Search Results (251)

Heat transport in heterogeneous materials can deviate markedly from classical Fourier behavior when microstructural disorder, trapping effects, nonlinear mobility, and long-range temporal correlations interact across multiple spatial and temporal scales. These mechanisms may produce delayed relaxation, persistent thermal footprints, front deformation, and non-classical spreading patterns that are not adequately represented by conventional integer-order diffusion models. In this study, a modeling and simulation framework is developed for anomalous heat transport in heterogeneous media using a two-dimensional time-fractional porous medium equation. The model combines a Caputo fractional time derivative, which represents thermal memory, with nonlinear degenerate porous-medium diffusion, spatially heterogeneous conductivity, localized volumetric heating, and Robin-type convective boundary exchange. A conservative fully discrete numerical scheme is constructed using flux-based finite differences for the heterogeneous nonlinear diffusion operator and an $L1$ approximation for the Caputo derivative. The nonlinear algebraic system at each time level is solved using an under-relaxed Picard frozen-coefficient iteration with non-negativity enforcement and sparse direct solution of the resulting linear systems. The numerical implementation is verified through a manufactured-solution convergence study, and additional analyses are performed to examine computational cost, Picard iteration behavior, coefficient-regularization sensitivity, strong-source effects, heterogeneous conductivity structures, and long-time thermal-footprint persistence. The results show that heterogeneous conductivity mainly redirects heat through preferential pathways and enlarges the spatial footprint while producing negligible changes in global heat content. Stronger fractional memory, represented by smaller fractional order, increases the persistence and spatial reach of moderate heating, whereas larger porous-medium exponents confine heat near the source and preserve higher local peaks. Source amplitude increases the thermal burden and footprint monotonically over the tested range, including strong forcing, without producing an abrupt localization-spreading transition. Boundary exchange remains secondary in the short-time interior-heating regime considered. These findings demonstrate that the proposed two-dimensional time-fractional porous medium framework provides a verified and physically interpretable model for non-Fourier heat transport in heterogeneous materials, where local intensity, global heat retention, and spatial thermal exposure must be assessed jointly. Full article

This paper proposes a novel hybrid numerical scheme that augments the classical L1 finite-difference approximation of the Caputo fractional derivative of order $\alpha \in (0,1]$ with a selective shifted Grünwald–Letnikov correction (controlled by a shift parameter $\beta \in [0,1)$) applied only to the most recent time increment. When $\beta =0$, the scheme reduces exactly to the classical L1 scheme and retains its optimal convergence rate $O\left(h^{2-\alpha }\right)$, where h denotes the uniform time-step size. For $\beta >0$ (optimally chosen as $\beta =1-\alpha /2$), extra numerical damping is introduced at the cost of a mildly reduced convergence order $O\left(h^{1-\alpha }\right)$, while long-term stability is significantly improved. The scheme is applied to the fractional Kelvin-Voigt and Standard Linear Solid models to analyze creep and relaxation responses. Numerical simulations demonstrate that the proposed hybrid scheme achieves improved accuracy, long-term stability, and computational efficiency compared to classical integer-order models and several existing fractional schemes reported in the recent literature. Results show that fractional orders capture anomalous creep behavior more accurately, aligning with experimental data from recent studies. The proposed method offers improved computational performance for real-time structural health monitoring applications. Full article

Carbon-fiber reinforced polymer (CFRP) tendons have attracted increasing attention as corrosion-resistant prestressing elements for prestressed concrete and cable-supported structures; however, their practical implementation requires reliable verification of long-term mechanical performance and anchorage reliability. In this study, a 9.5 mm pultruded CFRP tendon and compression-type anchorage system were developed and experimentally evaluated through relaxation, creep rupture, and fatigue tests. The tendon exhibited a tensile strength of 2501 MPa and an elastic modulus of 132.5 GPa. Relaxation tests were conducted at an initial load corresponding to 70% of the ultimate tensile capacity, and the measured relaxation loss after 1000 h was 1.02%. Based on logarithmic regression of the measured data, the relaxation loss at 1,000,000 h was estimated to be 2.11%; however, this value should be interpreted as an extrapolated long-term estimate rather than a directly verified result. Creep rupture tests performed at load ratios of 82.4–100.0% yielded an estimated 1,000,000 h creep rupture load ratio of approximately 80%, although the prediction is subject to uncertainty because of the limited number of specimens and scatter in rupture times. Fatigue tests indicated that the CFRP tendon–anchorage assembly maintained stable performance up to 2,000,000 cycles without measurable degradation in elastic stiffness under the adopted loading conditions. These results suggest that the developed CFRP tendon–anchorage system has promising potential for prestressing applications, while further long-term tests with a larger number of specimens are required to improve the statistical reliability of the extrapolated relaxation and creep rupture predictions. Full article

The problem of path following control for underactuated Unmanned Surface Vehicles (USVs) is tackled in this work, and a scheme based on Predicted Adaptive Line-of-Sight (PALOS) is put forward. At the guidance level, prediction techniques and adaptive mechanisms are incorporated to eliminate the inherent assumption of small sideslip angle in the conventional LOS methods, enabling online estimation and dynamic feedforward compensation of time-varying sideslip angles. On the control side, radial basis function neural networks are combined with virtual parameter learning techniques to achieve online approximation of the lumped uncertainties, which include modeling inaccuracies and external disturbances. An adaptive control scheme based on lifelong learning mechanisms is developed, wherein the historical knowledge is constructed and preserved through feedback terms to achieve knowledge retention and on-demand reuse, thereby enhancing control efficiency and mitigating catastrophic forgetting. Additionally, a self-triggered mechanism acts as a knowledge transfer instrument, reducing communication overhead, relaxing transmission conditions, and rigorously precluding Zeno behavior. Through theoretical derivations, one can prove that all closed-loop signals are uniformly ultimately bounded. Comprehensive numerical simulations based on the 1:70 CyberShip II scale-model ship dynamics under complex sea conditions verify the proposed approach to be both effective and practical. Full article

This study compares low-parameter fractional viscoelastic models for the unified characterization and extrapolation of creep and stress relaxation behaviors in polymer-based energetic materials, including polymer-bonded explosives (PBXs) and solid propellants. Fourteen candidate models composed of springs and spring-pot elements were considered under controlled parameter complexity. Their creep compliance and relaxation modulus were evaluated through Laplace-domain formulations, and the parameters were identified using a combined Talbot inverse Laplace transform and Gray Wolf Optimizer. Published creep and stress relaxation datasets were used to assess both fitting performance and early-stage data extrapolation behavior. The results show that the fractional Zener model and Model 13 can each describe both creep compliance and relaxation modulus within compact six-parameter rheological forms. Both models generally achieved coefficients of determination above 0.99. When the first 10% of the time span was used for calibration, the selected fractional models showed extrapolation capability over an approximately one-order-of-magnitude longer time window, with rRMSE values below 8.5% in reported cases and below 2% under suitable conditions. Compared with Prony series and power-law models, these fractional models offer compact alternatives for broad viscoelastic response characterization. These results provide guidance for selecting compact viscoelastic models for long-term response analysis of polymer-based energetic materials. Full article

This paper studies quantitative forms of approximate recurrence for bounded linear operators on Banach spaces through the notion of uniformly $\delta$-almost periodic vectors. For a prescribed tolerance $\delta \ge 0$, this notion relaxes classical almost periodicity by requiring uniform orbit repetitions up to an error controlled by $\delta$, along relatively dense sets of approximate periods. The main purpose of the paper is to refine this qualitative recurrence condition by introducing return-time profiles. These profiles measure, for each accuracy level, the minimal size of recurrence windows needed to guarantee the existence of an approximate period. Thus, they provide a quantitative refinement of the usual relatively dense return condition. We prove that uniform $\delta$-almost periodicity is equivalent to the finiteness of the associated return-time profile at every positive accuracy level. We also establish basic structural properties of these profiles, including monotonicity with respect to the accuracy and tolerance parameters, behavior under scalar multiplication and forward iteration, and an elementary additive property of approximate periods. The final part of the paper applies the general framework to weighted backward shifts on ${\ell }^p$-spaces. In this setting, the explicit coordinate representation of the iterates allows us to identify several recurrence and obstruction mechanisms. We describe stable threshold recurrence, finite-support recurrence, exact recurrence generated by periodic vectors, and coordinate-level obstructions to $\delta$-almost periodicity. The results provide a rigorous framework for measuring approximate almost periodicity in linear dynamics and clarify how recurrence-window profiles complement the classical qualitative theory of relatively dense returns. Full article

This paper designs a novel aperiodic intermittent control (AIC) strategy using discrete-time observation information. It can stabilize unstable hybrid McKean–Vlasov stochastic differential equations and reduce control consumption effectively. Key contributions include the following: (1) Lévy noise is introduced into the hybrid McKean–Vlasov framework to describe discontinuous disturbances. We further derive the existence, uniqueness and generalized Itô formula for the above system. (2) A new distribution-dependent Lyapunov functional to prove moment finiteness, mean square, and asymptotic exponential stability is constructed. (3) We derive explicit ranges for the AIC time rate and observation intervals. By tightening the state error bound via an innovative technique, the control design constraints are effectively relaxed. (4) We prove the equivalence of exponential stability between the controlled system and its particle approximation. This approach avoids the computational intractability of the exact probability distribution. Finally, the efficacy of our method is demonstrated through a numerical example. Full article

This study investigates the pressure-dependent structural, electronic, mechanical, and thermoelectric properties of LiYN (Y = Sr, Mg, Zn) half-Heusler compounds using first-principles calculations. The structural stability was analyzed by fitting the total energy versus volume curves using the Birch–Murnaghan equation of state, allowing the determination of equilibrium lattice parameters and bulk moduli at pressures of 0, 5, and 10 GPa. Elastic constants were calculated to assess the mechanical stability, and all compounds satisfy the Born stability criteria over the entire pressure range. The Pugh ratio (B/G) and Poisson’s ratio (ν) indicate that LiSrN, LiMgN, and LiZnN exhibit predominantly brittle behavior under 0 GPa. Electronic band structure calculations reveal that LiMgN and LiZnN exhibit direct band gaps, whereas LiSrN shows an indirect band gap. Increasing pressure leads to a systematic widening of the band gaps due to lattice compression. Thermoelectric properties were evaluated using the Boltzmann transport theory within the constant relaxation time approximation. The Seebeck coefficient, electrical conductivity, and figure of merit (ZT) were found to be strongly dependent on both temperature and pressure. Notably, at 300 K, the ZT values increase from 0.005, 0.35, and 0.54 at 0 GPa to 0.027, 1.12, and 1.13 at 10 GPa for LiMgN, LiSrN, and LiZnN, respectively. These results demonstrate that hydrostatic pressure significantly enhances the thermoelectric performance of LiYN compounds, highlighting their promising potential for thermoelectric energy conversion applications. Full article

To address the durability limitations of conventional crack sealants under coupled extreme temperatures and traffic loads in long-life pavements, a bio-oil composite-modified patching material was developed using 90# base asphalt as the matrix, synergistically modified with crumb rubber (CR) and epoxidized soybean oil (ESO). To resolve the contradictory requirements for high elasticity and thermal expansion/contraction coordination in sealants, ESO was introduced; its polar epoxy groups optimize phase compatibility and promote low-temperature stress relaxation without restricting thermal deformability. Rheological evaluations revealed that the optimal system (OPT) successfully extended the service temperature window from PG 76–−24 °C (baseline) to PG 82–−24 °C, significantly enhancing its adaptability to extreme climatic fluctuations. At −24 °C, OPT exhibited a reduced creep stiffness (S) of 164 MPa and an increased creep rate (m) of 0.312, with a cracking resistance ratio (k) as low as 525.6; the quantitative significance of these metrics lies in granting the sealant superior stress relaxation capacity, enabling it to accommodate dynamic crack widening without interfacial debonding or brittle fracture. Fatigue testing via time sweeps demonstrated that N_f50 reached 2890 cycles, highlighting robust long-term resistance against high-frequency shear strains induced by tire edges. Micro-mechanistic analyses (FTIR, TG/DTG, and DSC) confirmed that the modification is primarily driven by physical blending. The elevation of the thermal decomposition threshold (T5%) to 302.4 °C and the residue at 600 °C to 44.8% provide a critical safety margin for high-temperature construction heating, preventing thermal degradation. Furthermore, the glass transition temperature (T_g) decreased to approximately −35.2 °C. These findings establish a rigorous quantitative and mechanistic framework for designing sustainable, high-performance patching materials for resilient pavement maintenance. Full article

Ion-acoustic waves in dense quantum plasmas are strongly influenced by Fermi degeneracy, Landau quantization, and finite-temperature effects, and in many relevant environments, they also experience memory and nonlocal transport processes that cannot be captured within the planar integer Korteweg-de Vries (KdV) paradigm. In the present work, we revisit this problem by considering a two-fluid, partially degenerate electron-ion plasma in which electron trapping in the presence of a quantizing field and finite temperature is taken into account. Starting from the normalized fluid-Poisson system appropriate for such magnetized quantum plasmas, the reductive perturbation technique is used to derive the planar integer KdV equation for weakly nonlinear ion-acoustic disturbances. Within this integer-order KdV framework, we recast the evolution equation as a planar dynamical system, construct the associated Hamiltonian and effective Sagdeev-like potential, and demonstrate the existence of compressive solitary waves and nonlinear periodic modes via homoclinic and periodic phase-space orbits. Exact multi-soliton solutions and interaction states are then obtained by combining Hirota’s direct bilinear method with generalized Wronskian representations, allowing us to describe not only standard one-, two-, and three-soliton profiles but also positon-negaton interactions relevant to magnetized, partially degenerate plasmas. To incorporate hereditary and history-dependent effects that arise from anomalous transport and nonlocal temporal response in dense environments, we extend the model by introducing a Caputo time-fractional derivative, thereby obtaining a time-fractional KdV (FKdV) equation that continuously connects the classical KdV limit to fractional dynamics. The FKdV equation is analyzed using the Tantawy technique. This semi-analytical iterative scheme yields rapidly convergent series approximations for the fractional ion-acoustic soliton and provides explicit control of the approximation error. The fractional solutions show that varying the order of the Caputo derivative modifies the amplitude, width, and temporal relaxation of the solitary structures and can even split the pulse into two distinct lobes, in contrast with the nearly rigid propagation predicted by the integer-order KdV equation. Taken together, these results clarify how Landau quantization, finite electron temperature, and fractional-order memory jointly shape the morphology, robustness, and interaction properties of ion-acoustic structures in strongly magnetized quantum plasmas of astrophysical and high-energy-density laboratory interest. Full article

Unmanned aerial vehicles (UAVs) are increasingly employed for parcel logistics while simultaneously serving as aerial communication platforms. However, jointly optimizing pickup-and-delivery operations and wireless communication raises a large-scale mixed-integer nonlinear programming problem due to the coupling of binary logistics decisions, trajectory planning, time allocation, user scheduling, and transmit-power control. This paper proposes a two-phase optimization framework that enables a dual-purpose UAV mission by jointly considering parcel pickup-and-delivery and downlink communication within a single framework. The key strength of the proposed approach is that it separates the logistics-dominated delivery stage from the communication-oriented service stage, thereby reducing the difficulty of directly handling the highly coupled MINLP while exploiting the residual mission time for communication enhancement. In Phase 1, a pickup-and-delivery optimization problem is formulated to minimize the delivery completion time by determining the UAV trajectory, time-slot lengths, and item handling sequence, where the binary pickup/drop-off decisions are relaxed and progressively enforced through a penalty convex–concave procedure. In Phase 2, communication performance is enhanced by optimizing user scheduling and transmit power over the entire mission horizon, together with residual flight trajectory refinement after delivery completion using successive convex approximation and block coordinate descent. Simulation results show that the proposed algorithm substantially improves the minimum average spectral efficiency among ground nodes while achieving early completion of logistics tasks. Compared with baseline strategies, the proposed method delivers consistent performance gains under various system parameters. In particular, it improves the minimum average spectral efficiency by up to $15\%$ compared with the baseline that removes the proposed post-delivery trajectory refinement, demonstrating the benefit of exploiting the residual flight trajectory for communication enhancement after delivery completion. Full article

This paper presents a theoretically grounded integration of deterministic Q-learning with relational game theory (QLRG) for efficiently identifying minimal winning coalitions in Online Social Networks (OSNs). We address the fundamental challenge that coalition formation is NP-hard under traditional approaches by leveraging structural properties of relational dependencies and Armstrong’s axioms to transform the problem into one solvable in polynomial time. Our framework reduces the state space from exponential O(2ⁿ) to O(n²) through a sufficient statistic representation based on coalition size, follower reach, and terminal status, while achieving O(n⁴) time complexity under deterministic, static, and sufficiently symmetric influence structures. The QLRG framework introduces three critical innovations: (1) a principled agent selection mechanism derived directly from the Q-function that eliminates heuristic weight tuning; (2) a formal Boost action defined through temporal closure operators that captures influence spread dynamics; and (3) a constrained MDP formulation that enforces relational consistency through action elimination rather than penalty terms. We prove that the Bellman optimality operator forms a contraction mapping, guaranteeing deterministic convergence to optimal policies with established rates of O(1/√k) for decreasing learning rates or linear convergence up to bias for constant rates. To bridge the gap between this idealized model and the asymmetry inherent in real OSNs, we further develop a cluster-based sufficient statistics approach. By partitioning the network into communities with bounded internal variation, we relax the global symmetry requirement while preserving polynomial state space complexity, and obtaining a single within-community swap changes the optimal Q-value by at most ${\displaystyle \frac{{\epsilon }_i}{1-\gamma }}$, which is a local Lipschitz continuity result. The implications of this are both theoretical and practical, and they form the bedrock for relaxing the global symmetry assumption in the QLRG framework. Empirical validation on synthetic networks satisfying the symmetry assumption demonstrates that QLRG consistently identifies minimal winning coalitions matching the optimal solutions found by exhaustive search, while operating with polynomial-time complexity. Unlike conventional approaches, our framework simultaneously satisfies four critical properties: deterministic convergence, policy optimality, minimal coalition identification, and computational tractability. The work bridges computational social science and operations research, providing a mathematically rigorous foundation for strategic decision-making in influencer marketing and coalition formation. While the framework requires symmetry assumptions that may only hold approximately in real-world OSNs, it establishes an idealized baseline for future extensions addressing stochasticity, dynamics, and partial observability. This research represents a paradigm shift from empirical improvements to theoretically grounded convergence guarantees for coalition formation problems, demonstrating how structural mathematical insights can transform intractable problems into efficiently solvable ones without sacrificing solution quality. Full article

We study the discrete-time amplitude-constrained additive white Gaussian noise (AWGN) channel from the perspective of near-optimal input distributions in the high-SNR, or equivalently large-amplitude, regime. While it is known that the capacity-achieving input is discrete with finitely many mass points, the precise scaling of its support size as a function of the amplitude constraint remains an open problem. In this work, we instead consider the minimal support size required to achieve capacity up to an $\epsilon$-gap. We introduce the quantity $K_{\epsilon }\left(A\right)$, defined as the smallest support size among discrete inputs supported on $[-A,A]$ that achieves mutual information within $\epsilon$ of capacity. We show that this relaxed formulation is significantly more tractable and admits sharp characterizations in several vanishing-gap regimes. In particular, for polynomially decaying gaps, $\epsilon =A^{-\beta }$ with $\beta \ge 1$, we establish that $K_{\epsilon }\left(A\right)=\Theta \left(A\sqrt{logA}\right)$ as $A\to \infty$. For exponentially small gaps, we obtain bounds of order between $A\sqrt{logA}$ and $A^{3/2}$. Our approach combines approximation-theoretic bounds for Gaussian mixtures with information-theoretic control of entropy via ${\chi }^2$-divergence, together with a wrapping argument that relates the problem to approximating the uniform distribution on a circle. Beyond the technical results, our framework provides a conceptual explanation for the variety of scaling laws observed in prior numerical studies, suggesting that these may correspond to different regimes of $\epsilon$-optimality rather than intrinsic properties of the exact optimizer. Full article

The energy-intensive nature of primary aluminum production necessitates advanced computational tools for process optimization. This study presents a coupled electro-thermal model of an aluminum reduction cell, developed within the framework of smart manufacturing. Using the finite difference method (FDM) implemented in MATLAB R2025b, the model resolves the three-dimensional configuration of a cell with eight prebaked anodes across four distinct physical domains (electrolyte, anodes, cathode, and gas phase). The computational grid comprises approximately 45,000 nodes with refined vertical resolution (Δz = 0.025 m) in the interelectrode gap. The electrostatic solution converges within 150–200 iterations using successive over-relaxation (SOR, ω = 1.5), with a total runtime under 15 min for 30,000 s of simulated physical time on a standard desktop workstation. Simulation results reveal characteristic temperature profiles with maxima reaching 1150 °C and a thermal uniformity index of approximately 130 °C across the central cross-section. The predicted specific energy consumption of 14.0 MWh/t Al aligns with industrial benchmarks. This computationally accessible virtual testbed enables rapid assessment of design modifications and process parameters, supporting the goals of energy efficiency and enhanced operational stability in primary aluminum production. Full article

Time-interleaved analog-to-digital converters (TI-ADC) are sensitive to inter-phase timing skew, which degrades effective resolution unless mitigated by careful phase alignment or calibration. This paper presents a low-speed proof-of-concept four-phase TI-ADC based on dual-slope pulse-width modulation, incorporating an adjustable ON-TIME delay mechanism at the analog front end. The proposed approach enables controlled shifting of the effective sampling instant at the comparator/D-flip-flop interface without altering waveform amplitude or functional linearity. A four-phase up/down binary counter implemented using a Gray-code-based phase multiplier provides evenly spaced phases with reduced switching activity. Measurements from a breadboard prototype operating at approximately 1.5 MHz demonstrate that the adjustable ON-TIME delay can align adjacent phases and constrain observed inter-phase timing skew to the order of approximately 30 ns within the measurement resolution. The results indicate that analog front-end phase pre-alignment can complement or relax subsequent digital background calibration in time-interleaved ADC systems. Full article