation with any given accuracy has been well elaborated, the theory of best constrained constructive operator approximation is not so well developed. Despite increasing demands from various applications, this subject is minimally tractable because of intrinsic difficulties with associated approximation techniques. This paper concerns the best constrained approximation of a nonlinear operator in probability spaces. The main conceptual novelty of the proposed approach is that, unlike the known techniques, it targets a constructive optimal determination of all 3p+2 ingredients of the approximating operator where p is a nonnegative integer. The solution to the associated problem is represented by a combination of new best approximation techniques with a special iterative procedure. The proposed approximating model of the system has several degrees of freedom to minimize the associated error. In particular, one of the specific features of the developed approximating technique is special random vectors called injections. It is shown that the desired injection is determined from the solution of a special Fredholm integral equation of the second kind. Its solution is called the optimal injection. The determination of optimal injections in this way allows us to further minimize the associated error. Full article
12 pages, 1697 KiB  
Article
Ultrasound Measurements Are Useful to Estimate Hot Carcass Weight of Nellore Heifers Under Different Supplementation Strategies
by Patrick Bezerra Fernandes, Tiago do Prado Paim, Lucas Ferreira Gonçalves, Vanessa Nunes Leal, Darliane de Castro Santos, Josiel Ferreira, Rafaela Borges Moura, Isadora Carolina Borges Siqueira and Guilherme Antonio Alves dos Santos
AgriEngineering 2025, 7(3), 74; https://doi.org/10.3390/agriengineering7030074 (registering DOI) - 7 Mar 2025
Abstract
The use of non-invasive methods can contribute to the development of predictive models for measuring carcass yield (CY) and hot carcass weight (HCW) in domestic ruminants. In this study, in vivo measurements of subcutaneous fat thickness (SFT) and ribeye area (REA) were performed [...] Read more.
The use of non-invasive methods can contribute to the development of predictive models for measuring carcass yield (CY) and hot carcass weight (HCW) in domestic ruminants. In this study, in vivo measurements of subcutaneous fat thickness (SFT) and ribeye area (REA) were performed on 111 Nellore heifers using ultrasound imaging. The animals were managed in crop–livestock integrated systems with different supplementation levels (SL). Four multiple regression equations were developed to estimate CY and HCW, using five predictor variables: SFT, REA, REA per 100 kg of body weight (REA100), live weight (LW), and SL. For the CY prediction models, when ultrasound measurements (SFT, REA, and REA100) were considered, the generated equations showed low R2 and concordance correlation coefficient (CCC) values, indicating low predictive capacity for this trait. For HCW, the predictor variables stood out due to their high R2 values. Additionally, the equation based solely on ultrasound measurements achieved a CCC greater than 0.800, demonstrating high predictive capacity. Based on these results, it can be concluded that ultrasound-derived measurements are effective for generating useful models to predict HCW. Thus, it will be possible to estimate the amount of carcass that will be produced even before the animals are sent to slaughterhouses. Full article
(This article belongs to the Section Livestock Farming Technology)
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<p>Steps to perform the reading of ribeye area (REA) and subcutaneous fat thickness (SFT): (<b>1</b>)—Image positioning: The blue line indicates the boundary for obtaining images, positioned between the 12th and 13th ribs. (<b>2</b>)—Processing monitor: Used for viewing and processing the obtained images. (<b>3</b>)—Probe in the correct position: The probe must be properly positioned for efficient scanning of the desired areas. (<b>4</b>)—Visual highlights: Red lines with markers “×” indicate the SFT, while the yellow contour outlines the REA.</p>
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<p>Relationship between predicted and observed results for carcass yield of Nellore heifers under different supplementation strategies in integrated production systems. Predicted values are represented by the solid line, while observed data are represented by black circles. (<b>A</b>): Equation (1); (<b>B</b>): Equation (2); (<b>C</b>): Equation (3); (<b>D</b>): Equation (4).</p>
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<p>Relationship between predicted and observed results for the hot carcass weight of Nellore heifers under different supplementation strategies in integrated production systems. Predicted values are represented by the solid line, while observed data are represented by black circles. (<b>A</b>): Equation (5); (<b>B</b>): Equation (6); (<b>C</b>): Equation (7); (<b>D</b>): Equation (8).</p>
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23 pages, 3148 KiB  
Article
Performance Assessment Model for Petrol Stations Using a Multi-Criteria Condition Rating Index
by Altayeb Qasem
Sustainability 2025, 17(6), 2355; https://doi.org/10.3390/su17062355 (registering DOI) - 7 Mar 2025
Abstract
Saudi Arabia’s rapid urbanization and economic growth have increased the number of petrol stations crucial to national infrastructure. Despite oversight from seven local authorities, many stations fail to meet Ministry of Municipal and Rural Affairs (MMRA) standards due to decentralized management. This study [...] Read more.
Saudi Arabia’s rapid urbanization and economic growth have increased the number of petrol stations crucial to national infrastructure. Despite oversight from seven local authorities, many stations fail to meet Ministry of Municipal and Rural Affairs (MMRA) standards due to decentralized management. This study develops a Condition Rating Index (CRI) for petrol stations, designed to serve as the backbone of a comprehensive decision support system for the operation and rehabilitation processes of petrol stations in Saudi Arabia. It is based on dividing petrol stations into four key areas: refueling tanks, pump stations, car service buildings, and commercial spaces. Performance factors for each area are identified and categorized hierarchically into main and sub-factors. The Analytical Hierarchy Process (AHP) is used to determine relative importance weights for these factors, while Multi-Attribute Utility Theory (MAUT) is used to assign utility scores (1–10 scale) reflecting performance levels, where 1 is poor, and 10 is optimal. The overall CRI for each petrol station is calculated by aggregating the scores of all four spaces, combining their relative importance weights with the specific CRI scores aligned with each factor’s utility level. These space-specific CRI scores reveal particular performance levels and rehabilitation needs for each area. The developed CRI functions as a transparent, integrated tool for effectively communicating performance levels and rehabilitation needs among all stakeholders. It serves as an effective decision support tool for prioritizing rehabilitation interventions based on performance levels and budget constraints, offering a comprehensive approach for enhancing petrol station management across Saudi Arabia. This paper develops a transparent and adaptable Condition Rating Index (CRI) that bridges gaps in petrol station management and aligns with sustainability goals. Full article
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<p>Petrol station main spaces considered in this study.</p>
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<p>Research methodology phases.</p>
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<p>Petrol station spaces hierarchy.</p>
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<p>(<b>a</b>) The hierarchical structure for main spaces 1 and 2 main factors and sub-factors. (<b>b</b>) The hierarchical structure for main spaces 3 and 4 main factors and sub-factors.</p>
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<p>(<b>a</b>) The hierarchical structure for main spaces 1 and 2 main factors and sub-factors. (<b>b</b>) The hierarchical structure for main spaces 3 and 4 main factors and sub-factors.</p>
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<p>Relative importance weight for main and sub-criteria for petrol station spaces.</p>
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<p>The integrated AHP- MAUT technique.</p>
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<p>Petro station spaces.</p>
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<p>CRI for petrol station spaces.</p>
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26 pages, 34185 KiB  
Article
Design and Implementation of ESP32-Based Edge Computing for Object Detection
by Yeong-Hwa Chang, Feng-Chou Wu and Hung-Wei Lin
Sensors 2025, 25(6), 1656; https://doi.org/10.3390/s25061656 (registering DOI) - 7 Mar 2025
Abstract
This paper explores the application of the ESP32 microcontroller in edge computing, focusing on the design and implementation of an edge server system to evaluate performance improvements achieved by integrating edge and cloud computing. Responding to the growing need to reduce cloud burdens [...] Read more.
This paper explores the application of the ESP32 microcontroller in edge computing, focusing on the design and implementation of an edge server system to evaluate performance improvements achieved by integrating edge and cloud computing. Responding to the growing need to reduce cloud burdens and latency, this research develops an edge server, detailing the ESP32 hardware architecture, software environment, communication protocols, and server framework. A complementary cloud server software framework is also designed to support edge processing. A deep learning model for object recognition is selected, trained, and deployed on the edge server. Performance evaluation metrics, classification time, MQTT (Message Queuing Telemetry Transport) transmission time, and data from various MQTT brokers are used to assess system performance, with particular attention to the impact of image size adjustments. Experimental results demonstrate that the edge server significantly reduces bandwidth usage and latency, effectively alleviating the load on the cloud server. This study discusses the system’s strengths and limitations, interprets experimental findings, and suggests potential improvements and future applications. By integrating AI and IoT, the edge server design and object recognition system demonstrates the benefits of localized edge processing in enhancing efficiency and reducing cloud dependency. Full article
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<p>Installation process of ESP32-CAM in Arduino IDE.</p>
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<p>ESP32-CAM module: 1.8-inch LCD (<b>left</b>), onboard camera (<b>right</b>).</p>
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<p>MQTT communication in the edge–cloud environment.</p>
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<p>Overall software framework.</p>
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<p>The software framework for the ESP32-CAM edge device.</p>
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<p>Cloud server software framework.</p>
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<p>Entire process from data collection to model deployment.</p>
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<p>The experimental setup for the image capture and recognition.</p>
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<p>Samples of testing images.</p>
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<p>Complete object detection process in the edge–cloud system.</p>
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<p>Response time of the Mosquitto broker (Option 1).</p>
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<p>Response time of the Mosquitto broker (Option 2).</p>
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<p>Response time of the Mosquitto broker (Option 3).</p>
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<p>Response time of the MQTTGO broker (Option 1).</p>
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<p>Response time of the MQTTGO broker (Option 2).</p>
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<p>Response time of the MQTTGO broker (Option 3).</p>
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<p>Response of the Eclipse broker (Option 1).</p>
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<p>Response time of the Eclipse broker (Option 2).</p>
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<p>Response time of the Eclipse broker (Option 3).</p>
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<p>Samples of validation images: person (<b>a</b>,<b>b</b>,<b>d</b>,<b>f</b>,<b>g</b>,<b>k</b>,<b>l</b>,<b>m</b>,<b>n</b>), non-person (<b>c</b>,<b>e</b>,<b>h</b>,<b>i</b>,<b>j</b>,<b>o</b>,<b>p</b>,<b>q</b>,<b>r</b>,<b>s</b>,<b>t</b>).</p>
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<p>Snap shots of object recognition under domestic broker and Option 3: (<b>a</b>) a person is detected, (<b>b</b>) object recognition by the edge, (<b>c</b>) object recognition by the cloud.</p>
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18 pages, 458 KiB  
Article
Leveraging Federated Satellite Systems for Unmanned Medical Evacuation on the Battlefield
by Kasper Halme, Oskari Kirjamäki, Samuli Pietarinen, Mikko Majanen, Kai Virtanen and Marko Höyhtyä
Sensors 2025, 25(6), 1655; https://doi.org/10.3390/s25061655 (registering DOI) - 7 Mar 2025
Abstract
This paper evaluates the role of federated satellite systems (FSSs) in enhancing unmanned vehicle-supported military medical evacuation (MEDEVAC) missions. An FSS integrates multiple satellite systems, thus improving imaging and communication capabilities compared with standalone satellite systems. A simulation model is developed for a [...] Read more.
This paper evaluates the role of federated satellite systems (FSSs) in enhancing unmanned vehicle-supported military medical evacuation (MEDEVAC) missions. An FSS integrates multiple satellite systems, thus improving imaging and communication capabilities compared with standalone satellite systems. A simulation model is developed for a MEDEVAC mission where the FSS control of an unmanned aerial vehicle is distributed across different countries. The model is utilized in a simulation experiment in which the capabilities of the federated and standalone systems in MEDEVAC are compared. The performance of these systems is evaluated by using the most meaningful metrics, i.e., mission duration and data latency, for evacuation to enable life-saving procedures. The simulation results indicate that the FSS, using low-Earth-orbit constellations, outperforms standalone satellite systems. The use of the FSS leads to faster response times for urgent evacuations and low latency for the real-time control of unmanned vehicles, enabling advanced remote medical procedures. These findings suggest that investing in hybrid satellite architectures and fostering international collaboration promote scalability, interoperability, and frequent-imaging opportunities. Such features of satellite systems are vital to enhancing unmanned vehicle-supported MEDEVAC missions in combat zones. Full article
(This article belongs to the Section Sensors and Robotics)
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<p>The MEDEVAC mission. (<b>a</b>) The first phase begins with the MEDCOM requesting satellite imagery to confirm the casualty’s location. The imagery is captured and then transmitted via a ground station or an ISL. (<b>b</b>) The second phase involves the MEDCOM dispatching a UXV while monitoring it in real time. When the UXV reaches the casualty, the MEDEVAC mission ends in the simulation experiment.</p>
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<p>The coverage and access schedules for each SSS. Blue intervals indicate coverage periods, while orange intervals represent access periods. Sum refers to the aggregated coverage and access periods of the satellites.</p>
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<p>The coverage and access schedules for the FSS. Blue intervals indicate coverage periods, while orange intervals represent access periods. Sum refers to the aggregated coverage and access periods of the satellites.</p>
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<p>The mission duration for ‘France’, ‘Germany’, ‘Italy’, ‘EU’, and ‘Federated’ systems as a function of the start time of the mission. Dotted horizontal lines represent the limits between the classes of mission duration.</p>
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<p>Latency classifications for the ‘France’, ‘Germany’, ‘Italy’, ‘EU’, and ‘Federated’ systems.</p>
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25 pages, 7087 KiB  
Article
The Condition Evaluation of Bridges Based on Fuzzy BWM and Fuzzy Comprehensive Evaluation
by Yunyu Li, Jingwen Deng, Yongsheng Wang, Hao Liu, Longfan Peng, Hepeng Zhang, Yabin Liang and Qian Feng
Appl. Sci. 2025, 15(6), 2904; https://doi.org/10.3390/app15062904 (registering DOI) - 7 Mar 2025
Abstract
Accurate and objective evaluation of existing bridges is critical for ensuring the bridge’s safety and optimizing maintenance strategies. This study proposes an integrated Fuzzy Best and Worst Method and fuzzy comprehensive evaluation (FBWM-FCE) model to evaluate uncertainties in expert judgments and complex decision-making. [...] Read more.
Accurate and objective evaluation of existing bridges is critical for ensuring the bridge’s safety and optimizing maintenance strategies. This study proposes an integrated Fuzzy Best and Worst Method and fuzzy comprehensive evaluation (FBWM-FCE) model to evaluate uncertainties in expert judgments and complex decision-making. A four-layer evaluation indicator system and five distinct grades for bridges were established, aligned with the JTG 5120-2004 and JTG/T H21-2011 standards. The FBWM innovatively employs triangular fuzzy numbers (TFNs) to reduce linguistic uncertainties and cognitive bias in bridge evaluation. Subsequently, by integrating FCE for multi-level fuzzy comprehensive operations, the method translates qualitative evaluations into quantitative evaluations using membership matrices and weights. A case study of Ding Jia Bridge and Jigongling Bridge validated the FBWM-FCE model, revealing Class III Bridge (fail condition), consistent with on-site inspections in the 2020 Bridge Inspection and Evaluation Report (Highway Administration of Hubei Provincial Department of Transportation). Comparative analysis demonstrated FBWM’s operational efficiency, requiring 20% fewer pairwise comparisons than AHP while maintaining higher consistency than BWM. The model’s reliability stems from its systematic handling of epistemic uncertainties, offering a high reduction in procedural complexity compared to standardized methods. These advancements provide a scientifically rigorous yet practical tool for bridge management, balancing computational efficiency with evaluation accuracy to support maintenance decisions. Full article
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<p>The function curve of <span class="html-italic">T<sub>F</sub></span>.</p>
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<p>Flowchart of weight calculation using FBWM.</p>
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<p>(<b>a</b>) left semi-trapezoidal membership function; (<b>b</b>) right semi-trapezoidal membership function.</p>
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<p>Trapezoidal membership function.</p>
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<p>Flowchart of FCE method implementation for evaluation.</p>
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<p>The condition evaluation indicator system for bridges.</p>
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<p>Ding Jia bridge location schematic.</p>
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<p>(<b>a</b>) Defects on the bridge deck; (<b>b</b>) defects on the bottom of the T-beam; (<b>c</b>) defects on abutments.</p>
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<p>Jigongling bridge location schematic.</p>
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<p>The plan view of the bridge structure.</p>
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<p>(<b>a</b>) Transverse crack pattern at beam bottom; (<b>b</b>) vertical crack detail at left wall of bridge abutment; (<b>c</b>) transverse crack detail on bridge deck pavement; (<b>d</b>) severe blockage detail in expansion joint.</p>
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23 pages, 5699 KiB  
Article
A Light-Steered Self-Rowing Liquid Crystal Elastomer-Based Boat
by Zongsong Yuan, Jinze Zha and Junxiu Liu
Polymers 2025, 17(6), 711; https://doi.org/10.3390/polym17060711 (registering DOI) - 7 Mar 2025
Abstract
Conventional machines often face limitations due to complex controllers and bulky power supplies, which can hinder their reliability and operability. In contrast, self-excited movements can harness energy from a stable environment for self-regulation. In this study, we present a novel model of a [...] Read more.
Conventional machines often face limitations due to complex controllers and bulky power supplies, which can hinder their reliability and operability. In contrast, self-excited movements can harness energy from a stable environment for self-regulation. In this study, we present a novel model of a self-rowing boat inspired by paddle boats. This boat is powered by a liquid crystal elastomer (LCE) turntable that acts as a motor and operates under consistent illumination. We investigated the dynamic behavior of the self-rowing boat under uniform illumination by integrating the photothermal reaction theory of LCEs with a nonlinear dynamic framework. The primary equations were solved using the fourth-order Runge–Kutta method. Our findings reveal that the model exhibits two modes of motion under steady illumination: a static pattern and a self-rowing pattern. The transition between these modes is influenced by the interaction of the driving and friction torques generated by photothermal energy. This study quantitatively analyzes the fundamental conditions necessary for initiating a self-rowing motion and examines how various dimensionless parameters affect the speed of the self-rowing system. The proposed system offers several unique advantages, including a simple structure, easy control, and independence from electronic components. Furthermore, it has the potential for miniaturization and integration, enhancing its applicability in miniature machines and systems. Full article
(This article belongs to the Section Polymer Applications)
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<p>A self-rowing paddle boat system based on the LCE turntable system. (<b>a</b>) 3D view of LCE-based boat; (<b>b</b>) side view of LCE-based boat; (<b>c</b>) enlarged view of the engine; (<b>d</b>) reference state; (<b>e</b>) force analysis of the ball; (<b>f</b>) force analysis of the boat. Under steady illumination, the boat can self-rowing continuously.</p>
Full article ">Figure 2
<p>The time histories and phase trajectories of the LCE-based boat system for the two main motion modes. (<b>a</b>,<b>b</b>) Static pattern with parameters of <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>M</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>f</mi> </msub> <mo>=</mo> <mn>0.4</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>T</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>0</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>g</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>α</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>L</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>0</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>l</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>β</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>δ</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>l</mi> </msub> <mo>=</mo> <mn>20</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>s</mi> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.5</mn> <mi>π</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>θ</mi> <mo>=</mo> <mn>0.25</mn> <mi>π</mi> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>w</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>0</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>. (<b>c</b>,<b>d</b>) Self-rowing with parameters of <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>M</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>f</mi> </msub> <mo>=</mo> <mn>0.4</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>T</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>0</mn> </msub> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>g</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>α</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>L</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>0</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>l</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>β</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>δ</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>l</mi> </msub> <mo>=</mo> <mn>20</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>s</mi> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.5</mn> <mi>π</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>θ</mi> <mo>=</mo> <mn>0.25</mn> <mi>π</mi> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>w</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>0</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 3
<p>The cyclical variation in key kinematic parameters of the system in self-rowing mode. (<b>a</b>) Torque applied during self-rowing as a function of the angle of rotation; (<b>b</b>) torque from damping as a function of the angle of rotation; (<b>c</b>) boat self-rowing speed <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>v</mi> <mo stretchy="true">¯</mo> </mover> </mrow> </semantics></math> as a function of time; (<b>d</b>) change in position of the mass sphere <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>L</mi> <mo stretchy="true">¯</mo> </mover> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> as a function of time; (<b>e</b>) elastic force <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>F</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>l</mi> </msub> </mrow> </semantics></math> as a function of time; and (<b>f</b>) elastic force <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>F</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>l</mi> </msub> </mrow> </semantics></math> as a function of angle.</p>
Full article ">Figure 4
<p>The movement of a LCE-based boat throughout a self-rowing cycle. The boat is propelled forward continuously by the shrinkage and recovery of the LCE rope, driven by the photothermal effect, completing a full self-rowing cycle.</p>
Full article ">Figure 5
<p>Influence of the dimensionless maximum frictional torque <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>M</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>f</mi> </msub> </mrow> </semantics></math> on the self-rowing of the system, with <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>T</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>0</mn> </msub> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>g</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>α</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>L</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>0</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>l</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>β</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>δ</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>l</mi> </msub> <mo>=</mo> <mn>20</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>s</mi> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.5</mn> <mi>π</mi> </mrow> </semantics></math>. (<b>a</b>) Limit cycles; (<b>b</b>) The self-rowing speed of a boat driven by an LCE turntable. As <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>M</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>f</mi> </msub> </mrow> </semantics></math> increases, self-rowing speed <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>v</mi> <mo stretchy="true">¯</mo> </mover> </mrow> </semantics></math> of the system’s self-rowing decreases.</p>
Full article ">Figure 6
<p>Influence of the dimensionless limit temperature <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>T</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>0</mn> </msub> </mrow> </semantics></math> on the self-rowing of the system, with <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>M</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>f</mi> </msub> <mo>=</mo> <mn>0.4</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>g</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>α</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>L</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>0</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>l</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>β</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>δ</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>l</mi> </msub> <mo>=</mo> <mn>20</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>s</mi> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.5</mn> <mi>π</mi> </mrow> </semantics></math>. (<b>a</b>) Limit cycles; (<b>b</b>) the self-rowing speed of a boat driven by an LCE turntable. As <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>T</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>0</mn> </msub> </mrow> </semantics></math> increases, self-rowing speed <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>v</mi> <mo stretchy="true">¯</mo> </mover> </mrow> </semantics></math> of the system’s self-rowing increases.</p>
Full article ">Figure 7
<p>Influence of the dimensionless gravitational acceleration <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>g</mi> <mo stretchy="true">¯</mo> </mover> </mrow> </semantics></math> on the self-rowing of the system, with <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>M</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>f</mi> </msub> <mo>=</mo> <mn>0.4</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>T</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>0</mn> </msub> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>α</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>L</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>0</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>l</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>β</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>δ</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>l</mi> </msub> <mo>=</mo> <mn>20</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>s</mi> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.5</mn> <mi>π</mi> </mrow> </semantics></math>. (<b>a</b>) Limit cycles; (<b>b</b>) the self-rowing speed of a boat driven by an LCE turntable. As <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>g</mi> <mo stretchy="true">¯</mo> </mover> </mrow> </semantics></math> increases, self-rowing speed <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>v</mi> <mo stretchy="true">¯</mo> </mover> </mrow> </semantics></math> of the system’s self-rowing increases.</p>
Full article ">Figure 8
<p>Influence of the dimensionless thermal shrinkage coefficient <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>α</mi> <mo stretchy="true">¯</mo> </mover> </mrow> </semantics></math> on the self-rowing, with <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>M</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>f</mi> </msub> <mo>=</mo> <mn>0.4</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>T</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>0</mn> </msub> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>g</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>L</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>0</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>l</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>β</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>δ</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>l</mi> </msub> <mo>=</mo> <mn>20</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>s</mi> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.5</mn> <mi>π</mi> </mrow> </semantics></math>. (<b>a</b>) Limit cycles; (<b>b</b>) the self-rowing speed of a boat driven by an LCE turntable. As <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>α</mi> <mo stretchy="true">¯</mo> </mover> </mrow> </semantics></math> increases, the self-rowing speed <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>v</mi> <mo stretchy="true">¯</mo> </mover> </mrow> </semantics></math> of the system’s self-rowing increases.</p>
Full article ">Figure 9
<p>Influence of dimensionless initial position <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>L</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>0</mn> </msub> </mrow> </semantics></math> on the self-rowing of the system, with <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>M</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>f</mi> </msub> <mo>=</mo> <mn>0.4</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>T</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>0</mn> </msub> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>g</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>α</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>l</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>β</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>δ</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>l</mi> </msub> <mo>=</mo> <mn>20</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>s</mi> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.5</mn> <mi>π</mi> </mrow> </semantics></math>. (<b>a</b>) Limit cycles; (<b>b</b>) the self-rowing speed of a boat driven by an LCE turntable. As <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>L</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>0</mn> </msub> </mrow> </semantics></math> increases, the self-rowing speed <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>v</mi> <mo stretchy="true">¯</mo> </mover> </mrow> </semantics></math> of the system’s self-rowing decreases.</p>
Full article ">Figure 10
<p>Influence of the dimensionless length <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>l</mi> <mo stretchy="true">¯</mo> </mover> </mrow> </semantics></math> of paddle on the self-rowing of the system, with <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>M</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>f</mi> </msub> <mo>=</mo> <mn>0.4</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>T</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>0</mn> </msub> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>g</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>α</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>L</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>0</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>β</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>δ</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>l</mi> </msub> <mo>=</mo> <mn>20</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>s</mi> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.5</mn> <mi>π</mi> </mrow> </semantics></math>. (<b>a</b>) Limit cycles; (<b>b</b>) the self-rowing speed of a boat driven by an LCE turntable. As <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>l</mi> <mo stretchy="true">¯</mo> </mover> </mrow> </semantics></math> increases, the self-rowing speed <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>v</mi> <mo stretchy="true">¯</mo> </mover> </mrow> </semantics></math> of the system’s self-rowing increases and then decreases.</p>
Full article ">Figure 11
<p>Influence of the dimensionless damping factor <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>β</mi> <mo stretchy="true">¯</mo> </mover> </mrow> </semantics></math> on the self-rowing of the system, with <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>M</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>f</mi> </msub> <mo>=</mo> <mn>0.4</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>T</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>0</mn> </msub> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>g</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>α</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>L</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>0</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>l</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>δ</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>l</mi> </msub> <mo>=</mo> <mn>20</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>s</mi> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.5</mn> <mi>π</mi> </mrow> </semantics></math>. (<b>a</b>) Limit cycles; (<b>b</b>) the self-rowing speed of a boat driven by an LCE turntable. As <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>β</mi> <mo stretchy="true">¯</mo> </mover> </mrow> </semantics></math> increases, the self-rowing speed <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>v</mi> <mo stretchy="true">¯</mo> </mover> </mrow> </semantics></math> of the system’s self-rowing decreases.</p>
Full article ">Figure 12
<p>Influence of the dimensionless rolling resistance coefficient <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>δ</mi> <mo stretchy="true">¯</mo> </mover> </mrow> </semantics></math> on the self-rowing of the system, with <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>M</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>f</mi> </msub> <mo>=</mo> <mn>0.4</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>T</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>0</mn> </msub> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>g</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>α</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>L</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>0</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>l</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>β</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>l</mi> </msub> <mo>=</mo> <mn>20</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>s</mi> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.5</mn> <mi>π</mi> </mrow> </semantics></math>. (<b>a</b>) Limit cycles; (<b>b</b>) the self-rowing speed of a boat driven by an LCE turntable. As <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>δ</mi> <mo stretchy="true">¯</mo> </mover> </mrow> </semantics></math> increases, the self-rowing speed <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>v</mi> <mo stretchy="true">¯</mo> </mover> </mrow> </semantics></math> of the system’s self-rowing decreases.</p>
Full article ">Figure 13
<p>Influence of the dimensionless elastic stiffness of LCE−rope <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>l</mi> </msub> </mrow> </semantics></math> on the self-rowing of the system, with <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>M</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>f</mi> </msub> <mo>=</mo> <mn>0.4</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>T</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>0</mn> </msub> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>g</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>α</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>L</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>0</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>l</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>β</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>δ</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>s</mi> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.5</mn> <mi>π</mi> </mrow> </semantics></math>. (<b>a</b>) Limit cycles; (<b>b</b>) the self-rowing speed of a boat driven by an LCE turntable. As <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>l</mi> </msub> </mrow> </semantics></math> increases, self-rowing speed <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>v</mi> <mo stretchy="true">¯</mo> </mover> </mrow> </semantics></math> of the system’s self-rowing increases.</p>
Full article ">Figure 14
<p>Influence of the dimensionless elastic stiffness of spring <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>s</mi> </msub> </mrow> </semantics></math> on the self-rowing of the system, with <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>M</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>f</mi> </msub> <mo>=</mo> <mn>0.4</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>T</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>0</mn> </msub> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>g</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>α</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>L</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>0</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>l</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>β</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>δ</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>l</mi> </msub> <mo>=</mo> <mn>20</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.5</mn> <mi>π</mi> </mrow> </semantics></math>. (<b>a</b>) Limit cycles; (<b>b</b>) the self-rowing speed of a boat driven by an LCE turntable. As <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>s</mi> </msub> </mrow> </semantics></math> increases, the self-rowing speed <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>v</mi> <mo stretchy="true">¯</mo> </mover> </mrow> </semantics></math> of the system’s self-rowing decreases.</p>
Full article ">Figure 15
<p>Influence of <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mn>0</mn> </msub> </mrow> </semantics></math> on the self-rowing of the system, with <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>M</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>f</mi> </msub> <mo>=</mo> <mn>0.4</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>T</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>0</mn> </msub> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>g</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>α</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>L</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>0</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>l</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>β</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>δ</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>l</mi> </msub> <mo>=</mo> <mn>20</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mi>s</mi> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>. (<b>a</b>) Limit cycles; (<b>b</b>) the self-rowing speed of a boat driven by an LCE turntable. As <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mn>0</mn> </msub> </mrow> </semantics></math> increases, the self-rowing speed <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>v</mi> <mo stretchy="true">¯</mo> </mover> </mrow> </semantics></math> of the system’s self-rowing increases and then decreases.</p>
Full article ">
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