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Keywords = orbital forcing

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21 pages, 8384 KB  
Article
Study of Ultra-High-Speed Rarefied Flow for Nozzle Optimization with Multiscale Particle Simulations
by Wenjin Sun, Yuan Hu, Fei Fei, Chao Yang, Jinwen Cao, Xian Meng, Quanhua Sun and Heji Huang
Aerospace 2026, 13(6), 554; https://doi.org/10.3390/aerospace13060554 - 16 Jun 2026
Viewed by 176
Abstract
Ultra-high-speed rarefied gas wind tunnels (RGWTs) are critical for estimating the aerodynamic forces acting on spacecraft in very low Earth orbit (VLEO). These tunnels utilize nozzles with large expansion ratios to generate extreme freestream conditions (Ma>20, [...] Read more.
Ultra-high-speed rarefied gas wind tunnels (RGWTs) are critical for estimating the aerodynamic forces acting on spacecraft in very low Earth orbit (VLEO). These tunnels utilize nozzles with large expansion ratios to generate extreme freestream conditions (Ma>20, Kn>1). However, the large expansion ratio induces a multiscale flow within the nozzle that simultaneously spans the continuum and transitional regimes, making the investigation of such flows extremely challenging. The present work applies a multiscale particle method to investigate the RGWT nozzle flow in a unified manner. Simulations reveal that the nozzle flow is underexpanded and characterized by rarefaction effects, and can be categorized into a central core and a surrounding region comprising the shock wave and boundary layer. This surrounding region occupies a significant portion of the nozzle exit, notably degrading flow quality. The wall suction technique increases the uniform flow radius by 11% at a total pressure of 500 kPa, while its effectiveness is limited at 50 kPa due to heightened rarefaction. Finally, a wall smoothing technique is proposed to improve the quality of nozzle flow by recognizing that strongly rarefied flows are governed by gas-surface interactions. Full article
(This article belongs to the Section Astronautics & Space Science)
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29 pages, 28942 KB  
Article
Development of a Launch Mechanism for Small Satellites Using Laser Powder Bed Fusion Process
by Cosmin Gogu, Cătălin-Gheorghe Amza and Cristina Pupăză
J. Manuf. Mater. Process. 2026, 10(6), 204; https://doi.org/10.3390/jmmp10060204 - 11 Jun 2026
Viewed by 249
Abstract
The deployment of CubeSats requires reliable, lightweight, and space-efficient launch mechanisms. Traditional spring-based deployers often rely on standard off-the-shelf components, limiting the design flexibility. This study presents a pilot design-to-verification workflow for a CubeSat deployment mechanism manufactured by Laser Powder Bed Fusion from [...] Read more.
The deployment of CubeSats requires reliable, lightweight, and space-efficient launch mechanisms. Traditional spring-based deployers often rely on standard off-the-shelf components, limiting the design flexibility. This study presents a pilot design-to-verification workflow for a CubeSat deployment mechanism manufactured by Laser Powder Bed Fusion from 316L stainless steel. The workflow integrates analytical sizing, kinematic and numerical force assessment, FEM-based LPBF process simulation employed as a design-support tool to predict thermal displacements and residual stress that occur during manufacturing, prototype manufacturing and optical inspection. Optical scanning indicated that the main envelope dimensions remained close to the nominal CAD values, while the support-plate warping was localized at the plate corners due to the residual thermal stress after the support removal. The study validates the manufacturability of a single LPBF orbital-deployer lunch mechanism and assesses its dimensional accuracy and workflow feasibility, rather than its functional mechanical performance. It also includes mitigation strategies for deployer distortions. Full article
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17 pages, 2613 KB  
Article
Design and Dynamic Analysis of a Tethered-Net-Based Space Debris Capture System with Winch-Driven Closure Mechanism
by Hyeonjin Shin, Henzeh Leeghim, Taehwan Joo, Soonsik Jang and Gilsu Park
Appl. Sci. 2026, 16(12), 5759; https://doi.org/10.3390/app16125759 - 8 Jun 2026
Viewed by 148
Abstract
This study presents a design and performance analysis of a tethered-net-based space debris capture system using multibody dynamic simulation. The increasing accumulation of space debris in Low Earth Orbit (LEO) necessitates reliable capture mechanisms capable of handling non-cooperative targets with positional and velocity [...] Read more.
This study presents a design and performance analysis of a tethered-net-based space debris capture system using multibody dynamic simulation. The increasing accumulation of space debris in Low Earth Orbit (LEO) necessitates reliable capture mechanisms capable of handling non-cooperative targets with positional and velocity uncertainties. To address this, a node-based net model was developed, in which the net structure is represented by interconnected spring-damper elements to capture large deformation and nonlinear behavior. The dynamic analysis was conducted using the commercial multibody dynamics software RecurDyn, considering key design parameters such as ejection distance, angle, and velocity. The results show that the net deployment characteristics are strongly influenced by ejection conditions. An optimal configuration was identified at an ejection angle of 18° and an ejection velocity of 10 m/s, satisfying both deployment performance and the allowable tension limit of 300 N. The proposed capture mechanism enables the net to fully pass over the target before activating a winch to reel in the pulling rope, thereby minimizing impact forces and improving capture stability. Furthermore, the capture performance was quantitatively evaluated under relative position and velocity uncertainties. The maximum allowable lateral velocity was derived as a function of the available capture margin, yielding approximately 1.25 m/s without positional error and 0.30 m/s with a 1 m positional offset. These results provide practical design guidelines for net-based space debris capture systems and demonstrate the robustness of the proposed approach under realistic operational conditions. Full article
(This article belongs to the Special Issue Optimized Design and Analysis of Mechanical Structure)
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40 pages, 64591 KB  
Article
Dynamic Modeling and Thermo-Mechanical Coupling Analysis of Variable-Geometry Spacecraft Antenna with Clearance Hinges Under Extreme Thermal Environment
by Yuntao Hua, Ning Zhang, Yingyong Shen, Shengxin Sun, Hutao Cui and Wenlai Ma
Aerospace 2026, 13(6), 529; https://doi.org/10.3390/aerospace13060529 - 5 Jun 2026
Viewed by 148
Abstract
Extreme cyclic temperature fluctuations (−200 °C to 200 °C) and inherent clearance nonlinearity in deployment hinges severely threaten the on-orbit deployment accuracy and dynamic stability of large variable-geometry spacecraft antennas for geosynchronous Earth orbit applications. However, current modeling approaches suffer from three critical [...] Read more.
Extreme cyclic temperature fluctuations (−200 °C to 200 °C) and inherent clearance nonlinearity in deployment hinges severely threaten the on-orbit deployment accuracy and dynamic stability of large variable-geometry spacecraft antennas for geosynchronous Earth orbit applications. However, current modeling approaches suffer from three critical limitations: single-configuration models requiring manual switching, there are inherent geometric nonlinear errors from conventional floating frame formulations, and incomplete thermo-mechanical coupling neglects the temperature effects on contact stiffness and friction. To address these gaps, we propose a unified high-fidelity dynamic model based on the Absolute Nodal Coordinate Formulation (ANCF). This model eliminates geometric errors and mesh mismatch, enables seamless multi-configuration deployment without switching, and fully incorporates temperature-dependent material properties and nonlinear contact forces. An improved Hilber–Hughes–Taylor-α implicit integration algorithm with second-order accuracy and unconditional stability is adopted to solve the strongly nonlinear differential-algebraic equations. Numerical results demonstrate that the proposed model achieves a calculation error below 3% against experimental data, significantly outperforming the traditional floating frame of reference formulation with an error of 15–22%. Non-uniform temperature fields increase thermally induced vibration amplitudes by 32–45%, and every 0.1 increase in the friction coefficient raises the impact force at the clearance hinge by 15–20%. The proposed unified modeling framework provides a solid theoretical basis for deployment stability prediction and the on-orbit control optimization of large variable-geometry spacecraft antennas. Full article
(This article belongs to the Section Astronautics & Space Science)
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44 pages, 79396 KB  
Article
An Adaptive Dissipation–Precision Coordinated Multi-Scale Implicit Integration Algorithm for Thermo-Mechanical Coupled Dynamics of Flexible Multibody Systems with Temperature-Dependent Clearance Joints
by Yuntao Hua, Ning Zhang, Changzheng Qian, Shengxin Sun, Hutao Cui and Wenlai Ma
Appl. Sci. 2026, 16(11), 5461; https://doi.org/10.3390/app16115461 - 31 May 2026
Viewed by 166
Abstract
Extreme orbital thermal cycling and temperature-dependent clearance nonlinearity make it difficult to predict contact–impact, stick–slip, and bifurcation responses of flexible deployable space structures with sufficient stability, accuracy, and computational efficiency. An Adaptive Dissipation–Precision Coordinated Multi-Scale Implicit Integration Algorithm (ADPC-MSIIA) is proposed. First, an [...] Read more.
Extreme orbital thermal cycling and temperature-dependent clearance nonlinearity make it difficult to predict contact–impact, stick–slip, and bifurcation responses of flexible deployable space structures with sufficient stability, accuracy, and computational efficiency. An Adaptive Dissipation–Precision Coordinated Multi-Scale Implicit Integration Algorithm (ADPC-MSIIA) is proposed. First, an absolute nodal coordinate formulation (ANCF)-based thermo-mechanical clearance-joint model with thermal-viscosity-modified contact and frictional/impact heat feedback is established; second, a dual-time-scale implicit integration scheme with dual-α stability–dissipation control and third-order compensation is developed; finally, numerical validation is performed using a linear single-degree-of-freedom (SDOF) benchmark, a temperature-dependent clearance impact oscillator, finite-element and published benchmark comparisons, and a deployable annular truss antenna case. Simulation results show that ADPC-MSIIA achieves a high-frequency spectral radius of 0.867, an effective convergence order of 2.98, a maximum contact force error of 3.1%, and a 51.7% reduction in the global cumulative error compared with the generalized-α method. This study contributes to knowledge by linking temperature-driven clearance evolution, frictional heat feedback, and adaptive numerical dissipation within a unified framework for predicting non-smooth thermo-mechanical deployment dynamics of large flexible space structures with clearance joints. Full article
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18 pages, 2271 KB  
Article
Mechanism of Imidazole Collectors in the Hydrophobic Agglomeration and Flotation Behavior of Quartz
by Siyu Chen, Yuankun Yang, Yanming Wu, Shengli Yu, Bingchao Lv, Chongzhong Ouyang, Xiang Yao, Yuan Chen and Guohua Gu
Colloids Interfaces 2026, 10(3), 44; https://doi.org/10.3390/colloids10030044 - 29 May 2026
Viewed by 261
Abstract
Imidazole-based ionic liquids hold immense potential in the field of mineral flotation due to their tunable properties. In this study, three imidazole-based ionic liquids with varying carbon chain lengths (OMB, DMB, and HMB) were selected as collectors for quartz flotation to systematically investigate [...] Read more.
Imidazole-based ionic liquids hold immense potential in the field of mineral flotation due to their tunable properties. In this study, three imidazole-based ionic liquids with varying carbon chain lengths (OMB, DMB, and HMB) were selected as collectors for quartz flotation to systematically investigate the microscopic mechanisms by which carbon chain length influences the agglomeration and flotation behavior of quartz. Flotation tests and online particle-bubble monitoring (PBM) results indicate that the elongation of the collector’s carbon chain significantly enhances its collecting ability and reduces the required reagent dosage. To achieve the complete recovery of quartz in a neutral system, a dosage of 35 mg/L is required for OMB, whereas HMB requires only 8 mg/L. As the carbon chain lengthens, the optimal pH range for highly efficient flotation shifts from alkaline to neutral-acidic. Interfacial measurements and mechanistic analyses (Zeta potential and FTIR spectroscopy) confirm that the imidazole ring of the collector physically adsorbs onto the quartz surface through the synergistic action of electrostatic forces and hydrogen bonding, thereby inducing the hydrophobic agglomeration of particles. Notably, in a strongly alkaline system (pH = 11), the long-chain HMB promotes the formation of oversized quartz agglomerates. This leads to a depletion of free reagents in the liquid phase and destabilizes the bubble liquid film, ultimately triggering a sharp decline in recovery. Density functional theory (DFT) calculations further corroborate the structure–activity relationship at the molecular level: the extension of the carbon chain increases the highest occupied molecular orbital (HOMO) energy and electron-donating ability. The adsorption energy of HMB on the quartz (001) surface reached −350.2 kJ/mol, exhibiting the strongest solid–liquid interfacial affinity. This study elucidates the competitive mechanism of carbon chain length in regulating electrostatic adsorption, hydrophobic agglomeration, and froth stability, providing a solid theoretical foundation for the molecular design of novel green flotation reagents for quartz. Full article
(This article belongs to the Special Issue Colloids and Interfaces in Mineral Processing and Resource Recovery)
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17 pages, 1807 KB  
Article
Phase-Space Structure and Traveling-Wave Solutions of a (3 + 1)-Dimensional Extended Kadomtsev–Petviashvili Equation
by Yaling Lai, Xiyan Wu, Jiaye Lin, Changlong Chen, Junjie Li and Yucheng Chen
Mathematics 2026, 14(11), 1861; https://doi.org/10.3390/math14111861 - 27 May 2026
Viewed by 162
Abstract
This study investigates the (3+1)-dimensional extended Kadomtsev–Petviashvili equation via traveling-wave phase-space geometry. The equation is reduced to a planar Hamiltonian system with cubic nonlinearity, whose conserved energy partitions the phase space into periodic orbits, separatrices, and unbounded trajectories. Closed-form [...] Read more.
This study investigates the (3+1)-dimensional extended Kadomtsev–Petviashvili equation via traveling-wave phase-space geometry. The equation is reduced to a planar Hamiltonian system with cubic nonlinearity, whose conserved energy partitions the phase space into periodic orbits, separatrices, and unbounded trajectories. Closed-form profiles for the gradient variable φ=Uξ are obtained through separation of variables; the corresponding field U is recovered by quadrature and must satisfy a zero-mean condition for periodic reconstruction. In particular, for h1>0, the reconstructed field exhibits kink/antikink-type rather than localized-pulse behavior. Under weak periodic forcing, an explicit Melnikov amplitude factor is derived. Its exponential decay with the forcing frequency implies that the leading-order separatrix splitting distance μA(ω) becomes exponentially small at high frequency, while the simple-zero condition still predicts transverse intersections of stable and unstable manifolds and the onset of horseshoe chaos. Applying the complete discriminant method yields eight distinct solution families—hyperbolic, trigonometric, rational, and Jacobi elliptic—each associated with a unique orbital topology. These results enrich both the dynamical theory and the exact solution framework of higher-dimensional nonlinear evolution equations. Full article
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18 pages, 25539 KB  
Article
Astronomically Constrained Third-Order Sequence Stratigraphy of the Eocene Eh3 Member in the Lacustrine Biyang Depression, Central China
by Dan Ye, Yiping Zhang, Binbin Hao, Xuewei Xiao, Xue Yan, Jian Wang and Ke Xu
Appl. Sci. 2026, 16(10), 4881; https://doi.org/10.3390/app16104881 - 13 May 2026
Viewed by 364
Abstract
The middle Eocene represents a shift from the Early Eocene greenhouse climate to a subsequent cooling trend, during which orbital-scale forcing exerted a strong influence on continental depositional systems. The third Member of the Hetaoyuan Formation (Eh3) in the Biyang Depression [...] Read more.
The middle Eocene represents a shift from the Early Eocene greenhouse climate to a subsequent cooling trend, during which orbital-scale forcing exerted a strong influence on continental depositional systems. The third Member of the Hetaoyuan Formation (Eh3) in the Biyang Depression of the Nanxiang Basin preserves a thick lacustrine succession, but its third-order sequence subdivision has remained controversial because of insufficient temporal control. In this study, natural gamma-ray (GR) logs from wells A1 and A2 were analyzed using an integrated workflow that combines cyclostratigraphy, INPEFA (Integrated Prediction Error Filter Analysis), wavelet transform, and sedimentary noise modeling. The GR records reveal clear astronomical signals corresponding to ~405 kyr long eccentricity, ~100 kyr short eccentricity, ~40 kyr obliquity, and ~20 kyr precession. Astronomical tuning to the 405 kyr cycle yields a depositional duration of ~10.3 Myr and a basal age of ~49.6 Ma. Integrated stratigraphic analysis identifies nine third-order sequence boundaries and eight third-order sequences. In addition, sedimentary noise modeling detects a prominent ~1.2 Myr long-period obliquity modulation signal, which is interpreted to govern long-term lake-level fluctuations and third-order sequence development. These results provide a time-constrained framework for sequence subdivision and demonstrate the importance of orbital forcing in shaping lacustrine stratigraphic architecture. Full article
(This article belongs to the Section Earth Sciences)
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33 pages, 109990 KB  
Article
Design and Analysis of a Grasping Mechanism with an Actuated Palm for On-Orbit Servicing
by Zeyuan Yin, Bin Hu, Yuchen Cai, Guorui Ren, Chuang Li and Hui Zhao
Aerospace 2026, 13(5), 449; https://doi.org/10.3390/aerospace13050449 - 10 May 2026
Viewed by 283
Abstract
To address the inability of existing space grasping mechanisms to adapt to the varying shapes and sizes of space objects, we propose a novel three-fingered space robotic hand composed of an actuated palm and deployable fingers with the aim of successfully grasping a [...] Read more.
To address the inability of existing space grasping mechanisms to adapt to the varying shapes and sizes of space objects, we propose a novel three-fingered space robotic hand composed of an actuated palm and deployable fingers with the aim of successfully grasping a wider variety of space objects. We begin by elaborating on the design concept of the robotic hand. Compared to traditional robotic palms, the actuated palm possesses deployment and metamorphic functions, allowing it to adjust its dimensions to actively adapt to different items. The modular deployable fingers are designed based on a parallel scissor mechanism featuring folding and deployment functions. Next, a kinematic analysis and performance evaluation are performed. The force closure and contact force distribution are also analyzed. After that, a physical prototype is fabricated, and basic motion and grasping tests are performed. The proposed three-fingered robotic hand exhibits excellent adaptability. Finally, the design trade-offs are discussed, along with an analysis of the model’s limitations and future prospects, and it is demonstrated that the proposed novel robotic hand has broad application prospects in future on-orbit missions. Full article
(This article belongs to the Section Astronautics & Space Science)
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29 pages, 25251 KB  
Article
Dynamic Analysis of the Maglev Vehicle–Turnout System Considering Spatial Magnetic–Rail Interaction
by Qiliang Zhang, Enze Yu, Long Zhang, Xiulu Zhang, Guofang Li and Wangcai Ding
Appl. Sci. 2026, 16(9), 4132; https://doi.org/10.3390/app16094132 - 23 Apr 2026
Viewed by 240
Abstract
The dynamic performance of medium- and low-speed maglev vehicle–track coupling systems, as well as the dynamic response of the vehicle body and suspension frame under suspension electromagnet failure, is of great significance for the safe operation of maglev tracks. Based on vehicle–track coupling [...] Read more.
The dynamic performance of medium- and low-speed maglev vehicle–track coupling systems, as well as the dynamic response of the vehicle body and suspension frame under suspension electromagnet failure, is of great significance for the safe operation of maglev tracks. Based on vehicle–track coupling dynamics theory, and considering the spatial dynamic magnetic rail relationship in combination with the suspension control system, a dynamic vehicle–track model incorporating suspension electromagnet failure is established. The effect of such failures on electromagnet suspension force and overall vehicle performance are analyzed. The results indicate that the theoretically calculated electromagnetic force differs significantly from the actual force. Under four electromagnet operating conditions, lateral displacement has the greatest influence on suspension force. By considering the magnetic saturation of ferromagnetic materials and the leakage effect of suspension gaps, a spatial dynamic magnetic orbit relationship is established. A single-pole suspension electromagnet fault has little effect on overall vehicle performance. When the suspension electromagnet on one side fails, the suspension frame tilts toward that side and is supported and operated by a sled. When three suspension points fail, the entire suspension frame loses its suspension state and operates fully under sled support. When a suspension frame electromagnet becomes stuck, severe fluctuations in suspension force and vehicle vibration acceleration occur. These fluctuations increase with vehicle operating speed, seriously endangering operational performance. The findings provide a fundamental theoretical basis for the safe operation and maintenance of medium- and low-speed maglev vehicles under fault conditions. Full article
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20 pages, 4655 KB  
Article
Experimental Characterization and Non-Linear Dynamic Modelling of PCD Bearings: A Digital-Twin Approach for the Condition Monitoring of Rotating Machinery
by Alessio Cascino, Andrea Amedei, Enrico Meli and Andrea Rindi
Sensors 2026, 26(8), 2545; https://doi.org/10.3390/s26082545 - 20 Apr 2026
Cited by 1 | Viewed by 692
Abstract
This study proposes a comprehensive methodology for the experimental characterization and non-linear dynamic modelling of Polycrystalline Diamond (PCD) bearings, establishing a high-fidelity digital twin approach for the condition monitoring of rotating machinery. The research addresses complex rotor–stator interactions through the development of a [...] Read more.
This study proposes a comprehensive methodology for the experimental characterization and non-linear dynamic modelling of Polycrystalline Diamond (PCD) bearings, establishing a high-fidelity digital twin approach for the condition monitoring of rotating machinery. The research addresses complex rotor–stator interactions through the development of a multibody numerical framework. A structural 1D Finite Element (FE) model of the stator assembly was first calibrated via experimental modal analysis, achieving a high correlation with the first four bending modes and a maximum frequency discrepancy of only 1.4%. This validated structure was integrated into a non-linear multibody environment to simulate transient rub-impact events at rotational speeds up to 5500 rpm across varying clearance configurations. The model successfully captures the transition from stable periodic orbital motion to the stochastic and chaotic regimes observed in high-clearance setups. Frequency-domain validation further confirms the model’s accuracy in identifying supersynchronous harmonics and energy distribution patterns. Quantitative analysis shows that high-clearance configurations generate impact forces exceeding 6000 N, providing critical data for structural health assessment. These results demonstrate that the proposed digital twin serves as a robust physical foundation for diagnostic systems, enabling the identification of contact-induced vibrational signatures that are essential for training prognostic algorithms. This approach facilitates the autonomous monitoring of critical rotating machinery in demanding industrial and subsea applications, supporting the transition toward active balancing and model-based vibration control strategies. Full article
(This article belongs to the Special Issue Robust Measurement and Control Under Noise and Vibrations)
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20 pages, 4257 KB  
Article
Infrared Small Target Detection Method Fusing Accurate Registration and Weighted Difference
by Quan Liang, Teng Wang, Kefang Wang, Lixing Zhao, Xiaoyan Li and Fansheng Chen
Sensors 2026, 26(8), 2406; https://doi.org/10.3390/s26082406 - 14 Apr 2026
Viewed by 523
Abstract
Low-orbit thermal infrared bidirectional whisk-broom imaging offers wide-swath coverage and high spatial resolution for monitoring moving targets such as aircraft, but large scan angles and terrain undulation cause non-rigid geometric distortion and radiometric inconsistency between forward and backward scans. These effects generate strong [...] Read more.
Low-orbit thermal infrared bidirectional whisk-broom imaging offers wide-swath coverage and high spatial resolution for monitoring moving targets such as aircraft, but large scan angles and terrain undulation cause non-rigid geometric distortion and radiometric inconsistency between forward and backward scans. These effects generate strong clutter in difference images and degrade small and weak target detection. To address this problem, we propose an infrared small target detection method that fuses accurate registration and weighted difference. First, we propose a hybrid multi-scale registration algorithm that achieves coarse affine registration through sparse feature–point matching and then iteratively corrects nonlinear deformations by integrating a global grayscale-driven force with a local sparse-feature-guided force, yielding a registration error of 0.3281 pixels. On this basis, a multi-scale weighted convolutional morphological difference algorithm is proposed. A novel dual-structure hollow top-hat transform is constructed to accurately estimate the background, and a multi-directional convolution mechanism is introduced to effectively suppress anisotropic edge clutter and enhance target saliency. Experiments on SDGSAT-1 thermal infrared bidirectional whisk-broom data show an SCRG of 18.27, and a detection rate of 91.2% when the false alarm rate is below 0.15%. The method outperforms representative competing algorithms and provides a useful reference for space-based aerial moving target detection. Full article
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13 pages, 476 KB  
Article
Albedo-Induced Perturbation in the Sitnikov Three-Body Problem
by M. Shahbaz Ullah, M. Javed Idrisi and Sergey Ershkov
Physics 2026, 8(2), 41; https://doi.org/10.3390/physics8020041 - 13 Apr 2026
Viewed by 613
Abstract
In this paper, the circular Sitnikov three-body problem is studied under the combined influence of radiation pressure and albedo. The model consists of two equal-mass primaries moving in circular orbits about their center of mass and an infinitesimal body constrained to oscillate along [...] Read more.
In this paper, the circular Sitnikov three-body problem is studied under the combined influence of radiation pressure and albedo. The model consists of two equal-mass primaries moving in circular orbits about their center of mass and an infinitesimal body constrained to oscillate along the perpendicular axis. The radiative emission from one primary and the reflected radiation from the other are incorporated into the effective potential through radiation and reflectivity parameters. Using the Jacobi integral, we determine the energetically admissible region for vertical motion and examine how radiative effects modify the accessible phase space. The study shows that the system admits a single vertical equilibrium point at the origin, which remains linearly stable within the physically admissible parameter range. Radiation and albedo reduce the effective restoring force and increase the oscillation period, producing a measurable rescaling of the physical time without altering the geometrical structure of the phase trajectories. The phase-space dynamics are further explored by means of Poincare (first-return) maps obtained from numerical integration of the nonlinear equation of motion. The resulting invariant curves confirm that the motion remains regular and bounded, while their progressive contraction reflects the reduction in the oscillation amplitude with increasing radiative effects. Overall, the results show that albedo acts as a quantitative modifier of the vertical Sitnikov dynamics by changing the effective potential, the admissible energy domain, and the observable time scale, without generating new qualitative phase-space structures. Full article
(This article belongs to the Section Mathematical Physics and Mathematical Methods)
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30 pages, 7132 KB  
Review
A Review of the Non-Linear Motion Behaviour of Ball Bearing and Methods for Its Multibody Dynamics Analysis
by Jingwei Zhang, Enwen Zhou, Linting Guan, Xiaoyu Gai and Yuan Zhang
Lubricants 2026, 14(4), 165; https://doi.org/10.3390/lubricants14040165 - 11 Apr 2026
Viewed by 486
Abstract
Active magnetic levitation bearings incorporate backup bearings that support the rotor during a breakdown, allowing it to maintain its circular movement despite the loss of magnetic force. This safeguards both the stator of the magnetic levitation bearing and the motor stator from harm. [...] Read more.
Active magnetic levitation bearings incorporate backup bearings that support the rotor during a breakdown, allowing it to maintain its circular movement despite the loss of magnetic force. This safeguards both the stator of the magnetic levitation bearing and the motor stator from harm. Research reveals that ball bearings are susceptible to failure mechanisms, including raceway wear and scoring. The principal cause is the unregulated motion of the rolling parts, which are divided by the cage, once wear manifests, resulting in raceway lag. This leads to significant contact deformation between the rolling elements and the raceway, along with prolonged cumulative impacts between the rolling elements and the cage. Cage-free bearings prevent collisions between the cage and rolling elements; yet, the orbital motion of the rolling elements in these bearings demonstrates a level of independence and randomness relative to traditional caged ball bearings. This presents considerable obstacles to attaining standard orbital motion in cage-free ball bearings. Despite advancements in technology that have largely elucidated the non-linear motion dynamics of ball bearings, several critical hurdles in behavioral characterization persist. This work presents a thorough review of the non-linear motion behavior of ball bearings and the methodologies for their multi-body dynamic characterization. This report proposes future research topics to improve the design of high-performance bearings and augment their reliability. Full article
(This article belongs to the Special Issue Advances in Wear Life Prediction of Bearings)
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39 pages, 7931 KB  
Article
First-Principles Insights into Cr- and Mn-Doped Rocksalt ScN: Engineering Structural Stability and Magnetism
by Ahmad M. Alsaad
Magnetochemistry 2026, 12(4), 47; https://doi.org/10.3390/magnetochemistry12040047 - 7 Apr 2026
Viewed by 946
Abstract
The study presents a comprehensive first-principles investigation of the structural, electronic, and magnetic properties of rocksalt scandium nitride (ScN) and its Cr- and Mn-doped derivatives using spin-polarized density-functional theory within the GGA + U (UCr = 3.5 eV, UMn = 2.7 [...] Read more.
The study presents a comprehensive first-principles investigation of the structural, electronic, and magnetic properties of rocksalt scandium nitride (ScN) and its Cr- and Mn-doped derivatives using spin-polarized density-functional theory within the GGA + U (UCr = 3.5 eV, UMn = 2.7 eV) and HSE06 frameworks. Pristine ScN crystallizes in the cubic Fm3m structure and exhibits narrow-gap semiconducting behavior, with an indirect band gap of 0.82 eV obtained from hybrid-functional calculations, in excellent agreement with reported theoretical values. Substitutional doping with Cr and Mn introduces localized 3d states near the Fermi level, driving a transition toward spin-polarized metallic or half-metallic behavior accompanied by robust ferromagnetism. Density-of-states and band-structure analyses reveal that magnetism and charge transport in the doped systems are dominated by exchange-split transition-metal 3d states hybridized with N-2p orbitals. Total energy calculations confirm ferromagnetic ground states for both Cr- and Mn-doped ScN, with Mn substitution yielding stronger exchange stabilization and higher magnetic moments. Magnetocrystalline anisotropy energies, evaluated using the force-theorem approach, are found to be negligibly small, indicating weak anisotropy consistent with the moderate spin–orbit coupling strength in ScN-based nitrides. Nevertheless, symmetry breaking around dopant sites gives rise to a finite Dzyaloshinskii–Moriya interaction, leading to weak spin canting and non-collinear magnetic tendencies. The interplay between magnetic exchange coupling, spin–orbit interaction, and local inversion symmetry breaking positions of Cr- and Mn-doped ScN as promising dilute magnetic semiconductors with tunable spin polarization and chiral magnetic interactions, offering a viable platform for nitride-based spintronic and magneto-electronic applications. Full article
(This article belongs to the Section Magnetic Materials)
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