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Keywords = parabolic structure

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20 pages, 5591 KB  
Article
Mechanical Uniaxial Compression of 3D-Printed Non-Periodic ASA Lattice Structures Using Semi-Controlled Design Models
by Nebojša Rašović, Inga Krešić and Jasmin Kaljun
Polymers 2025, 17(20), 2775; https://doi.org/10.3390/polym17202775 - 16 Oct 2025
Abstract
This work examines the mechanical behaviour of 3D-printed stochastic lattice structures fabricated using a semi-controlled design. A primary goal is to predict and optimize the mechanical response of these Acrylic Styrene Acrylonitrile (ASA) filament structures when subjected to compressive stress. By transitioning from [...] Read more.
This work examines the mechanical behaviour of 3D-printed stochastic lattice structures fabricated using a semi-controlled design. A primary goal is to predict and optimize the mechanical response of these Acrylic Styrene Acrylonitrile (ASA) filament structures when subjected to compressive stress. By transitioning from a purely stochastic method to a semi-controlled tessellation approach within Rhinoceros 7 software, we effectively generated the proposed design models. This methodology results in mechanical responses that are both predictable and reliable. The design parameters, including nodal formation, strut thickness, and lattice generation based on a predefined geometric routine, are associated with the regulation of the relative density. This approach aims to minimize the effect of relative density on the actual stiffness and strength evaluation. Our findings are cantered on the compressive testing of structures, which were generated using a Voronoi population distributed along a parabolic curve. We analyzed their mechanical response to the point of failure by examining stress–strain fluctuations. Three distinct behaviour stages are observed: elastic range, plastic range, and collapse without densification. The influence of crosslink geometry on the elastic responses was highlighted, with parabolic configurations affecting the peak stresses and elastic line slopes. The structures exhibited purely brittle behaviour, characterized by abrupt local cracking and oscillatory plateau formation in the plastic stage. Full article
(This article belongs to the Special Issue Latest Research on 3D Printing of Polymer and Polymer Composites)
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15 pages, 3447 KB  
Article
Coaxial Laser Cladding of Novel Wear-Resistant Alloy Coatings on 60CrMnMo Steel Surface
by Min Chen, Liu Weng, Xuyang Liu, Zhongxue Feng, Xuan Xiao, Haoran Zhou and Xuefeng Zhang
Materials 2025, 18(20), 4696; https://doi.org/10.3390/ma18204696 - 13 Oct 2025
Viewed by 183
Abstract
Fe–Cr–Nb–Al–C alloy coatings were firstly fabricated on a high-carbon forged steel surface via coaxial laser cladding. The morphological evolution with varying Nb contents and wear mechanisms of the coatings were systematically investigated through comprehensive analysis. The results indicate that Nb content critically governs [...] Read more.
Fe–Cr–Nb–Al–C alloy coatings were firstly fabricated on a high-carbon forged steel surface via coaxial laser cladding. The morphological evolution with varying Nb contents and wear mechanisms of the coatings were systematically investigated through comprehensive analysis. The results indicate that Nb content critically governs the coating microstructure and mechanical properties. At low Nb levels, coarse grain-boundary networks of (Fe,Cr) solid solution embrittled by Cr23C6 are formed. Moderate Nb addition produces finely dispersed rod-shaped NbC precipitates. At higher Nb levels, the morphology evolves into a segregated martensite–ferrite dual-phase structure. The coating wear rate exhibits a parabolic dependence on Nb content, initially decreasing with moderate addition and then increasing with further Nb. Consequently, optimal wear resistance is achieved at a critical Nb content (3 wt.%) that establishes an optimal balance between NbC precipitation and phase uniformity, thereby minimizing debris generation and spalling. Full article
(This article belongs to the Section Metals and Alloys)
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38 pages, 6482 KB  
Review
Solar Heat for Industrial Processes (SHIP): An Overview of Its Categories and a Review of Its Recent Progress
by Osama A. Marzouk
Solar 2025, 5(4), 46; https://doi.org/10.3390/solar5040046 - 11 Oct 2025
Viewed by 175
Abstract
The term SHIP (solar heat for industrial processes) or SHIPs (solar heat for industrial plants) refers to the use of collected solar radiation for meeting industrial heat demands, rather than for electricity generation. The global thermal capacity of SHIP systems at the end [...] Read more.
The term SHIP (solar heat for industrial processes) or SHIPs (solar heat for industrial plants) refers to the use of collected solar radiation for meeting industrial heat demands, rather than for electricity generation. The global thermal capacity of SHIP systems at the end of 2024 stood slightly above 1 GWth, which is comparable to the electric power capacity of a single power station. Despite this relatively small presence, SHIP systems play an important role in rendering industrial processes sustainable. There are two aims in the current study. The first aim is to cover various types of SHIP systems based on the variety of their collector designs, operational temperatures, applications, radiation concentration options, and solar tracking options. SHIP designs can be as simple as unglazed solar collectors (USCs), having a stationary structure without any radiation concentration. On the other hand, SHIP designs can be as complicated as solar power towers (SPTs), having a two-axis solar tracking mechanism with point-focused concentration of the solar radiation. The second aim is to shed some light on the status of SHIP deployment globally, particularly in 2024. This includes a drop during the COVID-19 pandemic. The findings of the current study show that more than 1300 SHIP systems were commissioned worldwide by the end of 2024 (cumulative number), constituting a cumulative thermal capacity of 1071.4 MWth, with a total collector area of 1,531,600 m2. In 2024 alone, 120.3 MWth of thermal capacity was introduced in 106 SHIP systems having a total collector area of 171,874 m2. In 2024, 65.9% of the installed global thermal capacity of SHIP systems belonged to the parabolic trough collectors (PTCs), and another 22% of this installed global thermal capacity was attributed to the unevacuated flat plate collectors (FPC-Us). Considering the 106 SHIP systems installed in 2024, the average collector area per system was 1621.4 m2/project. However, this area largely depends on the SHIP category, where it is much higher for parabolic trough collectors (37,740.5 m2/project) but lower for flat plate collectors (805.2 m2/project), and it is lowest for unglazed solar collectors (163.0 m2/project). The study anticipates large deployment in SHIP systems (particularly the PTC type) in 2026 in alignment with gigascale solar-steam utilization in alumina production. Several recommendations are provided with regard to the SHIP sector. Full article
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19 pages, 1035 KB  
Article
Spectral Bounds and Exit Times for a Stochastic Model of Corruption
by José Villa-Morales
Math. Comput. Appl. 2025, 30(5), 111; https://doi.org/10.3390/mca30050111 - 8 Oct 2025
Viewed by 139
Abstract
We study a stochastic differential model for the dynamics of institutional corruption, extending a deterministic three-variable system—corruption perception, proportion of sanctioned acts, and policy laxity—by incorporating Gaussian perturbations into key parameters. We prove global existence and uniqueness of solutions in the physically relevant [...] Read more.
We study a stochastic differential model for the dynamics of institutional corruption, extending a deterministic three-variable system—corruption perception, proportion of sanctioned acts, and policy laxity—by incorporating Gaussian perturbations into key parameters. We prove global existence and uniqueness of solutions in the physically relevant domain, and we analyze the linearization around the asymptotically stable equilibrium of the deterministic system. Explicit mean square bounds for the linearized process are derived in terms of the spectral properties of a symmetric matrix, providing insight into the temporal validity of the linear approximation. To investigate global behavior, we relate the first exit time from the domain of interest to backward Kolmogorov equations and numerically solve the associated elliptic and parabolic PDEs with FreeFEM, obtaining estimates of expectations and survival probabilities. An application to the case of Mexico highlights nontrivial effects: while the spectral structure governs local stability, institutional volatility can non-monotonically accelerate global exit, showing that highly reactive interventions without effective sanctions increase uncertainty. Policy implications and possible extensions are discussed. Full article
(This article belongs to the Section Social Sciences)
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16 pages, 11267 KB  
Article
Seepage Characteristics and Critical Scale in Gas-Bearing Coal Pores Under Water Injection: A Multifractal Approach
by Qifeng Jia, Xiaoming Ni, Jingshuo Zhang, Bo Li, Lang Liu and Jingyu Wang
Fractal Fract. 2025, 9(10), 629; https://doi.org/10.3390/fractalfract9100629 - 27 Sep 2025
Viewed by 255
Abstract
To investigate the flow characteristics of movable water in coal under the influence of micro-nano pore fractures with multiple fractal structures, this study employed nuclear magnetic resonance (NMR) and multifractal theory to analyze gas–water seepage under different injection pressures. Then, the scale threshold [...] Read more.
To investigate the flow characteristics of movable water in coal under the influence of micro-nano pore fractures with multiple fractal structures, this study employed nuclear magnetic resonance (NMR) and multifractal theory to analyze gas–water seepage under different injection pressures. Then, the scale threshold for mobile water entering coal pores and fractures was determined by clarifying the relationship among “injection pressure-T2 dynamic multiple fractal parameter seepage resistance-critical pore scale”. The results indicate that coal samples from Yiwu (YW) and Wuxiang (WX) enter the nanoscale pore size range at an injection pressure of 8 MPa, while the coal sample from Malan (ML) enters the nanoscale pore size range at an injection pressure of 9 MPa. During the water injection process, there is a significant linear relationship between the multiple fractal parameters log X(q, ε) and log(ε) of the sample. The generalized fractal dimension D(q) decreases monotonically with increasing q in an inverse S-shape. This decrease occurs in two distinct stages: D(q) decreases rapidly in the low probability interval q < 0; D(q) decreases slowly in the high probability interval q > 0. The multiple fractal singularity spectrum function f(α) has an asymmetric upward parabolic convex function relationship with α, which is divided into a rapidly increasing left branch curve and a slowly decreasing right branch curve with α0 as the boundary. Supporting evidence indicates the feasibility of a methodology for identifying the variation in multiple fractal parameters of gas–water NMR seepage and the critical scale transition conditions. This investigation establishes a methodological foundation for analyzing gas–water transport pathways within porous media materials. Full article
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22 pages, 4675 KB  
Article
Thermal Stress of Fractured Rock Under Solar Radiation Based on a Typical Shape Function Method
by Yang Wang and Wenhua Chen
Mathematics 2025, 13(17), 2864; https://doi.org/10.3390/math13172864 - 5 Sep 2025
Viewed by 471
Abstract
Tunnel portal rocks in southern China, which are exposed to intense solar radiation and temperature fluctuations, are susceptible to thermal stress, which directly or indirectly affects the safety, stability, and normal use of a tunnel and its peripheral structures. Fractures act as conduits [...] Read more.
Tunnel portal rocks in southern China, which are exposed to intense solar radiation and temperature fluctuations, are susceptible to thermal stress, which directly or indirectly affects the safety, stability, and normal use of a tunnel and its peripheral structures. Fractures act as conduits for solar radiation energy, converting it into thermal energy within the rock, thereby altering the thermal stress field. As formation mechanisms of rock, fractures are complex, and the nonlinear thermal conduction at fracture tips leads to thermal stress concentration. A parabolic shape function for the heat source and thermal stress at tips of rock fractures is herein proposed, and the thermal stress field of fractured rocks under solar radiation is obtained. The applicability of different fracture heat source functions for analyzing the effects of heat on rocks with varying thermodynamic properties is discussed. Compared with a linear heat source function, the thermal stress values of rock fracture tips are larger. The daily maximum σθmax increases by 8.14% when αc=0.05 based on the parabolic heat source function, providing more conservative results for the thermal stability analysis of fractured rock under solar radiation. Parabolic heat source functions are more reasonable for soft rocks with high thermal conductivity and low thermal deformation, while linear heat source functions are more appropriate for hard rocks. A parabolic heat source function is a typical function for analyzing the effects of heat on fractured rocks under solar radiation. Full article
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21 pages, 34958 KB  
Article
Investigation of Fluid–Structure Interactions of an Uncontrolled Flexible Hemisphere Utilising Non-Simultaneous Stereo Particle Image Velocimetry and Digital Image Correlation
by Nishanth Menakath, Gareth A. Vio and Nicholas J. Lawson
Aerospace 2025, 12(9), 769; https://doi.org/10.3390/aerospace12090769 - 27 Aug 2025
Viewed by 467
Abstract
This research investigates the interaction between a flexible thin-walled hemisphere and the surrounding wake at ReD=2×105 acting as a simplified model of a flexible surface protuberance immersed within a turbulent boundary layer (BL). A flexible model [...] Read more.
This research investigates the interaction between a flexible thin-walled hemisphere and the surrounding wake at ReD=2×105 acting as a simplified model of a flexible surface protuberance immersed within a turbulent boundary layer (BL). A flexible model and a rigid model, both 100 mm in diameter, are experimentally tested to observe and contrast the flow variation between a rigid structure and a freely deforming structure. Two experiments were conducted. To capture fluid flow behaviour, stereo particle image velocimetry (SPIV) was used. To capture structural deformation of the model, digital image correlation (DIC) was utilised. Experimental testing was conducted non-simultaneously. From the experimental testing, it was observed that the flexible model experienced a leading edge (LE) deformation at 29° of the altitude angle (θ), showing an average deformation of 2.11 mm. All regions of the structure experienced non-zero distortion due to the incoming wind load. This was similar to behaviour observed in previous literature. This caused a modulation in the wake region, giving a parabolic wake velocity contour to form about θ20°. A velocity inflection point is observed for the flexible model at an average of θ=23.39° within the wake. This inflection region extends surrounding the area of maximum structural deflection up to θ40°. This indicates that the deflection across the LE centreline has a direct interaction with location and size of the near wake. Turbulent kinetic energy (TKE) in the wake was observed to drop with the introduction of the flexible model, with a lower dissipation rate observable. This is indicative of energy transfer from the flow to the structure, allowing deformation. The maximum region of TKE coincides with the recirculation vortex core region, which was shown to move from z/D= 0.19 to z/D= 0.35 for the rigid and flexible models, respectively. The results indicate that, with the Reynolds number tested, the rigid behaviour is in line with previous literature trends. The flexibility of the model, therefore, highly influences the wake region, with general shape deformation causing a decrease in near wake TKE and change in wake shape and recirculation core location. Full article
(This article belongs to the Section Aeronautics)
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20 pages, 8356 KB  
Article
A Fundamental Study on a Porous Carbon Nanotubes Macroelectrode in Weakly Supported Electrolyte: A Novel Criterion for Distinguishing Diffusion Domains
by Josipa Dugeč, Ivana Škugor Rončević, Nives Vladislavić and Marijo Buzuk
Int. J. Mol. Sci. 2025, 26(17), 8262; https://doi.org/10.3390/ijms26178262 - 26 Aug 2025
Viewed by 549
Abstract
A new approach is presented to elucidate the phenomena that occur within a porous single-walled carbon nanotubes (SWCNTs) modified glassy carbon electrode (GCE) and that influence the electrochemical behavior of the modified electrode. By employing cyclic voltammetry, reverse pulse voltammetry, and double potential [...] Read more.
A new approach is presented to elucidate the phenomena that occur within a porous single-walled carbon nanotubes (SWCNTs) modified glassy carbon electrode (GCE) and that influence the electrochemical behavior of the modified electrode. By employing cyclic voltammetry, reverse pulse voltammetry, and double potential step chronoamperometry, insights into the structural changes in the electrochemical double layer and the mass transport regimes are gained. An analysis of the reduction of the electrochemically generated [Fe(CN)6]3− shows that the SWCNTs layer can be considered inactive. However, their pronounced influence on the electrochemical signal arises from their capacitive behavior. Furthermore, a novel criterion for distinguishing the mass transport domains is proposed, which allows the estimation of the points at which a change in the mass transport regime occurs. The results also show the role of the porous SWCNTs layer in preventing the expansion of the double layer as well as in the process of ion condensation in the Gouy-Chapman layer. Finally, the counterintuitive and unexpected voltametric behavior, such as the independence of the current peak heights from the ionic strength of the support, the parabolic dependence of the peak potential on the scan rates, and the occurrence of steady-state currents, are discussed. Full article
(This article belongs to the Special Issue Recent Advances in Electrochemical-Related Materials)
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13 pages, 9516 KB  
Article
Rapid Full-Field Surface Topography Measurement of Large-Scale Wafers Using Interferometric Imaging
by Ruifang Ye, Jiarui Zeng, Heyan Zhang, Yujie Su and Huihui Li
Photonics 2025, 12(9), 835; https://doi.org/10.3390/photonics12090835 - 22 Aug 2025
Viewed by 776
Abstract
Rapid full-field surface topography measurement for large-scale wafers remains challenging due to limitations in speed, system complexity, and scalability. This work presents a interferometric system based on thin-film interference for high-precision wafer profiling. An optical flat serves as the reference surface, forming a [...] Read more.
Rapid full-field surface topography measurement for large-scale wafers remains challenging due to limitations in speed, system complexity, and scalability. This work presents a interferometric system based on thin-film interference for high-precision wafer profiling. An optical flat serves as the reference surface, forming a parallel air-gap structure with the wafer under test. A large-aperture collimated beam is introduced via an off-axis parabolic mirror to generate high-contrast interference fringes across the entire field of view. Once the wafer is fully illuminated, topographic information is directly extracted from the fringe pattern. Comparative measurements with a commercial interferometer show relative deviations below 3% in bow and warp, confirming the system’s accuracy and stability. With its simple optical layout, low cost, and robust performance, the proposed method shows strong potential for industrial applications in wafer inspection and online surface monitoring. Full article
(This article belongs to the Special Issue Advances in Interferometric Optics and Applications)
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24 pages, 9267 KB  
Article
Tendon Profile Layout Impact on the Shear Capacity of Unbonded Post-Tensioned Prestressed Concrete Bridge I-Girders
by Swar I. Hasib, Assim M. Lateef and Omar Q. Aziz
Infrastructures 2025, 10(9), 222; https://doi.org/10.3390/infrastructures10090222 - 22 Aug 2025
Viewed by 805
Abstract
The main objective of this research is to investigate the impact of the tendon profile layout on the shear strength of unbonded post-tensioned prestressed concrete bridge I-girders. This study involves an experimental investigation where ten unbonded post-tensioned bridge girders are cast and subjected [...] Read more.
The main objective of this research is to investigate the impact of the tendon profile layout on the shear strength of unbonded post-tensioned prestressed concrete bridge I-girders. This study involves an experimental investigation where ten unbonded post-tensioned bridge girders are cast and subjected to four-point loads. The focus of the investigation is on the effect of different tendon profile layouts, including trapezoidal, parabolic, and harped shapes. The experimental results reveal that the shear behavior of the specimens progresses through three distinct stages: the elastic stage, the elastic–plastic stage, and the plastic stage, with all specimens ultimately failing due to shear. The results show that tendon profiles with higher eccentricity at the end of the beams (80 mm above the neutral axis) had the highest ultimate load capacity for each tendon profile shape, coupled with the largest deflection. Conversely, profiles with lower eccentricity (80 mm below the neutral axis) demonstrated the lower ultimate load capacity for each tendon profile shape and minimal deflection. Among the various tendon profile layouts that were tested, the specimen with the harped tendon profile (GF-1 HA) showed the highest ultimate load capacity, with an increasing rate of 17.52% in ultimate load and a 45.55% increase in ultimate deflection compared to the control beam (GF-1 ST) with a straight tendon profile. On the other hand, the harped tendon profile specimen (GF-1 HA) exhibited the lowest deflection among the various tendon profile shapes with an increasing rate of 5.7% in ultimate load deflection in comparison with the control beam (GF-1 ST) with a straight tendon profile. These improvements in stiffness, load capacity, and deflection are attributed to enhanced resistance, particularly at the supports. Consequently, the optimized tendon layouts offer an increase in the overall structural efficiency, leading to potential cost savings in bridge girder production. Full article
(This article belongs to the Section Infrastructures and Structural Engineering)
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21 pages, 3814 KB  
Article
Features of the Structure of Layered Epoxy Composite Coatings Formed on a Metal-Ceramic-Coated Aluminum Base
by Volodymyr Korzhyk, Volodymyr Kopei, Petro Stukhliak, Olena Berdnikova, Olga Kushnarova, Oleg Kolisnichenko, Oleg Totosko, Danylo Stukhliak and Liubomyr Ropyak
Materials 2025, 18(15), 3620; https://doi.org/10.3390/ma18153620 - 1 Aug 2025
Viewed by 651
Abstract
Difficult, extreme operating conditions of parabolic antennas under precipitation and sub-zero temperatures require the creation of effective heating systems. The purpose of the research is to develop a multilayer coating containing two metal-ceramic layers, epoxy composite layers, carbon fabric, and an outer layer [...] Read more.
Difficult, extreme operating conditions of parabolic antennas under precipitation and sub-zero temperatures require the creation of effective heating systems. The purpose of the research is to develop a multilayer coating containing two metal-ceramic layers, epoxy composite layers, carbon fabric, and an outer layer of basalt fabric, which allows for effective heating of the antenna, and to study the properties of this coating. The multilayer coating was formed on an aluminum base that was subjected to abrasive jet processing. The first and second metal-ceramic layers, Al2O3 + 5% Al, which were applied by high-speed multi-chamber cumulative detonation spraying (CDS), respectively, provide maximum adhesion strength to the aluminum base and high adhesion strength to the third layer of the epoxy composite containing Al2O3. On this not-yet-polymerized layer of epoxy composite containing Al2O3, a layer of carbon fabric (impregnated with epoxy resin) was formed, which serves as a resistive heating element. On top of this carbon fabric, a layer of epoxy composite containing Cr2O3 and SiO2 was applied. Next, basalt fabric was applied to this still-not-yet-polymerized layer. Then, the resulting layered coating was compacted and dried. To study this multilayer coating, X-ray analysis, light and raster scanning microscopy, and transmission electron microscopy were used. The thickness of the coating layers and microhardness were measured on transverse microsections. The adhesion strength of the metal-ceramic coating layers to the aluminum base was determined by both bending testing and peeling using the adhesive method. It was established that CDS provides the formation of metal-ceramic layers with a maximum fraction of lamellae and a microhardness of 7900–10,520 MPa. In these metal-ceramic layers, a dispersed subgrain structure, a uniform distribution of nanoparticles, and a gradient-free level of dislocation density are observed. Such a structure prevents the formation of local concentrators of internal stresses, thereby increasing the level of dispersion and substructural strengthening of the metal-ceramic layers’ material. The formation of materials with a nanostructure increases their strength and crack resistance. The effectiveness of using aluminum, chromium, and silicon oxides as nanofillers in epoxy composite layers was demonstrated. The presence of structures near the surface of these nanofillers, which differ from the properties of the epoxy matrix in the coating, was established. Such zones, specifically the outer surface layers (OSL), significantly affect the properties of the epoxy composite. The results of industrial tests showed the high performance of the multilayer coating during antenna heating. Full article
(This article belongs to the Section Metals and Alloys)
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23 pages, 4708 KB  
Article
Mechanical Characteristics and Precision Analysis of Inflatable Deployable Parabolic Membrane Antenna Structures
by Yu Hu, Huichao Ji and Wujun Chen
Aerospace 2025, 12(8), 677; https://doi.org/10.3390/aerospace12080677 - 29 Jul 2025
Viewed by 518
Abstract
As accuracy of the reflector surface of a space parabolic deployable antenna is an important factor to determine its electrical characteristics (transmission gain and side lobes), mechanical characteristics of parabolic antennas under various internal pressures should be studied. The objective of this paper [...] Read more.
As accuracy of the reflector surface of a space parabolic deployable antenna is an important factor to determine its electrical characteristics (transmission gain and side lobes), mechanical characteristics of parabolic antennas under various internal pressures should be studied. The objective of this paper is to explore the force analysis of parabolic antennas by theoretical method and to estimate the effect of different air pressures on the surface precision of parabolic antennas via experiments in horizontal and vertical directions, and then a numerical analysis of the vibration characteristics of the parabolic antenna is proposed to explore the transient response of parabolic antennas. It is found that the ratio of tension reduces as depth of the parabolic membrane increases and can infinitely converge to 1/2. For precision analysis, it is concluded that precision of the parabolic membrane surface in a vertical state is higher than that in a horizontal state. Full article
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14 pages, 1578 KB  
Article
On the Canonical Form of Singular Distributed Parameter Systems
by Zhongchen Meng, Yushan Jiang, Nier Dong, Wanyue Wang, Yunxiao Chang and Ruoxiang Ma
Axioms 2025, 14(8), 583; https://doi.org/10.3390/axioms14080583 - 27 Jul 2025
Viewed by 425
Abstract
This study addresses the standardization of Singular Distributed Parameter Systems (SDPSs). It focuses on classifying and simplifying first- and second-order linear SDPSs using characteristic matrix theory. First, the study classifies first-order linear SDPSs into three canonical forms based on characteristic curve theory, with [...] Read more.
This study addresses the standardization of Singular Distributed Parameter Systems (SDPSs). It focuses on classifying and simplifying first- and second-order linear SDPSs using characteristic matrix theory. First, the study classifies first-order linear SDPSs into three canonical forms based on characteristic curve theory, with an example illustrating the standardization process for parabolic SDPSs. Second, under regular conditions, first-order SDPSs can be decomposed into fast and slow subsystems, where the fast subsystem reduces to an Ordinary Differential Equation (ODE) system, while the slow subsystem retains the spatiotemporal characteristics of the original system. Third, the standardization and classification of second-order SDPSs is proposed using three reversible transformations that achieve structural equivalence. Finally, an illustrative example of a building temperature control is built with SDPSs. The simulation results show the importance of system standardization in real-world applications. This research provides a theoretical foundation for SDPS standardization and offers insights into the practical implementation of distributed temperature systems. Full article
(This article belongs to the Special Issue Differential Equations and Inverse Problems, 2nd Edition)
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12 pages, 16238 KB  
Article
Degradation of HVOF-MCrAlY + APS-Nanostructured YSZ Thermal Barrier Coatings
by Weijie R. Chen, Chao Li, Yuxian Cheng, Hongying Li, Xiao Zhang and Lu Wang
Coatings 2025, 15(8), 871; https://doi.org/10.3390/coatings15080871 - 24 Jul 2025
Viewed by 548
Abstract
The degradation process of HVOF-MCrAlY + APS-nanostructured YSZ (APS-nYSZ) thermal barrier coatings, produced using gas turbine OEM-approved MCrAlY powders, is investigated by studying the TGO growth and crack propagation behaviors in a thermal cycling environment. The TGO growth yields a parabolic mechanism on [...] Read more.
The degradation process of HVOF-MCrAlY + APS-nanostructured YSZ (APS-nYSZ) thermal barrier coatings, produced using gas turbine OEM-approved MCrAlY powders, is investigated by studying the TGO growth and crack propagation behaviors in a thermal cycling environment. The TGO growth yields a parabolic mechanism on the surfaces of all HVOF-MCrAlYs, and the growth rate increases with the aluminum content in the “classical” MCrAlYs. The APS-nYSZ layer comprises micro-structured YSZ (mYSZ) and nanostructured YSZ (nYSZ) zones. Both mYSZ/mYSZ and mYSZ/nYSZ interfaces appear to be crack nucleation sites, resulting in crack propagation and consequent crack coalescence within the APS-nYSZ layer in the APS-nYSZ/HVOF-MCrAlY vicinity. Crack propagation in the TBCs can be characterized as a steady-state crack propagation stage, where crack length has a nearly linear relationship with TGO thickness, and an accelerating crack propagation stage, which is apparently a result of the coalescence of neighboring cracks. All TBCs fail in the same way as APS-/HVOF-MCrAlY + APS-conventional YSZ analogs, but the difference in thermal cycling lives is not substantial, although the HVOF-low Al-NiCrAlY encounters chemical failure in the early stage of thermal cycling. Full article
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15 pages, 4349 KB  
Article
The Roles of Leaflet Geometry in the Structural Deterioration of Bioprosthetic Aortic Valves
by Yaghoub Dabiri and Kishan Narine
Prosthesis 2025, 7(4), 86; https://doi.org/10.3390/prosthesis7040086 - 18 Jul 2025
Viewed by 648
Abstract
Objectives: Our goal was to assess the role of leaflet geometry on the structural deterioration of bioprosthetic aortic valves (BAVs) in a closed configuration. Methods: With a Fung-type orthotropic model, finite element modeling was used to create ten cases with parabolic, circular and [...] Read more.
Objectives: Our goal was to assess the role of leaflet geometry on the structural deterioration of bioprosthetic aortic valves (BAVs) in a closed configuration. Methods: With a Fung-type orthotropic model, finite element modeling was used to create ten cases with parabolic, circular and spline leaflet curvatures and six leaflet angles. Results: A circular circumferential curvature led to lower von Mises and compressive stresses in both the coaptation and load-bearing areas, reduced tensile stresses in the coaptation regions, and increased tensile stresses in the load-bearing areas. A parabolic radial curvature reduced von Mises stresses in the coaptation, as well as the load-bearing regions, reduced compressive stresses in the coaptation, and reduced tensile stresses in the load-bearing regions, leading to a slight increase in the minimized tensile stress in the coaptation regions (1.794 vs. 1.765 MPa) and the minimized compressive stress in the load-bearing regions (0.772 vs. 0.768 MPa). Within a range of downward inclination of the leaflets, all stresses in the coaptation regions decreased. A parabolic circumferential curvature, a linear radial curvature, and, for most cases, upward leaflet inclinations were associated with larger contact pressures between the leaflets. Conclusions: A parabolic radial curvature and downward leaflet inclination likely lead to the longer durability of BAVs. Full article
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