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21 pages, 6078 KB  
Article
Integrating Microstructures and Dual Constitutive Models in Instrumented Indentation Technique for Mechanical Properties Evaluation of Metallic Materials
by Yubiao Zhang, Bin Wang, Yonggang Zhang, Shuai Wang, Shun Zhang and He Xue
Materials 2025, 18(17), 4159; https://doi.org/10.3390/ma18174159 - 4 Sep 2025
Abstract
Local variations in mechanical properties are commonly observed in engineering structures, driven by complex manufacturing histories and harsh service environments. The evaluation of mechanical properties accurately constitutes a fundamental requirement for structural integrity assessment. The Instrumented Indentation Technique (IIT) can play a critical [...] Read more.
Local variations in mechanical properties are commonly observed in engineering structures, driven by complex manufacturing histories and harsh service environments. The evaluation of mechanical properties accurately constitutes a fundamental requirement for structural integrity assessment. The Instrumented Indentation Technique (IIT) can play a critical role in the in-site testing of local properties. However, it could be often a challenge to correlate indentation characteristics with uniaxial stress–strain relationships. In this study, we investigated quantitatively the connection between the indentation responses of commonly used metals and their plastic properties using the finite element inversion method. Materials typically exhibit plastic deformation mechanisms characterized by either linear or power-law hardening behaviors. Consequently, conventional prediction methods based on a single constitutive model may no longer be universally applicable. Hence, this study developed methods for acquiring mechanical properties suitable for either the power-law and linear hardening model, or combined, respectively, based on analyses of microstructures of materials exhibiting different hardening behaviors. We proposed a novel integrated IIT incorporating microstructures and material-specific constitutive models. Moreover, the inter-dependency between microstructural evolution and hardening behaviors was systematically investigated. The proposed method was validated on representative engineering steels, including austenitic stainless steel, structural steel, and low-alloy steel. The predicted deviations in yield strength and strain hardening exponent are broadly within 10%, with the maximum error at 12%. This study is expected to provide a fundamental framework for the advancement of IIT and structural integrity assessment. Full article
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21 pages, 1696 KB  
Article
Residual Stress Estimation in Structures Composed of One-Dimensional Elements via Total Potential Energy Minimization Using Evolutionary Algorithms
by Fatih Uzun and Alexander M. Korsunsky
J. Manuf. Mater. Process. 2025, 9(9), 292; https://doi.org/10.3390/jmmp9090292 - 28 Aug 2025
Viewed by 458
Abstract
This study introduces a novel energy-based inverse method for estimating residual stresses in structures composed of one-dimensional elements undergoing elastic–plastic deformation. The problem is reformulated as a global optimization task governed by the principle of minimum total potential energy. Rather than solving equilibrium [...] Read more.
This study introduces a novel energy-based inverse method for estimating residual stresses in structures composed of one-dimensional elements undergoing elastic–plastic deformation. The problem is reformulated as a global optimization task governed by the principle of minimum total potential energy. Rather than solving equilibrium equations directly, the internal stress distribution is inferred by minimizing the structure’s total potential energy using a real-coded genetic algorithm. This approach avoids gradient-based solvers, matrix assembly, and incremental loading, making it suitable for nonlinear and history-dependent systems. Plastic deformation is encoded through element-wise stress-free lengths, and a dynamic fitness exponent strategy adaptively controls selection pressure during the evolutionary process. The method is validated on single- and multi-bar truss structures under axial tensile loading, using a bilinear elastoplastic material model. The results are benchmarked against nonlinear finite element simulations and analytical calculations, demonstrating excellent predictive capability with stress errors typically below 1%. In multi-material systems, the technique accurately reconstructs tensile and compressive residual stresses arising from elastic–plastic mismatch using only post-load geometry. These results demonstrate the method’s robustness and accuracy, offering a fully non-incremental, variational alternative to traditional inverse approaches. Its flexibility and computational efficiency make it a promising tool for residual stress estimation in complex structural applications involving plasticity and material heterogeneity. Full article
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23 pages, 6258 KB  
Article
Study on Mine Water Inflow Prediction for the Liangshuijing Coal Mine Based on the Chaos-Autoformer Model
by Jin Ma, Dangliang Wang, Zhixiao Wang, Chenyue Gao, Hu Zhou, Mengke Li, Jin Huang, Yangguang Zhao and Yifu Wang
Water 2025, 17(17), 2545; https://doi.org/10.3390/w17172545 - 27 Aug 2025
Viewed by 391
Abstract
Mine water hazards represent one of the principal threats to safe coal mine operations; therefore, accurately predicting mine water inflow is critical for drainage system design and water hazard mitigation. Because mine water inflow is governed by the combined influence of multiple hydrogeological [...] Read more.
Mine water hazards represent one of the principal threats to safe coal mine operations; therefore, accurately predicting mine water inflow is critical for drainage system design and water hazard mitigation. Because mine water inflow is governed by the combined influence of multiple hydrogeological factors and thus exhibits pronounced non-linear characteristics, conventional approaches are inadequate in terms of forecasting accuracy and medium- to long-term predictive capability. To address this issue, this study proposes a Chaos-Autoformer-based method for predicting mine water inflow. First, the univariate inflow series is mapped into an m-dimensional phase space by means of phase-space reconstruction from chaos theory, thereby fully preserving its non-linear features; the reconstructed vectors are then used to train and forecast inflow with an improved Chaos-Autoformer model. On top of the original Autoformer architecture, the proposed model incorporates a Chaos-Attention mechanism and a Lyap-Dropout scheme, which enhance sensitivity to small perturbations in initial conditions and complex non-linear propagation paths while improving stability in long-horizon forecasting. In addition, the loss function integrates the maximum Lyapunov exponent error and earth mode decomposition (EMD) indices so as to jointly evaluate dynamical consistency and predictive performance. An empirical analysis based on monitoring data from the Liangshuijing Coal Mine for 2022–2025 demonstrates that the trained model delivers high accuracy and stable performance. Ablation experiments further confirm the significant contribution of the chaos-aware components: when these modules are removed, forecasting accuracy declines to only 76.5%. Using the trained model to predict mine water inflow for the period from June 2024 to June 2025 yields a root mean square error (RMSE) of 30.73 m3/h and a coefficient of determination (R2) of 0.895 against observed data, indicating excellent fitting and predictive capability for medium- to long-term tasks. Extending the forecast to July 2025–November 2027 reveals a pronounced annual cyclical pattern in future mine water inflow, with markedly higher inflow in summer than in winter and an overall slowly declining trend. These findings show that the Chaos-Autoformer can achieve high-precision medium- and long-term predictions of mine water inflow, thereby providing technical support for proactive deployment and refined management of mine water hazard prevention. Full article
(This article belongs to the Section Hydrogeology)
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21 pages, 7268 KB  
Article
Effect of Specimen Dimensions and Strain Rate on the Longitudinal Compressive Strength of Chimonobambusa utilis
by Xudan Wang, Meng Zhang, Chunnan Liu, Bo Xu, Wei Li, Yonghong Deng, Yu Zhang, Chunlei Dong and Qingwen Zhang
Materials 2025, 18(17), 4013; https://doi.org/10.3390/ma18174013 - 27 Aug 2025
Viewed by 256
Abstract
The combined influence of specimen size and strain rate on the mechanical behaviour of small-diameter bamboo culms remains insufficiently characterised. This study investigates the longitudinal compressive strength of Chimonobambusa utilis through axial compression tests on specimens measuring 15 × 15 × 5 mm, [...] Read more.
The combined influence of specimen size and strain rate on the mechanical behaviour of small-diameter bamboo culms remains insufficiently characterised. This study investigates the longitudinal compressive strength of Chimonobambusa utilis through axial compression tests on specimens measuring 15 × 15 × 5 mm, 18 × 18 × 6 mm, and 21 × 21 × 7 mm under strain rates of 10−4, 10−3, and 10−2 s−1. Coupling experimental data with theoretical analysis, this study develops a size–strain rate interaction model to quantitatively assess the effects of specimen size and strain rate on the compressive strength of small-diameter bamboo. Increasing specimen size reduced strength and shifted failure modes from shear to buckling and splitting. At a strain rate of 10−4 s−1, strength decreased from 73.35 MPa for the 15 × 15 × 5 mm specimens to 62.84 MPa for the 21 × 21 × 7 mm specimens. Conversely, increasing the strain rate from 10−4 s−1 to 10−2 s−1 for the 15 × 15 × 5 mm specimens increased strength from 73.35 MPa to 80.27 MPa, indicating suppressed crack propagation. The Type II Weibull model exhibited higher predictive accuracy and parameter stability than the Type I variant. Coupling the Type II Weibull function with a power-law strain rate term and an interaction exponent developed a predictive equation, achieving relative errors below 5%. The findings demonstrate that specimen size predominantly governs strength, whereas strain rate exerts a secondary but enhancing influence. The proposed coupling model enables reliable axial load prediction for small-diameter bamboo culms, supporting material selection and dimensional optimisation in structural applications. Full article
(This article belongs to the Section Mechanics of Materials)
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32 pages, 1113 KB  
Article
Interval Power Integration-Based Nonlinear Suppression Control for Uncertain Systems and Its Application to Superheated Steam Temperature Control
by Gang Zhao, Hongxia Zhu and Hang Yi
Energies 2025, 18(16), 4242; https://doi.org/10.3390/en18164242 - 9 Aug 2025
Viewed by 247
Abstract
The control of many industrial processes, such as superheated steam temperature control, exhibits poor robustness and degraded accuracy in the presence of model parameter uncertainties. This paper addresses this issue by developing a novel interval power integration-based nonlinear suppression scheme for a class [...] Read more.
The control of many industrial processes, such as superheated steam temperature control, exhibits poor robustness and degraded accuracy in the presence of model parameter uncertainties. This paper addresses this issue by developing a novel interval power integration-based nonlinear suppression scheme for a class of uncertain nonlinear systems with unknown but bounded parameters. The efficacy of this approach is specifically demonstrated for the superheated steam temperature control in thermal power plants. By integrating Lyapunov stability theory and homogeneous system theory, this method extends the traditional homogeneous degree theory to the interval domain, establishes interval boundary conditions for time-varying parameters, and constructs a Lyapunov function with interval numbers to recursively design the controller. Furthermore, the interval monotonic homogeneous degree and an admissibility index are introduced to ensure system stability under parameter uncertainties. The effectiveness of the proposed method is verified through numerical simulations of superheated steam temperature control. Simulation results demonstrate that the method effectively suppresses nonlinearities and achieves robust asymptotic stability, even when model parameters vary within bounded intervals. In the varying-exponent scenario, the proposed controller achieved an Integral of Absolute Error (IAE) of 70.78 and a convergence time of 37s for the superheated steam temperature control. This represents a performance improvement of 42.79% in IAE and 53.16% in convergence time compared to a conventional PID controller, offering a promising solution for complex thermal processes with inherent uncertainties. Full article
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21 pages, 6784 KB  
Article
A Second-Order LADRC-Based Control Strategy for Quadrotor UAVs Using a Modified Crayfish Optimization Algorithm and Fuzzy Logic
by Kelin Li, Guangzhao Wang and Yalei Bai
Electronics 2025, 14(15), 3124; https://doi.org/10.3390/electronics14153124 - 5 Aug 2025
Viewed by 388
Abstract
To enhance the rapid and stable tracking of a specified trajectory by quadcopter drones, while ensuring a degree of resistance to external wind disturbances, this paper proposes an integrated control strategy that combines an optimization algorithm and fuzzy control. In this system, both [...] Read more.
To enhance the rapid and stable tracking of a specified trajectory by quadcopter drones, while ensuring a degree of resistance to external wind disturbances, this paper proposes an integrated control strategy that combines an optimization algorithm and fuzzy control. In this system, both the position and attitude loops utilize second-order Linear Active Disturbance Rejection Control (LADRC) controllers, supplemented by fuzzy controllers. These controllers have been optimized using a modified crayfish optimization algorithm (MCOA), resulting in a dual-closed-loop control system. In comparisons with both the dual-closed-loop LADRC controller and the dual-closed-loop fuzzy control LADRC controller, the proposed method reduces the rise time by 52.87% in the X-channel under wind-free conditions, reduces the maximum trajectory tracking error by 86.37% under wind-disturbed conditions, and reduces the ITAE exponent by 66.2%, which demonstrates that the newly designed system delivers excellent tracking speed and accuracy along the specified trajectory. Furthermore, it remains effective even in the presence of external disturbances, it can reliably maintain the target position and the attitude angle, demonstrating strong resistance to interference and stability. Full article
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17 pages, 3180 KB  
Article
Ensemble-Based Correction for Anomalous Diffusion Exponent Estimation in Single-Particle Tracking
by Roman Lavrynenko, Lyudmyla Kirichenko, Sergiy Yakovlev, Sophia Lavrynenko and Nataliya Ryabova
Appl. Sci. 2025, 15(14), 8000; https://doi.org/10.3390/app15148000 - 18 Jul 2025
Viewed by 319
Abstract
The analysis of anomalous diffusion characteristics within single-particle tracking data is a key problem in several applied-science domains, including biosignal processing, bioinformatics, and biotechnology. This task becomes particularly challenging in the presence of short trajectories, localization errors, and non-ergodicity, features that are common [...] Read more.
The analysis of anomalous diffusion characteristics within single-particle tracking data is a key problem in several applied-science domains, including biosignal processing, bioinformatics, and biotechnology. This task becomes particularly challenging in the presence of short trajectories, localization errors, and non-ergodicity, features that are common in real experimental data. To address these limitations, this work proposes an approach that improves the robustness and accuracy of estimating the anomalous diffusion exponent α, even for very short trajectories of up to 10 points. The approach includes an ensemble-based variance estimation of the exponent α, along with a bias correction based on time–ensemble averaged mean squared displacement, which reduces the systematic bias. These components integrate well into neural network architectures and are suitable for analyzing experimental trajectories in biotechnology and bioprocess engineering applications. Full article
(This article belongs to the Section Applied Biosciences and Bioengineering)
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14 pages, 3542 KB  
Article
Study on Angular Velocity Measurement for Characterizing Viscous Resistance in a Ball Bearing
by Kyungmok Kim
Machines 2025, 13(7), 578; https://doi.org/10.3390/machines13070578 - 3 Jul 2025
Viewed by 366
Abstract
This article describes a machine vision-based method for measuring the angular velocity of a rotating disk to characterize the viscous resistance of a ball bearing. A bright marker was attached to a disk connected to a shaft supported by two ball bearings. Rotation [...] Read more.
This article describes a machine vision-based method for measuring the angular velocity of a rotating disk to characterize the viscous resistance of a ball bearing. A bright marker was attached to a disk connected to a shaft supported by two ball bearings. Rotation of the marker was recorded with a digital camera. A simple algorithm was developed to track the trajectory of the marker and calculate angular displacement of the disk. For accurate detection of the rotating marker, the algorithm employed Multi-Otsu thresholding and the Least Squares Method (LSM). Verification of the proposed method was carried out through a direct comparison between the predicted rotational speeds and measured ones by a commercial tachometer. It was demonstrated that the percentage error of the proposed method was less than 1.75 percent. The evolution of angular velocity after motor power-off was measured and found to follow an exponential decay law. The exponent was found to remain consistent regardless of the induced rotational speed. This proposed measurement method will offer a simple and accurate non-contact solution for monitoring angular velocity and characterizing the resistance of a bearing. Full article
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27 pages, 5382 KB  
Article
PI-DÆ: An Adaptive PID Controller Utilizing a New Adaptive Exponent (Æ) Algorithm to Solve Derivative Term Issues
by Juan M. Barrera-Fernández, Juan Pablo Manzo Hernández, Kevin Miramontes Escobedo, Alberto Vázquez-Cervantes and Julio-César Solano-Vargas
Algorithms 2025, 18(7), 391; https://doi.org/10.3390/a18070391 - 27 Jun 2025
Viewed by 545
Abstract
This study proposes an enhanced derivative control strategy, named PI-DÆ, designed to overcome key limitations of the derivative (D) term, such as noise amplification, derivative kick (D-k), and tuning difficulties. These [...] Read more.
This study proposes an enhanced derivative control strategy, named PI-DÆ, designed to overcome key limitations of the derivative (D) term, such as noise amplification, derivative kick (D-k), and tuning difficulties. These issues often arise in high-frequency or rapidly changing systems, in which traditional PID controllers struggle. The proposed solution introduces a novel adaptive exponent algorithm (Æ) that dynamically modulates the D term based on the evolving relationship between system output and setpoint. This yields the PI-DÆ controller, which adapts in real time to changing conditions. The results show significant performance improvements. Simulation results on two systems demonstrate that PI-DÆ achieves a 90% faster response time, a 35% reduction in peak time, and a 100% improvement in settling time compared with conventional PID controllers, all while maintaining a near-zero steady-state error even under external disturbances. Unlike more-complex alternatives such as fuzzy logic, neural networks, or sliding mode control, PI-DÆ retains the simplicity and robustness of PID, avoiding high computational costs or intricate setups. This adaptive exponent strategy offers a practical and scalable enhancement to classical PID, improving performance and robustness without added complexity, and thus provides a promising control solution for real-world applications in which simplicity, adaptability, and reliability are essential. Full article
(This article belongs to the Special Issue Algorithmic Approaches to Control Theory and System Modeling)
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32 pages, 441 KB  
Article
The Method of Types for the AWGN Channel
by Sergey Tridenski and Anelia Somekh-Baruch
Entropy 2025, 27(6), 621; https://doi.org/10.3390/e27060621 - 11 Jun 2025
Viewed by 395
Abstract
For the discrete-time AWGN channel with a power constraint, we give an alternative derivation for the sphere-packing upper bound on the optimal block error exponent and an alternative derivation for the analogous lower bound on the optimal correct-decoding exponent. The derivations use the [...] Read more.
For the discrete-time AWGN channel with a power constraint, we give an alternative derivation for the sphere-packing upper bound on the optimal block error exponent and an alternative derivation for the analogous lower bound on the optimal correct-decoding exponent. The derivations use the method of types with finite alphabets of sizes depending on the block length n and with the number of types sub-exponential in n. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
19 pages, 279 KB  
Article
NTRU-MCF: A Chaos-Enhanced Multidimensional Lattice Signature Scheme for Post-Quantum Cryptography
by Rong Wang, Bo Yuan, Minfu Yuan and Yin Li
Sensors 2025, 25(11), 3423; https://doi.org/10.3390/s25113423 - 29 May 2025
Viewed by 796
Abstract
To address the growing threat of quantum computing to classical cryptographic primitives, this study introduces NTRU-MCF, a novel lattice-based signature scheme that integrates multidimensional lattice structures with fractional-order chaotic systems. By extending the NTRU framework to multidimensional polynomial rings, NTRU-MCF exponentially expands the [...] Read more.
To address the growing threat of quantum computing to classical cryptographic primitives, this study introduces NTRU-MCF, a novel lattice-based signature scheme that integrates multidimensional lattice structures with fractional-order chaotic systems. By extending the NTRU framework to multidimensional polynomial rings, NTRU-MCF exponentially expands the private key search space, achieving a key space size 2256 for dimensions m2 and rendering brute-force attacks infeasible. By incorporating fractional-order chaotic masks generated via a hyperchaotic Lü system, the scheme introduces nonlinear randomness and robust resistance to physical attacks. Fractional-order chaotic masks, generated via a hyperchaotic Lü system validated through NIST SP 800-22 randomness tests, replace conventional pseudorandom number generators (PRNGs). The sensitivity to initial conditions ensures cryptographic unpredictability, while the use of a fractional-order L hyperchaotic system—instead of conventional pseudorandom number generators (PRNGs)—leverages multiple Lyapunov exponents and initial value sensitivity to embed physically unclonable properties into key generation, effectively mitigating side-channel analysis. Theoretical analysis shows that NTRU-MCF’s security reduces to the Ring Learning with Errors (RLWE) problem, offering superior quantum resistance compared to existing NTRU variants. While its computational and storage complexity suits high-security applications like military and financial systems, it is less suitable for resource-constrained devices. NTRU-MCF provides robust quantum resistance and side-channel defense, advancing PQC for classical computing environments. Full article
14 pages, 617 KB  
Article
Iterative Forecasting of Financial Time Series: The Greek Stock Market from 2019 to 2024
by Evangelos Bakalis and Francesco Zerbetto
Entropy 2025, 27(5), 497; https://doi.org/10.3390/e27050497 - 4 May 2025
Viewed by 1492
Abstract
Predicting the evolution of financial data, if at all possible, would be very beneficial in revealing the ways in which different aspects of a global environment can impact local economies. We employ an iterative stochastic differential equation that accurately forecasts an economic time [...] Read more.
Predicting the evolution of financial data, if at all possible, would be very beneficial in revealing the ways in which different aspects of a global environment can impact local economies. We employ an iterative stochastic differential equation that accurately forecasts an economic time series’s next value by analysing its past. The input financial data are assumed to be consistent with an α-stable Lévy motion. The computation of the scaling exponent and the value of α, which characterises the type of the α-stable Lévy motion, are crucial for the iterative scheme. These two indices can be determined at each iteration from the form of the structure function, for the computation of which we use the method of generalised moments. Their values are used for the creation of the corresponding α-stable Lévy noise, which acts as a seed for the stochastic component. Furthermore, the drift and diffusion terms are calculated at each iteration. The proposed model is general, allowing the kind of stochastic process to vary from one iterative step to another, and its applicability is not restricted to financial data. As a case study, we consider Greece’s stock market general index over a period of five years, from September 2019 to September 2024, after the completion of bailout programmes. Greece’s economy changed from a restricted to a free market over the chosen era, and its stock market trading increments are likely to be describable by an α-stable L’evy motion. We find that α=2 and the scaling exponent H varies over time for every iterative step we perform. The forecasting points follow the same trend, are in good agreement with the actual data, and for most of the forecasts, the percentage error is less than 2%. Full article
(This article belongs to the Special Issue Entropy-Based Applications in Sociophysics II)
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35 pages, 5603 KB  
Article
Zero–Average Dynamics Technique Applied to the Buck–Boost Converter: Results on Periodicity, Bifurcations, and Chaotic Behavior
by Diego A. Londoño Patiño, Simeón Casanova Trujillo and Fredy E. Hoyos
Energies 2025, 18(8), 2051; https://doi.org/10.3390/en18082051 - 16 Apr 2025
Viewed by 355
Abstract
This study addresses chaos control in a Buck–Boost converter using ZAD technique and FPIC. The system analysis identified 1-periodic orbits and observed the occurrence of flip bifurcations, indicating chaotic behavior characterized by sensitivity to initial conditions. To mitigate these instabilities, FPIC was successfully [...] Read more.
This study addresses chaos control in a Buck–Boost converter using ZAD technique and FPIC. The system analysis identified 1-periodic orbits and observed the occurrence of flip bifurcations, indicating chaotic behavior characterized by sensitivity to initial conditions. To mitigate these instabilities, FPIC was successfully applied, stabilizing periodic orbits and significantly reducing chaos in the system. Numerical simulations verified the presence of chaos, confirmed by positive Lyapunov exponents, and demonstrated the effectiveness of the applied control methods. Steady-state and transient responses of the open-loop model and experimental system were evaluated, showing a strong correlation between them. Under varying load conditions, the numerical model accurately predicted the converter’s real dynamics, validating the proposed approach. Additionally, closed-loop control with ZAD exhibited robust performance, maintaining stable inductor current even during abrupt load changes, thus achieving effective control in non-minimum phase systems. This work contributes to the design of robust control strategies for power converters, optimizing their stability and dynamic response in applications that require precise management of power under variable conditions. Finally, a comparison was made between the performance of the Buck–Boost converter controlled with ZAD and the one controlled by PID. It was observed that both controllers effectively regulate the current, with a steady-state error of less than 1%. However, the system controlled with ZAD maintains a fixed switching frequency, whereas the PID-controlled system lacks a fixed switching frequency and operates with a very high PWM frequency. This high frequency in the PID-controlled system presents a disadvantage, as it leads to issues such as chattering, duty cycle saturation, and consequently, overheating of the MOSFET. Full article
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14 pages, 1814 KB  
Article
Analysis of Phosphorus Soil Sorption Data: Improved Results from Global Least-Squares Fitting
by Joel Tellinghuisen, Paul Holford and Paul J. Milham
Soil Syst. 2025, 9(1), 22; https://doi.org/10.3390/soilsystems9010022 - 4 Mar 2025
Cited by 1 | Viewed by 707
Abstract
Phosphate sorption data are often analyzed by least-squares fitting to the two- or three-parameter Freundlich model. The standard methods are flawed by (1) treating the measured pseudo-equilibrium concentration C as the independent (hence error-free) variable and (2) neglecting the weighting that should accommodate [...] Read more.
Phosphate sorption data are often analyzed by least-squares fitting to the two- or three-parameter Freundlich model. The standard methods are flawed by (1) treating the measured pseudo-equilibrium concentration C as the independent (hence error-free) variable and (2) neglecting the weighting that should accommodate the varying precision of the data. Here, we address both of these shortfalls and use a global fit model to achieve optimal precision in fitting data for five acidic Australian soil types. Each individual dataset consists of measured C values for up to nine phosphate spiking levels C0. For each soil type, there are three–five such datasets from varying levels of phosphate fertilizer pre-exposure (Pf) two years earlier. These datasets are fitted simultaneously by expressing the Freundlich capacity factor a and exponent b as theoretically predicted functions of the assay amounts of Fe, Al, and P measured for each Pf. The analysis allows for uncertainty in both C and C0, with inverse-variance weighting from variance functions estimated by residuals analysis. The estimated presorbed P amounts Q depend linearly on Pf, with positive intercepts at Pf = 0, indicating residual phosphate in the soils prior to the laboratory phosphate treatments. The key takeaway points are as follows: (1) global analysis yields optimal estimates and improved precision for the fit parameters; (2) allowing for uncertainty in C is essential when the data include C values near 0; (3) varying data precision requires weighting to yield optimal parameter estimates and reliable uncertainties. Full article
(This article belongs to the Special Issue Adsorption Processes in Soils and Sediments)
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18 pages, 1341 KB  
Article
Performance Analysis for High-Dimensional Bell-State Quantum Illumination
by Jeffrey H. Shapiro
Physics 2025, 7(1), 7; https://doi.org/10.3390/physics7010007 - 3 Mar 2025
Viewed by 1374
Abstract
Quantum illumination (QI) is an entanglement-based protocol for improving LiDAR/radar detection of unresolved targets beyond what a classical LiDAR/radar of the same average transmitted energy can do. Originally proposed by Seth Lloyd as a discrete-variable quantum LiDAR, it was soon shown that his [...] Read more.
Quantum illumination (QI) is an entanglement-based protocol for improving LiDAR/radar detection of unresolved targets beyond what a classical LiDAR/radar of the same average transmitted energy can do. Originally proposed by Seth Lloyd as a discrete-variable quantum LiDAR, it was soon shown that his proposal offered no quantum advantage over its best classical competitor. Continuous-variable, specifically Gaussian-state, QI has been shown to offer a true quantum advantage, both in theory and in table-top experiments. Moreover, despite its considerable drawbacks, the microwave version of Gaussian-state QI continues to attract research attention. A recent QI study by Armanpreet Pannu, Amr Helmy, and Hesham El Gamal (PHE), however, has: (i) combined the entangled state from Lloyd’s QI with the channel models from Gaussian-state QI; (ii) proposed a new positive operator-valued measurement for that composite setup; and (iii) claimed that, unlike Gaussian-state QI, PHE QI achieves the Nair–Gu lower bound on QI target-detection error probability at all noise brightnesses. PHE’s analysis was asymptotic, i.e., it presumed infinite-dimensional entanglement. The current paper works out the finite-dimensional performance of PHE QI. It shows that there is a threshold value for the entangled-state dimensionality below which there is no quantum advantage, and above which the Nair–Gu bound is approached asymptotically. Moreover, with both systems operating with error-probability exponents 1 dB lower than the Nair–Gu bound, PHE QI requires enormously higher entangled-state dimensionality than does Gaussian-state QI to achieve useful error probabilities in both high-brightness (100 photons/mode) and moderate-brightness (1 photon/mode) noise. Furthermore, neither system has an appreciable quantum advantage in low-brightness (much less than 1 photon/mode) noise. Full article
(This article belongs to the Section Atomic Physics)
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