Search Results (828)

We study the phase-space dynamics of quantum systems with $\mathrm{SU}(1,1)$ group symmetry using coherent-state representations on the Poincaré disk. The resulting evolution equation combines transport terms with nonlocal contributions generated with the spectral functions of the Casimir operator, which admit a natural interpretation as pseudodifferential operators associated with the hyperbolic Laplace–Beltrami operator. Using this pseudodifferential structure, we classify the phase-space generators according to the type of the underlying PDE: compact quadratic dynamics ($\widehat{H}\propto {\widehat{K}}_0^2$) yield a degenerate hyperbolic operator of the transport type, and noncompact dynamics ($\widehat{H}\propto {\widehat{K}}_2^2$) give rise to a mixed-order differential–pseudodifferential operator. For numerical evaluation, we reformulate the propagator as an oscillatory integral and develop two complementary strategies: a Fourier-series reduction exploiting the periodicity of compact orbits and a Levin-type spectral collocation method for the noncompact case. Both approaches are stable, accurate, and free of the stiffness issues that afflict direct PDE evolution on the Poincaré disk. Full article

This study investigates how key milling parameters influence both cutting noise and surface quality during the machining of laminated bamboo lumber. Using a multifactorial optimal response surface methodology, the effects of fibre orientation (0–135°), spindle speed (7000–10,000 r/min), feed rate (0.5–2.0 m/min) and milling depth (0.5–2.0 mm) were quantified through 25 experimental runs. Cutting noise, measured as peak sound pressure level (SPL), ranged from 86.8 to 95.2 dB, increasing markedly with fibre angle, feed rate, and milling depth, but exhibiting a non-linear response to spindle speed. Surface roughness (S_a) varied from 2.6 to 11.7 µm and was most strongly governed by milling depth, followed by fibre orientation and feed rate, with a significant interaction between fibre orientation and spindle speed. Quadratic regression models demonstrated strong predictive performance (R² = 0.97 for SPL; R² = 0.85 for S_a). Based on the response surfaces, optimal low-noise, high-quality machining was achieved at moderate spindle speeds, low feed rates, and shallow milling depths. These findings provide a mechanistic basis for understanding noise–roughness coupling in bamboo machining and offer practical guidance for computer numerical control processing, tool selection, and industrial noise reduction strategies in bamboo manufacturing. Full article

The multi-finger robotic hand offers great potential for precise control due to its high degrees of freedom. Yet, manipulating objects forms a closed-chain kinematic system, which compounds the dimensionality and computational complexity of trajectory tracking. To tackle this challenge, and inspired by the widespread application of the zeroing neurodynamics (ZND) in robotic control, this study proposes a novel direct-discrete robust neurodynamics (DDRN) algorithm. The proposed algorithm advances the ZND methodology by employing a direct discretization design strategy. This strategy is crucial for two reasons. First, it fits naturally with the discrete-time nature of digital systems, enabling practical implementation. Second, it enhances precision by avoiding the integration errors inherent in continuous-to-discrete transformations. By simultaneously integrating this direct discretization with explicit noise suppression mechanisms, the DDRN algorithm efficiently solves the high-dimensional tracking problem formulated as a constrained time-varying quadratic programming (CTVQP) problem. Theoretical analyses demonstrate that under various noise environments, the steady-state residuals (SSRs) achieve global convergence, guaranteeing the algorithm’s strong robustness and high accuracy. Furthermore, comprehensive numerical simulations substantiate its superior performance. Practically, this DDRN algorithm enables more reliable and precise real-time control of dexterous robotic hands, with potential benefits for advanced manufacturing, prosthetic hands, and automated assembly where accurate trajectory tracking under sensor noise is critical. Full article

With the increasing demand for higher efficiency in semiconductor machining, air spindles with compensation systems have attracted growing attention. The pneumatic nozzle–cylindrical flapper is a promising sensing approach due to its high precision and suitability for displacement measurement of high-speed rotating bodies. However, its complex three-dimensional flow behavior leads to significant deviations from conventional nozzle–flat flapper models, limiting its practical application. This study aims to clarify the flow mechanisms governing the nozzle–cylindrical flapper system and to establish a reliable framework for predicting its static characteristics. A computational fluid dynamics model is developed to analyze gas flow within the micron-scale clearance under varying gap sizes and angular orientations, and the results are validated against experimental measurements. The analysis shows that curvature plays a dominant role in the flow behavior. Increasing curvature enhances inertia-driven acceleration and weakens viscous effects while simultaneously inducing strong recirculation due to flow wrapping around the cylindrical surface. These competing mechanisms explain the observed deviations from conventional models and cannot be captured by two-dimensional approaches. Based on the numerical results, a mass flow rate compensation coefficient is introduced and correlated with the momentum compensation coefficient. A quadratic relationship between the two coefficients is identified, indicating a common recirculation-driven mechanism. These findings support previous semi-empirical assumptions and provide a basis for predicting static characteristics with reduced reliance on experimental calibration. Full article

Background/Objectives: Whole-blood viscosity (WBV) is increasingly used in cardiovascular risk assessment; however, inter-device comparability may depend on shear-rate definition. We performed a paired comparison of two scanning capillary viscometers to evaluate shear-dependent analytical agreement and its impact on clinical classification. Methods: In 300 identical blood samples, WBV was measured using Rheovis 2000A and Hemovister. Systolic WBV was defined at 300 s⁻¹ for both devices (shear-matched), whereas clinically defined diastolic WBV corresponded to 1 s⁻¹ for Rheovis 2000A and 5 s⁻¹ for Hemovister. Agreement was assessed using linear regression and Bland–Altman analysis. Hematocrit tertiles were examined as effect modifiers. Clinical agreement was evaluated using quadratic weighted Cohen’s κ. Results: Across matched shear rates (1000 to 1 s⁻¹), Hemovister yielded consistently higher WBV values than Rheovis 2000A, with statistically significant inter-device differences at all shear levels except 1000 s⁻¹. The magnitude of bias increased progressively as shear rate decreased, reaching −8.34 mPa·s at 1 s⁻¹. Under shear-matched systolic conditions (300 s⁻¹), the mean difference was −0.25 mPa·s (limits of agreement −1.72 to 1.22). In contrast, under clinically defined diastolic conditions (1 vs. 5 s⁻¹), the mean difference was 14.54 mPa·s (3.93 to 25.15), increasing across hematocrit tertiles. Clinical agreement was fair for systolic (κ = 0.31; 95% CI 0.24 to 0.39) and moderate for diastolic WBV (κ = 0.44; 95% CI 0.37 to 0.51). Notably, among samples classified as high by Hemovister, 72.8% (systolic) and 54.0% (diastolic) were reclassified as normal by Rheovis 2000A. Conclusions: Inter-device agreement in WBV measurement is strongly shear-dependent. Although numerical divergence increases at low shear, categorical concordance may remain moderate when device-specific reference thresholds are applied. Harmonization of shear definitions and reference frameworks may therefore be essential for consistent cross-platform interpretation. Full article

In advanced technology nodes, mixed-cell-height circuit designs have become increasingly prevalent, posing significant challenges for legalization. We first formulate the legalization as a class of variational inequality (VI) problems defined over convex sets and then employ an existing self-adaptive inertial projection and contraction algorithm (SIPCA) to solve it. Building upon this framework, we further propose an improved self-adaptive inertial projection and contraction algorithm (SIPCA_IP) by incorporating the subgradient extragradient technique to enhance convergence efficiency and numerical stability. The proposed method preserves the advantages of projection and contraction schemes for handling VIs with nonsymmetric positive semidefinite system matrices while demonstrating faster convergence and improved robustness compared with the baseline SIPCA. Moreover, a rigorous convergence analysis is established to provide theoretical guarantees for the effectiveness of the proposed method. Numerical experiments demonstrate that the proposed method effectively addresses the mixed-cell-height legalization problem and provides a rigorous and extensible framework for solving related quadratic optimization problems. Full article

Large language model (LLM)-based document translation systems typically treat each segment independently, discarding terminology decisions, human corrections, and discourse cues after each generation step. This stateless approach causes terminology inconsistency across segments, failure to propagate approved post-edits downstream, and redundant prompt-token consumption. Existing solutions—document-level MT, retrieval-augmented generation, and computer-assisted translation (CAT) tools as a general category—address individual aspects but lack a unified, state-aware architecture with provenance, update rules, and rollback semantics. We propose Language Twin, a shared-state architecture that organizes translation projects into seven versioned layers (L0–L6), supporting selective context loading, scoped human-edit propagation, and reversible updates. A pilot study translated three curated English-to-Korean document bundles (17 segments) using GPT-4o with a temperature of 0.3. The Language Twin condition (P1) achieved numerically higher preferred-term accuracy than the strongest baseline (17/21 vs. 14/21; not statistically significant at this sample size) and showed no repeated downstream errors in the monitored set (0/5 vs. 5/5 against the propagation-disabled ablation; Fisher’s exact test: p = 0.008), while reducing prompt tokens by 39.2% relative to full-context loading (A4). In blinded human evaluation (quadratic-weighted κ = 0.71–0.78), P1 achieved the highest terminology rating (4.38/5 vs. 3.97/5) and lowest post-editing time (16.9 s vs. 19.1 s per segment). These pilot-scale results indicate that governed shared state can improve terminology consistency and editing efficiency. Full article

The study addresses a selected issue in industrial cooling, that is, how to transport heat more efficiently when the process involves fiber spinning and extrusion, in which conventional fluids usually cannot work. We considered a ternary nanofluid that passed around a porous stretching cylinder and particularly considered the synergistic effect of quadratic thermal buoyancy, and the thermally generated double-diffusive heat and solute (TGDHS) effect. Through the Casson fluid model and considering the magnetic fields, radiations, and nonlinear chemical reactions, we reduced complex PDEs to simple ODEs. The results were evident using the BVP4C numerical method. Although in reality, magnetic fields and thermal radiation become a retarding force, the quadratic thermal buoyancy is the driving force behind accelerating the flow. An important trade-off that we discovered is that a heavier Casson fluid reduces heat and mass transfer. The addition of Nimonic 80A, AA7072, and AA7075 nanoparticles to ethylene glycol consistently enhances heat transfer, outperforming the base fluid by 7.8% even at low concentrations. While AA7072 and AA7075 drive significant increases of over 16%, Nimonic 80A offers a much more marginal contribution of 1.23%. Consequently, the Nusselt number is far more sensitive to the concentration of the aluminum alloys than to the Nimonic 80A. Finally, this work demonstrates that the most significant parameter in intensifying convective heat and mass transfer in such industrial systems is the strong forces of buoyancy. Full article

This paper presents a symmetric positive definite (SPD) coupling between the boundary element method (BEM) and the finite element method (FEM) in the framework of the numerical manifold method (NMM) for two-dimensional linear elastic static problems. The BEM subdomain is treated as a single mathematical patch whose local approximation is derived from the displacement boundary integral equation, thereby preserving the nonlocal nature of BEM. The remaining domain is covered by a finite element mesh, with each node defining a patch and the associated shape functions serving as weight functions. Weight functions are defined over the entire mathematical cover, with explicit zero values outside the support of each patch. This global definition ensures that the partition of unity holds everywhere and enables the global displacement approximation to be expressed as a superposition of contributions from all patches. Within this unified framework, the interface between the BEM and FEM subdomains emerges naturally as a transition zone of weight functions, rather than a distinct boundary. Displacement continuity is automatically satisfied through the partition of unity, and traction equilibrium is approximately enforced through the variational formulation. To fully incorporate the coupling formulation into the minimum potential energy framework, the tractions on the BEM patch are eliminated in favor of displacements using the displacement boundary integral equation (BIE). Prescribed tractions on the BEM patch are enforced via a penalty method. The resulting algebraic system is symmetric by construction and remains positive definite when either constant or isoparametric boundary elements are used. This work serves as a proof-of-concept study for the SPD coupling framework with constant elements. Numerical examples demonstrate the accuracy and convergence of the method. The results show that the coupling procedure preserves the intrinsic convergence properties of each subdomain: the BEM part converges at a rate close to unity for displacements and approximately 2.0 for stresses, while the FEM part achieves quadratic convergence for both. The study also reveals that near-singular integrals in the strain BIE can affect the convergence rate when the element size becomes sufficiently small. Full article

Generalized Sinusoidal Frequency Modulation (GSFM) signals can enhance Continuous Active Sonar (CAS) performance by providing high sub-signal processing gain while achieving high target update rates. However, conventional processing methods for GSFM often exhibit high sidelobe levels arising from the waveform’s autocorrelation which degrade detection performance, especially in severe multipath environments. To address this issue, a Mismatched-Channel Filtering (MMCF) method for GSFM in CAS is proposed to focus multipath energy while suppressing sidelobe levels. Adopting the sub-pulse processing scheme, we incorporate the orthogonality of GSFM sub-signals (optimized via a genetic algorithm) and sparse channel estimates into the MMCF design for each sub-signal. The design is formulated as a Quadratically Constrained Quadratic Program (QCQP) and solved iteratively using the Alternating Direction Method of Multipliers (ADMM) for long-duration signal processing in CAS. Numerical simulations demonstrate that, compared with the matched filtering and matched channel filtering methods, the proposed MMCF method effectively suppresses sidelobe levels by approximately 20 dB and produces a Dirack-like main-lobe peak, while efficiently focusing multipath energy. The method’s effectiveness is further validated using experimental data from a lake trial. Therefore, this algorithm has distinct advantages for signal processing in multipath environments. Full article

A novel flexible single-parameter polynomial distribution is presented in this study. The forms of hazard rate and density functions are examined. Additionally, exact formulas for a number of numerical characteristics of distributions are obtained. Stochastic ordering, the moment technique, the maximum likelihood, and a Bayesian analysis of this novel distribution based on type II censored data are used to derive the extreme order statistics. We construct Bayes estimators and the associated posterior risks using a variety of loss functions, such as the generalized quadratic, entropy, and Linex functions. Since tractable analytical formulations of these estimators are unattainable, we suggest using a simulation technique based on Markov chain Monte-Carlo (MCMC) to examine their performance. Furthermore, we construct maximum likelihood estimators given initial values for the model’s parameters. Additionally, we use integrated mean square error and Pitman’s proximity criteria to compare their performance with that of the Bayesian estimators. Lastly, we apply the new family to many real-world datasets to show its versatility, and we model cancer survival data using this new distribution to explain our methodology. Full article

In response to the problem that the gears for offshore wind power are prone to cyclic stress and pitting damage under specific conditions, a finite element analysis method was adopted to establish numerical models for the distribution of cyclic stress on the gears and the dynamic expansion of pitting. Based on the material properties of ASTM5140 alloy structural steel, simulations were conducted using ANSYS 2024 R1 for contact stress analysis during gear meshing and COMSOL 6.3 for the evolution of pitting in a corrosive environment over a 120-h period. The results showed significant stress concentration in the tooth root fillet area under cyclic loads, with a maximum equivalent contact stress of 2.838 × 10⁸ Pa, which was identified as the key region for fatigue damage. Based on the simulated stress amplitude and material fatigue parameters, the predicted fatigue life of the gear under typical offshore operating conditions was approximately 13.3 years. In the corrosive environment, pitting pits exhibited an accelerating expansion trend, with pit volume increasing by approximately 125% and internal surface area by approximately 54% over 120 h. The volume growth followed a cubic polynomial, and the surface area growth followed a quadratic polynomial over time. These research results provide a quantitative basis for fatigue life assessment and corrosion protection design of offshore wind power gears. Full article

The thermal safety and longevity of lithium-ion batteries are critically constrained by excessive temperature rise and spatial thermal non-uniformity, particularly during high-rate discharges. Most existing numerical investigations rely on simplified heat generation models that fail to capture the spatiotemporal heterogeneity of electrochemical heat sources, leading to compromised predictive accuracy. To address this deficiency, this study develops a comprehensive three-dimensional electrochemical–thermal coupled framework, integrating the Newman pseudo-two-dimensional (P2D) electrochemical model with conjugate heat transfer and laminar flow dynamics. The predictive robustness of this framework is rigorously validated against experimental data across multiple discharge rates (3 C and 5 C). The validated model is then deployed to evaluate a water-cooled microchannel cold plate designed for prismatic $\mathrm{L}\mathrm{i}\mathrm{M}{\mathrm{n}}_2{\mathrm{O}}_4$/graphite cells under a demanding 5 C discharge. A systematic parametric investigation is conducted to quantify the effects of ambient temperature (293–343 K), microchannel number (2–6), and coolant inlet velocity (0.1–0.6 m/s) on the maximum battery temperature (${\mathrm{T}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$) and temperature difference ($\mathsf{\Delta }\mathrm{T}$). Results demonstrate that the proposed system exhibits exceptional environmental robustness: over a 50 K ambient temperature span, ${\mathrm{T}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ increases by merely 2.0 K, remaining safely below the 323 K industry limit. Densifying the channel count from 2 to 6 further reduces ${\mathrm{T}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ by 1.55 K and narrows $\mathsf{\Delta }\mathrm{T}$ to 4.25 K, successfully satisfying the strict 5 K temperature uniformity standard. Furthermore, the thermal benefit of elevating inlet velocity exhibits a pronounced diminishing-return trend governed by the asymptotic reduction in bulk coolant temperature rise, dictating a critical trade-off against the quadratically escalating pumping power. Ultimately, these findings provide robust theoretical guidelines for the rational design of safe and energy-efficient battery thermal management systems. Full article

This paper focuses on the dynamics modeling and control methods for an underactuated Dual-Unmanned Aerial Helicopter Slung Load System (DUH-SLS), which consists of two Unmanned Aerial Helicopters (UAHs) connected to the suspended load via two sling cables. The DUH-SLS is a multi-body coupled system with internal ideal constraint forces and has seven motion degrees of freedom (DOFs) in the longitudinal plane. In this paper, a set of independent and complete generalized coordinates is selected to describe the system’s motion. The dynamics model of DUH-SLS is established using Lagrange analytical mechanics. This approach, which avoids system internal forces, greatly improves modeling efficiency. Finally, the correctness of this dynamics model is validated using a virtual prototype of the DUH-SLS developed in the multi-body dynamics simulation software ADAMS. The DUH-SLS is a complex nonlinear controlled object, and the iterative Linear Quadratic Regulator (iLQR) method is introduced to design an integrated optimal controller to achieve trajectory tracking and swing suppression for the DUH-SLS. This method transforms the quadratic optimal control problem of nonlinear systems into a series of linear quadratic optimal control (LQR) problems through iterative optimization in function space, thus obtaining an optimal solution. The iLQR optimal controller requires offline iterative computation, but the optimal control obtained has a state feedback closed-loop form, which ensures robustness during online control. Numerical simulation results demonstrate that the proposed iLQR optimal controller exhibits excellent control performance in complex multi-task scenarios. Particularly in trajectory tracking tasks, the maximum average position tracking error of the iLQR controller is only 0.14 m, compared to 3.57 m and 3.11 m for the LQR and LMC (Lyapunov Method Controller) controllers, respectively. Furthermore, the controller demonstrates strong robustness against internal parameter perturbations and external complex wind disturbances, fully validating the effectiveness and superiority of the proposed approach. Full article

We develop a fast numerical method for solving nonlinear diffusion equations with memory phenomena, a class of problems arising within viscoelastic materials, anomalous transport, and hereditary systems. The primary computational problem is the nonlocal temporal dependence captured by Volterra-type memory operators, which makes direct evaluation scale quadratically with the number of time steps ($O\left(N_t^2\right)$), rendering prolonged simulations prohibitively expensive. To address this bottleneck, we develop a novel synthesis that combines a high-order spectral method for spatial discretization with a fast memory algorithm based on a sum-of-exponentials approximation. The spectral method obtains exponential spatial convergence for smooth solutions. At the same time, the fast memory algorithm reduces memory usage and computational complexity to $O\left(N_t\right)$, yielding computational speedups exceeding 414x for prolonged simulations. We rigorously prove that the proposed scheme preserves the discrete energy dissipation law of the continuous system under mild assumptions on the memory kernel, thereby ensuring unconditional stability. Error analysis verifies spectral accuracy in space and first-order temporal convergence. Extensive numerical experiments using exponentially decaying and weakly singular kernels validate the theoretical results and illustrate the method’s effectiveness for modeling viscoelastic transport phenomena and irregular diffusion in complex systems. Full article