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Search Results (2,014)

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22 pages, 18877 KiB  
Article
Multi-Centroid Extraction Method for High-Dynamic Star Sensors Based on Projection Distribution of Star Trail
by Xingyu Tang, Qipeng Cao, Zongqiang Fu, Tingting Xu, Rui Duan and Xiubin Yang
Remote Sens. 2025, 17(2), 266; https://doi.org/10.3390/rs17020266 - 13 Jan 2025
Abstract
To improve the centroid extraction accuracy and efficiency of high-dynamic star sensors, this paper proposes a multi-centroid localization method based on the prior distribution of star trail projections. First, the mapping relationship between attitude information and star trails is constructed based on a [...] Read more.
To improve the centroid extraction accuracy and efficiency of high-dynamic star sensors, this paper proposes a multi-centroid localization method based on the prior distribution of star trail projections. First, the mapping relationship between attitude information and star trails is constructed based on a geometric imaging model, and an endpoint centroid group extraction strategy is designed from the perspectives of time synchronization and computational complexity. Then, the endpoint position parameters are determined by fitting the star trail grayscale projection using a line spread function, and accurate centroid localization is achieved through principal axis analysis and inter-frame correlation. Finally, the effectiveness of the proposed method under different dynamic scenarios was tested using numerical simulations and semi-physical experiments. The experimental results show that when the three-axis angular velocity reaches 8°/s, the centroid extraction accuracy of the proposed method remains superior to 0.1 pixels, achieving an improvement of over 30% compared to existing methods and simultaneously doubling the attitude measurement frequency. This demonstrates the superiority of this method in high-dynamic attitude measurement tasks. Full article
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Figure 1

Figure 1
<p>Star sensor coordinate relationships.</p>
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<p>The process of centroid coordinates and centroid groups changing over time during the exposure period. For clarity, only two centroids are plotted as an illustrative representation.</p>
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<p>One-dimensional point spread functions (PSFs) and line spread functions (LSFs) at different spot radii. (<b>a</b>) PSFs with different central positions. (<b>b</b>) LSFs are obtained by integrating the PSFs in (<b>a</b>) along the <span class="html-italic">X</span>-axis.</p>
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<p>The trail of a star moving along the <span class="html-italic">X</span>-axis. Each horizontal line (parallel to the star’s motion, shown in orange) follows an LSF in grayscale, and each vertical line (perpendicular to the star’s motion, shown in blue) follows a PSF in grayscale. The respective structures are still preserved in the projection distributions.</p>
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<p>The trail of a star moving along both the <span class="html-italic">X</span>-axis and <span class="html-italic">Y</span>-axis. The projection distributions in both directions conform to the LSF structure, containing the coordinate information of the start and end points.</p>
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<p>Schematic diagram of the multi-centroid extraction method for the star trail.</p>
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<p>An example of determining coordinate parameters through grayscale projection distribution fitting.</p>
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<p>Schematic diagram of principal axis analysis. (<b>Left</b>): two possible scenarios for the endpoint centroid coordinates when the 4 positional parameters have been determined, identified using a green stripe and an orange stripe. (<b>Right</b>): the different ranges of principal axis angles correspond to two possible scenarios shown in green and orange respectively.</p>
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<p>Schematic diagram of the temporal sequence analysis of centroid groups. (<b>Left</b>): Two endpoint centroid groups without determined temporal order. (<b>Middle</b>): The centroid group at time <span class="html-italic">t<sub>1</sub></span> is closer to the centroid group at time <span class="html-italic">t</span><sub>0</sub>. (<b>Right</b>): The centroid group at time <span class="html-italic">t</span><sub>2</sub> is closer to the centroid group at time <span class="html-italic">t</span><sub>0</sub>.</p>
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<p>Three image plane positions used in the simulation experiments, where a, b, and c represent the center, the right edge, and the lower left edge of the image plane coordinate system, respectively. The local enlargement figure shows the grayscale distribution of the star trail. The continuous red dots superimposed on it are the centroid positions generated based on the attitude information. The green squares represent the centroid coordinates selected at specific reference times.</p>
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<p>The impact of three-axis attitude angles on the accuracy of the centroid extraction method proposed in this paper and the classical methods. (<b>a</b>–<b>d</b>), (<b>e</b>–<b>h</b>), and (<b>i</b>–<b>l</b>) display the results for the center, right edge, and lower left corner of the image plane, respectively.</p>
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<p>The impact of Gaussian noise with different variances on the centroid localization accuracy of the proposed method.</p>
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<p>Multi-centroid extraction from consecutive star images. (<b>a</b>–<b>d</b>) show the results of multi-centroid extraction from the 1st, 3rd, 6th, and 8th images, respectively, out of 8 simulated dynamic star images.</p>
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<p>High-frame-rate attitude determination results. (<b>a</b>–<b>c</b>) shows the attitude angle calculation results for the <span class="html-italic">X</span>-axis, <span class="html-italic">Y</span>-axis, and <span class="html-italic">Z</span>-axis, respectively.</p>
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<p>Dynamic star images semi-physical experimental system.</p>
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<p>Semi-physical experimental results. The green and orange points in each image represent the starting centroid group and the ending centroid group, respectively. And the three-axis attitude angles are displayed in green and orange, representing the attitude angles corresponding to the start and end of the exposure, respectively.</p>
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17 pages, 1285 KiB  
Article
Deep Temporal Clustering of Pathological Gait Patterns in Post-Stroke Patients Using Joint Angle Trajectories: A Cross-Sectional Study
by Gyeongmin Kim, Hyungtai Kim, Yun-Hee Kim, Seung-Jong Kim and Mun-Taek Choi
Bioengineering 2025, 12(1), 55; https://doi.org/10.3390/bioengineering12010055 - 11 Jan 2025
Viewed by 270
Abstract
Rehabilitation of gait function in post-stroke hemiplegic patients is critical for improving mobility and quality of life, requiring a comprehensive understanding of individual gait patterns. Previous studies on gait analysis using unsupervised clustering often involve manual feature extraction, which introduces limitations such as [...] Read more.
Rehabilitation of gait function in post-stroke hemiplegic patients is critical for improving mobility and quality of life, requiring a comprehensive understanding of individual gait patterns. Previous studies on gait analysis using unsupervised clustering often involve manual feature extraction, which introduces limitations such as low accuracy, low consistency, and potential bias due to human intervention. This cross-sectional study aimed to identify and cluster gait patterns using an end-to-end deep learning approach that autonomously extracts features from joint angle trajectories for a gait cycle, minimizing human intervention. A total of 74 sub-acute post-stroke hemiplegic patients with lower limb impairments were included in the analysis. The dataset comprised 219 sagittal plane joint angle and angular velocity trajectories from the hip, knee, and ankle joints during gait cycles. Deep temporal clustering was employed to cluster them in an end-to-end manner by simultaneously optimizing feature extraction and clustering, with hyperparameter tuning tailored for kinematic gait cycle data. Through this method, six optimal clusters were selected with a silhouette score of 0.2831, which is a relatively higher value compared to other clustering algorithms. To clarify the characteristics of the selected groups, in-depth statistics of spatiotemporal, kinematic, and clinical features are presented in the results. The results demonstrate the effectiveness of end-to-end deep learning-based clustering, yielding significant performance improvements without the need for manual feature extraction. While this study primarily utilizes sagittal plane data, future analysis incorporating coronal and transverse planes as well as muscle activity and gait symmetry could provide a more comprehensive understanding of gait patterns. Full article
(This article belongs to the Section Biosignal Processing)
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Figure 1

Figure 1
<p>The architecture of deep temporal clustering for gait patterns.</p>
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<p>Silhouette score per number of clusters.</p>
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<p>Loss curve for the optimal 7 clusters representing both pre-training and training.</p>
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<p>Average joint-level angular trajectories for each cluster on the affected side. (<b>a</b>) Hip, (<b>b</b>) Knee, (<b>c</b>) Ankle.</p>
Full article ">Figure 4 Cont.
<p>Average joint-level angular trajectories for each cluster on the affected side. (<b>a</b>) Hip, (<b>b</b>) Knee, (<b>c</b>) Ankle.</p>
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<p>Averaged joint angle trajectories for Group B on both affected and unaffected sides. (<b>a</b>) Hip, (<b>b</b>) Knee, (<b>c</b>) Ankle.</p>
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<p>Averaged joint angle trajectories for Group B on both affected and unaffected sides. (<b>a</b>) Hip, (<b>b</b>) Knee, (<b>c</b>) Ankle.</p>
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21 pages, 5510 KiB  
Article
Research into the Possibilities of Improving the Adhesion Properties of a Locomotive
by Vadym Ishchuk, Kateryna Kravchenko, Miroslav Blatnický, Alyona Lovska and Ján Dižo
Machines 2025, 13(1), 44; https://doi.org/10.3390/machines13010044 - 10 Jan 2025
Viewed by 178
Abstract
Locomotives are important vehicles, which serve for towing wagons, i.e., trains. Many factors influence the safe and cost-effective operation of locomotives and trains in general. One of these factors is adhesion at the wheel/rail contact. The adhesion determines how much power the locomotive [...] Read more.
Locomotives are important vehicles, which serve for towing wagons, i.e., trains. Many factors influence the safe and cost-effective operation of locomotives and trains in general. One of these factors is adhesion at the wheel/rail contact. The adhesion determines how much power the locomotive can deliver and how the braking system will ensure that the train stops. The main way to improve adhesion is to use sand at the wheel/rail contact point. The aim of this study is to improve the efficiency of the sand system of the locomotive. For this purpose, a new sand system nozzle mounting design was proposed. The newly proposed sanding system is equipped with a nozzle mounted to the axlebox unlike the original one, which uses the nozzle attached to the bogie frame. To compare the proposed and existing design, simulation calculations were performed in Simpack software 2024.3. For the simulation computation of the locomotive bogie, two types of railway tracks were chosen. A straight track section with two angular frequencies and three amplitudes of track irregularities was created, and a real track section corresponding to several kilometers of track was modeled in the Simpack software. During the simulations, it was determined that the proposed nozzle mounting design has a smaller amplitude of motion, compared to the existing one; therefore, there is a more accurate and efficient operation of the sand system. This in turn has a favorable effect on the adhesion of the wheel with the rail. It was found out that the newly designed sanding system has a significant positive economic effect regarding saving sand. There is no sand loss during sandblasting compared with the original sanding system. This directly relates to saving costs during locomotive operation. Full article
(This article belongs to the Special Issue Research and Application of Rail Vehicle Technology)
21 pages, 14214 KiB  
Article
Polarization and Forward Scattering Effects in Low Energy Positron Collisions with H2
by Wagner Tenfen, Josiney de Souza Glória, Sarah Esther da Silva Saab, Eliton Popovicz Seidel and Felipe Arretche
Hydrogen 2025, 6(1), 2; https://doi.org/10.3390/hydrogen6010002 - 10 Jan 2025
Viewed by 395
Abstract
Positron physical-chemistry has been one important focus of scientific investigation of the last decades, however their low energy scattering by atoms and molecules still offers many questions to be answered, as the low angle scattering effects on the measured cross sections and how [...] Read more.
Positron physical-chemistry has been one important focus of scientific investigation of the last decades, however their low energy scattering by atoms and molecules still offers many questions to be answered, as the low angle scattering effects on the measured cross sections and how the degree of target polarization manifest in the comparison between theoretical and experimental results. In this work, we investigate low energy positron collisions by H2 molecules, with particular attention to the convergence of the polarization contribution on the scattering potential. The interaction between positron and molecule was represented by a model potential conceived from the composition of a free electron gas correlation term with an asymptotic polarization potential, obtained from perturbation theory. In particular, we investigated how polarization effects beyond the second order perturbation affect the scattering observables. Our results show that the model which includes up to the quadrupole polarization contribution presents better agreement to the recent experimental data when corrected for forward scattering effects, since they were measured from a transmission beam technique. The angular distributions were also examined through the comparison between our results to the folded differential cross sections measurements available in the literature. We propose a simple correction scheme to the experimental folded differential cross sections for energies below 1 eV which then, as we argue, favorably compares to the quadrupole polarization model. Finally, the comparison between our phase shifts and scattering lengths with recent full many body ab initio results that explicitly include virtual positronium effects suggests that these are intrisically included in the adopted model correlation potential. Full article
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Figure 1

Figure 1
<p>Spherical component of the positron-H<sub>2</sub> interaction potential with the abscissa and ordinate axis given in units of Borhs and Hartrees, respectively. The repulsive static potential is provided as the dashed-point black curve where we can readily identify the position of the H atom and the short range asymptotic behaviour of the potential. The static plus correlation-polarization potential is provided as the full curve where the reader can verify from the inset that the different levels of molecular polarization essentially affect the cut radius at the molecular border. Legends are the same as given in the text after Equation (<a href="#FD7-hydrogen-06-00002" class="html-disp-formula">7</a>).</p>
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<p>Original critical missing angles as given in Zecca et al. [<a href="#B66-hydrogen-06-00002" class="html-bibr">66</a>] (blue squares), the fitted function <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mi>E</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo form="prefix">arcsin</mo> <mfenced separators="" open="(" close=")"> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <mn>0.300059</mn> <mspace width="4.pt"/> <msup> <mi>eV</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> </mrow> <msqrt> <mi>E</mi> </msqrt> </mfrac> </mstyle> </mfenced> </mrow> </semantics></math> (continuous red line) and the critical missing angles for each energy where there is a TCS measurement available in [<a href="#B17-hydrogen-06-00002" class="html-bibr">17</a>] (black filled circles).</p>
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<p><span class="html-italic">s</span>-wave phase shifts obtained in the present work adopting the different polarization approaches as discussed around Equation (<a href="#FD7-hydrogen-06-00002" class="html-disp-formula">7</a>) compared to the values from Rawlins et al. [<a href="#B13-hydrogen-06-00002" class="html-bibr">13</a>] and Frighetto et al. [<a href="#B30-hydrogen-06-00002" class="html-bibr">30</a>]. Present results: black dash dotted line represents the <math display="inline"><semantics> <msub> <mi>δ</mi> <mn>0</mn> </msub> </semantics></math> obtained within the electrostatic approximation, while PD is given by the blue long dashed line, PQ is the yellow short dashed line, PB is the dotted green line and PG is the red solid line. The blue squares represent the results in the static approximation, the purple triangles are the GW + <math display="inline"><semantics> <mo>Γ</mo> </semantics></math> results and the light green circles are the GW + <math display="inline"><semantics> <mrow> <mo>Γ</mo> <mo>+</mo> <mo>Λ</mo> </mrow> </semantics></math> results from Rawlins et al. [<a href="#B13-hydrogen-06-00002" class="html-bibr">13</a>]. The grey open circles is the SMC-SP results from Frighetto et al. [<a href="#B30-hydrogen-06-00002" class="html-bibr">30</a>].</p>
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<p><span class="html-italic">p</span>-wave phase shifts obtained in the present work adopting the different polarization approaches as discussed around Equation (<a href="#FD7-hydrogen-06-00002" class="html-disp-formula">7</a>) compared to the MERT fits from Fedus et al. [<a href="#B68-hydrogen-06-00002" class="html-bibr">68</a>]. The present results for each polarization approximation is given by the same curve and color as in <a href="#hydrogen-06-00002-f003" class="html-fig">Figure 3</a>. The blue squares represent the MERT fitted data from the forward uncorrected measurements and the light green circles represent the fitted data from the forward corrected measurements of Machacek et al. [<a href="#B18-hydrogen-06-00002" class="html-bibr">18</a>].</p>
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<p>Present ICS compared to the theoretical results of Rawlins et al. [<a href="#B13-hydrogen-06-00002" class="html-bibr">13</a>] (light green short dashed dotted line) and to the experimental data of Machacek et al. [<a href="#B18-hydrogen-06-00002" class="html-bibr">18</a>] (magenta triangles) and Zecca et al. [<a href="#B17-hydrogen-06-00002" class="html-bibr">17</a>] (open black circles—original data, filled black circles—forward corrected data). The present results for each polarization approximation is given by the same curve and color as in <a href="#hydrogen-06-00002-f003" class="html-fig">Figure 3</a>.</p>
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<p>Present FDCS for 0.5 eV in panel (<b>a</b>) and 1.0 eV in panel (<b>b</b>) compared to the experimental data of Sullivan et al. [<a href="#B65-hydrogen-06-00002" class="html-bibr">65</a>] panel (<b>a</b>) and Machacek et al. [<a href="#B18-hydrogen-06-00002" class="html-bibr">18</a>] panel (<b>b</b>), and the MERT derived FDCS from Fedus et al. [<a href="#B68-hydrogen-06-00002" class="html-bibr">68</a>]. In panel (<b>a</b>) we present also the measured FDCS of Sullivan et al. [<a href="#B65-hydrogen-06-00002" class="html-bibr">65</a>] corrected for the forward scattering effects as the open black circles (see details in the text). The MERT data of Fedus et al. [<a href="#B68-hydrogen-06-00002" class="html-bibr">68</a>] is presented as the long dash dotted light green line (forward corrected) and the long dashed double dotted black line (forward uncorrected). The present results for each polarization approximation is given by the same curve and color as in <a href="#hydrogen-06-00002-f003" class="html-fig">Figure 3</a>.</p>
Full article ">Figure 7
<p>Present FDCS for 3.0 eV compared to the experimental data of Machacek et al. [<a href="#B18-hydrogen-06-00002" class="html-bibr">18</a>] and the MERT derived FDCS from Fedus et al. [<a href="#B68-hydrogen-06-00002" class="html-bibr">68</a>]. The MERT data of Fedus et al. [<a href="#B68-hydrogen-06-00002" class="html-bibr">68</a>] is presented as the long dash dotted light green line (forward corrected) and the long dashed double dotted black line (forward uncorrected). The present results for each polarization approximation is given by the same curve and color as in <a href="#hydrogen-06-00002-f003" class="html-fig">Figure 3</a>.</p>
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<p>Present FDCS for 7.0 eV in panel (<b>a</b>) and 10.0 eV in panel (<b>b</b>) compared to the experimental data of Machacek et al. [<a href="#B18-hydrogen-06-00002" class="html-bibr">18</a>] and the MERT derived FDCS from Fedus et al. [<a href="#B68-hydrogen-06-00002" class="html-bibr">68</a>]. The MERT data of Fedus et al. [<a href="#B68-hydrogen-06-00002" class="html-bibr">68</a>] is presented as the long dash dotted light green line (forward corrected) and the long dashed double dotted black line (forward uncorrected). The present results for each polarization approximation is given by the same curve and color as in <a href="#hydrogen-06-00002-f003" class="html-fig">Figure 3</a>.</p>
Full article ">
17 pages, 854 KiB  
Article
Non-Stationary Flow of a Viscous Incompressible Electrically Conductive Liquid on a Rotating Plate in the Presence of Media Injection (Suction), Considering Induction and Diffusion Effects
by Anatoly A. Gurchenkov and Ivan A. Matveev
Physics 2025, 7(1), 1; https://doi.org/10.3390/physics7010001 - 10 Jan 2025
Viewed by 267
Abstract
The branch of physics known as magnetohydrodynamics (MHD) emerged in the middle of the 20th century. MHD models, being substantially nonlinear, are quite challenging for theoretical study and allow nontrivial consideration only in particular limited cases. Thus, due to the exceptional growth of [...] Read more.
The branch of physics known as magnetohydrodynamics (MHD) emerged in the middle of the 20th century. MHD models, being substantially nonlinear, are quite challenging for theoretical study and allow nontrivial consideration only in particular limited cases. Thus, due to the exceptional growth of calculation power, research on MHD is now primarily concentrated on numerical modeling. The achievements are considerable; however, there is a possibility of overlooking some phenomena or missing an optimal approach to modeling and calculating that could be identified with theoretical guidance. The paper presents a theoretical study of a particular class of boundary and initial conditions. The flow of a viscous, electrically conductive fluid on a rotating plate in the presence of a magnetic field is considered. The fluid and the bounding plate rotate together with a constant angular velocity around an axis that is not perpendicular to the plane. The flow is induced by sudden longitudinal vibrations of the plate, injection (suction) of the medium through the plate, and an applied magnetic field directed normal to the plate. The full equation of magnetic induction is used, taking into account both the induction effect and energy dissipation due to the flow of electric currents. An analytical solution of three-dimensional magnetohydrodynamics equations in a half-space bounded by a plate is presented. The solution is given in the form of a superposition of plane waves propagating with certain wave numbers along the y-coordinate axis. For certain regions of system parameters, the vibration of the bounding plate does not cause waves in the media. Full article
(This article belongs to the Section Classical Physics)
Show Figures

Figure 1

Figure 1
<p>Schematic geometry of the problem. See text for details.</p>
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<p>Regions of solution on the (<span class="html-italic">Y</span>–<math display="inline"><semantics> <msup> <mi>U</mi> <mo>*</mo> </msup> </semantics></math>)-plane, where <span class="html-italic">Y</span> is a dimensionless frequency variable (<a href="#FD28-physics-07-00001" class="html-disp-formula">28</a>) and <math display="inline"><semantics> <msup> <mi>U</mi> <mo>*</mo> </msup> </semantics></math> is a dimensionless injection velocity (<a href="#FD30-physics-07-00001" class="html-disp-formula">30</a>).</p>
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<p>Wave surfaces of function <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>(</mo> <msup> <mi>U</mi> <mo>*</mo> </msup> <mo>,</mo> <mi>Y</mi> <mo>)</mo> </mrow> </semantics></math>, case of injection. Pale red and pale blue lines on the (<span class="html-italic">Y</span>–<math display="inline"><semantics> <msup> <mi>U</mi> <mo>*</mo> </msup> </semantics></math>)-plane indicate the boundaries of the regions in <a href="#physics-07-00001-f002" class="html-fig">Figure 2</a> shown with same colors. The upper pale blue line denotes the projection of the region drawn for clarity. The bright red and bright blue lines represent the intersection of the <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>(</mo> <mi>Y</mi> <mo>,</mo> <msup> <mi>U</mi> <mo>*</mo> </msup> <mo>)</mo> </mrow> </semantics></math> surface with the <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>=</mo> <mn>50</mn> </mrow> </semantics></math> plane. The bright green curves correspond to the lines of constant <span class="html-italic">Y</span> and the dark green curves represent the lines of constant <math display="inline"><semantics> <msup> <mi>U</mi> <mo>*</mo> </msup> </semantics></math>.</p>
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<p>Wave surfaces of function <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>(</mo> <msup> <mi>U</mi> <mo>*</mo> </msup> <mo>,</mo> <mi>Y</mi> <mo>)</mo> </mrow> </semantics></math>, case of injection. Pale red and pale blue lines on the (<span class="html-italic">Y</span>–<math display="inline"><semantics> <msup> <mi>U</mi> <mo>*</mo> </msup> </semantics></math>)-plane indicate the boundaries of the regions in <a href="#physics-07-00001-f002" class="html-fig">Figure 2</a> shown with same colors. The upper pale blue line denotes the projection of the region drawn for clarity. The bright red and bright blue lines in <a href="#physics-07-00001-f004" class="html-fig">Figure 4</a> depict the intersection of the <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>(</mo> <mi>Y</mi> <mo>,</mo> <msup> <mi>U</mi> <mo>*</mo> </msup> <mo>)</mo> </mrow> </semantics></math> surface with the region given by Equation (<a href="#FD31-physics-07-00001" class="html-disp-formula">31</a>). The bright green curves correspond to the lines of constant <span class="html-italic">Y</span> and the dark green curves represent the lines of constant <math display="inline"><semantics> <msup> <mi>U</mi> <mo>*</mo> </msup> </semantics></math>.</p>
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<p>Wave surfaces of function <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>(</mo> <msup> <mi>U</mi> <mo>*</mo> </msup> <mo>,</mo> <mi>Y</mi> <mo>)</mo> </mrow> </semantics></math>, case of suction for root <math display="inline"><semantics> <msub> <mover accent="true"> <mi>χ</mi> <mo>˜</mo> </mover> <mn>1</mn> </msub> </semantics></math>. Pale red and pale blue lines on the (<span class="html-italic">Y</span>–<math display="inline"><semantics> <msup> <mi>U</mi> <mo>*</mo> </msup> </semantics></math>)-plane indicate the boundaries of the regions in <a href="#physics-07-00001-f002" class="html-fig">Figure 2</a> shown with same colors. The upper pale blue line denotes the projection of the region drawn for clarity. The bright red and bright blue lines represent the intersection of the <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>(</mo> <mi>Y</mi> <mo>,</mo> <msup> <mi>U</mi> <mo>*</mo> </msup> <mo>)</mo> </mrow> </semantics></math> surface with the <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>=</mo> <mn>50</mn> </mrow> </semantics></math> plane. The bright green curves correspond to the lines of constant <span class="html-italic">Y</span> and the dark green curves represent the lines of constant <math display="inline"><semantics> <msup> <mi>U</mi> <mo>*</mo> </msup> </semantics></math>.</p>
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<p>Wave surfaces of function <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>(</mo> <msup> <mi>U</mi> <mo>*</mo> </msup> <mo>,</mo> <mi>Y</mi> <mo>)</mo> </mrow> </semantics></math>, case of suction for root <math display="inline"><semantics> <msub> <mover accent="true"> <mi>χ</mi> <mo>˜</mo> </mover> <mn>1</mn> </msub> </semantics></math>. Pale red and pale blue lines on the (<span class="html-italic">Y</span>–<math display="inline"><semantics> <msup> <mi>U</mi> <mo>*</mo> </msup> </semantics></math>)-plane indicate the boundaries of the regions in <a href="#physics-07-00001-f002" class="html-fig">Figure 2</a> shown with same colors. The upper pale blue line denotes the projection of the region drawn for clarity. The bright red and bright blue lines in <a href="#physics-07-00001-f004" class="html-fig">Figure 4</a> depict the intersection of the <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>(</mo> <mi>Y</mi> <mo>,</mo> <msup> <mi>U</mi> <mo>*</mo> </msup> <mo>)</mo> </mrow> </semantics></math> surface with the region given by Equation (<a href="#FD31-physics-07-00001" class="html-disp-formula">31</a>). The bright green curves correspond to the lines of constant <span class="html-italic">Y</span> and the dark green curves represent the lines of constant <math display="inline"><semantics> <msup> <mi>U</mi> <mo>*</mo> </msup> </semantics></math>.</p>
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<p>Wave surfaces of function <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>(</mo> <msup> <mi>U</mi> <mo>*</mo> </msup> <mo>,</mo> <mi>Y</mi> <mo>)</mo> </mrow> </semantics></math>, case of suction for root <math display="inline"><semantics> <msub> <mover accent="true"> <mi>χ</mi> <mo>˜</mo> </mover> <mn>2</mn> </msub> </semantics></math>. See text for details. The bright green curves correspond to the lines of constant <span class="html-italic">Y</span> and the dark green curves represent the lines of constant <math display="inline"><semantics> <msup> <mi>U</mi> <mo>*</mo> </msup> </semantics></math>.</p>
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<p>Wave surfaces of function <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>(</mo> <msup> <mi>U</mi> <mo>*</mo> </msup> <mo>,</mo> <mi>Y</mi> <mo>)</mo> </mrow> </semantics></math>, case of suction for root <math display="inline"><semantics> <msub> <mover accent="true"> <mi>χ</mi> <mo>˜</mo> </mover> <mn>2</mn> </msub> </semantics></math>. See text for details. The bright green curves correspond to the lines of constant <span class="html-italic">Y</span> and the dark green curves represent the lines of constant <math display="inline"><semantics> <msup> <mi>U</mi> <mo>*</mo> </msup> </semantics></math>.</p>
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18 pages, 7228 KiB  
Article
Motion Smoothness Analysis of the Gait Cycle, Segmented by Stride and Associated with the Inertial Sensors’ Locations
by Leonardo Eliu Anaya-Campos, Luis Pastor Sánchez-Fernández and Ivett Quiñones-Urióstegui
Sensors 2025, 25(2), 368; https://doi.org/10.3390/s25020368 - 9 Jan 2025
Viewed by 342
Abstract
Portable monitoring devices based on Inertial Measurement Units (IMUs) have the potential to serve as quantitative assessments of human movement. This article proposes a new method to identify the optimal placements of the IMUs and quantify the smoothness of the gait. First, it [...] Read more.
Portable monitoring devices based on Inertial Measurement Units (IMUs) have the potential to serve as quantitative assessments of human movement. This article proposes a new method to identify the optimal placements of the IMUs and quantify the smoothness of the gait. First, it identifies gait events: foot-strike (FS) and foot-off (FO). Second, it segments the signals of linear acceleration and angular velocities obtained from the IMUs at four locations into steps and strides. Finally, it applies three smoothness metrics (SPARC, PM, and LDLJ) to determine the most reliable metric and the best location for the sensor, using data from 20 healthy subjects who walked an average of 25 steps on a flat surface for this study (117 measurements were processed). All events were identified with less than a 2% difference from those obtained with the photogrammetry system. The smoothness metric with the least variance in all measurements was SPARC. For the smoothness metrics with the least variance, we found significant differences between applying the metrics with the complete signal (C) and the signal segmented by strides (S). This method is practical, time-effective, and low-cost in terms of computation. Furthermore, it is shown that analyzing gait signals segmented by strides provides more information about gait progression. Full article
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<p>Placement of data collection methods. (<b>a</b>) In gray circles, placement of 14 mm VICON markers according to the Plug-In Gait Lower Body AI model. (<b>b</b>) In orange rectangles, the XSENS IMUs are placed symmetrically on the lower limbs: on the lateral part of the thigh and leg, the dorsum of the foot, and the posterior part of the hip. (<b>c</b>) In blue chips, TRIDENT VICON: IMUs are placed symmetrically on the side of the thigh, leg, and back of each foot. (<b>d</b>) GAITRite mat is 5.79 m long and 0.89 m wide.</p>
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<p>Diagram of the methodology (from left to right) implemented as part of the measurement protocol: data acquisition, data processing, and signal filtering. (1) Sensors indicate the four methods of obtaining data. (2) Placement, location of the sensors on the diagram, and the subject’s body for measurement. (<b>a</b>) In gray circles, placement of 14 mm VICON markers. (<b>b</b>) In orange rectangles, the XSENS IMUs. (<b>c</b>) In blue chips, TRIDENT VICON. (<b>d</b>) GAITRite mat. (3) Raw data and graphs of the unprocessed signals from each sensor detecting the right foot’s magnitude. (4) Filters describe the filter equation used for the raw data.</p>
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<p>Diagram of the methodology (from left to right) implemented as part of the measurement protocol: the processed data from each sensor, the event detection algorithm, the events detected in the acceleration signals, and the signals segmented by the events marked in all the signals. (5) Filtered signals from all sensors consist of signals from the right foot’s magnitude. (6) The event detection algorithm is explained in MATLAB code. (7) The event detection algorithm is applied to each magnitude and component of the IMU signals, and each gear’s foot-off and foot-strike events are detected. (7A) The y component of the linear acceleration is shown. (7B) The y component of the angular acceleration is shown. (8) The events detected by the algorithm in each of the acceleration signals from each sensor are shown.</p>
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<p>Diagram of the methodology (from left to right) implemented as part of the measurement protocol: equations of the smoothness metrics, application of the smoothness metrics to the entire gait signal, and application of the smoothness metrics to the segmented stride signals of each march. (9) Equations of the smoothness metrics (Equations (1)–(5)), are used to evaluate the motor gesture of walking. (10) Smoothness metrics are applied to the complete signal in its components and magnitude. (11) Smoothness metrics are applied to acceleration signals in their components, and magnitude is applied to the signal segmented by gait strides.</p>
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<p>Both graphs show the events marked by the signal maxima to determine the foot-off and foot-strike events; the white flag indicates the detection of standing foot-offs, and the black flag indicates the detection of foot-strikes. White triangles indicate the signal zone between standing foot-off and foot-strike, indicating the swing phase. The black triangles indicate the signal zone between the foot-strike and the following standing foot-off, indicating the stance phase. (Left) graph (<b>A</b>) shows the linear acceleration signal on the <span class="html-italic">y</span>-axis (pitch), and (right) graph (<b>B</b>) the angular acceleration on the <span class="html-italic">y</span>-axis (pitch).</p>
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<p>The XSENS IMUs obtained these seven signals. The solid line represents the foot-strike, and the dashed line represents the foot-off in each graphic.</p>
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<p>The graphs obtained from the SPARC metric in analyzing the entire gait (<b>A</b>) and the study of a stride with the SPARC metric in magnitude (<b>B</b>).</p>
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<p>The smoothness in the SPARC metric in the stance phase on the left side (<b>C</b>) and in the swing phase on the right side (<b>D</b>) for a stride.</p>
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<p>The graph shows the average (blue box) ±1 standard deviation (dashed line) of each smoothness metric (magnitude (M), yaw (X), pitch (Y), and roll (Z)) of the complete gait and the average per stride according to the IMUs placed on the feet, legs, thighs, and hips.</p>
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11 pages, 1889 KiB  
Article
Chemical Lasers Based on Polyatomic Reaction Dynamics: Research of Vibrational Excitation in a Reactive
by José Daniel Sierra Murillo
Atoms 2025, 13(1), 5; https://doi.org/10.3390/atoms13010005 - 9 Jan 2025
Viewed by 251
Abstract
The research presented by the author investigates a polyatomic reaction occurring in the gas phase. This study employs the Quasi-Classical Trajectory (QCT) approach using the Wu–Schatz–Lendvay–Fang–Harding (WSLFH) potential energy surface (PES), recognized as one of the most reliable PES models for this type [...] Read more.
The research presented by the author investigates a polyatomic reaction occurring in the gas phase. This study employs the Quasi-Classical Trajectory (QCT) approach using the Wu–Schatz–Lendvay–Fang–Harding (WSLFH) potential energy surface (PES), recognized as one of the most reliable PES models for this type of analysis. The substantial sample size enables the derivation of detailed results that corroborate previous findings while also identifying potential objectives for future experimental work. The Gaussian Binning (GB) technique is utilized to more effectively highlight the variation in the total angular momentum (J′) of the excited product molecule, HOD*. A key aim of the study is to explore the reaction dynamics due to their importance in excitation and emission processes, which may contribute to the development of a chemical laser based on this reaction. Increasing the vibrational level, v, of one reactant, D2, significantly enhances the excitation of HOD* and shifts the P(J′) distributions towards higher J′ values, while also broadening the distribution. Although the current research focuses on a few initial conditions, the author plans to extend the study to encompass a wider range of initial conditions within the reaction chamber of this type of chemical laser. Full article
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<p>(<b>a</b>–<b>e</b>). P(J’) after a second selection, R–GB. P(J′) distributions are divided in 40 bin’s (J′ = 1,…, 40) and normalized to the unity the sum of the set of all probability distributions. The P(J′)(all) distribution is the sum of all possible distributions, P(J′)(v<sub>HO</sub>′, v<sub>HOD</sub>′, v<sub>OD</sub>′).</p>
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<p>(<b>a</b>–<b>e</b>). P(J’) after a second selection, R–GB. P(J′) distributions are divided in 40 bin’s (J′ = 1,…, 40) and normalized to the unity the sum of the set of all probability distributions. The P(J′)(all) distribution is the sum of all possible distributions, P(J′)(v<sub>HO</sub>′, v<sub>HOD</sub>′, v<sub>OD</sub>′).</p>
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<p>(<b>a</b>–<b>e</b>). P(J’) after a second selection, R–GB. P(J′) distributions are divided in 40 bin’s (J′ = 1,…, 40) and normalized to the unity the sum of the set of all probability distributions. The P(J′)(all) distribution is the sum of all possible distributions, P(J′)(v<sub>HO</sub>′, v<sub>HOD</sub>′, v<sub>OD</sub>′).</p>
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11 pages, 271 KiB  
Article
Hydrogen and Pionic Atoms Under the Effects of Oscillations in the Global Monopole Spacetime
by R. L. L. Vitória and Kleber Anderson T. da Silva
Symmetry 2025, 17(1), 88; https://doi.org/10.3390/sym17010088 - 8 Jan 2025
Viewed by 319
Abstract
In this analysis, we investigate hydrogen and pionic atoms subjected to Dirac and Klein-Gordon oscillators, respectively, in the global monopole spacetime. Through a purely analytical analysis, we determine solutions of bound state, in which we define the allowed energy values for the lowest [...] Read more.
In this analysis, we investigate hydrogen and pionic atoms subjected to Dirac and Klein-Gordon oscillators, respectively, in the global monopole spacetime. Through a purely analytical analysis, we determine solutions of bound state, in which we define the allowed energy values for the lowest energy state of both proposed systems. In addition to the influence of the topological defect on the results obtained, we note another quantum effect: the oscillation frequencies of both systems depend on the system quantum numbers, that is, the angular frequencies are quantized. Full article
(This article belongs to the Special Issue Symmetry in Topological Physics)
22 pages, 17029 KiB  
Article
Cross-Line Fusion of Ground Penetrating Radar for Full-Space Localization of External Defects in Drainage Pipelines
by Yuanjin Fang, Feng Yang, Xu Qiao, Maoxuan Xu, Liang Fang, Jialin Liu and Fanruo Li
Remote Sens. 2025, 17(2), 194; https://doi.org/10.3390/rs17020194 - 8 Jan 2025
Viewed by 281
Abstract
Drainage pipelines face significant threats to underground safety due to external defects. Ground Penetrating Radar (GPR) is a primary tool for detecting such defects from within the pipeline. However, existing methods are limited to single or multiple axial scan lines, which cannot provide [...] Read more.
Drainage pipelines face significant threats to underground safety due to external defects. Ground Penetrating Radar (GPR) is a primary tool for detecting such defects from within the pipeline. However, existing methods are limited to single or multiple axial scan lines, which cannot provide the precise spatial coordinates of the defects. To address this limitation, this study introduces a novel GPR-based drainage pipeline inspection robot system integrated with multiple sensors. The system incorporates MEMS-IMU, encoder modules, and ultrasonic ranging modules to control the GPR antenna for axial and circumferential scanning. A novel Cross-Line Fusion of GPR (CLF-GPR) method is introduced to integrate axial and circumferential scan data for the precise localization of external pipeline defects. Laboratory simulations were performed to assess the effectiveness of the proposed technology and method, while its practical applicability was further validated through real-world drainage pipeline inspections. The results demonstrate that the proposed approach achieves axial positioning errors of less than 2.0 cm, spatial angular positioning errors below 2°, and depth coordinate errors within 2.3 cm. These findings indicate that the proposed approach is reliable and has the potential to support the transparency and digitalization of urban underground drainage networks. Full article
(This article belongs to the Special Issue Advanced Ground-Penetrating Radar (GPR) Technologies and Applications)
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<p>Schematic diagram of GPR detection principle for drainage pipelines. (<b>a</b>) Actual working conditions. (<b>b</b>) Detection principle.</p>
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<p>Diagram of GPR pipeline robot. (<b>a</b>) Extended state of prototype robot. (<b>b</b>) Collapsed state of telescopic antenna module. (<b>c</b>) Collapsed state of telescopic driving module. (<b>d</b>) Circular scanning state of GPR pipeline robot.</p>
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<p>Operational principle of GPR pipeline robot system.</p>
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<p>Definition of coordinate system. (<b>a</b>) Robot coordinate system. (<b>b</b>) Pipeline coordinate system and ground coordinate system.</p>
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<p>Geometric diagram of (<b>a</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>n</mi> </mrow> </semantics></math> and (<b>b</b>) circumferential scan.</p>
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<p>Diagram of simulated defect and experimental setup.</p>
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<p>Processing of axial scan in experiment 1#: (<b>a</b>) Raw image of circumferential GPR signal; (<b>b</b>) GPR image after denoising and reconstructed; (<b>c</b>) edge detection and center point determination.</p>
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<p>Processing of circular scan in experiment 1#: (<b>a</b>) Raw image of circumferential GPR signal; (<b>b</b>) GPR image after denoising and reconstructed; (<b>c</b>) edge detection and center point determination.</p>
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<p>Zero-point calibration for GPR image; (<b>a</b>) raw image of GPR signal; (<b>b</b>) detailed waveforms of initial GPR signal traces.</p>
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<p>CLF-GPR resolution; (<b>a</b>) the CLF-GPR image of experiment 1#; (<b>b</b>) antenna angles corresponding to different GPR traces selected; (<b>c</b>) filtered and reconstructed GPR signals selected.</p>
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<p>The results of the estimated distance between the simulated defect and inner pipe wall.</p>
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<p>The CLF-GPR image and the results. (<b>a</b>), (<b>e</b>), and (<b>i</b>) are CLF-GPR images of 2#, 3#, and 4#, respectively; (<b>b</b>), (<b>f</b>), and (<b>j</b>) show the antenna angles corresponding to different GPR traces selected in 2#, 3#, and 4#, respectively; (<b>c</b>), (<b>g</b>), and (<b>k</b>) illustrate the GPR signals selected after filtering and reconstructing in 2#, 3#, and 4#, respectively; (<b>d</b>), (<b>h</b>), and (<b>l</b>) are the results of the estimated distance between the simulated defect and inner pipe wall in 2#, 3#, and 4#, respectively.</p>
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<p>Filed testing. (<b>a</b>) Field overview. (<b>b</b>) Simulated defect location; (<b>c</b>) wooden box placement; (<b>d</b>) Robot Advancement; Antenna Swing to (<b>e</b>) angle 1, (<b>f</b>) angle 2, and (<b>g</b>) angle 3.</p>
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<p>The CLF-GPR resolution of the experiment; (<b>a</b>) the CLF-GPR image; (<b>b</b>) antenna angles corresponding to different GPR traces selected; (<b>c</b>) filtered and reconstructed GPR signals selected; (<b>d</b>) the estimated distance between the simulated defect and inner pipe wall.</p>
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<p>Variation in MSE with the number of selected points.</p>
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11 pages, 1809 KiB  
Article
Comparative Analysis of Nickel–Titanium Instrumentation Systems for Root Canal Anatomy Preservation: An In Vitro Study
by Eszter Nagy, Niki Kotaki, Máté Dudás, Dániel Gerhard Gryschka, Gábor Braunitzer and Mark Adam Antal
Appl. Sci. 2025, 15(1), 429; https://doi.org/10.3390/app15010429 - 5 Jan 2025
Viewed by 658
Abstract
This study aimed to evaluate the efficacy of various nickel–titanium (Ni-Ti) root canal instrumentation systems in preserving root canal anatomy, focusing on their capacity to limit changes in canal angulation. One hundred canals in fifty extracted human molars were prepared with different techniques: [...] Read more.
This study aimed to evaluate the efficacy of various nickel–titanium (Ni-Ti) root canal instrumentation systems in preserving root canal anatomy, focusing on their capacity to limit changes in canal angulation. One hundred canals in fifty extracted human molars were prepared with different techniques: Step-Back, Reciproc, MTwo, ProTaper Universal (PTU), and ProTaper Next (PTN). The curvature of each canal was measured before and after treatment using Schneider’s methodology, a widely accepted method for assessing canal curvature. Descriptive and statistical analyses, including the Kruskal–Wallis test, were employed to compare angular changes across the systems. The results indicated that all techniques effectively reduced canal curvature, with each system exhibiting a reduction in mean canal angle after instrumentation. Although the Reciproc system showed the smallest mean change in angulation, no statistically significant differences were identified between any of the systems (p = 0.182). This finding suggests that while minor differences in performance may exist, they do not translate into clinically meaningful distinctions in preserving root canal anatomy. The Reciproc system’s slight advantage aligns with other studies, highlighting its conservative design and minimal dentinal stress; however, its superiority was not statistically validated in this study. The results suggest that all five systems are clinically comparable in preserving root canal anatomy, highlighting that dentists can choose from these widely available techniques without compromising anatomical preservation. While this study had limitations, including a relatively small sample size and an in vitro design, it aligns with previous findings on the mechanical behavior of Ni-Ti systems in endodontic practice. Full article
(This article belongs to the Special Issue State-of-the-Art Operative Dentistry)
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<p>Flowchart showing the five study groups with the different root canal treatment protocols. G1: Step-Back, G2: Reciproc, G3: MTwo, G4: ProTaper Universal, G5: ProTaper Next.</p>
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<p>Sequence of radiographs from different stages of the root canal treatment (G1). Abbreviations: IAF = Initial Apical File, MAF = Master Apical File, FF = Final File (applicable only to the step-back technique). FINAL shows the final condition of the root canals without instruments.</p>
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<p>Schematic picture of reference points, lines and angles and root canal curvature. (M-mesial, D-distal)</p>
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48 pages, 2344 KiB  
Article
Neural Network and Hybrid Methods in Aircraft Modeling, Identification, and Control Problems
by Gaurav Dhiman, Andrew Yu. Tiumentsev and Yury V. Tiumentsev
Aerospace 2025, 12(1), 30; https://doi.org/10.3390/aerospace12010030 - 3 Jan 2025
Viewed by 413
Abstract
Motion control of modern and advanced aircraft has to be provided under conditions of incomplete and inaccurate knowledge of their parameters and characteristics, possible flight modes, and environmental influences. In addition, various abnormal situations may occur during flight, in particular, equipment failures and [...] Read more.
Motion control of modern and advanced aircraft has to be provided under conditions of incomplete and inaccurate knowledge of their parameters and characteristics, possible flight modes, and environmental influences. In addition, various abnormal situations may occur during flight, in particular, equipment failures and structural damage. These circumstances cause the problem of a rapid adjustment of the used control laws so that the control system can adapt to the mentioned changes. However, most adaptive control schemes have a model of the control object, which plays a crucial role in adjusting the control law. That is, it is required to solve also the identification problem for dynamical systems. We propose an approach to solving the above-mentioned problems based on artificial neural networks (ANNs) and hybrid technologies. In the class of traditional neural network technologies, we use recurrent neural networks of the NARX type, which allow us to obtain black-box models for controlled dynamical systems. It is shown that in a number of cases, in particular, for control objects with complicated dynamic properties, this approach turns out to be inefficient. One of the possible alternatives to this approach, investigated in the paper, consists of the transition to hybrid neural network models of the gray box type. These are semi-empirical models that combine in the resulting network structure both empirical data on the behavior of an object and theoretical knowledge about its nature. They allow solving with high accuracy the problems inaccessible by the level of complexity for ANN models of the black-box type. However, the process of forming such models requires a very large consumption of computational resources. For this reason, the paper considers another variant of the hybrid ANN model. In it, the hybrid model consists not of the combination of empirical and theoretical elements, resulting in a recurrent network of a special kind, but of the combination of elements of feedforward networks and recurrent networks. Such a variant opens up the possibility of involving deep learning technology in the construction of motion models for controlled systems. As a result of this study, data were obtained that allow us to evaluate the effectiveness of two variants of hybrid neural networks, which can be used to solve problems of modeling, identification, and control of aircraft. The capabilities and limitations of these variants are demonstrated on several examples. Namely, on the example of the problem of aircraft longitudinal angular motion, the possibilities of modeling the motion using the NARX network as applied to a supersonic transport aircraft (SST) are first considered. It is shown that under complicated operating conditions this network does not always provide acceptable modeling accuracy. Further, the same problem, but applied to a maneuverable aircraft, as a more complex object of modeling and identification, is solved using both a NARX network (black box) and a semi-empirical model (gray box). The significant advantage of the gray box model over the black box one is shown. The capabilities of the hybrid model realizing deep learning technologies are demonstrated by forming a model of the control object (SST) and neurocontroller on the example of the MRAC adaptive control scheme. The efficiency of the obtained solution is illustrated by comparing the response of the control object with a failure situation (a decrease in the efficiency of longitudinal control by 50%) with and without adaptation. Full article
(This article belongs to the Section Aeronautics)
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<p>General structure of a controlled dynamical system.</p>
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<p>Scheme of generating a training example based on the results of the experiment with the control object.</p>
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<p>Typical test excitations used in the study of the controlled systems dynamics: (<b>a</b>)—step; (<b>b</b>)—rectangular pulse; (<b>c</b>)—doublet.</p>
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<p>Test excitations as functions of time (in seconds) used in the study of the dynamics of controlled systems: (<b>a</b>)—random signal; (<b>b</b>)—polyharmonic signal. Here, <math display="inline"><semantics> <msub> <mi>ϕ</mi> <mrow> <mi>a</mi> <mi>c</mi> <mi>t</mi> </mrow> </msub> </semantics></math> is the command signal of the elevator actuator; the red dashed–dotted line shows the trimming value of the elevator deflection angle, providing horizontal flight of the airplane for the given values of altitude and airspeed.</p>
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<p>Structure of the NARX model; see Equation (<a href="#FD29-aerospace-12-00030" class="html-disp-formula">29</a>) and its explanations for variable designations.</p>
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<p>Scheme of neural network identification of the control object. Here, <span class="html-italic">u</span> is control, <math display="inline"><semantics> <msub> <mi>y</mi> <mi>p</mi> </msub> </semantics></math> is output of the control object, <math display="inline"><semantics> <msub> <mi>y</mi> <mi>m</mi> </msub> </semantics></math> is output of the ANN model of the control object, <span class="html-italic">e</span> is the difference between the outputs of the control object and the ANN model, and <math display="inline"><semantics> <mi>ξ</mi> </semantics></math> is a correcting action.</p>
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<p>Training results for ANN model of SST with number of neurons in the hidden layer = 15, delays = 2; training epochs = 30,000.</p>
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<p>Canonical form of the recurrent neural network.</p>
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<p>Canonical semi-empirical form of source model (<a href="#FD36-aerospace-12-00030" class="html-disp-formula">36</a>) discretized using explicit Euler method; only the subnetwork whose elements are marked in color is being trained.</p>
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<p>Canonical semi-empirical form of source model (<a href="#FD36-aerospace-12-00030" class="html-disp-formula">36</a>) discretized using explicit Adams method; only the subnetwork whose elements are marked in color is being trained.</p>
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<p>Example comparing the capabilities of black-box and gray-box approaches with modeling dynamical systems with neural networks: Source ODE system (1) in this figure corresponds to dynamical system (<a href="#FD34-aerospace-12-00030" class="html-disp-formula">34</a>), (<a href="#FD34-aerospace-12-00030" class="html-disp-formula">34</a>), while (2) and (3) are its variants with complicated dynamics; trained elements of the semi-empirical ANN model and the NARX model are marked in color.</p>
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<p>An example of using the direct and indirect approaches to find relationships for the coefficients of aerodynamic forces and moments affecting an aircraft. Trained elements of the semi-empirical ANN model and the representation of functions are marked in color. In the semi-empirical ANN model, the left subnetwork marked in color represents the <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mi>L</mi> </msub> <mrow> <mo>(</mo> <mi>α</mi> <mo>,</mo> <mi>q</mi> <mo>,</mo> <mi>φ</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> function and the right subnetwork represents the <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mi>m</mi> </msub> <mrow> <mo>(</mo> <mi>α</mi> <mo>,</mo> <mi>q</mi> <mo>,</mo> <mi>φ</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> function.</p>
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<p>Semi-empirical ANN model for longitudinal angular aircraft motion (based on the Euler scheme). In this model, the left subnetwork marked in color represents the <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mi>L</mi> </msub> <mrow> <mo>(</mo> <mi>α</mi> <mo>,</mo> <mi>q</mi> <mo>,</mo> <mi>φ</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> function and the right subnetwork represents the <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mi>m</mi> </msub> <mrow> <mo>(</mo> <mi>α</mi> <mo>,</mo> <mi>q</mi> <mo>,</mo> <mi>φ</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> function. Only these marked out elements of the model are to be trained.</p>
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<p>Empirical ANN model for longitudinal angular aircraft motion (NARX). In this model, unlike the model in <a href="#aerospace-12-00030-f013" class="html-fig">Figure 13</a>, all elements are to be trained and are marked in color.</p>
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<p>Accuracy evaluation of the semi-empirical ANN model shown in <a href="#aerospace-12-00030-f013" class="html-fig">Figure 13</a>. The red dashed–dotted line shows the trimming value of the elevator deflection angle, providing horizontal flight of the airplane for the given values of altitude and airspeed.</p>
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<p>Accuracy assessment of the empirical ANN model shown in <a href="#aerospace-12-00030-f014" class="html-fig">Figure 14</a>.</p>
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<p>Example of pitching moment coefficient reconstitution for a maneuverable aircraft with a wide range of flight modes: (<b>a</b>)—coefficient <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mi>m</mi> </msub> <mrow> <mo>(</mo> <mi>α</mi> <mo>,</mo> <msub> <mi>δ</mi> <mi>e</mi> </msub> <mo>)</mo> </mrow> </mrow> </semantics></math> for various elevator deflection angle <math display="inline"><semantics> <msub> <mi>δ</mi> <mi>e</mi> </msub> </semantics></math> values according to [<a href="#B111-aerospace-12-00030" class="html-bibr">111</a>]; (<b>b</b>)—approximation error <math display="inline"><semantics> <msub> <mi>E</mi> <msub> <mi>C</mi> <mi>m</mi> </msub> </msub> </semantics></math> for fixed values of pitch rate <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> deg/s and airspeed <math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mi>T</mi> </msub> <mo>=</mo> <mn>150</mn> </mrow> </semantics></math> m/s.</p>
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<p>Error values for <math display="inline"><semantics> <msub> <mi>C</mi> <mi>L</mi> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>C</mi> <mi>Y</mi> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>C</mi> <mi>l</mi> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>C</mi> <mi>m</mi> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>C</mi> <mi>n</mi> </msub> </semantics></math> according to the reconstructed dependencies for them in the process of testing the hybrid ANN model (referred to the ranges of change for these variables obtained during testing).</p>
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<p>The architecture of the SST motion model in the form of a deep neural network.</p>
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<p>Training results of the SST motion model in the form of a deep neural network.</p>
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<p>Adaptive control of a dynamical system using the MRAC scheme.</p>
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<p>Neurocontroller architecture and its interaction with the ANN model of the control object.</p>
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<p>Source data for training the combined network including the neurocontroller (NC) and the ANN model and its results (angle of attack tracking error <math display="inline"><semantics> <msub> <mi>e</mi> <mi>α</mi> </msub> </semantics></math> is measured in degrees).</p>
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<p>SST response to a failure situation without adaptation (failure at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>40</mn> </mrow> </semantics></math> s; angle of attack tracking error <math display="inline"><semantics> <msub> <mi>e</mi> <mi>α</mi> </msub> </semantics></math> is measured in degrees).</p>
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<p>SST response to a failure situation with adaptation (failure at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>40</mn> </mrow> </semantics></math> s; angle of attack tracking error <math display="inline"><semantics> <msub> <mi>e</mi> <mi>α</mi> </msub> </semantics></math> is measured in degrees).</p>
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20 pages, 1163 KiB  
Review
The Challenges and Opportunities for Performance Enhancement in Resonant Fiber Optic Gyroscopes
by Sumathi Mahudapathi, Sumukh Nandan R, Gowrishankar R and Balaji Srinivasan
Sensors 2025, 25(1), 223; https://doi.org/10.3390/s25010223 - 3 Jan 2025
Viewed by 416
Abstract
In the last decade, substantial progress has been made to improve the performance of optical gyroscopes for inertial navigation applications in terms of critical parameters such as bias stability, scale factor stability, and angular random walk (ARW). Specifically, resonant fiber optic gyroscopes (RFOGs) [...] Read more.
In the last decade, substantial progress has been made to improve the performance of optical gyroscopes for inertial navigation applications in terms of critical parameters such as bias stability, scale factor stability, and angular random walk (ARW). Specifically, resonant fiber optic gyroscopes (RFOGs) have emerged as a viable alternative to widely popular interferometric fiber optic gyroscopes (IFOGs). In a conventional RFOG, a single-wavelength laser source is used to generate counter-propagating waves in a ring resonator, for which the phase difference is measured in terms of the resonant frequency shift to obtain the rotation rate. However, the primary limitation of RFOG performance is the bias drift, which can be attributed to nonreciprocal effects such as Rayleigh backscattering, back-reflections, polarization instabilities, Kerr nonlinearity, and environmental fluctuations. In this paper, we review the challenges and opportunities of achieving performance enhancement in RFOGs. Full article
(This article belongs to the Special Issue Advances in Optical Fiber Sensors and Fiber Lasers)
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<p>Performance comparison of various gyroscope technologies used for inertial/tactical/ control grades; adopted from [<a href="#B4-sensors-25-00223" class="html-bibr">4</a>].</p>
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<p>A schematic diagram illustrating the working principle of resonant fiber optic gyroscopes (RFOGs). Any rotation experienced by the fiber ring resonator (FRR) will result in an upward or downward shift in the resonance frequency for the two counter-propagating waves (CW and CCW, respectively). This frequency shift may be demodulated into an intensity change by typically locking the source frequency with respect to the FRR resonance.</p>
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<p>A typical lock-in detection-based readout system for RFOGs (reproduced from [<a href="#B26-sensors-25-00223" class="html-bibr">26</a>]). The input CW and CCW light beams are either phase or frequency-modulated to enable lock-in detection. One of the output signals (CCW in the above figure) is used to keep the source laser locked to the FRR resonance, whereas the other (CW) is used to read out the rotation rate.</p>
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<p>Schematic diagram illustrating the various algorithmic blocks implemented in an FPGA for signal detection [<a href="#B20-sensors-25-00223" class="html-bibr">20</a>].</p>
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<p>Bar graph showing the improvement in bias stability of RFOGs over the past three decades.</p>
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<p>Schematic diagram of a single-coupler resonator with reflector (SCRWR) gyroscope configuration with an intensity-based readout [<a href="#B80-sensors-25-00223" class="html-bibr">80</a>].</p>
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<p>Beat frequency for different rotation induced phase changes [<a href="#B11-sensors-25-00223" class="html-bibr">11</a>].</p>
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<p>Change in beat frequency vs. rotational bias for different values of reflectivity [<a href="#B11-sensors-25-00223" class="html-bibr">11</a>].</p>
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<p>Schematic diagram of a frequency comb source-based RFOG. Two mode-locked lasers are used to generate a separate comb of frequencies for the CW and CCW light beams. The rotation rate is measured by beating the two frequency combs as they are modulated by using FRR resonance shift through closed-loop feedback.</p>
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<p>A simulated frequency comb from which a set of frequencies are carved out in the central region.</p>
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<p>Comparison of (<b>a</b>) HC-PBGF, (<b>b</b>) NANF structures [<a href="#B75-sensors-25-00223" class="html-bibr">75</a>] (<b>c</b>), and CTF structures [<a href="#B95-sensors-25-00223" class="html-bibr">95</a>].</p>
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<p>Schematic diagram of an RFOG using an ASE source in a reflected resonator open-loop configuration [<a href="#B76-sensors-25-00223" class="html-bibr">76</a>].</p>
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24 pages, 7613 KiB  
Article
A Novel Hybrid Die Design for Enhanced Grain Refinement: Vortex Extrusion–Equal-Channel Angular Pressing (Vo-CAP)
by Hüseyin Beytüt, Kerim Özbeyaz and Şemsettin Temiz
Appl. Sci. 2025, 15(1), 359; https://doi.org/10.3390/app15010359 - 2 Jan 2025
Viewed by 362
Abstract
A novel hybrid Severe Plastic Deformation (SPD) method called Vortex Extrusion–Equal-Channel Angular Pressing (Vo-CAP) was developed and applied to AA6082 workpieces in this study. Before experimental application, a comprehensive optimization of the die design was performed considering effective strain, strain inhomogeneity, and pressing [...] Read more.
A novel hybrid Severe Plastic Deformation (SPD) method called Vortex Extrusion–Equal-Channel Angular Pressing (Vo-CAP) was developed and applied to AA6082 workpieces in this study. Before experimental application, a comprehensive optimization of the die design was performed considering effective strain, strain inhomogeneity, and pressing load parameters. The optimization process utilized an integrated approach combining Finite Element Analysis (FEA), artificial neural networks (ANNs), and the non-dominated sorting genetic algorithm II (NSGA-II). The optimized die successfully achieved a balance between maximizing effective strain while minimizing pressing load and strain inhomogeneity. The Vo-CAP process incorporates a unique conical die design that enables assembly without traditional fasteners. Moreover, this novel die combines VE and ECAP advantages in a single-pass operation. While VE has been previously studied, experimental work was limited to specific configurations, and its integration with ECAP had not been explored. Through the development of Vo-CAP, this research gap has been addressed. The results showed substantial enhancements in hardness values, ultimate tensile strength, and strain homogeneity. These findings demonstrate that Vo-CAP represents a significant advancement in SPD, offering an efficient single-pass process for improving the mechanical properties of aluminum alloys through grain refinement. Full article
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<p>Design of novel Vo-CAP die. (<b>a</b>) 3D view of the die. (<b>b</b>) Detailed view of the zones (VE and ECAP).</p>
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<p>FEM setup of Vo-CAP.</p>
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<p>Optimization framework for Vo-CAP.</p>
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<p>Selected point across the cross-sectional plane.</p>
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<p>Geometric representation of variables.</p>
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<p>Basic structure of the implemented ANN model.</p>
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<p>Assembly of parts. (<b>a</b>) Assembly, (<b>b</b>) die holder, (<b>c</b>) fixed part-1, (<b>d</b>) workpiece, (<b>e</b>) resistor rods, (<b>f</b>) punch, (<b>g</b>) M18×20 bolt, (<b>h</b>) fixed part-2, and (<b>i</b>) die.</p>
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<p>Experimental setup.</p>
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<p>Tensile test sample. (<b>a</b>) Geometrical dimensions. (<b>b</b>) Prepared round test specimen.</p>
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<p>Validation of the FEM setup and comparison of the VE and the Vo-CAP at different twist angles [<a href="#B24-applsci-15-00359" class="html-bibr">24</a>].</p>
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<p>Zones of Vo-CAP process and stroke–pressing load curve.</p>
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<p>Comparison of experimental and FEM results during different stages of Vo-CAP process: experimental samples (<b>left</b>), effective strain distributions (<b>middle</b>), and pressing load–stroke curves (<b>right</b>) at die strokes of 8.3, 17.8, 20.2, and 32.4 mm.</p>
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<p>The comparison between prediction values and targets of (<b>a</b>) effective strain, (<b>b</b>) max. pressing load, and (<b>c</b>) strain inhomogeneity.</p>
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<p>Pareto-optimal solutions generated by NSGA-II (optimum point ε̅ = 16.49, ML = 15.69, and CVεp = 0.375).</p>
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<p>Optimum design variables of Vo-CAP. (<b>a</b>) Geometrical details. (<b>b</b>) Manufactured Vo-CAP die.</p>
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<p>(<b>a</b>) View of the workpiece (red dashed line) emerging through the exit channel during the Vo-CAP process. (<b>b</b>) Vo-CAP-processed AA6082.</p>
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<p>Deformation path geometry in Vo-CAP die.</p>
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<p>Hardness values of annealed and Vo-CAP-processed samples.</p>
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<p>Stress–strain curve of annealed and Vo-CAP-processed samples.</p>
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<p>Fracture surface of tensile test specimen.</p>
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<p>OM images. (<b>a</b>) Annealed and (<b>b</b>) Vo-CAP-processed workpiece.</p>
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23 pages, 7167 KiB  
Article
Features of Structure and Flow Field in Homemade Co-Current Cavitation Water Jet Nozzle
by Chenhao Guo, Xing Dong, Haorong Song and Yun Jiang
Materials 2025, 18(1), 146; https://doi.org/10.3390/ma18010146 - 2 Jan 2025
Viewed by 315
Abstract
The cavitation water jet cleaning and coating removal technique represents an innovative sustainable method for cleaning and removing coatings, with the nozzle serving as a crucial component of this technology. Developing an artificially submerged nozzle with a reliable structure and excellent cavitation performance [...] Read more.
The cavitation water jet cleaning and coating removal technique represents an innovative sustainable method for cleaning and removing coatings, with the nozzle serving as a crucial component of this technology. Developing an artificially submerged nozzle with a reliable structure and excellent cavitation performance is essential for enhancing cavitation water jets’ cleaning and coating removal efficacy in an atmosphere environment (non-submerged state). This study is based on the shear flow cavitation mechanism of an angular nozzle, the resonance principle of an organ pipe, and the jet pump principle. A dual-nozzle co-current cavitation water jet nozzle structure was designed and manufactured. The impact of the nozzle’s inlet pressure on the vapor volume percentage, as well as the axial and radial velocities inside the flow field, were examined utilizing ANSYS Fluent software with the CFD method. The dynamic change rule of the cavitation cloud is derived by analyzing the picture of the cavitation cloud in the nozzle’s outflow field utilizing pseudo-color imaging techniques. The results show that the maximum vapor volume percentage is more significant than 95% for different inlet pressures in the internal nozzle. The changes that occur in the cavitation cloud exhibit notable regularity, including the four stages of cavitation, which are inception, development, shedding, and collapse. A change period is 1.5 ms, which proves that the homemade co-current cavitation water jet nozzle can achieve good cavitation effects. Full article
(This article belongs to the Topic Fluid Mechanics, 2nd Edition)
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<p>Schematic structure of homemade co-current cavitation water jet nozzle.</p>
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<p>Homemade co-current cavitation water jet nozzle physical picture.</p>
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<p>Dimensions of the internal organ pipe self-oscillating angular cavitation nozzle.</p>
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<p>Finite element model.</p>
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<p>Variation curve of maximum vapor volume percentage for different numbers of meshes.</p>
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<p>Cloud diagram of maximum vapor volume percentage distributions at (<b>a</b>) 10 MPa, (<b>b</b>) 15 MPa, (<b>c</b>) 20 MPa, (<b>d</b>) 25 MPa, and (<b>e</b>) 30 MPa.</p>
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<p>Cloud diagram of axial velocity distribution at different inlet pressures of (<b>a</b>) 10 MPa, (<b>b</b>) 15 MPa, (<b>c</b>) 20 MPa, (<b>d</b>) 25 MPa, and (<b>e</b>) 30 MPa.</p>
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<p>Radial distribution of jet velocity at different inlet pressures of (<b>a</b>) 10 MPa, (<b>b</b>) 15 MPa, (<b>c</b>) 20 MPa, (<b>d</b>) 25 MPa, and (<b>e</b>) 30 MPa.</p>
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<p>Radial distribution of jet velocity at different inlet pressures of (<b>a</b>) 10 MPa, (<b>b</b>) 15 MPa, (<b>c</b>) 20 MPa, (<b>d</b>) 25 MPa, and (<b>e</b>) 30 MPa.</p>
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<p>Visualization test system diagram of co-current cavitation water jet nozzle. (<b>a</b>) Visualization of system diagram. (<b>b</b>) Visualization of system physical photos.</p>
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<p>Visualization test system diagram of co-current cavitation water jet nozzle. (<b>a</b>) Visualization of system diagram. (<b>b</b>) Visualization of system physical photos.</p>
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<p>Dynamic evolution process diagram of cavitation cloud. (<b>a</b>) Original images. (<b>b</b>) Grayscale images. (<b>c</b>) Pseudo-color images.</p>
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19 pages, 319 KiB  
Article
Noncommutative Reissner–Nordström Black Hole from Noncommutative Charged Scalar Field
by Marija Dimitrijević Ćirić, Nikola Konjik, Tajron Jurić, Andjelo Samsarov and Ivica Smolić
Symmetry 2025, 17(1), 54; https://doi.org/10.3390/sym17010054 - 31 Dec 2024
Viewed by 424
Abstract
Within the framework of noncommutative (NC) deformation of gauge field theory by the angular twist, we first rederive the NC scalar and gauge field model from our previous papers, and then generalize it to the second order in the Seiberg–Witten (SW) map. It [...] Read more.
Within the framework of noncommutative (NC) deformation of gauge field theory by the angular twist, we first rederive the NC scalar and gauge field model from our previous papers, and then generalize it to the second order in the Seiberg–Witten (SW) map. It turns out that SW expansion is finite and that it ceases at the second order in the deformation parameter, ultimately giving rise to the equation of motion for the scalar field in the Reissner–Nordström (RN) metric that is nonperturbative and exact at the same order. As a further step, we show that the effective metric put forth and constructed in our previous work satisfies the equations of Einstein–Maxwell gravity, but only within the first order of deformation and when the gauge field is fixed by the Coulomb potential of the charged black hole. Thus, the obtained NC deformation of the Reissner–Nordström (RN) metric appears to have an additional off-diagonal element which scales linearly with a deformation parameter. We analyze various properties of this metric. Full article
(This article belongs to the Special Issue Symmetry in Researches of Neutron Stars and Black Holes)
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