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12 pages, 4250 KiB  
Article
SIW Directional Coupler with Improved Isolation for X-Band Applications
by Thuy-Linh Nguyen, Duy-Manh Luong, Ta Van Mai, Huy Hoang Nguyen, Tuan Hung Nguyen, Thi Thu Huong Tran and Khac Phuong Kieu
Electronics 2025, 14(4), 774; https://doi.org/10.3390/electronics14040774 - 17 Feb 2025
Viewed by 57
Abstract
This paper presents the design of a high-isolation directional coupler for X-band applications, utilizing substrate-integrated waveguide (SIW) technology. The coupler features a simple structure, compact size, and ease of integration with other planar circuits. Typically, the S-parameters of a directional coupler are determined [...] Read more.
This paper presents the design of a high-isolation directional coupler for X-band applications, utilizing substrate-integrated waveguide (SIW) technology. The coupler features a simple structure, compact size, and ease of integration with other planar circuits. Typically, the S-parameters of a directional coupler are determined by the dimensions of the SIW and the aperture (or hole) of the coupler. In this study, we introduce additional via lines to modify the SIW and the coupler aperture, aiming to achieve high isolation. First, two via lines are embedded in the center, converging into two central vias that form the coupler’s aperture. The power ratio within the coupler is controlled by adjusting the width of the aperture and the overall width of the SIW. Specifically, the width of the SIW at the aperture position is affected by adding vias on the two outer sides of the SIW. By incorporating these vias, we can effectively manage the power distribution across the four ports while ensuring sufficient isolation among them. The proposed design achieves an insertion loss of 3.3 dB, a coupling factor of 6 dB, and an isolation factor of 28.6 dB at 10 GHz. The experimental results demonstrate that the coupler maintains S41 less than −20 dB over a 30% fractional bandwidth, ranging from 8.6 GHz to 11.6 GHz. Full article
(This article belongs to the Section Circuit and Signal Processing)
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<p>The substrate-integrated waveguide transmission line: (<b>a</b>) Structure of SIW [<a href="#B4-electronics-14-00774" class="html-bibr">4</a>]; (<b>b</b>) Electric field distribution of the <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>T</mi> <mi>E</mi> </mrow> <mrow> <mn>10</mn> </mrow> </msub> </mrow> </semantics></math> mode in SIW.</p>
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<p>The fundamental parameters of the SIW line.</p>
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<p>The basic structure of the four-port coupler.</p>
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<p>The basic structure of the single-aperture SIW coupler.</p>
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<p>Simulated S-parameter of the basic X-band directional coupler.</p>
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<p>Simulated electric field distribution of the basic X band coupler at 10 GHz.</p>
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<p>The structure of the proposed SIW coupler.</p>
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<p>Effects of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>X</mi> </mrow> <mrow> <mi>a</mi> </mrow> </msub> </mrow> </semantics></math> of the additional vias on the performance of the coupler: (<b>a</b>) Simulated electric field distribution of the coupler at 10 GHz in the case of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>X</mi> </mrow> <mrow> <mi>a</mi> </mrow> </msub> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>; (<b>b</b>) Simulated electric field distribution of the coupler at 10 GHz in the case of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>X</mi> </mrow> <mrow> <mi>a</mi> </mrow> </msub> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>; (<b>c</b>) Simulated electric field distribution of the coupler at 10 GHz in the case of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>X</mi> </mrow> <mrow> <mi>a</mi> </mrow> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>; (<b>d</b>) Simulated electric field distribution of the coupler at 10 GHz in the case of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>X</mi> </mrow> <mrow> <mi>a</mi> </mrow> </msub> <mo>=</mo> <mn>0.3</mn> </mrow> </semantics></math>; (<b>e</b>) Comparison of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>S</mi> </mrow> <mrow> <mn>41</mn> </mrow> </msub> </mrow> </semantics></math> simulated results.</p>
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<p>Simulated S-parameter of the proposed coupler.</p>
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<p>Simulated electric field distribution of the proposed coupler at 10 GHz.</p>
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<p>Simulated <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>S</mi> </mrow> <mrow> <mn>41</mn> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>S</mi> </mrow> <mrow> <mn>31</mn> </mrow> </msub> </mrow> </semantics></math> of the basic X-band coupler and the proposed coupler.</p>
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<p>The photograph of the two fabricated X-band couplers: (<b>a</b>) Basic SIW directional coupler; (<b>b</b>) The high-isolation directional coupler.</p>
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<p>Measured S-parameters of the basic X-band coupler.</p>
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<p>Measured S-Parameters of the proposed coupler.</p>
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<p>Measured <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>S</mi> </mrow> <mrow> <mn>41</mn> </mrow> </msub> </mrow> </semantics></math> results of the two couplers.</p>
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22 pages, 8673 KiB  
Article
A Dual-Polarized and Broadband Multiple-Antenna System for 5G Cellular Communications
by Haleh Jahanbakhsh Basherlou, Naser Ojaroudi Parchin and Chan Hwang See
Sensors 2025, 25(4), 1032; https://doi.org/10.3390/s25041032 - 9 Feb 2025
Viewed by 568
Abstract
This study presents a new multiple-input multiple-output (MIMO) antenna array system designed for sub-6 GHz fifth generation (5G) cellular applications. The design features eight compact trapezoid slot elements with L-shaped CPW (Coplanar Waveguide) feedlines, providing broad bandwidth and radiation/polarization diversity. The antenna elements [...] Read more.
This study presents a new multiple-input multiple-output (MIMO) antenna array system designed for sub-6 GHz fifth generation (5G) cellular applications. The design features eight compact trapezoid slot elements with L-shaped CPW (Coplanar Waveguide) feedlines, providing broad bandwidth and radiation/polarization diversity. The antenna elements are compact in size and function within the frequency spectrum spanning from 3.2 to 6 GHz. They have been strategically positioned at the peripheral corners of the smartphone mainboard, resulting in a compact overall footprint of 75 mm × 150 mm FR4. Within this design framework, there are four pairs of antennas, each aligned to offer both horizontal and vertical polarization options. In addition, despite the absence of decoupling structures, the adjacent elements in the array exhibit high isolation. The array demonstrates a good bandwidth of 2800 MHz, essential for 5G applications requiring high data rates and reliable connectivity, high radiation efficiency, and dual-polarized/full-coverage radiation. Furthermore, it achieves low ECC (Envelope Correlation Coefficient) and TARC (Total Active Reflection Coefficient) values, measuring better than 0.005 and −20 dB, respectively. With its compact and planar configuration, quite broad bandwidth, acceptable SAR (Specific Absorption Rate) and excellent radiation characteristics, this suggested MIMO antenna array design shows good promise for integration into 5G hand-portable devices. Furthermore, a compact phased-array millimeter-wave (mmWave) antenna with broad bandwidth is introduced as a proof of concept for higher frequency antenna integration. This design underscores the potential to support future 5G and 6G applications, enabling advanced connectivity in smartphones. Full article
(This article belongs to the Special Issue Antenna Design and Optimization for 5G, 6G, and IoT)
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<p>(<b>a</b>) Side and (<b>b</b>) front views of the introduced antenna design.</p>
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<p>S-parameters of the suggested antenna design.</p>
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<p>(<b>a</b>) S<sub>nn</sub> and (<b>b</b>) S<sub>mn</sub> results for different values of L<sub>1</sub>.</p>
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<p>Current densities at (<b>a</b>) 3.2, (<b>b</b>) 4.7, and (<b>c</b>) 5.5 GHz.</p>
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<p>Efficiency results across the antenna’s broad bandwidth.</p>
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<p>Linear-scaled (<b>a</b>) 3D and (<b>b</b>) 2D dual-polarized radiation patterns at 4.5 GHz.</p>
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<p>3D radiation patterns of the dual-polarized antenna at (<b>a</b>) 3.5 and (<b>b</b>) 5.5 GHz.</p>
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<p>Schematic of the introduced MIMO antenna.</p>
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<p>(<b>a</b>) S<sub>nn</sub> and (<b>b</b>) S<sub>mn</sub> results of the antenna elements.</p>
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<p>Three-dimensional radiation patterns at (<b>a</b>) 3.5 GHz and (<b>b</b>) 5.5 GHz.</p>
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<p>(<b>a</b>) Radiation and (<b>b</b>) total efficiency results of the elements over 3–6 GHz.</p>
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<p>(<b>a</b>) Prototyped sample and (<b>b</b>) feeding method.</p>
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<p>Measured/simulated S-parameters.</p>
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<p>Measured/simulated 2D radiation patterns of the pair at (<b>a</b>) 3.5 GHz and (<b>b</b>) 5.5 GHz.</p>
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<p>Measured/simulated comparison for (<b>a</b>) ECC and (<b>b</b>) TARC.</p>
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<p>(<b>a</b>) Talk-mode and SAR analysis at (<b>b</b>) 3.5 GHz and (<b>c</b>) 5.5 GHz.</p>
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<p>Schematic of the phased array.</p>
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<p>(<b>a</b>) S-parameters and (<b>b</b>) gain comparison of the designed phased array.</p>
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<p>Beam-steering of the phased array at (<b>a</b>) 0, (<b>b</b>) 30, and (<b>c</b>) 60 degrees.</p>
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<p>Possible placements of the mmWave phased array.</p>
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16 pages, 4009 KiB  
Article
Curved Fabry-Pérot Ultrasound Detectors: Optical and Mechanical Analysis
by Barbara Rossi, Maria Alessandra Cutolo, Martino Giaquinto, Andrea Cusano and Giovanni Breglio
Sensors 2025, 25(4), 1014; https://doi.org/10.3390/s25041014 - 8 Feb 2025
Viewed by 437
Abstract
Optical fiber-based acoustic detectors for ultrasound imaging in medical field feature plano-concave Fabry–Perot cavities integrated on fiber tips, realized via dip-coating. This technique imposes constraints on sensor geometry, potentially limiting performance. Lab-on-Fiber technology enables complex three-dimensional structures with precise control over geometric parameters, [...] Read more.
Optical fiber-based acoustic detectors for ultrasound imaging in medical field feature plano-concave Fabry–Perot cavities integrated on fiber tips, realized via dip-coating. This technique imposes constraints on sensor geometry, potentially limiting performance. Lab-on-Fiber technology enables complex three-dimensional structures with precise control over geometric parameters, such as the curvature radius. A careful investigation of the optical and mechanical aspects involved in the sensors’ performances is crucial for determining the design rules of such probes. In this study, we numerically analyzed the impact of curvature on the optical and acoustic properties of a plano-concave cavity using the Finite Element Method. Performance metrics, including sensitivity, bandwidth, and directivity, were compared to planar Fabry–Perot configurations. The results suggest that introducing curvature significantly enhances sensitivity by improving light confinement, especially for cavity thicknesses exceeding half the Rayleigh zone (∼45 μm), reaching an enhancement of 2.5 a L = 60 μm compared to planar designs. The curved structure maintains high spectral quality (FOM) despite 2% fabrication perturbations. A mechanical analysis confirms no disadvantages in acoustic response and bandwidth (∼40 MHz). These findings establish curved plano-concave structures as robust and reliable for high-sensitivity polymeric lab-on-fiber ultrasound detectors, offering improved performance and fabrication tolerance for MHz-scale bandwidth applications. Full article
(This article belongs to the Special Issue Feature Papers in Optical Sensors 2025)
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<p>Schematic representation of the model with sensitive element (orange) on the optical fiber tip (gray).</p>
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<p>Diagram of FEM models in Comsol Multphysics, illustrating the interaction between the acoustic–mechanical and optical models used. The acoustic–mechanical model, solved using Pressure Acoustics and Structural Mechanics physics in COMSOL coupled with the Acoustic-Solid Interaction interface, simulates the structural response to an incident acoustic wave. The acoustic–mechanical model’s output, representing the polymer’s deformation <math display="inline"><semantics> <mrow> <mo>(</mo> <mo>Δ</mo> <mi>L</mi> <mo>)</mo> </mrow> </semantics></math>, serves as the initial condition for the optical analysis, affecting the cavity thickness (<math display="inline"><semantics> <mrow> <msub> <mi>L</mi> <mi>Deformed</mi> </msub> <mo>=</mo> <mi>L</mi> <mo>−</mo> <mo>Δ</mo> <mi>L</mi> </mrow> </semantics></math>) and reflection spectrum. The optical model, using the Electromagnetic Wave, Beam Envelopes Physics module, computes the reflection spectra and optical sensitivity. The overall sensitivity of the sensor is determined by combining the acoustic and optical sensitivities.</p>
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<p>Reflectivity spectrum of curved surface FP (red solid line) and planar surface (black dashed line) for a 45 µm cavity length.</p>
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<p>(<b>a</b>–<b>c</b>) Optical parameters FOM, Q-factor, and Visibility of the Ideal Fabry Perot (yellow dash and dot line), Planar FP (black dash line), and Curved FP (red solid line).</p>
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<p>(<b>a</b>) Reflection Spectra evolution of Curved FP as a function of the cavity length variation around a nominal value of 20 µm. (<b>b</b>) <math display="inline"><semantics> <msub> <mi>S</mi> <mi>R</mi> </msub> </semantics></math> and (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>λ</mi> </mrow> </semantics></math> as a function of the cavity length of the Ideal Fabry Perot (yellow dashed point line), Planar Fabry Perot (black dashed line), and Curved FP (red solid line).</p>
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<p>(<b>a</b>) Reflection spectra of a curved FP as a function of radius of curvature perturbation. (<b>b</b>) Reflection spectra of a planar FP as a function of the variation in the inclination of the upper plane. (<b>c</b>) FOM as a function of the perturbation applied to the optimum condition of a planar FP (black dashed line) and a curved FP (red solid line).</p>
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<p>Longitudinal displacement field maps evaluated in the correspondence of a flat band in the case of (<b>a</b>) the planar FP and (<b>b</b>) the curved FP. Longitudinal displacement for three different acoustic wave frequencies: flat band (1 kHz) (blue solid line), peak frequency in the bandwidth (13 MHz) (orange solid line), and cut-off frequency (42 MHz) (yellow solid line) of the planar FP (<b>c</b>). Longitudinal displacement for three different acoustic wave frequencies: flat band (1 kHz) (blue solid line), peak frequency in the bandwidth (14 MHz) (orange solid line), and cut-off frequency (41 MHz) (yellow solid line) of the curved FP (<b>d</b>). (<b>e</b>) Schematic representation of average displacement <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi mathvariant="normal">L</mi> </mrow> </semantics></math> calculated in the region of interest irradiated with light (11.8 µm). (<b>f</b>) Longitudinal displacement of the area illuminated by the beam (5.8 µm) as a function of frequency for the planar FP (black dashed line) and curved FP (red solid line).</p>
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<p>Displacement and cut-off frequency as a function of the cavity length.</p>
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<p>(<b>a</b>) Longitudinal displacement as a function of the angle of incidence. (<b>b</b>) Longitudinal displacement along the planar (dashed line) and curved (solid line) FP in the flat band and peak frequency.</p>
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<p>Sensitivity as a function of the acoustic frequency of a curved surface and a planar surface for different cavity lengths, 20 μm (<b>a</b>), 45 μm (<b>b</b>), and 60 μm (<b>c</b>).</p>
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22 pages, 5963 KiB  
Article
A Light Field Depth Estimation Algorithm Considering Blur Features and Prior Knowledge of Planar Geometric Structures
by Shilong Zhang, Zhendong Liu, Xiaoli Liu, Dongyang Wang, Jie Yin, Jianlong Zhang, Chuan Du and Baocheng Yang
Appl. Sci. 2025, 15(3), 1447; https://doi.org/10.3390/app15031447 - 31 Jan 2025
Viewed by 429
Abstract
Light field camera depth estimation is a core technology for high-precision three-dimensional reconstruction and realistic scene reproduction. We propose a depth estimation algorithm that fuses blurry features and planar geometric structure priors, aimed at overcoming the limitations of traditional methods in neighborhood selection [...] Read more.
Light field camera depth estimation is a core technology for high-precision three-dimensional reconstruction and realistic scene reproduction. We propose a depth estimation algorithm that fuses blurry features and planar geometric structure priors, aimed at overcoming the limitations of traditional methods in neighborhood selection and mismatching in weak texture regions. First, by constructing a multi-constraint adaptive neighborhood microimage set, the microimages with the lowest blur degree are selected to calculate matching costs, and sparse feature correspondence relationships are used to propagate depth information. Second, planar prior knowledge is introduced to optimize pixel matching costs in weak texture regions, and weights are dynamically adjusted and pixel matching costs are updated during the iterative propagation process within microimages based on matching window completeness. Then, potential mismatched points are eliminated using epipolar geometric relationships. Finally, experiments were conducted using public and real-world datasets for verification and analysis. Compared with famous depth estimation algorithms, such as Zeller and BLADE, the Our method demonstrates superior performance in quantitative depth estimation metrics, scene reconstruction completeness, object edge clarity, and depth scene coverage, providing richer and more accurate depth information. Full article
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<p>Workflow of Our method.</p>
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<p>Epipolar constraint. (<b>a</b>) Epipolar Geometry and (<b>b</b>) polar correction.</p>
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<p>Neighborhood baseline ranges. The blue solid lines represent the baseline lengths, and the red dashed lines indicate the baseline search ranges.</p>
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<p>Relationship between the overlapping regions of different microimages and their disparity <span class="html-italic">d<sub>p</sub></span>. The two blue circles are two different microimages.</p>
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<p>Arrangement of microlenses in a multifocal light field camera, with three different colors representing three types of microlenses.</p>
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<p>Neighborhoods of images with different blur levels. Red circle represents the clearest microimage, green circle represents the least clear microimage, and yellow circle represents the fuzziest microimage.</p>
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<p>Overlapping regions between microimages. (<b>a</b>,<b>b</b>) Adjacent microimages with different levels of blur; (<b>c</b>) the overlapping region.</p>
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<p>Sparse reliable correspondences and triangulation results. (<b>a</b>) Sparse point cloud, the blue is the background and the green is the point cloud; (<b>b</b>) triangulation result, the solid red lines are triangulation nets.</p>
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<p>Matching window completeness. The black wire frame represents a micro image, the blue and red photo frames represent the matching window, and the blue photo frame belongs entirely to the black photo frame. The red dashed wireframe is not in the image; it is incomplete.</p>
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<p>Geometric position relationships of six microlenses in the inner ring. Three different colored circles represent three microimages with different levels of blur and the solid blue line represents the baseline and geometric position relationship of the six microlens images.</p>
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<p>Light field cameras. (<b>a</b>) Raytrix R12 camera; (<b>b</b>) Raytrix R32 camera; (<b>c</b>) HR260 camera.</p>
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<p>Depth estimation results for R32-Indoor. The first column shows the original light field images, the second column displays laser scanning point clouds, the third to fifth columns represent depth values generated by our algorithm, Zeller, and BLADE, respectively, with our and Zeller’s depth values shown in grayscale images, and BLADE’s depth values displayed as RGB images.</p>
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<p>Depth estimation results for R12-Indoor. The first column shows the original light field images, the second column displays laser scanning point clouds, the third to fifth columns represent depth values generated by Our, Zeller, and BLADE, respectively, with Our and Zeller’s depth values shown in grayscale images, and BLADE’s depth values displayed as RGB images.</p>
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<p>Depth estimation results for HR260-Outdoor. The first column shows the original light field images, the second column displays laser scanning point clouds, the third to fifth columns represent depth values generated by Our, Zeller, and BLADE, respectively, with Our and Zeller’s depth values shown in grayscale images, and BLADE’s depth values displayed as RGB images.</p>
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19 pages, 5153 KiB  
Article
Aluminum Reservoir Welding Surface Defect Detection Method Based on Three-Dimensional Vision
by Hanjie Huang, Bin Zhou, Songxiao Cao, Tao Song, Zhipeng Xu and Qing Jiang
Sensors 2025, 25(3), 664; https://doi.org/10.3390/s25030664 - 23 Jan 2025
Viewed by 486
Abstract
Welding is an important process in the production of aluminum reservoirs for motor vehicles. The welding quality affects product performance. However, rapid and accurate detection of weld surface defects remains a huge challenge in the field of industrial automation. To address this problem, [...] Read more.
Welding is an important process in the production of aluminum reservoirs for motor vehicles. The welding quality affects product performance. However, rapid and accurate detection of weld surface defects remains a huge challenge in the field of industrial automation. To address this problem, we proposed a 3D vision-based aluminum reservoir welding surface defect detection method. First of all, a scanning system based on laser line scanning camera was constructed to acquire the point cloud data of weld seams on the aluminum reservoir surface. Next, a planar correction algorithm was used to adjust the slope of the contour line according to the slope of the contour line in order to minimize the effect of systematic disturbances when acquiring weld data. Then, the surface features of the weld, including curvature and normal vector direction, were extracted to extract holes, craters, and undercut defects. For better extraction of the defect, a double-aligned template matching method was used to ensure comprehensive extraction and measurement of defect areas. Finally, the detected defects were categorized according to their morphology. Experimental results show that the proposed method using 3D laser scanning data can detect and classify typical welding defects with an accuracy of more than 97.1%. Furthermore, different types of defects, including holes, undercuts, and craters, can also be accurately detected with precision 98.9%. Full article
(This article belongs to the Collection 3D Imaging and Sensing System)
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<p>Reservoirs and welds with different types of defects. Defects are circled in red: (<b>a</b>) normal weld; (<b>b</b>) hole defects; (<b>c</b>) arc crater defects; (<b>d</b>) undercut defects.</p>
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<p>Weld inspection system.</p>
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<p>Flow of defect detection method.</p>
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<p>Planar correction process: (<b>a</b>) eccentric rotation of the reservoir; (<b>b</b>) pre-correction point cloud; (<b>c</b>) correction step; (<b>d</b>) post-correction point cloud.</p>
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<p>Defect depth map and curvature and normal vector scalar map: (<b>a</b>) elevation map of hole defects; (<b>b</b>) curvature map of hole defects; (<b>c</b>) elevation map of arc crater defects; (<b>d</b>) normal vector direction map of curvature defects.</p>
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<p>Weld nibbling region profile with the direction of the normal vector in the region: (<b>a</b>) point cloud depth map; (<b>b</b>) curvature and normal vector direction map; (<b>c</b>) curvature and normal vector direction extraction results; (<b>d</b>) point cloud clustering results.</p>
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<p>Principle of normal vector direction calculation.</p>
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<p>Contour lines of undercut defects with the direction of the normal vector of the region.</p>
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<p>Weld contour lines and their widths and heights for target and template point clouds.</p>
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<p>Differential thin plate detection process: (<b>a</b>) pre-alignment template with target point cloud; (<b>b</b>) post-alignment template with target point cloud; (<b>c</b>) post-alignment side view of defective region; (<b>d</b>) defective region extraction results.</p>
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<p>Correction effect of different methods on the point cloud: (<b>a</b>) pre-calibration point cloud; (<b>b</b>) calibration results using the RANSAC method; (<b>c</b>) calibration results using our method.</p>
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<p>Relative errors of defect extraction with different neighborhood radius and curvature thresholds.</p>
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<p>(<b>a</b>) Difference results between target and template point clouds; (<b>b</b>) extraction results with a height threshold of −0.7; (<b>c</b>) extraction results with a height threshold of −1; (<b>d</b>) extraction results with a height threshold of −1.5.</p>
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<p>Different types of defects and their extraction results: (<b>a</b>) depth map of hole and crater defects; (<b>b</b>) hole and crater defect extraction results; (<b>c</b>) depth map of undercut defects; (<b>d</b>) undercut defect extraction results; (<b>e</b>) depth map of crater defects; (<b>f</b>) crater defect extraction results.</p>
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20 pages, 7483 KiB  
Article
An Enhanced LiDAR-Based SLAM Framework: Improving NDT Odometry with Efficient Feature Extraction and Loop Closure Detection
by Yan Ren, Zhendong Shen, Wanquan Liu and Xinyu Chen
Processes 2025, 13(1), 272; https://doi.org/10.3390/pr13010272 - 19 Jan 2025
Viewed by 871
Abstract
Simultaneous localization and mapping (SLAM) is crucial for autonomous driving, drone navigation, and robot localization, relying on efficient point cloud registration and loop closure detection. Traditional Normal Distributions Transform (NDT) odometry frameworks provide robust solutions but struggle with real-time performance due to the [...] Read more.
Simultaneous localization and mapping (SLAM) is crucial for autonomous driving, drone navigation, and robot localization, relying on efficient point cloud registration and loop closure detection. Traditional Normal Distributions Transform (NDT) odometry frameworks provide robust solutions but struggle with real-time performance due to the high computational complexity of processing large-scale point clouds. This paper introduces an improved NDT-based LiDAR odometry framework to address these challenges. The proposed method enhances computational efficiency and registration accuracy by introducing a unified feature point cloud framework that integrates planar and edge features, enabling more accurate and efficient inter-frame matching. To further improve loop closure detection, a parallel hybrid approach combining Radius Search and Scan Context is developed, which significantly enhances robustness and accuracy. Additionally, feature-based point cloud registration is seamlessly integrated with full cloud mapping in global optimization, ensuring high-precision pose estimation and detailed environmental reconstruction. Experiments on both public datasets and real-world environments validate the effectiveness of the proposed framework. Compared with traditional NDT, our method achieves trajectory estimation accuracy increases of 35.59% and over 35%, respectively, with and without loop detection. The average registration time is reduced by 66.7%, memory usage is decreased by 23.16%, and CPU usage drops by 19.25%. These results surpass those of existing SLAM systems, such as LOAM. The proposed method demonstrates superior robustness, enabling reliable pose estimation and map construction in dynamic, complex settings. Full article
(This article belongs to the Section Manufacturing Processes and Systems)
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<p>The system structure.</p>
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<p>Combined feature point cloud. (<b>a</b>) is the raw point cloud acquired by LiDAR, and (<b>b</b>) is the feature point cloud. The feature point cloud is composed of planar points, edge points, and ground points; the outlier points and small-scale points in the environment are removed; and only large-scale point clouds are retained. Compared to the original point cloud, the feature point cloud significantly reduces the number of points while effectively preserving environmental features.</p>
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<p>(<b>a</b>) KITTI data acquisition platform, equipped with an inertial navigation system (GPS/IMU) OXTS RT 3003, a Velodyne HDL-64E LiDAR, two 1.4 MP grayscale cameras, two 1.4 MP color cameras, and four zoom lenses. (<b>b</b>) Sensor installation positions on the platform.</p>
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<p>Comparison of trajectories across different algorithm frameworks for Sequence 00-10. The trajectories generated during mapping for LOAM, LeGO-LOAM, DLO, the original NDT, and our method are compared.</p>
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<p>Loop closure detection results for various methods on Sequence 09. It can be seen that our improved method effectively identifies the loop closure. The parallel strategy using two loop closure detection methods greatly improves detection accuracy.</p>
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<p>(<b>a</b>–<b>c</b>) Inter-frame registration time, memory usage, and CPU usage before and after the improvement. Our improved method effectively reduces matching time and computational load.</p>
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<p>Mobile robot platform.</p>
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<p>Maps generated using the improved method. (<b>a</b>–<b>d</b>) The one-way corridor, round-trip corridor, loop corridor, and long, feature-sparse corridor, respectively.</p>
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<p>(<b>a</b>–<b>d</b>) Maps generated by the original method. Significant mapping errors occurred in larger environments, such as (<b>c</b>,<b>d</b>).</p>
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<p>(<b>a</b>–<b>d</b>) Maps generated by the original method. Significant mapping errors occurred in larger environments, such as (<b>c</b>,<b>d</b>).</p>
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<p>Detailed comparison between the improved and original methods. (<b>a</b>,<b>b</b>) The improved and original methods, respectively. The improved method balances detail preservation and computation speed, while the original sacrifices some environmental accuracy for mapping results.</p>
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<p>Map comparison. (<b>a</b>) The Google Earth image. (<b>b</b>) LeGO-LOAM failed to close the loop due to the lack of IMU data, leading to Z-axis drift. (<b>c</b>) The original NDT framework experienced significant drift in large-scale complex environments. (<b>d</b>) The improved method produced maps closely matching the real environment.</p>
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<p>Detail of Scenario 2. The improved method preserved environmental details without artifacts or mismatches.</p>
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<p>(<b>a</b>–<b>c</b>) Scenario 2 map comparison. (<b>b</b>) The map generated by the original NDT method lacked details. (<b>c</b>) The improved method effectively preserved details.</p>
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25 pages, 4089 KiB  
Article
Taguchi Method-Based Synthesis of a Circular Antenna Array for Enhanced IoT Applications
by Wided Amara, Ramzi Kheder, Ridha Ghayoula, Issam El Gmati, Amor Smida, Jaouhar Fattahi and Lassaad Latrach
Telecom 2025, 6(1), 7; https://doi.org/10.3390/telecom6010007 - 14 Jan 2025
Viewed by 625
Abstract
Linear antenna arrays exhibit radiation patterns that are restricted to a half-space and feature axial radiation, which can be a significant drawback for applications that require omnidirectional coverage. To address this limitation, the synthesis method utilizing the Taguchi approach, originally designed for linear [...] Read more.
Linear antenna arrays exhibit radiation patterns that are restricted to a half-space and feature axial radiation, which can be a significant drawback for applications that require omnidirectional coverage. To address this limitation, the synthesis method utilizing the Taguchi approach, originally designed for linear arrays, can be effectively extended to two-dimensional or planar antenna arrays. In the context of a linear array, the synthesis process primarily involves determining the feeding law and/or the spatial distribution of the elements along a single axis. Conversely, for a planar array, the synthesis becomes more complex, as it requires the identification of the complex weighting of the feed and/or the spatial distribution of sources across a two-dimensional plane. This adaptation to planar arrays is facilitated by substituting the direction θ with the pair of directions (θ,ϕ), allowing for a more comprehensive coverage of the angular domain. This article focuses on exploring various configurations of planar arrays, aiming to enhance their performance. The primary objective of these configurations is often to minimize the levels of secondary lobes and/or array lobes while enabling a full sweep of the angular space. Secondary lobes can significantly impede system performance, particularly in multibeam applications, where they restrict the minimum distance for frequency channel reuse. This restriction is critical, as it affects the overall efficiency and effectiveness of communication systems that rely on precise beamforming and frequency allocation. By investigating alternative planar array designs and their synthesis methods, this research seeks to provide solutions that improve coverage, reduce interference from secondary lobes, and ultimately enhance the functionality of antennas in diverse applications, including telecommunications, radar systems, and wireless communication. Full article
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<p>Electronic-scanning of the space with a secondary lobe level of −8 dB for a circular antenna array of 24 elements.</p>
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<p>Electronic-scanning of the space with a secondary lobe level of −28 dB for a circular antenna array of 16 elements.</p>
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<p>Geometry of the proposed antenna.</p>
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<p>Design and simulation of a circular antenna array with 10 elements.</p>
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<p>Reflection coefficient of the proposed antenna and 3D radiation pattern at 2.45 GHz.</p>
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<p>Polar radiation patterns for a circular antenna array with 10-elements at 2.45 GHz.</p>
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<p>Simulated results for 3D circular antenna array radiation pattern synthesis with 10-elements using PSO and GA algorithms at 2.45 GHz.</p>
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<p>Circular antenna array with 16-elements at 2.45 GHz. (<b>a</b>) Uniform excitation (16 antennas). (<b>b</b>) Taguchi excitation (16 antennas).</p>
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<p>Circular antenna array with 24-elements at 2.45 GHz. (<b>a</b>) Uniform excitation (24-antennas). (<b>b</b>) Taguchi excitation (24-antennas).</p>
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<p>Circular antenna array in concentric rings with isotropic elements.</p>
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<p>Simulation results of a concentric ring array (<math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>6</mn> </mrow> </semantics></math>).</p>
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<p>Simulation results of a concentric ring array (<math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>6</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>).</p>
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<p>Simulation results of a concentric ring array (<math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>6</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>).</p>
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<p>Simulation results of a concentric ring array (<math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>12</mn> </mrow> </semantics></math>).</p>
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<p>Simulation results of a concentric ring array (<math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>6</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>4</mn> </msub> <mo>=</mo> <mn>12</mn> </mrow> </semantics></math>).</p>
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<p>Reduction of the side-lobe level for concentric ring arrays.</p>
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<p>Optimal excitation values found using the Taguchi method.</p>
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<p>Synthesis of 3D radiation patterns for an 18-element array (<math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>6</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>) at 2.45 GHz. (<b>a</b>) Structure of the concentric ring array (<math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>6</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>). (<b>b</b>) Uniform excitations. (<b>c</b>) Excitations with Evolutionary Programming (EP). (<b>d</b>) Excitations with Firefly Algorithm (FA). (<b>e</b>) Excitations with Taguchi method.</p>
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<p>Synthesis of 3D radiation patterns for a 24-element array (<math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>6</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>) at 2.45 GHz. (<b>a</b>) Structure of the concentric ring array (<math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>6</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>). (<b>b</b>) Uniform excitations. (<b>c</b>) Excitations with Taguchi method.</p>
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<p>Synthesis of 3D radiation patterns for a 30-element array (<math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>12</mn> </mrow> </semantics></math>) at 2.45 GHz. (<math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>12</mn> </mrow> </semantics></math>), (<b>a</b>) Structure of the concentric ring array and (<b>b</b>) Uniform excitations. (<b>c</b>) Excitations with Evolutionary Programming (EP). (<b>d</b>) Excitations with the Firefly Algorithm (FA). (<b>e</b>) Excitations with Taguchi.</p>
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<p>Synthesis of 3D radiation patterns for a 36-element array (<math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>6</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>4</mn> </msub> <mo>=</mo> <mn>12</mn> </mrow> </semantics></math>) at <math display="inline"><semantics> <mrow> <mn>2.45</mn> </mrow> </semantics></math> GHz. (<b>a</b>) Structure of the concentric ring array (<math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>6</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>4</mn> </msub> <mo>=</mo> <mn>12</mn> </mrow> </semantics></math>). (<b>b</b>) Uniform excitations. (<b>c</b>) Excitations with Taguchi optimization.</p>
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8 pages, 7391 KiB  
Proceeding Paper
Comparative Analysis of LiDAR Inertial Odometry Algorithms in Blueberry Crops
by Ricardo Huaman, Clayder Gonzalez and Sixto Prado
Eng. Proc. 2025, 83(1), 9; https://doi.org/10.3390/engproc2025083009 - 9 Jan 2025
Viewed by 405
Abstract
In recent years, LiDAR Odometry (LO) and LiDAR Inertial Odometry (LIO) algorithms for robot localization have considerably improved, with significant advancements demonstrated in various benchmarks. However, their performance in agricultural environments remains underexplored. This study addresses this gap by evaluating five state-of-the-art LO [...] Read more.
In recent years, LiDAR Odometry (LO) and LiDAR Inertial Odometry (LIO) algorithms for robot localization have considerably improved, with significant advancements demonstrated in various benchmarks. However, their performance in agricultural environments remains underexplored. This study addresses this gap by evaluating five state-of-the-art LO and LIO algorithms—LeGO-LOAM, DLO, DLIO, FAST-LIO2, and Point-LIO—in a blueberry farm setting. Using an Ouster OS1-32 LiDAR mounted on a four-wheeled mobile robot, the algorithms were evaluated using the translational error metric across four distinct sequences. DLIO showed the highest accuracy across all sequences, with a minimal error of 0.126 m over a 230 m path, while FAST-LIO2 achieved its lowest translational error of 0.606 m on a U-shaped path. LeGO-LOAM, however, struggled due to the environment’s lack of linear and planar features. The results underscore the effectiveness and potential limitations of these algorithms in agricultural environments, offering insights into future improvements and adaptations. Full article
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<p>Designated paths for each sequence followed by the robot at the blueberry farm, where each letter represents a waypoint along the trajectories.</p>
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<p>Wheeled mobile robot at the blueberry farm. (<b>a</b>) The robot in its initial position within an inter-row space. (<b>b</b>) The robot transitioning between blocks of crops and the separation between these marked with a yellow measuring tape.</p>
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<p>Estimated trajectories by each algorithm during sequences AB and AC.</p>
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<p>Estimated trajectories by each algorithm during sequences AD and AF.</p>
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<p>Close-up views of the 3D maps generated using DLIO, with each label designating the corresponding sequence from the Blueberry Crop Dataset. The path taken to create these maps is shown in yellow. The point cloud color indicates the intensity of the point return.</p>
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18 pages, 349 KiB  
Article
DP-4-Colorability on Planar Graphs Excluding 7-Cycles Adjacent to 4- or 5-Cycles
by Fan Yang, Xiangwen Li and Ziwen Huang
Mathematics 2025, 13(2), 190; https://doi.org/10.3390/math13020190 - 8 Jan 2025
Viewed by 564
Abstract
In order to resolve Borodin’s Conjecture, DP-coloring was introduced in 2017 to extend the concept of list coloring. In previous works, it is proved that every planar graph without 7-cycles and butterflies is DP-4-colorable. And any planar graph that does not have 5-cycle [...] Read more.
In order to resolve Borodin’s Conjecture, DP-coloring was introduced in 2017 to extend the concept of list coloring. In previous works, it is proved that every planar graph without 7-cycles and butterflies is DP-4-colorable. And any planar graph that does not have 5-cycle adjacent to 6-cycle is DP-4-colorable. The existing research mainly focus on the forbidden adjacent cycles that guarantee the DP-4-colorability for planar graph. In this paper, we demonstrate that any planar graph G that excludes 7-cycles adjacent to k-cycles (for each k=4,5), and does not feature a Near-bow-tie as an induced subgraph, is DP-4-colorable. This result extends the findings of the previous works mentioned above. Full article
(This article belongs to the Section E: Applied Mathematics)
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<p><math display="inline"><semantics> <msub> <mi>H</mi> <mn>1</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>H</mi> <mn>2</mn> </msub> </semantics></math> are two distinct covers of <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>C</mi> <mn>4</mn> </msub> <mo>,</mo> <mi>L</mi> <mo>)</mo> </mrow> </semantics></math> with <math display="inline"><semantics> <mrow> <mo>|</mo> <mi>L</mi> <mo>(</mo> <msub> <mi>v</mi> <mi>i</mi> </msub> <mo>)</mo> <mo>|</mo> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> for each <math display="inline"><semantics> <mrow> <mi>i</mi> <mo>∈</mo> <mo>[</mo> <mn>4</mn> <mo>]</mo> </mrow> </semantics></math>. (<b>a</b>) 4-cycle <math display="inline"><semantics> <msub> <mi>C</mi> <mn>4</mn> </msub> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <msub> <mi>H</mi> <mn>1</mn> </msub> </semantics></math>. (<b>c</b>) <math display="inline"><semantics> <msub> <mi>H</mi> <mn>2</mn> </msub> </semantics></math>.</p>
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<p>Near-bow-tie and butterfly. (<b>a</b>) Near-bow-tie, where <span class="html-italic">v</span> is a 7-vertex. (<b>b</b>) butterfly.</p>
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<p>All non-isomorphic <span class="html-italic">k</span>-clusters for each <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>∈</mo> <mo>{</mo> <mn>4</mn> <mo>,</mo> <mn>5</mn> <mo>,</mo> <mn>6</mn> <mo>,</mo> <mn>7</mn> <mo>}</mo> </mrow> </semantics></math>.</p>
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<p>Different cover <math display="inline"><semantics> <msub> <mi mathvariant="script">M</mi> <mrow> <mo>(</mo> <msub> <mi>K</mi> <mn>3</mn> </msub> <mo>,</mo> <mi>L</mi> <mo>)</mo> </mrow> </msub> </semantics></math> of <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>K</mi> <mn>3</mn> </msub> <mo>,</mo> <mi>L</mi> <mo>)</mo> </mrow> </semantics></math>, where <math display="inline"><semantics> <msub> <mi>L</mi> <msub> <mi>v</mi> <mi>i</mi> </msub> </msub> </semantics></math> is a clique for each <math display="inline"><semantics> <mrow> <mi>i</mi> <mo>∈</mo> <mo>[</mo> <mn>3</mn> <mo>]</mo> </mrow> </semantics></math>. (<b>a</b>) <math display="inline"><semantics> <msub> <mi>E</mi> <mi>M</mi> </msub> </semantics></math> is a union of two 3-cycles. (<b>b</b>) <math display="inline"><semantics> <msub> <mi>E</mi> <mi>M</mi> </msub> </semantics></math> is not a union of two 3-cycles.</p>
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<p>Special or poor vertex: all <math display="inline"><semantics> <msub> <mi>K</mi> <mn>1</mn> </msub> </semantics></math> is special and internal and <math display="inline"><semantics> <msub> <mi>K</mi> <mn>2</mn> </msub> </semantics></math> is special. (<b>a</b>) Special 6-vertex <span class="html-italic">v</span>. (<b>b</b>) Poor 6-vertex <span class="html-italic">v</span>. (<b>c</b>) Poor 7-vertex <span class="html-italic">v</span> when <math display="inline"><semantics> <mrow> <mi>u</mi> <mo>,</mo> <mi>w</mi> <mo>∈</mo> <msub> <mi mathvariant="script">A</mi> <mn>1</mn> </msub> </mrow> </semantics></math>. (<b>d</b>) Special 7-vertex <span class="html-italic">v</span> when <math display="inline"><semantics> <mrow> <msup> <mi>u</mi> <mo>′</mo> </msup> <mo>∈</mo> <msub> <mi mathvariant="script">A</mi> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msup> <mi>w</mi> <mo>′</mo> </msup> <mo>∈</mo> <msub> <mi mathvariant="script">A</mi> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
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35 pages, 33466 KiB  
Article
Exploring the Influence of Microtopography on the Spatial Genes of Urban Historical Streets and Alleys in Xuzhou
by Yan Lin, Shuhan Zhang and Yi Jian
Sustainability 2025, 17(2), 427; https://doi.org/10.3390/su17020427 - 8 Jan 2025
Viewed by 627
Abstract
Spatial genes represent the fundamental interplay among the morphological characteristics of historical districts. Identifying and analyzing these morphological elements can enhance our understanding of urban spatial development, uncover spatial meanings, and provide informed recommendations for future development. This study focuses on the Xuzhou [...] Read more.
Spatial genes represent the fundamental interplay among the morphological characteristics of historical districts. Identifying and analyzing these morphological elements can enhance our understanding of urban spatial development, uncover spatial meanings, and provide informed recommendations for future development. This study focuses on the Xuzhou Huilongwo historical district, employing geographic information system, Global Mapper, and other digital technologies to determine the area’s microtopographic features. Qualitative methodologies extract the spatial genes of street segments, entry spaces, and node spaces. By summarizing the microtopography’s influence on street and alley characteristics, valuable spatial samples were selected and visually represented for analysis. This included examining the street segment interface, entry space sequences, and the planar morphology of node spaces. The findings reveal that Huilongwo architecture aligns with topographical features, exhibiting a multi-directional distribution. Height differences help establish street boundaries and enhance pathways’ experiential quality. Additionally, topography significantly influences street spaces, leading to undulating sequences in entry spaces. This study provides insights into the preservation and enhancement of streets and alleys within Xuzhou’s historical district. Full article
(This article belongs to the Special Issue Architecture, Urban Space and Heritage in the Digital Age)
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<p>Theoretical framework.</p>
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<p>The study area (the city of Xuzhou).</p>
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<p>Historical maps of Xuzhou and photos of Huilongwo.</p>
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<p>Functional distribution of Huilongwo district.</p>
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<p>Research framework.</p>
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<p>Elevation analysis of Huilongwo district.</p>
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<p>Huilongwo district gradient and slope analysis.</p>
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<p>Analysis perspective generation framework.</p>
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<p>Alley elevation distribution and marking.</p>
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<p>Lane 1: planar views and photo.</p>
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<p>Lane 5: planar views and photo.</p>
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<p>Lanes 8 and 9: planar views and photos.</p>
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<p>Elevated positions and flow lines for elevation as a site boundary.</p>
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<p>Lanes 7, 13, and 14.</p>
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<p>Lane 2: planar views and photos.</p>
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<p>Lane 4: planar views and photos.</p>
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<p>Lane 10: planar views and photos.</p>
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<p>Lane 11: planar views and photos.</p>
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<p>Elevated positions and flow lines for elevation as an enriching experience.</p>
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<p>Lane 3: planar views, elevated positions, flow lines, and photos.</p>
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<p>Relationship between façade profile and ground elevation.</p>
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<p>Lane 5 and 6 façades.</p>
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<p>Boundary extraction of a street segment.</p>
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<p>Lanes 6 and 7: planar views, elevated positions, flow lines, and photos.</p>
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<p>Entry space distribution.</p>
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<p>Courtyard spatial distribution.</p>
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<p>The Hotel of Flowers’ multi-perspective analysis.</p>
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<p>Pengcheng Gift Store’s multi-perspective analysis.</p>
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<p>Waku Teahouse’s multi-perspective analysis.</p>
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<p>The corridor’s spatial distribution.</p>
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<p>Hanfeng Cultural and Creative Store’s multi-perspective analysis.</p>
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<p>Banyunting Restaurant’s and Flower Stream Bookstore’s multi-perspective analyses.</p>
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<p>The platform’s spatial distribution.</p>
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<p>Platform entry space multi-perspective analysis.</p>
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<p>Distribution of node spaces.</p>
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<p>Node 1 multi-perspective analysis.</p>
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<p>Node 2 multi-perspective analysis.</p>
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<p>Nodes 3 and 5 multi-perspective analyses.</p>
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<p>Nodes 4 and 6 multi-perspective analyses.</p>
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<p>Node 7 multi-perspective analysis.</p>
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<p>Street segment spatial genes summary.</p>
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<p>Entry space genes summary.</p>
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<p>Node space genes summary.</p>
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<p>Spatial genetic system of streets and alleys.</p>
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20 pages, 9558 KiB  
Article
Enhancing Thermal Performance Investigations of a Methane-Fueled Planar Micro-Combustor with a Counter-Flow Flame Configuration
by Liaoliao Li, Yuze Sun, Xinyu Huang, Lixian Guo and Xinyu Zhao
Energies 2025, 18(1), 195; https://doi.org/10.3390/en18010195 - 5 Jan 2025
Viewed by 491
Abstract
To enhance the performance of combustors in micro thermophotovoltaic systems, this study employs numerical simulations to investigate a planar microscale combustor featuring a counter-flow flame configuration. The analysis begins with an evaluation of the effects of (1) equivalence ratio Φ and (2) inlet [...] Read more.
To enhance the performance of combustors in micro thermophotovoltaic systems, this study employs numerical simulations to investigate a planar microscale combustor featuring a counter-flow flame configuration. The analysis begins with an evaluation of the effects of (1) equivalence ratio Φ and (2) inlet flow rate Vi on key thermal and combustion parameters, including the average temperature of the combustor main wall (T¯w), wall temperature non-uniformity (R¯Tw) and radiation efficiency (ηr). The findings indicate that increasing Φ causes these parameters to initially increase and subsequently decrease. Similarly, increasing the inlet flow rate leads to a monotonic decline in ηr, while the T¯w and R¯Tw exhibit a rise-then-fall trend. A comparative study between the proposed combustor and a conventional planar combustor reveals that, under identical inlet flow rate and equivalence ratio conditions, the use of the counterflow flame configuration can increase the T¯w while reducing the R¯Tw. The Nusselt number analysis shows that the counter-flow flame configuration micro-combustor achieves a larger area with positive Nusselt numbers and higher average Nusselt numbers, which highlights improved heat transfer from the fluid to the solid. Furthermore, the comparison of blow-off limits shows that the combustor with counter-flow flame configuration exhibits superior flame stability and a broader flammability range. Overall, this study provides a preliminary investigation into the use of counter-flow flame configurations in microscale combustors. Full article
(This article belongs to the Special Issue Challenges and Research Trends of Exhaust Emissions)
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Figure 1

Figure 1
<p>(<b>a</b>) Schematic of conventional micro-planar combustor; (<b>b</b>) Schematic of counter-flow flame micro-planar combustor; (<b>c</b>) x–y cross-sectional schematic of the present combustion; (<b>d</b>) Mesh model of the counter-flow flame micro-planar combustor.</p>
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<p>Mesh independence study.</p>
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<p>Model validation results: comparison of centerline temperature profiles.</p>
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<p>Variation of <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>T</mi> </mrow> <mo>¯</mo> </mover> </mrow> <mrow> <mi>w</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>R</mi> </mrow> <mo>¯</mo> </mover> </mrow> <mrow> <mi>T</mi> <mi>w</mi> </mrow> </msub> </mrow> </semantics></math> with <span class="html-italic">Φ</span>, where <span class="html-italic">V</span><sub><span class="html-italic">i</span></sub> = 28.8 mL/s.</p>
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<p>Fluid field temperature distributions at z = 0 plane in combustors under various <span class="html-italic">Φ</span>, where <span class="html-italic">V<sub>i</sub></span> = 28.8 mL/s.</p>
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<p>Main wall temperature distributions under various <span class="html-italic">Φ</span>, where <span class="html-italic">V<sub>i</sub></span> = 28.8 mL/s.</p>
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<p>Variation of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>η</mi> </mrow> <mrow> <mi>r</mi> </mrow> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>η</mi> </mrow> <mrow> <mi>c</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>η</mi> </mrow> <mrow> <mi>o</mi> </mrow> </msub> </mrow> </semantics></math> with <span class="html-italic">Φ</span>, where <span class="html-italic">V<sub>i</sub></span> = 28.8 mL/s.</p>
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<p>Variation of <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>T</mi> </mrow> <mo>¯</mo> </mover> </mrow> <mrow> <mi>w</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>R</mi> </mrow> <mo>¯</mo> </mover> </mrow> <mrow> <mi>T</mi> <mi>w</mi> </mrow> </msub> </mrow> </semantics></math> with <span class="html-italic">V<sub>i</sub></span>, where <span class="html-italic">Φ</span> = 1.0.</p>
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<p>Fluid field temperature distributions at <span class="html-italic">z</span> = 0 plane in combustors under various <span class="html-italic">V<sub>i</sub></span>, where <span class="html-italic">Φ</span> = 1.0.</p>
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<p>Main wall temperature distributions under various <span class="html-italic">V<sub>i</sub></span>, where <span class="html-italic">Φ</span> = 1.0.</p>
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<p>Variation of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>Q</mi> </mrow> <mrow> <mi>r</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>η</mi> </mrow> <mrow> <mi>r</mi> </mrow> </msub> </mrow> </semantics></math> with <span class="html-italic">V<sub>i</sub></span>, where <span class="html-italic">Φ</span> = 1.0.</p>
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<p>Variation <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>T</mi> </mrow> <mo>¯</mo> </mover> </mrow> <mrow> <mi>w</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>R</mi> </mrow> <mo>¯</mo> </mover> </mrow> <mrow> <mi>T</mi> <mi>w</mi> </mrow> </msub> </mrow> </semantics></math> between conventional and present combustors under various <span class="html-italic">Φ</span>, where <span class="html-italic">V<sub>i</sub></span> = 14.4 mL/s.</p>
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<p>Variation <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>η</mi> </mrow> <mrow> <mi>r</mi> </mrow> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>η</mi> </mrow> <mrow> <mi>c</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>η</mi> </mrow> <mrow> <mi>o</mi> </mrow> </msub> </mrow> </semantics></math> between conventional and present combustors under various <span class="html-italic">Φ</span>, where <span class="html-italic">V<sub>i</sub></span> = 14.4 mL/s.</p>
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<p>Fluid field temperature distributions at z = 0 plane in combustors under various <span class="html-italic">Φ</span> of (<b>a</b>) Conventional combustor; and (<b>b</b>) counter-flow flame combustor, where <span class="html-italic">V<sub>i</sub></span> = 14.4 mL/s.</p>
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<p>Main wall Temperature distributions under various <span class="html-italic">Φ</span> of (<b>a</b>) Conventional combustor; and (<b>b</b>) counter-flow flame combustor, where <span class="html-italic">V<sub>i</sub></span> = 14.4 mL/s.</p>
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<p>(<b>a</b>) Local Nusselt number distribution in two different combustors (<b>left</b>: Conventional combustor, <b>right</b>: Counter-flow flame combustor); (<b>b</b>) Comparison of average Nusselt number under various <span class="html-italic">Φ</span> between two different combustors.</p>
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<p>Comparison of flammability behaviors between two different combustors: (<b>a</b>) Conventional combustor; and (<b>b</b>) counter-flow flame combustor.</p>
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17 pages, 26057 KiB  
Article
Staggered Design of UV–Curable Polymer Microneedle Arrays with Increased Vertical Action Space
by Baoling Jia, Tiandong Xia, Yangtao Xu and Bei Li
Polymers 2025, 17(1), 104; https://doi.org/10.3390/polym17010104 - 2 Jan 2025
Viewed by 599
Abstract
Recent studies have identified microneedle (MN) arrays as promising alternatives for transdermal drug delivery. This study investigated the properties of novel staggered MN arrays design featuring two distinct heights of MNs. The staggered MN arrays were precisely fabricated via PμSL light-cured 3D printing [...] Read more.
Recent studies have identified microneedle (MN) arrays as promising alternatives for transdermal drug delivery. This study investigated the properties of novel staggered MN arrays design featuring two distinct heights of MNs. The staggered MN arrays were precisely fabricated via PμSL light-cured 3D printing technology. The arrays were systematically evaluated for their morphology, fracture force, skin penetration ability, penetration mechanism, and drug delivery capability. The results demonstrated that the staggered MN arrays punctured the skin incrementally, leveraging the benefits of skin deformation during the puncture process. This approach effectively reduced the puncture force needed, achieving a maximum reduction of approximately 80.27% due to variations in the staggered height. Additionally, the staggered design facilitated skin penetration, as confirmed by the results of the rat skin hematoxylin-eosin (H&E) staining experiments. Compared with 3D-printed planar structures and highly uniform MN arrays, the staggered design exhibited enhanced hydrophilicity, as evidenced by a reduction in the contact angle from approximately 93° to 70°. Simulated drug release images of both coated and hollow staggered MNs illustrated the release and delivery capabilities of these structures across various skin layers, and the staggered design expanded the effective area of the MN arrays within the vertical dimension of the skin layers. This study offers both experimental and theoretical foundations for developing MN arrays with three–dimensional structural distributions, thereby facilitating advancements in MN array technology. Full article
(This article belongs to the Special Issue Advanced Processing Strategy for Functional Polymer Materials)
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Figure 1
<p>Arrangement of the MNs in array patches: (<b>a</b>) #1 MN arrays with a height of 0.8 mm; (<b>b</b>) #2 MN arrays with heights of 0.8 mm and 0.96 mm; (<b>c</b>) #3 MN arrays with heights of 0.8 mm and 1.04 mm; and (<b>d</b>) #4 MN arrays with heights of 0.8 mm and 1.12 mm.</p>
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<p>Photographs of MN patches puncture rats: (<b>a</b>) #1 MN arrays; (<b>b</b>) #2 MN arrays; (<b>c</b>) #3 MN arrays; (<b>d</b>) # 4MN arrays.</p>
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<p>Schematic of the mechanical properties of the MN patches: (<b>a</b>) the fracture force, and (<b>b</b>) penetration force test on porcine skin.</p>
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<p>Morphology of the MN arrays: (<b>a</b>) digital microscope images and (<b>b</b>) SEM micrographs.</p>
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<p>Mechanical compression tests of MN arrays: (<b>a</b>) fracture force of MN arrays and (<b>b</b>) fracture force of individual MNs.</p>
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<p>Force diagram of MN arrays puncturing porcine skin: (<b>a</b>) penetration force curves of MN arrays; (<b>b</b>) penetration force of MN arrays; and (<b>c</b>) displacement curves of MN arrays.</p>
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<p>H&amp;E staining of the rat skin penetrated by MNs: (<b>a</b>) #1 MN arrays; (<b>b</b>) #2 MN arrays; (<b>c</b>) #3 MN arrays; and (<b>d</b>) #4 MN arrays. Graphical representation: The black dotted line indicates the puncture outline, and the red dotted line indicates the puncture depth.</p>
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<p>Puncture processes of staggered MN arrays: (<b>a</b>) physical pictures and (<b>b</b>) schematic diagrams.</p>
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<p>The hydrophilicity for MN arrays: (<b>a</b>) backing layer; (<b>b</b>) #1 MN arrays; (<b>c</b>) #2 MN arrays; (<b>d</b>) #3 MN arrays; (<b>e</b>) #4 MN arrays; and (<b>f</b>) contact angle of MN arrays.</p>
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<p>Drug release behavior of the coated MN arrays: (<b>a</b>) photographs of the rhodamine-B-coated MNs; (<b>b</b>) photographs of the released rhodamine B from the MN patches into the agarose gel; and (<b>c</b>) the color of the agarose gel containing released rhodamine B over time.</p>
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<p>Drug release behavior of the hollow MN arrays: (<b>a</b>) morphology of the hollow MN arrays; (<b>b</b>) physical picture of the hollow MN puncture into the agarose gel; and (<b>c</b>) the color of the agarose gel over time.</p>
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18 pages, 5088 KiB  
Article
Dynamical Visualization and Qualitative Analysis of the (4+1)-Dimensional KdV-CBS Equation Using Lie Symmetry Analysis
by Maria Luz Gandarias, Nauman Raza, Muhammad Umair and Yahya Almalki
Mathematics 2025, 13(1), 89; https://doi.org/10.3390/math13010089 - 29 Dec 2024
Viewed by 614
Abstract
This study investigates novel optical solitons within the intriguing (4+1)-dimensional Korteweg–de Vries–Calogero–Bogoyavlenskii–Schiff (KdV-CBS) equation, which integrates features from both the Korteweg–de Vries and the Calogero–Bogoyavlenskii–Schiff equations. Firstly, all possible symmetry generators are found by applying Lie symmetry analysis. By using these generators, the [...] Read more.
This study investigates novel optical solitons within the intriguing (4+1)-dimensional Korteweg–de Vries–Calogero–Bogoyavlenskii–Schiff (KdV-CBS) equation, which integrates features from both the Korteweg–de Vries and the Calogero–Bogoyavlenskii–Schiff equations. Firstly, all possible symmetry generators are found by applying Lie symmetry analysis. By using these generators, the given model is converted into an ordinary differential equation. An adaptive approach, the generalized exp(-S(χ)) expansion technique has been utilized to uncover closed-form solitary wave solutions. The findings reveal a range of soliton types, including exponential, rational, hyperbolic, and trigonometric functions, represented as bright, singular, rational, periodic, and new solitary waves. These results are illustrated numerically and accompanied by insightful physical interpretations, enriching the comprehension of the complex dynamics modeled by these equations. Our approach’s novelty lies in applying a new methodology to this problem, yielding a variety of novel optical soliton solutions. Additionally, we employ bifurcation and chaos techniques for a qualitative analysis of the model, extracting a planar system from the original equation and mapping all possible phase portraits. A thorough sensitivity analysis of the governing equation is also presented. These results highlight the effectiveness of our methodology in tackling nonlinear problems in both mathematics and engineering, surpassing previous research efforts. Full article
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Figure 1
<p>Figure (<b>a</b>) shows the 3D visualization, (<b>b</b>) the contour plot, and (<b>c</b>) the 2D view of <math display="inline"><semantics> <mrow> <mo>[</mo> <msub> <mi mathvariant="script">E</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>]</mo> </mrow> </semantics></math>.</p>
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<p>Figure (<b>a</b>) shows the 3D visualization, (<b>b</b>) the contour plot, and (<b>c</b>) the 2D view of <math display="inline"><semantics> <mrow> <mo>[</mo> <msub> <mi mathvariant="script">E</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>]</mo> </mrow> </semantics></math>.</p>
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<p>Figure (<b>a</b>) shows the 3D visualization, (<b>b</b>) the contour plot, and (<b>c</b>) the 2D view of <math display="inline"><semantics> <mrow> <mo>[</mo> <msub> <mi mathvariant="script">E</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>]</mo> </mrow> </semantics></math>.</p>
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<p>Figure (<b>a</b>) shows the 3D visualization, (<b>b</b>) the contour plot, and (<b>c</b>) the 2D view of <math display="inline"><semantics> <mrow> <mo>[</mo> <msub> <mi mathvariant="script">E</mi> <mn>6</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>]</mo> </mrow> </semantics></math>.</p>
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<p>Figure (<b>a</b>) shows the 3D visualization, (<b>b</b>) the contour plot, and (<b>c</b>) the 2D view of <math display="inline"><semantics> <mrow> <mo>[</mo> <msub> <mi mathvariant="script">E</mi> <mn>10</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>]</mo> </mrow> </semantics></math>.</p>
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<p>Bifurcation analysis for <math display="inline"><semantics> <mrow> <msup> <mi>A</mi> <mn>2</mn> </msup> <mo>+</mo> <mn>6</mn> <mi>B</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math> with <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>A</mi> <mo>=</mo> <mn>2.5</mn> </mrow> </semantics></math>.</p>
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<p>Bifurcation analysis for <math display="inline"><semantics> <mrow> <msup> <mi>A</mi> <mn>2</mn> </msup> <mo>+</mo> <mn>6</mn> <mi>B</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> with <math display="inline"><semantics> <mrow> <mi>A</mi> <mo>=</mo> <msqrt> <mn>6</mn> </msqrt> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mo>−</mo> <mn>1</mn> </mrow> </semantics></math>.</p>
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<p>Chaotic behavior is detected using time series when <math display="inline"><semantics> <mrow> <mi>A</mi> <mo>=</mo> <mo>−</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>ς</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>2.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>χ</mi> <mo>=</mo> <mn>4.5</mn> </mrow> </semantics></math>, and satisfies <math display="inline"><semantics> <mrow> <mi>I</mi> <mo>.</mo> <mi>C</mi> <mo>=</mo> <mo>[</mo> <mn>0.5</mn> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mn>0.5</mn> <mo>]</mo> </mrow> </semantics></math>.</p>
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<p>Chaotic behavior is detected using phase portrait when <math display="inline"><semantics> <mrow> <mi>A</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>1.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>ς</mi> <mn>0</mn> </msub> <mo>=</mo> <mrow> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>]</mo> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>χ</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>, and satisfies <math display="inline"><semantics> <mrow> <mi>I</mi> <mo>.</mo> <mi>C</mi> <mo>=</mo> <mo>[</mo> <mn>0.5</mn> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mn>0.5</mn> <mo>]</mo> </mrow> </semantics></math>.</p>
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<p>Chaotic behavior is detected using the Poincaré map when <math display="inline"><semantics> <mrow> <mi>A</mi> <mo>=</mo> <mn>3.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mo>−</mo> <mn>0.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>ς</mi> <mn>0</mn> </msub> <mo>=</mo> <mrow> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>]</mo> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>χ</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>, and satisfies <math display="inline"><semantics> <mrow> <mi>I</mi> <mo>.</mo> <mi>C</mi> <mo>=</mo> <mo>[</mo> <mn>0.7</mn> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mn>0.7</mn> <mo>]</mo> </mrow> </semantics></math>.</p>
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<p>Chaotic behavior is detected using the bifurcation diagram when <math display="inline"><semantics> <mrow> <mi>A</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>7.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>ς</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>1.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>χ</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>, and satisfies <math display="inline"><semantics> <mrow> <mi>I</mi> <mo>.</mo> <mi>C</mi> <mo>=</mo> <mo>[</mo> <mn>0.5</mn> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mn>0.5</mn> <mo>]</mo> </mrow> </semantics></math>.</p>
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<p>Chaotic behavior is detected using the Lyapunov exponent when <math display="inline"><semantics> <mrow> <mi>A</mi> <mo>=</mo> <mn>0.09</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>1.2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>ς</mi> <mn>0</mn> </msub> <mo>=</mo> <mo>−</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>χ</mi> <mo>=</mo> <mn>11</mn> </mrow> </semantics></math>, and satisfies <math display="inline"><semantics> <mrow> <mi>I</mi> <mo>.</mo> <mi>C</mi> <mo>=</mo> <mo>[</mo> <mo>−</mo> <mn>0.4</mn> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mo>−</mo> <mn>0.4</mn> <mo>]</mo> </mrow> </semantics></math>.</p>
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<p>Sensitivity plots for (<a href="#FD31-mathematics-13-00089" class="html-disp-formula">31</a>) with two initial conditions: <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="script">F</mi> <mo>,</mo> <mo>∧</mo> <mo>)</mo> <mo>=</mo> <mo>(</mo> <mn>0.1</mn> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="script">F</mi> <mo>,</mo> <mo>∧</mo> <mo>)</mo> <mo>=</mo> <mo>(</mo> <mn>0.2</mn> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> </semantics></math>.</p>
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<p>Sensitivity plots for (<a href="#FD31-mathematics-13-00089" class="html-disp-formula">31</a>) with two initial conditions: <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="script">F</mi> <mo>,</mo> <mo>∧</mo> <mo>)</mo> <mo>=</mo> <mo>(</mo> <mn>0.1</mn> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="script">F</mi> <mo>,</mo> <mo>∧</mo> <mo>)</mo> <mo>=</mo> <mo>(</mo> <mn>0.3</mn> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> </semantics></math>.</p>
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<p>Sensitivity plots for (<a href="#FD31-mathematics-13-00089" class="html-disp-formula">31</a>) with two initial conditions: <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="script">F</mi> <mo>,</mo> <mo>∧</mo> <mo>)</mo> <mo>=</mo> <mo>(</mo> <mn>0.2</mn> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="script">F</mi> <mo>,</mo> <mo>∧</mo> <mo>)</mo> <mo>=</mo> <mo>(</mo> <mn>0.3</mn> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> </semantics></math>.</p>
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<p>Sensitivity plots for (<a href="#FD31-mathematics-13-00089" class="html-disp-formula">31</a>) with two initial conditions: <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="script">F</mi> <mo>,</mo> <mo>∧</mo> <mo>)</mo> <mo>=</mo> <mo>(</mo> <mn>0.1</mn> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="script">F</mi> <mo>,</mo> <mo>∧</mo> <mo>)</mo> <mo>=</mo> <mo>(</mo> <mn>0.2</mn> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="script">F</mi> <mo>,</mo> <mo>∧</mo> <mo>)</mo> <mo>=</mo> <mo>(</mo> <mn>0.3</mn> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> </semantics></math>.</p>
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21 pages, 6696 KiB  
Article
Quantitative Physiologic MRI Combined with Feature Engineering for Developing Machine Learning-Based Prediction Models to Distinguish Glioblastomas from Single Brain Metastases
by Seyyed Ali Hosseini, Stijn Servaes, Brandon Hall, Sourav Bhaduri, Archith Rajan, Pedro Rosa-Neto, Steven Brem, Laurie A. Loevner, Suyash Mohan and Sanjeev Chawla
Diagnostics 2025, 15(1), 38; https://doi.org/10.3390/diagnostics15010038 - 27 Dec 2024
Viewed by 719
Abstract
Background: The accurate and early distinction of glioblastomas (GBMs) from single brain metastases (BMs) provides a window of opportunity for reframing treatment strategies enabling optimal and timely therapeutic interventions. We sought to leverage physiologically sensitive parameters derived from diffusion tensor imaging (DTI) [...] Read more.
Background: The accurate and early distinction of glioblastomas (GBMs) from single brain metastases (BMs) provides a window of opportunity for reframing treatment strategies enabling optimal and timely therapeutic interventions. We sought to leverage physiologically sensitive parameters derived from diffusion tensor imaging (DTI) and dynamic susceptibility contrast (DSC)–perfusion-weighted imaging (PWI) along with machine learning-based methods to distinguish GBMs from single BMs. Methods: Patients with histopathology-confirmed GBMs (n = 62) and BMs (n = 26) and exhibiting contrast-enhancing regions (CERs) underwent 3T anatomical imaging, DTI and DSC-PWI prior to treatment. Median values of mean diffusivity (MD), fractional anisotropy, linear, planar and spheric anisotropic coefficients, and relative cerebral blood volume (rCBV) and maximum rCBV values were measured from CERs and immediate peritumor regions. Data normalization and scaling were performed. In the next step, most relevant features were extracted (non-interacting features), which were subsequently used to generate a set of new, innovative, high-order features (interacting features) using a feature engineering method. Finally, 10 machine learning classifiers were employed in distinguishing GBMs and BMs. Cross-validation and receiver operating characteristic (ROC) curve analyses were performed to determine the diagnostic performance. Results: A random forest classifier with ANOVA F-value feature selection algorithm using both interacting and non-interacting features provided the best diagnostic performance in distinguishing GBMs from BMs with an area under the ROC curve of 92.67%, a classification accuracy of 87.8%, a sensitivity of 73.64% and a specificity of 97.5%. Conclusions: A machine learning based approach involving the combined use of interacting and non-interacting physiological MRI parameters shows promise to differentiate between GBMs and BMs with high accuracy. Full article
(This article belongs to the Special Issue Clinical Advances and Applications in Neuroradiology)
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Figure 1
<p>The image processing pipeline provides an overview of the data analytical components including image registration, tissue segmentation, feature selection, model building machine learning-based algorithms, and diagnostic performance metrics.</p>
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<p>Image data distribution before pre-processing based on minimum, first quartile (Q1), median, third quartile (Q3), and maximum. The box itself represents the interquartile range (IQR), which is the range between the first quartile (25th percentile) and the third quartile (75th percentile). The horizontal line inside the box indicates the median of the data. The “whiskers” extend from the box to the smallest and largest values within 1.5 × IQR from the Q1 and Q3, respectively. Points outside of the whiskers are considered outliers and are represented as individual dots. Abbreviations: contrast-enhanced region (CER), immediate peritumoral region (IPR), mean diffusivity (MD), fractional anisotropy (FA), coefficient of linear anisotropy (CL), planar anisotropy (CP), spherical anisotropy (CS) maps, relative cerebral blood volume (rCBV), and maximum rCBV (rCBV<sub>max</sub>).</p>
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<p>The effect of the number of trees on the classification accuracy between GBMs and BMs.</p>
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<p>A 65-year-old male patient with a glioblastoma in the left parietal-occipital region. Axial post contrast T1-weighted, and T2-FLAIR images show ring-enhancement and extensive vasogenic edema. DTI derived maps (MD, FA, CL, CP and CS) are shown and CBV map showing high perfusion from CER and IPR of neoplasm indicating neoplastic infiltration (arrow).</p>
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<p>A 51 year old male patient with metastatic lung adenocarcinoma in the left occipital lobe. Axial post contrast T1-weighted, and T2-FLAIR images show ring-enhancement and extensive edema. DTI derived maps (MD, FA, CL, CP and CS) are shown and CBV map showing high perfusion from CER of neoplasm. Please note lower CBV value of this BM from IPR than that of GBM (shown in <a href="#diagnostics-15-00038-f004" class="html-fig">Figure 4</a>).</p>
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<p>Correlation matrix between various image features extracted in this study. In this matrix: Each cell in the grid represents the value of the correlation coefficient between two variables. The correlation coefficient values range from −1 to 1, where 1 indicates a perfect positive linear relationship, −1 shows a perfect negative linear relationship, and 0 indicates no linear relationship. Abbreviations: contrast-enhanced region (CER), immediate peritumoral region (IPR), mean diffusivity (MD), fractional anisotropy (FA), coefficient of linear anisotropy (CL), planar anisotropy (CP), spherical anisotropy (CS) maps, relative cerebral blood volume (rCBV), and maximum rCBV (rCBV<sub>max</sub>).</p>
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<p>Ranked feature importance based on the random forest classifier are shown. Abbreviations: contrast-enhanced region (CER), immediate peritumoral region (IPR), mean diffusivity (MD), fractional anisotropy (FA), coefficient of linear anisotropy (CL), planar anisotropy (CP), spherical anisotropy (CS) maps, relative cerebral blood volume (rCBV), and maximum rCBV (rCBV<sub>max</sub>).</p>
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<p>Diagnostic performance metric (AUC ROC, accuracy, sensitivity, specificity, and F1 score) heatmap of various feature selections and multiple machine learning classifiers belonging to the ‘Original Method’ implemented in the current study.</p>
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<p>Diagnostic performance metric (AUC ROC, accuracy, sensitivity, specificity, and F1 score) heatmap of various feature selections and multiple machine learning classifiers belonging to the ‘Innovative Method’ implemented in the current study.</p>
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<p>Diagnostic performance metric (AUC ROC, accuracy, sensitivity, specificity, and F1 score) heatmap of various feature selections and multiple machine learning classifiers belonging to the ‘Combined Method’ implemented in the current study.</p>
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12 pages, 2993 KiB  
Technical Note
py.Aroma: An Intuitive Graphical User Interface for Diverse Aromaticity Analyses
by Zhe Wang
Chemistry 2024, 6(6), 1692-1703; https://doi.org/10.3390/chemistry6060103 - 23 Dec 2024
Viewed by 937
Abstract
The nucleus-independent chemical shift (NICS) criterion plays a significant role in evaluating (anti-)aromaticity. While being readily accessible even for non-computational chemists, adding ghost atoms for multi-points NICS evaluations poses a significant challenge. In this article, I introduce py.Aroma 4, a freely available and [...] Read more.
The nucleus-independent chemical shift (NICS) criterion plays a significant role in evaluating (anti-)aromaticity. While being readily accessible even for non-computational chemists, adding ghost atoms for multi-points NICS evaluations poses a significant challenge. In this article, I introduce py.Aroma 4, a freely available and open-source Python package designed specifically for analyzing (anti-)aromaticity. Through its user-friendly graphical interface, py.Aroma simplifies and enhances aromaticity analyses by offering key features such as HOMA/HOMER index computation, Gaussian-type input file generation for diverse NICS calculations and corresponding output processing, NMR spectra plotting, and computational supporting information (SI) generation for scientific manuscripts. Additionally, NICS is suggested for evaluating (anti-)aromaticity for non-planar or tilted rings. Pre-compiled executables for macOS and Windows are freely available online. Facilitate accessibility for users lacking programming experience or time constraints. Full article
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Graphical abstract

Graphical abstract
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<p>Startup window of py.Aroma.</p>
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<p>HOMA analysis of triphenylene by py.Aroma. The calculated HOMA values are presented in a dedicated text box, while the user interface enables the specification of the examined cyclic structure by inputting the relevant atom sequence.</p>
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<p>Screenshots of the menu bar for creating NICS input files and examples generated by py.Aroma: (<b>a</b>) NICS probes for calculating NICS(0) and NICS(1) of benzene; (<b>b</b>) NICS-<span class="html-italic">XY</span>-scan along the long axis of pentalene above the molecular plane by 1 Å; (<b>c</b>) region of NICS probes for the 2D NICS of benzene; (<b>d</b>) region of NICS probes for the 3D NICS of benzene; (<b>e</b>) NICS probes for the INICS calculation of (1-bromoethyl)benzene, in the range of –8 to 8 Å, with an interval of 0.2 Å.</p>
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<p>(<b>a</b>) An example of shielding tensors from the NICS output. (<b>b</b>) The best-fit plane is marked in a rectangle for a phenyl ring in [7]cycloparaphenylene.</p>
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<p>Geometries used for NICS calculations: (<b>a</b>) <b>[8]CPP</b>; (<b>b</b>) <b>[8]LPP</b>. The numbers in the figure represent the atom numbers for Bq atoms used in the calculations.</p>
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<p>NICS outputs processed by py.Aroma: (<b>a</b>) NICS(0)<sub>ZZ</sub> and NICS(1)<sub>ZZ</sub> of benzene; (<b>b</b>) NICS-<span class="html-italic">XY</span>-scan trace for pentalene; (<b>c</b>) 2D NICS(0)<sub>ZZ</sub> heatmap of benzene; (<b>d</b>) 3D NICS<sub>ZZ</sub> iso-surface (red: −25 ppm, green: 10 ppm) visualized by ChimeraX; (<b>e</b>) INICS<sub>ZZ</sub> trance for (1-bromoethyl)benzene. The table summarizes the INICS indices of all NICS components.</p>
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<p>(<b>a</b>) Screenshot of the NMR module in py.Aroma; (<b>b</b>) A comparison of two H NMR spectra of intricarene plotted with different FWHM (0.01 and 0.06) values; NMR calculated at (SCRF = CHCl<sub>3</sub>) mPW1PW91/6-311+G(2d,p)//B3LYP/6-31+G(d,p) level of theory [<a href="#B68-chemistry-06-00103" class="html-bibr">68</a>,<a href="#B69-chemistry-06-00103" class="html-bibr">69</a>].</p>
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