Search Results (1,533)

This paper proposes a finite element approach to the numerical solution of boundary value problems of linear elasticity theory formulated directly in terms of the stress tensor components. In contrast to the classical finite element formulation, in which displacements are the primary unknowns, the approach considered here treats the stress components as the sought quantities. Two forms of the boundary value problem are investigated. The first is based on the joint use of the equilibrium equations and the Beltrami–Michell equations, while the second is a transformed system of Poisson-type equations for the stress tensor components. Variational relations based on the Galerkin method are obtained for both formulations. Using linear basis functions on triangular finite elements, local matrices are constructed, and global systems of algebraic equations are formed, whose unknowns are the nodal values of the stresses. The numerical implementation of the developed schemes is carried out in an in-house C++ program and in the FreeFEM++ software environment. To verify the reliability of the proposed mathematical and numerical models, the classical Kirsch problem of a stretched elastic plate with a circular hole—characterized by a pronounced stress concentration near the edge of the hole—is solved. The numerical values of the stress components are compared with the analytical solution obtained using the Airy stress function method, as well as with the results of calculations performed with the FreeFEM++ software package. The comparison shows good agreement between the obtained solutions and confirms the possibility of determining stresses directly, without first computing the displacement field. A mesh-refinement study further showed a systematic reduction in the numerical error: on the finest mesh considered, the relative error decreased to 3.189% for formulation A and to 7.415% for formulation B. The proposed approach extends the applicability of the finite element method to boundary value problems of elasticity theory formulated in terms of stresses and can be used to study problems with complex geometry and local stress concentration. Full article

Equivalent-circuit models (ECMs) are widely used in battery management systems. However, scheduled resistance and capacitance changes can make numerical histories inconsistent with physical polarisation states. This paper introduces BATTLM, a Transmission-Line Modelling (TLM) realisation of lithium-ion battery ECMs. Each capacitor in a resistor–capacitor (RC) branchcapacitor is represented by an open-circuit TLM stub using incident and reflected variables. When parameters change, the incident history is reconstructed from the endpoint polarisation voltage. The fixed-step algebraic formulation extends from 1RC to arbitrary nRC order and reproduces the corresponding trapezoidal update. Assessment uses Panasonic 18650PF and Stanford second-life cell data. Among 1RC, 2RC, 3RC, and 4RC candidates, frequency-point testing favours 4RC for all 180 Stanford spectra, whereas the corrected Akaike information criterion selects 4RC for 108 spectra and 3RC for 72. Median impedance test root-mean-square error (RMSE) values are 2.166, 1.146, 0.912, and 0.848 mΩ, respectively. Electrochemical impedance spectroscopy (EIS)-derivedparameters are applied to 177 measured pulses without pulse-domain fitting. Median voltage RMSE values, referenced to the measured pre-pulse voltage, are 5.359, 1.656, 0.884, and 0.623 mV. The results support state-consistent TLM implementation while identifying application-dependent model-order trade-offs. On a dedicated Panasonic temperature-rise record excluded from parameter identification, scheduling with measured battery temperature reduced terminal-voltage RMSE from 177.55 to 86.92 mV relative to freezing the temperature dependence at the initial condition. Full article

To address the dependence of uncertainty analysis methods on assumed probability density functions of wind power output and the computational burden of time-domain simulations in transient stability-constrained optimal power flow (TSCOPF) problems, this paper proposes a chance-constrained transient stability-constrained optimal power flow (CCTSCOPF) solution method based on data-driven polynomial chaos expansion (DDPCE) and the maximum entropy method (MEM). The method eliminates the need for predefined distribution assumptions for wind power variables. Specifically, using N = 5000 historical wind power forecast error samples, raw statistical moments up to order 2p = 8 are extracted, and orthogonal polynomial basis functions up to order p = 4 are derived by solving a 5 × 5 linear algebraic equation system constructed from these moments. Based on the constructed polynomials, Gaussian quadrature collocation points of wind power output are obtained, and time-domain simulations are performed at these points to solve the expansion coefficients, establishing a surrogate model that maps wind power fluctuations to transient responses. The surrogate model then computes the statistical moments of transient stability indices. MEM is subsequently used to reconstruct the probability density function of the transient stability index, and the transient stability chance constraint is converted into an algebraic boundary condition. Finally, an optimization model incorporating power system operating constraints is formulated and solved. Case studies conducted on the modified IEEE 39-bus test system with two 100 MW wind farms demonstrate that the proposed surrogate model achieves high accuracy with R² = 0.987, significantly improving uncertainty quantification accuracy over the standard Wiener–Askey polynomial chaos expansion (PCE) method. Furthermore, the total computational runtime is reduced from 66,280.00 s under full-scale Monte Carlo simulations to 47.92 s, achieving a 1383× computational speedup while strictly satisfying transient stability chance constraints. Full article

This study examined quiescent optical structures in a cubic–quintic nonlinear Schrödinger model that combines intensity-dependent dispersion with a weakly nonlocal intensity-curvature response. A real phase–amplitude reduction establishes the compatibility conditions for stationary localized profiles. The enhanced direct algebraic method then produces regular bright and dark states, singular hyperbolic states, and Jacobi and Weierstrass elliptic families. Spatially shifted formulas are identified as translated representatives rather than new orbit types. Each family is validated through the auxiliary equation, the stationary residual, explicit reality and nondegeneracy restrictions, and an independent first-integral formulation. The quintic response changes the dominant balance and the admissible coefficient manifolds relative to the corresponding Kerr-only setting. Parameter continuations illustrate distinct roles of cubic, quintic, dispersive, and weakly nonlocal effects without implying unconstrained one-parameter dynamics. For a representative regular bright state, refined Chebyshev collocation locates no persistent unstable eigenvalue and direct Fourier propagation under simultaneous amplitude and phase perturbations remains bounded. The numerical conclusion is restricted to the tested branch and finite propagation interval. Full article

The quantification of structural resilience and sub-percentile tail risk represents a major challenge across both corporate financial engineering and modern industrial logistics. Traditional aggregation architectures, such as linear risk matrices and parametric copulas, can exhibit computational and sensitivity challenges when modeling extreme tail-risk dependencies under sparse data regimes. While parametric copulas are highly effective under standard conditions, they can be sensitive to parameter specifications and sample size limitations in deep-tail regions. This paper highlights a numerical limitation of the Gumbel extreme-value copula in deep-tail regions (F ≥ 0.999). Analytical results indicate that the logarithmic structure of the tail generator produces progressively higher sensitivity near the distribution boundary, yielding an empirical condition number greater than 1220 at the regulatory 99.9% Value-at-Risk (VaR) threshold. This numerical conditioning issue increases sensitivity to sample noise and data scarcity, resulting in a 36.5% underestimation of systemic tail damage. The proposed model formalizes risk scenarios by mapping multi-node threats as normalized directional unit vectors within a compact 3D vector space. Interactions are then calculated algebraically using geometric invariants—the Dot Product for root-cause convergence and the Cross Product Norm for dynamic, second-order risk resonance—effectively contracting high-dimensional combinations into a stable framework. Rather than treating risks as frame-dependent scalar probabilities, this generalized High-Dimensional Geometric Invariant Operational Risk Framework extends legacy structures with domain-agnostic invariants capturing dynamic risk resonance and multi-trigger cascades. Simulation results across rugged operational environments, acute data scarcity (Ntrain = 100), and high-dimensional scaling (50 risk factors) demonstrate that the proposed model outperforms standard alternatives by a factor of approximately 13 in out-of-sample predictive accuracy (MSE = 0.08193) while maintaining absolute parametric stability. Furthermore, a Taylor-series tensor contraction successfully collapses 1275 second-order interactions into just 2 free parameters. This framework bypasses iterative Maximum Likelihood Estimation (MLE) bottlenecks, unlocking real-time, low-latency Monte Carlo stress testing for systemic banking compliance and global supply chain risk governance. Full article

College students’ physical activity may decline when academic demands are high, even among those who previously intended to exercise. This three-wave longitudinal study examined whether T2 physical activity, modeled conditional on T1 exercise intention and T1 physical activity, was involved in a time-ordered indirect association between T1 academic stress and T3 depressive and anxiety symptoms. Of 982 students who completed the baseline survey in September 2025, 750 provided complete matched data in December 2025 and March 2026 (retention = 76.4%). Primary models used raw T2 physical activity and adjusted all component, direct, and total-effect equations for the identical covariate set: gender, age, BMI, T1 exercise intention, T1 physical activity, T1 PHQ-9, and T1 GAD-7. A sign-reversed residualized activity score was examined only as an algebraically equivalent parameterization. T1 exercise intention predicted higher T2 physical activity (β = 0.308), whereas T1 academic stress was associated with lower T2 physical activity (B = −12.771, p < 0.001). Under identical adjustment, raw T2 physical activity was inversely associated with T3 depressive symptoms (B = −0.0024) and anxiety symptoms (B = −0.0013); the corresponding sign-reversed residualized coefficients were equal in magnitude and opposite in sign, with identical R² values (0.4257 and 0.2720). Full-process bootstrap indirect associations were significant for depressive symptoms (B = 0.0309, 95% CI [0.0229, 0.0396]) and anxiety symptoms (B = 0.0162, 95% CI [0.0099, 0.0236]). The Stress × Intention interaction and quadratic residualized-activity terms were not significant. No observed T1 variable differed significantly between retained and attrited participants. Higher academic stress was associated with relatively lower subsequent physical activity, which was in turn statistically associated with later depressive and anxiety symptoms. The findings do not establish causality, disruption of intention enactment, or a distinct psychological residual mechanism. Full article

This paper presents the design, development, and evaluation of a machine-learning system built to forecast agricultural crop yields across Indian states between 2000 and 2026, together with a complementary, national-scale verification of predicted crop yield using a MODIS-derived NDVI time series (MOD13A3.061 Vegetation Indices Monthly L3 Global 1 km SIN Grid). Although many prior studies address crop-yield prediction with linear regression, random forest, gradient boosting, and related methods, a complementary, aggregate-level verification method for predicted crop yield has rarely been proposed. This article contributes such a method, together with a complementary NDVI-based estimation approach for total foodgrain output. Crop yield and MODIS-derived NDVI are strongly correlated (r = 0.84 for annual maximum NDVI; r = 0.78 for annual mean NDVI), and a simple regression of total foodgrains on annual maximum NDVI alone reaches R² = 0.70. Four modeling approaches—linear regression, random forest, gradient boosting, and CatBoost—were built and compared using a chronology-preserving, expanding-window walk-forward validation procedure with a final, untouched 2024–2026 holdout, rather than a random split; a companion leakage check confirmed that reported production is almost algebraically identical to reported yield and therefore had to be excluded from the feature set. Random forest produced the most reliable and consistent forecasts, reaching a mean absolute percentage error (MAPE) of 11.4% and R² = 0.982 on the final holdout, ahead of CatBoost (MAPE = 11.6%, R² = 0.969) and gradient boosting (MAPE = 13.0%, R² = 0.908), and substantially ahead of linear regression, which failed to generalize to the holdout period (R² = −10.67); across the walk-forward folds preceding this holdout, however, the three tree ensembles were statistically indistinguishable. A four-configuration ablation study confirms that most of this performance gain is attributable to the inclusion of MODIS-derived NDVI rather than to model choice alone. Prediction error varies considerably by crop, from under 10% MAPE for major staples (rice, wheat, maize, sugarcane, moong) to well over 80% MAPE for several lower-volume crops (soyabean, garlic, Sunn hemp, tobacco, potato). The paper also documents two consequential data-quality findings—a near-perfect algebraic relationship between production and yield, and a structural administrative reporting gap in 2020—and closes with directions for future work, including higher-resolution satellite inputs, temporal deep-learning architectures, additional environmental covariates, and explainable-AI analysis of feature contributions. Full article

Background/Objectives: Subarachnoid analgesia (SA) is increasingly used as an adjunct to general anesthesia in robotic ERAS pathways, but the contribution of the intrathecal local anesthetic, as distinct from that of the intrathecal opioids, has not been isolated. Methods: This study comprised a single-center retrospective cohort of adults undergoing elective robotic surgery (May 2024–July 2025). The exposure was the intrathecal regimen, serving as mutually exclusive categories. The primary outcome was intraoperative opioid exposure (model-derived area under the concentration–time curve per hour, AUC/h); secondary outcomes were standardized intraoperative fluid administration and a stringent pain-free 48 h course (NRS = 0 throughout). Multivariable Gamma and logistic models were supplemented by provider-adjusted mixed-effects analyses, E-values, and a model-free robustness analysis. Results: Of 207 patients, 83.1% received SA; all were given intrathecal morphine and 62.3% levobupivacaine. Compared with no SA, morphine alone was not associated with AUC/h (+14.0%; 95% CI, −0.9 to +31.1), whereas all levobupivacaine-containing regimens were: −36.4% (IM + L5), −24.3% (IM + L5 + S3), and −44.8% (IM + L10 + S3); overall p < 0.001. Algebraically equivalent component reparameterization attributed this to levobupivacaine dose (−44.3% at 5 mg; −59.3% at 10 mg). Remifentanil was used in 98.7%, 88.6%, and 10.0% of patients receiving 0, 5, and 10 mg, respectively. Fluid administration was lower with IM + L5 (−24.9%) and IM + L10 + S3 (−31.0%) after adjustment, but was not with levobupivacaine-graded unadjustment. SA was associated with a pain-free course (adjusted OR, 3.33; 95% CI, 1.06–11.79), an estimate not robust to minimal unmeasured confounding. Conclusions: Levobupivacaine-containing regimens were consistently associated with lower intraoperative opioid exposure, but regimen and opioid strategy were chosen jointly by the same clinician; therefore, these associations between strategies are specific to the delivery context of this study. The fluid and pain-free findings are hypothesis-generating. Trials should vary the local anesthetic dose independently of intrathecal opioids. Full article

Extreme weather events increasingly affect the safety, durability, and operational performance of road infrastructure, creating the need for sustainable thermal management solutions. Among the available technologies, low-enthalpy geothermal systems offer significant advantages by providing continuous heating and cooling capabilities with reduced environmental impact compared to conventional maintenance practices. This study presents the methodology developed within the GEO-ROAD project to assess shallow geothermal resources across Spain and support the future deployment of geothermal road systems. The proposed framework integrates geological, thermal, and satellite-derived geophysical information through a unified GIS-based workflow, combining multivariate statistical analysis, map algebra, and automated geospatial processing to generate a regional geothermal potential model. In addition to conventional geological characterization, the methodology incorporates magnetic and gravity data from satellite missions, airborne surveys, and ground-based observations to improve the spatial representation of subsurface conditions. The resulting geothermal potential assessment constitutes a key component of the GEO-ROAD digital platform, where it will be combined with climatic risk maps and road infrastructure information to identify the most suitable locations for geothermal applications. By linking geothermal resource assessment with infrastructure-oriented decision-making, the proposed methodology provides a scalable and transferable framework for supporting the planning of sustainable and climate-resilient road thermal management systems. Full article

Weakly nonlinear free-surface flows past disturbances are traditionally modeled using the forced Korteweg–de Vries (fKdV) equation with a prescribed instantaneous pressure field. However, physical wake responses possess finite relaxation times and advection scales that diagnostic algebraic closures fail to capture. This paper introduces a novel coupled system in which the surface pressure is a dynamical field governed by an advection–reaction–diffusion equation driven by band-limited curvature. Using linear spectral theory and numerical validation, we derive a phase-speed criterion demonstrating that energy transfer is determined by the comparison between the pressure drift speed and the surface phase speed. A sharp stability theorem proves that, to leading order in the coupling strength and for a non-negative even response transfer function whose drift speed exceeds the Froude detuning, the system is spectrally stable if and only if the response is band-limited below a critical wavenumber $k_c$. Furthermore, an exact energy identity establishes that passivity and linear stability are equivalent. Finally, we demonstrate resonance steering: while coupling typically increases the wave resistance for monotone spectra, tuning the response to a spectral zero of a multi-lobe footprint reduces the drag significantly relative to its classical value. This result identifies an explicit performance–strongness trade-off, providing a mathematically strong structure for wave drag minimization through dynamic pressure control. Full article

Higher-order boundary value problems model several physical phenomena in fluid dynamics, astrophysics, hydrodynamics, beam theory, astronomy, hydromagnetic stability, and engineering. Eighth-order boundary value problems arise in the physics of various hydrodynamic stability problems, advanced structural mechanics, and several other real-world systems. This paper applies an efficient collocation method based on the shifted Horadam polynomials to obtain approximate solutions of an eighth-order boundary value problem in ordinary differential equations. The Horadam collocation method expresses the solution of the proposed problem as a shifted Horadam polynomial series. Using the zeros of the shifted Horadam polynomials as the collocation points, the proposed boundary value problem is reduced to a set of algebraic equations in the expansion coefficients of the series solution. The obtained algebraic equations are then solved for the unknown expansion coefficients using Newton’s iterative method. Two illustrative examples of the proposed boundary value problem are considered for the purpose of accuracy, efficiency, and reliability of the proposed method. Numerical solutions obtained are compared with the exact solutions and other existing solutions. Comparisons of results are demonstrated in tables and graphs. It is observed that the proposed method yields higher accuracy compared to the existing methods. This research work shows that the Horadam polynomial-based collocation method is an efficient method for obtaining accurate and reliable approximate solutions of higher-order boundary value problems in ordinary differential equations. Full article

Financial returns have heavy tails and nonzero skewness. Machine learning risk models typically return isolated quantiles or rest on thin-tailed laws. We introduce a skewed, heavy-tailed distribution that is as easy to use as the normal and that converts any machine learning forecast of conditional moments into a full density. The law splices the left half of one logistic density onto the right half of another. A prescribed mean, variance, and skewness map into its three parameters by elementary algebra. Value at Risk (VaR), Expected Shortfall (ES), optimal holdings, and risk premia then have closed-form expressions. The attainable third-moment interval is wider than that of the smooth half-normal law and even a small departure from symmetry already moves the implied tails away from the Gaussian benchmark. The logistic base has a kurtosis of $4.2$ and above, so tail-risk estimates are more conservative than those of thin-tailed alternatives. Gradient-boosted trees predict the conditional mean, volatility, and skewness that enter the closed-form formulas. The resulting one-day-ahead VaR and ES forecasts are well calibrated and pass standard coverage tests. Unlike quantile-based machine learning forecasts, they deliver the entire conditional density in analytic form. Exponentially weighted moving average moments, fed through the same formulas, already give accurate ES forecasts. An application to stock-index, commodity, and foreign-exchange returns shows that the distribution tracks sample asymmetry and tail behavior. A three-moment calibration matches mean, variance, and skewness. The implied kurtosis is that of the logistic base and is not a free parameter. Full article

The island formula recovers a unitary Page curve in controlled gravitational models, but the dominance of an island saddle, the existence of a radiation recovery channel, and the cost of implementing that channel are logically distinct statements. We formulate this distinction as a two-stage framework. In the first stage, candidate islands and the physical Page transition are determined exclusively by the standard generalized entropy and quantum-extremal-surface (QES) prescription. In the second stage, an explicitly model-dependent reconstruction score ranks the QES candidates by normalized recovery, connectivity, algebraic, and complexity diagnostics. The score is not proposed as a new gravitational entropy formula. For a nondegenerate island/no-island crossing we derive the first- and second-order displacement of the operational reconstruction-support transition relative to the Page transition. We define operator recovery on a code subspace without assuming an interior–exterior tensor factorization, state the Fawzi–Renner recoverability implication with its correct conditional-mutual-information hypothesis, and derive a dimension-normalized mutual-information network diagnostic bounded in $\left[0,1\right]$. We then test the diagnostics in a fully reproducible random-Clifford evaporation model. A self-contained binary stabilizer calculation uses n = 12, 16, and 20 black-hole qubits and 256 seeded realizations per size and ensemble. The entropy peak converges to an emitted fraction k/n = 1/2, whereas a reference qubit becomes equally correlated with radiation and the remaining register near the same point. A stricter decoupling criterion occurs later. Pairwise radiation–network connectivity and multipartite total correlation exhibit sharply different behavior, demonstrating that a pairwise network cannot by itself certify interior reconstruction. These results support reconstruction support as an operational layer placed on top of—not inside—the island rule, and they give falsifiable criteria for future tensor-network, random-circuit, and semiclassical calculations. Full article

Barrier-based safety systems are fundamental to preventing accidents in high-hazard industrial operations. However, traditional Hazard Identification (HAZID) and risk screening frameworks aggregate safety safeguards at a macro-hazard level, creating a systemic blind spot that masks threat-specific vulnerabilities and single points of failure. To address this gap, this study develops ‘Maximum-Vulnerability Diagrams’ (MVD), a network-based modeling approach that maps and quantifies threat–barrier pathways using matrix algebra and conditional probability. Validated across empirical cases of working-at-height (H-06.01) and heavy rotary equipment (H-08.01) operations in the oil extraction industry, the MVD successfully isolates high-criticality, zero-redundancy pathways. We mathematically establish that multiplexed defenses require a target individual efficiency of η ≥ 95% to reliably suppress system failure probability below a strict 5% operational threshold. The findings demonstrate that aggregate safeguard volume is a deceptive safety metric, and that systemic resilience depends entirely on network architecture. This framework transitions risk governance from passive compliance checking to predictive, threat-driven barrier management, offering an actionable methodology to optimize safety resources before accidents occur. Full article

Modular satellite architectures can shorten development cycles and support flexible mission configurations; however, their thermal management is complicated by inter-module coupling, variable operating conditions, and stringent temperature limits. This study proposes a Thermal Digital Datasheet (TDD) framework that provides a standardized representation of module-level thermal information for data exchange, rapid system analysis, and consistent characterization across suppliers. The TDD organizes the passive thermal properties, active control capabilities, and operational constraints of each module in a unified format. To populate the datasheet with physically consistent parameters, a physics-constrained algebraic identification method is developed using excitation-based thermal response data and a structured least-squares formulation derived from the energy-balance equations. The resulting TDD representation is then integrated with a graph neural network (GNN), in which the modular interconnection topology is represented explicitly as a graph for network-wide temperature prediction. On the simulated modular satellite dataset, TDD-GNN achieves a mean absolute error of 0.096 °C and an $R^2$ of 0.962 for one-step temperature-increment prediction, maintaining high accuracy over autoregressive horizons of up to 2 h. In an end-to-end evaluation in which the thermal parameters of each test configuration are independently identified before GNN inference, the model retains $R^2=0.959$, demonstrating robustness to realistic parameter-identification errors. Perturbation-based sensitivity analysis further shows that the learned parameter ranking is consistent with the expected thermal behavior. These simulation results indicate that the proposed framework can support computationally efficient thermal-state prediction for modular satellite systems. Full article