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Search Results (5,120)

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Keywords = Singularity

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21 pages, 5199 KB  
Article
Real-Time Trajectory Replanning and Tracking Control of Cable-Driven Continuum Robots in Uncertain Environments
by Yanan Qin and Qi Chen
Actuators 2026, 15(2), 83; https://doi.org/10.3390/act15020083 (registering DOI) - 1 Feb 2026
Abstract
To address trajectory tracking of cable-driven continuum robots (CDCRs) in the presence of obstacles, this paper proposes an integrated control framework that combines online trajectory replanning, obstacle avoidance, and tracking control. The control system consists of two modules. The first is a trajectory [...] Read more.
To address trajectory tracking of cable-driven continuum robots (CDCRs) in the presence of obstacles, this paper proposes an integrated control framework that combines online trajectory replanning, obstacle avoidance, and tracking control. The control system consists of two modules. The first is a trajectory replanning controller developed on an improved model predictive control (IMPC) framework. The second is a trajectory-tracking controller that integrates an adaptive disturbance observer with a fast non-singular terminal sliding mode control (ADO-FNTSMC) strategy. The IMPC trajectory replanning controller updates the trajectory of the CDCRs to avoid collisions with obstacles. In the ADO-FNTSMC strategy, the adaptive disturbance observer (ADO) compensates for uncertain dynamic factors, including parametric uncertainties, unmodeled dynamics, and external disturbances, thereby enhancing the system’s robustness and improving trajectory tracking accuracy. Meanwhile, the fast non-singular terminal sliding mode control (FNTSMC) guarantees fast, stable, and accurate trajectory tracking. The average tracking errors for IMPC-ADO-FNTSMC, MPC-FNTSMC, and MPC-SMC are 1.185 cm, 1.540 cm, and 1.855 cm, with corresponding standard deviations of 0.035 cm, 0.057 cm, and 0.078 cm in the experimental results. Compared with MPC-FNTSMC and MPC-SMC, the IMPC-ADO-FNTSMC controller reduces average tracking errors by 29.96% and 56.54%. Simulation and experimental results demonstrate that the designed two-module controller (IMPC-ADO-FNTSMC) achieves fast, stable, and accurate trajectory tracking in the presence of obstacles and uncertain dynamic conditions. Full article
(This article belongs to the Section Control Systems)
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22 pages, 1401 KB  
Article
Deep Learning-Enhanced Hybrid Beamforming Design with Regularized SVD Under Imperfect Channel Information
by S. Pourmohammad Azizi, Amirhossein Nafei, Shu-Chuan Chen and Rong-Ho Lin
Mathematics 2026, 14(3), 509; https://doi.org/10.3390/math14030509 (registering DOI) - 31 Jan 2026
Abstract
We propose a low-complexity hybrid beamforming method for massive Multiple-Input Multiple-Output (MIMO) systems that is robust to Channel State Information (CSI) estimation errors. These errors stem from hardware impairments, pilot contamination, limited training, and fast fading, causing spectral-efficiency loss. However, existing hybrid beamforming [...] Read more.
We propose a low-complexity hybrid beamforming method for massive Multiple-Input Multiple-Output (MIMO) systems that is robust to Channel State Information (CSI) estimation errors. These errors stem from hardware impairments, pilot contamination, limited training, and fast fading, causing spectral-efficiency loss. However, existing hybrid beamforming solutions typically either assume near-perfect CSI or rely on greedy/black-box designs without an explicit mechanism to regularize the error-distorted singular modes, leaving a gap in unified, low-complexity, and theoretically grounded robustness. We unfold the Alternating Direction Method of Multipliers (ADMM) into a trainable Deep Learning (DL) network, termed DL-ADMM, to jointly optimize Radio-Frequency (RF) and baseband precoders and combiners. In DL-ADMM, the ADMM update mappings are learned (layer-wise parameters and projections) to amortize the joint RF/baseband optimization, whereas Regularized Singular Value Decomposition (RSVD) acts as an analytical regularizer that reshapes the observed channel’s singular values to suppress noise amplification under imperfect CSI. RSVD is integrated to stabilize singular modes and curb noise amplification, yielding a unified and scalable design. For σe2=0.1, the proposed DL-ADMM-Reg achieves approximately 8–11 bits/s/Hz higher spectral efficiency than Orthogonal Matching Pursuit (OMP) at Signal-to-Noise Ratio (SNR) =20–40 dB, while remaining within <1 bit/s/Hz of the digital-optimal benchmark across both (Nt,Nr)=(32,32) and (64,64) settings. Simulations confirm higher spectral efficiency and robustness than OMP and Adaptive Phase Shifters (APSs). Full article
(This article belongs to the Special Issue Computational Methods in Wireless Communications with Applications)
27 pages, 5529 KB  
Essay
The Meaning of “Big Bang”
by Emilio Elizalde
Galaxies 2026, 14(1), 8; https://doi.org/10.3390/galaxies14010008 - 30 Jan 2026
Viewed by 32
Abstract
What does “Big Bang” mean? What was the actual origin of these two words? There are many aspects hidden under this name, which are seldom explained. They are discussed here. To frame the analysis, help will be sought from the highly authoritative voices [...] Read more.
What does “Big Bang” mean? What was the actual origin of these two words? There are many aspects hidden under this name, which are seldom explained. They are discussed here. To frame the analysis, help will be sought from the highly authoritative voices of two exceptional writers: William Shakespeare and Umberto Eco. Both have explored the tension existing between words and the realities they name. And this includes names given to outstanding theorems and spectacular discoveries, too. Stigler’s law of eponymy is recalled in this context. These points will be at the heart of the quest here, concerning the concept of “Big Bang”, which only a few people know what it means, actually. Fred Hoyle was the first to pronounce these words, in a BBC radio program, with a meaning that was later called inflation. But listeners were left with the image he was trying to destroy: the explosion of Lemaître’s primeval atom (an absolutely wrong concept). Hoyle’s Steady State will be carefully compared with inflation cosmology. They are quite different, and yet, in both cases, the possibility of creating matter/energy out of expanding space is rooted in the same fundamental principles: those of General Relativity. As is also, the possibility of having a universe with zero total energy, anticipated by R.C. Tolman, in 1934 already. It will be shown, how to obtain accelerated expansion from negative pressure; how to reconcile energy conservation with matter creation in an expanding universe; and a curious relation between de Sitter spacetime and Steady State cosmology. Concerning the naming issue, it will be remarked that, today, the same label “Big Bang” is used in very different contexts: (a) the Big Bang Singularity; (b) as the equivalent of cosmic inflation; (c) speaking of the Big Bang cosmological model; (d) to name a very popular TV program; and more. Full article
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28 pages, 6880 KB  
Article
Non-Appearance-Based Discrimination of UAVs and Birds in Optical Remote Sensing: Using Kinematic and Time–Frequency Features
by Yifei Yao, Jiazhou Geng, Guiting Chen, Tao Lei, Lvjiyuan Jiang and Yi Cui
Drones 2026, 10(2), 98; https://doi.org/10.3390/drones10020098 - 29 Jan 2026
Viewed by 74
Abstract
Unmanned aerial vehicles (UAVs) and birds are typical low-altitude small targets in optical remote sensing, often occupying only a few pixels and exhibiting highly similar appearances, which limits the effectiveness of appearance-based discrimination at long distances and low resolutions. To overcome this, we [...] Read more.
Unmanned aerial vehicles (UAVs) and birds are typical low-altitude small targets in optical remote sensing, often occupying only a few pixels and exhibiting highly similar appearances, which limits the effectiveness of appearance-based discrimination at long distances and low resolutions. To overcome this, we propose a non-appearance-based classification framework using kinematic and time–frequency features. At the trajectory level, kinematic features—including the coefficient of variation of velocity and acceleration, the Spatiotemporal Box-counting Fractal Dimension (SBFD), and the Local Higuchi Fractal Dimension (LHFD)—quantify multi-scale trajectory complexity. At the scale-variation level, time–frequency features, specifically the Time-Frequency Aware Singular Value Entropy (TF-SVE) derived from bounding-box area sequences, capture non-stationary oscillations from bird wing flapping, reflecting behavioral differences from rigid UAV motion. Experiments on a complex real-world dataset show that stacking these features achieves 99.47% classification accuracy, demonstrating a robust, resolution-invariant, and practically effective approach for non-appearance-based recognition of low-altitude targets. Full article
33 pages, 6290 KB  
Article
Empirical Research and Optimization Strategies for the Retrofitting and Renewal of Existing Super High-Rise Buildings from the Perspective of Urbanity
by Huiqiong Tian, Zhendong Wang and Cheng Liu
Buildings 2026, 16(3), 561; https://doi.org/10.3390/buildings16030561 - 29 Jan 2026
Viewed by 58
Abstract
As a dominant typology of urban development and a critical component of public infrastructure, super high-rise buildings have transitioned from a speed-driven expansion model to one that emphasizes a balanced approach between development pace and quality. Within the context of urban stock renewal, [...] Read more.
As a dominant typology of urban development and a critical component of public infrastructure, super high-rise buildings have transitioned from a speed-driven expansion model to one that emphasizes a balanced approach between development pace and quality. Within the context of urban stock renewal, numerous super high-rise buildings now face pressing needs for retrofitting to enhance their sustainability and urban integration. This study establishes “urbanity”—defined as the capacity of the built environment to foster vibrant, inclusive, and sustainable urban life—as a core evaluation criterion for assessing the retrofitting and renewal of super high-rise buildings. Based on a comprehensive literature review and field investigations, 21 representative indicators were identified, and the key factors influencing the upgrading of such buildings were determined. Subsequently, 20 super high-rise buildings in Shanghai were selected as case studies, and their urbanity performance was assessed using a fuzzy comprehensive evaluation model (FCEM). The findings reveal common challenges, including architectural homogenization, functional singularity, limited vitality in near-ground spaces, weak integration with surrounding infrastructure, and inefficient utilization of urban landscape resources. Furthermore, the study analyzes urbanity-oriented enhancement strategies implemented in the selected cases and proposes targeted improvement measures across five key dimensions: building morphology, functional configuration, near-ground space, infrastructure, and urban landscape. The research contributes to the body of knowledge on sustainable urban regeneration by providing a practical evaluation framework and actionable strategies for retrofitting super high-rise buildings. The findings aim to support more livable, inclusive, and resilient urban environments, with implications for both Chinese and global cities facing similar challenges in high-density urban contexts. Full article
(This article belongs to the Section Architectural Design, Urban Science, and Real Estate)
26 pages, 5834 KB  
Article
Research and Implementation of Localization of Multiple Local Discharge Sources in Switchgear Based on Ultrasound
by Dijian Xu, Yao Huang, Apurba Deb Mitra, Simon X. Yang, Ping Li, Mengqiu Xiao, Longbo Su and Lepeng Song
Sensors 2026, 26(3), 884; https://doi.org/10.3390/s26030884 - 29 Jan 2026
Viewed by 89
Abstract
At present, most of the switchgear partial discharge detection means are offline detection and cannot monitor multiple partial discharge sources online at the same time. Based on this, this paper investigates the application of ultrasonic technology in localized discharge fault localization in high-voltage [...] Read more.
At present, most of the switchgear partial discharge detection means are offline detection and cannot monitor multiple partial discharge sources online at the same time. Based on this, this paper investigates the application of ultrasonic technology in localized discharge fault localization in high-voltage switchgear, removes the background noise of localized discharge in switchgear by using soft and hard filtering; proposes a generalized cubic correlation algorithm on the basis of TODA, improves the accuracy of the time difference acquisition in the case of low signal-to-noise ratio; determines the number of multiple localized discharging power sources by using the single-channel signal blind source separation technique and singularity spectral analysis; and determines the number of multiple localized discharging power sources by using independent component analysis to separate them. As well as for the problem that TDOA cannot be directly applied to the localization of multiple partial discharge sources, independent component analysis is used to separate the mixed signals, and the disordered coordinate selection method is proposed to determine the coordinates of multiple partial discharge sources. The experimental results show that (1) the noise reduction method is able to remove the excess interference while preserving the localized discharge signals; (2) the improved generalized cubic inter-correlation algorithm is more resistant to interference and has less error than other time delay estimation algorithms. The localization error is reduced by 60 mm~68 mm compared to the basic correlation algorithm, 41 mm~47 mm compared to the twice correlation algorithm, and 17 mm~20 mm compared to the three times correlation algorithm, which is a big improvement compared to the pre-improved algorithm. (3) It is able to locate the multiple localized power sources, and the accuracy of the number of localized power sources reaches 88%. Full article
(This article belongs to the Section Physical Sensors)
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7 pages, 235 KB  
Article
Singular Equivalences and ϕ-Dimensions
by Jinrui Yang and Yongyun Qin
Axioms 2026, 15(2), 96; https://doi.org/10.3390/axioms15020096 - 28 Jan 2026
Viewed by 73
Abstract
The ϕ-dimension of an algebra is a homological invariant arising from the Igusa–Todorov function. In this paper, we establish a new bound on the ϕ-dimensions of two algebras related by singular equivalences of the Morita-type with level. Full article
(This article belongs to the Special Issue Advances in Representation Theory of Algebras)
29 pages, 1928 KB  
Article
Denoising Stock Price Time Series with Singular Spectrum Analysis for Enhanced Deep Learning Forecasting
by Carol Anne Hargreaves and Zixian Fan
Analytics 2026, 5(1), 9; https://doi.org/10.3390/analytics5010009 - 27 Jan 2026
Viewed by 201
Abstract
Aim: Stock price prediction remains a highly challenging task due to the complex and nonlinear nature of financial time series data. While deep learning (DL) has shown promise in capturing these nonlinear patterns, its effectiveness is often hindered by the low signal-to-noise ratio [...] Read more.
Aim: Stock price prediction remains a highly challenging task due to the complex and nonlinear nature of financial time series data. While deep learning (DL) has shown promise in capturing these nonlinear patterns, its effectiveness is often hindered by the low signal-to-noise ratio inherent in market data. This study aims to enhance the stock predictive performance and trading outcomes by integrating Singular Spectrum Analysis (SSA) with deep learning models for stock price forecasting and strategy development on the Australian Securities Exchange (ASX)50 index. Method: The proposed framework begins by applying SSA to decompose raw stock price time series into interpretable components, effectively isolating meaningful trends and eliminating noise. The denoised sequences are then used to train a suite of deep learning architectures, including Convolutional Neural Networks (CNN), Long Short-Term Memory (LSTM), and hybrid CNN-LSTM models. These models are evaluated based on their forecasting accuracy and the profitability of the trading strategies derived from their predictions. Results: Experimental results demonstrated that the SSA-DL framework significantly improved the prediction accuracy and trading performance compared to baseline DL models trained on raw data. The best-performing model, SSA-CNN-LSTM, achieved a Sharpe Ratio of 1.88 and a return on investment (ROI) of 67%, indicating robust risk-adjusted returns and effective exploitation of the underlying market conditions. Conclusions: The integration of Singular Spectrum Analysis with deep learning offers a powerful approach to stock price prediction in noisy financial environments. By denoising input data prior to model training, the SSA-DL framework enhanced signal clarity, improved forecast reliability, and enabled the construction of profitable trading strategies. These findings suggested a strong potential for SSA-based preprocessing in financial time series modeling. Full article
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22 pages, 1147 KB  
Article
Frictional Contact of Functionally Graded Piezoelectric Materials with Arbitrarily Varying Properties
by Xiuli Liu, Kaiwen Xiao, Changyao Zhang, Xinyu Zhou, Lingfeng Gao and Jing Liu
Mathematics 2026, 14(3), 450; https://doi.org/10.3390/math14030450 - 27 Jan 2026
Viewed by 74
Abstract
This study investigates the two-dimensional (2D) steady-state frictional contact behavior of functionally graded piezoelectric material (FGPM) coatings under a high-speed rigid cylindrical punch. An electromechanical coupled contact model considering inertial effects is established, while a layered model is employed to simulate arbitrarily varying [...] Read more.
This study investigates the two-dimensional (2D) steady-state frictional contact behavior of functionally graded piezoelectric material (FGPM) coatings under a high-speed rigid cylindrical punch. An electromechanical coupled contact model considering inertial effects is established, while a layered model is employed to simulate arbitrarily varying material parameters. Based on piezoelectric elasticity theory, the steady-state governing equations for the coupled system are derived. By utilizing the transfer matrix method and the Fourier integral transform, the boundary value problem is converted into a system of coupled Cauchy singular integral equations of the first and second kinds in the frequency domain. These equations are solved semi-analytically, using the least squares method combined with an iterative algorithm. Taking a power-law gradient distribution as a case study, the effects of the gradient index, relative sliding speed, and friction coefficient on the contact pressure, in-plane stress, and electric displacement are systematically analyzed. Furthermore, the contact responses of FGPM coatings with power-law, exponential, and sinusoidal gradient profiles are compared. The findings provide a theoretical foundation for the optimal design of FGPM coatings and for enhancing their operational reliability under high-speed service conditions. Full article
23 pages, 4514 KB  
Article
Fitness-for-Service Analysis of the Interplay Between a Quarter-Circle Corner Crack and a Parallel Semi-Elliptical Surface Crack in a Semi-Infinite Solid Subjected to In-Plane Bending Part II—The Effect on the Semi-Elliptical Surface Crack
by Mordechai Perl, Cesar Levy and Qin Ma
Appl. Sci. 2026, 16(3), 1240; https://doi.org/10.3390/app16031240 - 26 Jan 2026
Viewed by 111
Abstract
The impact of a quarter-circle corner crack on an adjacent parallel semi-elliptical surface crack (SESC) located in a semi-infinite solid subjected to in-plane bending is studied using a 3-D finite element analysis. The stress intensity factor (SIF) distributions along the front of the [...] Read more.
The impact of a quarter-circle corner crack on an adjacent parallel semi-elliptical surface crack (SESC) located in a semi-infinite solid subjected to in-plane bending is studied using a 3-D finite element analysis. The stress intensity factor (SIF) distributions along the front of the SESC are evaluated to determine said impact. The SESC’s semi-major axis ranged from a1 = 10 mm to 30 mm with ellipticities of b1/a1 varying from 0.1 to 1.0 for a constant quarter-circle corner crack length of a2 = 15 mm. Furthermore, several crack configurations are considered where the normalized vertical and horizontal gaps between the two cracks are taken to be H/a2 = 0.4 and 1.2 and S/a2 = −0.5 and 1.0, respectively. The results show that the effect of the quarter-circle corner crack on the SESC can be considerable both in amplifying and in attenuating the SIFs along the semi-elliptical surface crack front. Moreover, these opposite effects can occur simultaneously, but in different sections of the SESC’s crack front. The magnitude and pattern of these effects depend on the length and ellipticity of the SESC. It is further concluded that when considering the fitness-for-service of a critical real mechanical component, a complete 3-D analysis is needed to provide a reliable solution for such crack configurations. Full article
(This article belongs to the Special Issue Fatigue and Fracture Behavior of Engineering Materials)
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13 pages, 3626 KB  
Article
Hypromellose Acetate Succinates as a Single Mebeverine Hydrochloride Release-Modifying Excipient for Fused Deposition Modeling
by Mateusz Kurek, Margarida Berardo Lopes Nunes, Witold Jamróz, Justyna Knapik-Kowalczuk, Marian Paluch and Aleksander Mendyk
Appl. Sci. 2026, 16(3), 1237; https://doi.org/10.3390/app16031237 - 26 Jan 2026
Viewed by 106
Abstract
Background: Three-dimensional (3D) printing has been established in pharmaceutical sciences for preparing customized dosage forms with intricate release profiles. However, realizing this potential requires complex design strategies and the careful use of various excipients. This study was designed to evaluate the utility of [...] Read more.
Background: Three-dimensional (3D) printing has been established in pharmaceutical sciences for preparing customized dosage forms with intricate release profiles. However, realizing this potential requires complex design strategies and the careful use of various excipients. This study was designed to evaluate the utility of hypromellose acetate succinate (HPMC-AS) as a singular release-modifying excipient for manufacturing oral solid dosage forms via fused deposition modeling (FDM) 3D printing. Methods: The scope of work encompassed comprehensive material characterization, formulation and production of drug-loaded filaments using hot-melt extrusion (HME), subsequent FDM 3D printing of tablet geometries, and in vitro dissolution studies using mebeverine hydrochloride (MebH) as the model drug. Results: Initial HME processing indicated that the HPMC-AS-based filaments were brittle, presenting technical challenges for direct 3D printing. This issue was successfully overcome by incorporating an additional preheating stage into the FDM printing process, which enabled production of the tablets. Dissolution analysis demonstrated that the 3D-printed mebeverine hydrochloride tablets exhibited delayed and sustained-release characteristics. Conclusions: These results confirm the viability of HPMC-AS as a standalone functional excipient in FDM 3D printing to produce tailored, complex drug delivery systems. Full article
(This article belongs to the Special Issue Contemporary Pharmacy: Advances and Challenges)
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36 pages, 1564 KB  
Article
Transformer-Based Multi-Source Transfer Learning for Intrusion Detection Models with Privacy and Efficiency Balance
by Baoqiu Yang, Guoyin Zhang and Kunpeng Wang
Entropy 2026, 28(2), 136; https://doi.org/10.3390/e28020136 - 24 Jan 2026
Viewed by 292
Abstract
The current intrusion detection methods suffer from deficiencies in terms of cross-domain adaptability, privacy preservation, and limited effectiveness in detecting minority-class attacks. To address these issues, a novel intrusion detection model framework, TrMulS, is proposed that integrates federated learning, generative adversarial networks with [...] Read more.
The current intrusion detection methods suffer from deficiencies in terms of cross-domain adaptability, privacy preservation, and limited effectiveness in detecting minority-class attacks. To address these issues, a novel intrusion detection model framework, TrMulS, is proposed that integrates federated learning, generative adversarial networks with multispace feature enhancement ability, and transformers with multi-source transfer ability. First, at each institution (source domain), local spatial features are extracted through a CNN, multiple subsets are constructed (to solve the feature singularity problem), and the multihead self-attention mechanism of the transformer is utilized to capture the correlation of features. Second, the synthetic samples of the target domain are generated on the basis of the improved Exchange-GAN, and the cross-domain transfer module is designed by combining the Maximum Mean Discrepancy (MMD) to minimize the feature distribution difference between the source domain and the target domain. Finally, the federated transfer learning strategy is adopted. The model parameters of each local institution are encrypted and uploaded to the target server and then aggregated to generate the global model. These steps iterate until convergence, yielding the globally optimal model. Experiments on the ISCX2012, KDD99 and NSL-KDD intrusion detection standard datasets show that the detection accuracy of this method is significantly improved in cross-domain scenarios. This paper presents a novel paradigm for cross-domain security intelligence analysis that considers efficiency, privacy and balance. Full article
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18 pages, 412 KB  
Review
Singularities and Universals: Case Reports, Clinical Trials, and an Enduring Epistemic Tension
by Carlo Galli and Marco Meleti
Histories 2026, 6(1), 11; https://doi.org/10.3390/histories6010011 - 24 Jan 2026
Viewed by 176
Abstract
This manuscript examines how distinct epistemic attitudes toward singularity and generality have been articulated in medical writing across different historical contexts, offering a conceptual and meta-historical analysis of two enduring genres in biomedical literature: the individualized case report and the systematically aggregated clinical [...] Read more.
This manuscript examines how distinct epistemic attitudes toward singularity and generality have been articulated in medical writing across different historical contexts, offering a conceptual and meta-historical analysis of two enduring genres in biomedical literature: the individualized case report and the systematically aggregated clinical trial. Hippocratic case narratives are considered as a particularly lucid articulation of a mode of inquiry that privileges detailed observation of individual patients, while medieval Aristotelian natural philosophy exemplifies a contrasting emphasis on regularity, intelligibility, and general explanation. Renaissance medical and philosophical traditions are treated as a mediating moment in which attention to anomaly, wonder, and singularity was explicitly re-legitimized within learned medicine. These historically situated articulations are not presented as stages in a progressive narrative, but as recurrent epistemic orientations that are repeatedly reconfigured under different theoretical, institutional, and technological conditions. The paper argues that the tension between attention to exceptional cases and the pursuit of generalizable knowledge continues to structure modern biomedical writing, where case reports remain essential for identifying rare, novel, or anomalous phenomena, while clinical trials formalize strategies for producing reproducible, population-level evidence. Full article
14 pages, 7232 KB  
Article
Localized Induction Heating for Crack Healing of AISI 1020 Steel
by Aprilia Aprilia, Zixuan Ling, Vincent Gill, Nicholas Chia, Martyn A. Jones, Paul E. Williams and Wei Zhou
Materials 2026, 19(3), 451; https://doi.org/10.3390/ma19030451 - 23 Jan 2026
Viewed by 214
Abstract
This study investigates crack healing of AISI 1020 steel using localized induction heating with a pancake coil. A wire-cut slit sample and a repetitive-bent sample containing fine cracks were subjected to induction heating. Geometrical changes in the slit and cracks before and after [...] Read more.
This study investigates crack healing of AISI 1020 steel using localized induction heating with a pancake coil. A wire-cut slit sample and a repetitive-bent sample containing fine cracks were subjected to induction heating. Geometrical changes in the slit and cracks before and after heating were evaluated. Healing of fine cracks and local melting of the slit tip were observed. Numerical simulations were conducted to understand the current flow, current density distribution and Joule heating behavior within the samples. Results showed that current detours around cracks and concentrates at crack tips during induction heating. This enables the ability of induction heating to selectively locate and treat cracks effectively. Localized induction heating using a pancake coil enhances the crack-healing effectiveness by providing a non-singular current flow direction within the material. It also offers the flexibility to treat a specific localized region in a component. While localized induction heating demonstrates strong potential for crack-healing applications, its effectiveness is primarily limited to fine surface cracks. Full article
(This article belongs to the Section Metals and Alloys)
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11 pages, 4878 KB  
Technical Note
NBODYCL: A Program to Generate Regularized Classical Trajectories for the n–Body Coulomb Problem
by Mbuso K. Matfunjwa, Harindranath B. Ambalampitiya and Ilya I. Fabrikant
Atoms 2026, 14(2), 8; https://doi.org/10.3390/atoms14020008 - 23 Jan 2026
Viewed by 385
Abstract
A program package for calculating regularized classical trajectories for Coulomb n–body problem is developed. The Coulomb singularities from the equations of motion are removed by transformations of variables including the time. This effectively conserves the energy of the time-independent systems to a [...] Read more.
A program package for calculating regularized classical trajectories for Coulomb n–body problem is developed. The Coulomb singularities from the equations of motion are removed by transformations of variables including the time. This effectively conserves the energy of the time-independent systems to a high accuracy for long time propagation. Sample calculations are shown for the cases of 2, 3, 4, and 5 particle systems giving comparisons with the un-regularized trajectories. The program can be used for general purposes including the classical-trajectory Monte-Carlo simulations for charged-particle collisions in free or laser environments. Full article
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