Search Results (259)

We conducted a theoretical analysis on the diffusiophoretic motion of a dielectric droplet in a cylindrical pore in the presence of an induced diffusion potential, such as that in a NaCl electrolyte solution. The fundamental electrokinetic governing equations are solved using a patched pseudo-spectral method based on Chebyshev polynomials, coupled with a geometric mapping scheme to handle the irregular solution domain. The impact of the boundary confinement effect on droplet mobility is examined in detail. Interesting electrokinetic phenomena are found in this work, such as mobility reversal in narrow cylindrical pores with the droplet moving against the direction expected based on the classical Coulomb electrostatic law due to the strong boundary confinement effect. Moreover, “solidification phenomenon” is also found at some specific pore radius where the droplets move as rigid particles with no interior recirculating vortex flows regardless of the droplet viscosities. Corresponding critical points of ${\mathrm{R}}_{\mathrm{w}}^{\mathrm{*}}$, the ratio of droplet radius to the cylindrical radius are found where the spinning orientation on the droplet surface changes each time as it passes them. The profound boundary confinement effect, both electrostatically and hydrodynamically, is responsible for these peculiar phenomena. The results presented here have direct applications in microfluidic and nanofluidic operations as well as drug delivery applications. Full article

Cloud detection in high-resolution Gaofen-1 (GF-1) imagery is challenging due to the absence of short-wave infrared (SWIR) bands, which prevents the use of physically interpretable indices such as the Normalized Difference Snow Index (NDSI) and often leads to severe cloud–snow confusion. To address this limitation, we propose a unified framework, termed the Cross-Modality Spectral Expansion and Dual-Prior Network (CMSE-DPNet), that integrates cross-modality spectral expansion with physical–semantic dual priors. First, an improved CycleGAN reconstructs 13-band pseudo-Sentinel-2 spectra from four-band GF-1 imagery, enabling the computation of snow-sensitive physical indices. Second, a Snow-Aware Feature Attention Guidance Module (SAFAGM) introduces pixel-level physical priors derived from NDSI, while a Label-Guided Channel Attention Module (LG-CAM) injects scene-level semantic priors inferred from geographic metadata using a large language model. These complementary priors guide the network to better distinguish clouds from spectrally similar backgrounds. Experiments on the GF-1 dataset show that the proposed method achieves an F1-score of 94.41% and an Intersection over Union (IoU) of 89.40%, outperforming several state-of-the-art cloud detection methods. The results indicate that cross-modality spectral expansion combined with physical–semantic prior guidance effectively improves cloud detection performance in complex cloud–snow coexistence scenarios. Full article

In this paper, a radial basis function (RBF) neural network based trajectory generation strategy is proposed to solve the online rapid generation of initial reference trajectory for low-cost hypersonic glide vehicles (HGV) under initial state perturbation. Firstly, the feasible trajectories that constitute the sample sets are offline generated by pseudospectral method according to the possible distribution of heights and velocities. Then, the sample set is randomly divided into training subset and test subset, by which the RBF neural network is trained and verified. Moreover, the input of the RBF neural network is a vector comprised by height and velocity from the initial state, whereas the output is a discrete state-control sequence which represents the trajectory from the current state to the expected final state. The simulation results validate that the proposed method has high confidence and small errors, which can improve the on-line generation efficiency of the trajectory. Full article

Background/Objectives: Spectral resolution is strongly associated with speech perception for adult cochlear implant users, but the developmental trajectory of spectral resolution in childhood is more complex and far less understood. Music-based training presents a unique opportunity to address this gap, as musical stimuli feature spectral complexity and fine frequency cues which map to spectral resolution. This study explored if a 12-week music-based intervention could support better spectral resolution in children with cochlear implants. Methods: Twelve children with cochlear implants participated in this longitudinal, repeated-measures study. The music training intervention consisted of group-based in-person music therapy and a take-home music app. Participants (six boys, six girls; M age = 7.3 years) were pseudo-randomized into an immediate training group (n = 4) or delayed-start waitlisted group (n = 8). Inclusion criteria required bilateral moderate-to-profound sensorineural hearing loss, prelingual device fitting, and consistent bilateral device use. Eight children had bilateral CIs and four were bimodal listeners. Results: Spectral resolution perception was significantly enhanced after participating in the music intervention with a mean increase of 2 rpo, F(3, 10.7) = 3.859, p = 0.017. Previous engagement with music and age were not associated with spectral resolution. Conclusions: Despite the known limitations of CIs on spectral resolution, the results of this study indicate that music training can improve spectral resolution perception in children using CIs. Full article

We develop a high-order space-time spectral method for nonlinear convection–diffusion equations with a Riemann–Liouville time-fractional derivative and a spectrally defined space-fractional Laplacian. The spatial discretization uses a Fourier spectral method that diagonalizes the fractional Laplacian under periodic boundary conditions. The temporal discretization employs a Petrov–Galerkin method based on generalized Jacobi functions which capture the initial singularity exactly. The nonlinear convection term is treated pseudo-spectrally, and the resulting algebraic system is solved with a damped Newton iteration. Rigorous error analysis proves exponential convergence in both space and time. Numerical experiments for various fractional orders confirm the spectral accuracy. Simulations of the fractional Burgers equation demonstrate that increasing the viscosity enhances diffusion and stabilizes the solution, while a nonlinear coefficient that significantly exceeds the viscosity leads to error growth over long time intervals. The method provides an efficient and accurate tool for simulating anomalous transport phenomena. Full article

Indirect methods based on Pontryagin’s Maximum Principle (PMP) offer theoretical rigor for nonlinear optimal control but suffer from extreme sensitivity to costate initialization. Physics-Informed Neural Networks (PINNs) provide a promising data-free approach to globally approximate trajectories and overcome this initialization barrier. However, they often lack strict numerical precision due to their reliance on soft penalty constraints. To bridge this gap, this paper proposes a hybrid framework that synergizes the global search capability of a structurally modified PINN with the rigorous precision of high-order Chebyshev–Gauss–Lobatto (CGL) spectral discretization. Within this framework, we first introduce a novel neural architecture that enforces the PMP stationarity condition as a hard constraint by analytically eliminating control inputs via costates, thereby reducing the optimization search space and ensuring strict optimality during training. The neural-generated trajectories subsequently provide a high-quality warm start for a CGL pseudospectral solver, transforming the problem into a single-shot convex quadratic programming formulation. Numerical experiments on the Van der Pol oscillator and elliptic PDE optimal control problems demonstrate that this strategy effectively mitigates the initialization sensitivity of indirect methods. The results show that the proposed method achieves superior accuracy and convergence stability compared to standalone PINN solvers, providing a robust initialization-free approach for complex nonlinear optimal control. Full article

Object detection in high-resolution remote sensing images under complex industrial environments is fundamentally constrained by the inherent limitations of single-modality sensors. Optical imagery is prone to background confusion and pseudo-target interference, while synthetic aperture radar (SAR) imagery suffers from speckle noise and structural ambiguity. This work investigates a critical evaluation gap in multimodal fusion, where traditional image-level quality metrics do not consistently reflect downstream detection performance. To address this issue, we propose a task-oriented framework termed the Multi-Source Fusion for Enhanced Object Detection Network (MSFE-Net). The proposed method integrates pixel-level optical–SAR fusion with a YOLOv11-based detector, enabling the learning of task-relevant representations by exploiting complementary optical spectral cues and SAR scattering characteristics. Extensive experiments are conducted across multiple fusion strategies and representative detection architectures on two industrial datasets covering oil tanks and photovoltaic arrays. The results consistently reveal a nonlinear decoupling between image-level fusion metrics and detection accuracy, indicating that improvements in global statistical image quality do not necessarily lead to superior task performance. Furthermore, the proposed framework demonstrates improved robustness in complex scenarios involving multi-scale and weak targets. Specifically, MSFE-Net achieves 99.1% mAP@50 for oil tank detection (19.5% improvement over SAR-only baselines) and 90.2% mAP@50 for photovoltaic array detection, with stable performance across different evaluation settings. These results highlight the importance of task-oriented evaluation in multimodal remote sensing fusion and suggest that downstream detection performance provides a more reliable criterion than conventional image-quality metrics. Full article

Prediction of the reachable domain for high-threat unmanned aerial vehicles (UAVs) is critical for enabling cross-domain flight vehicles to perform proactive avoidance maneuvers. To address this challenge, this paper proposes a novel generic framework that integrates a Radau pseudospectral method (RPM) with a BP neural network, supported by information acquired from satellites. The framework begins by estimating a preliminary state vector of the non-cooperative target, including its coarse position and velocity, via a Newton iterative algorithm. To refine this initial estimate and enable continuous tracking, an Extended Kalman Filter (EKF) is fused with a flight vehicle dynamics model. Subsequently, the RPM is employed to solve the trajectory planning problem, generating a comprehensive database for offline training. This database is then used to train a multilayer feedforward neural network within an offline training and online application framework, which drastically reduces computational complexity and time. Finally, numerical simulations demonstrate the method’s high prediction accuracy and strong robustness against tracking uncertainties. Crucially, the neural network predicts the reachable domain in just 0.01 s, making it highly viable for real-time online applications. Full article

Rapid and robust trajectory planning for the Terminal Area Energy Management (TAEM) phase of horizontal-landing Reusable Launch Vehicles (RLVs) is critical but challenging due to large initial deviations, stringent terminal constraints, and strong model nonlinearities. To address the limitations of existing methods in convergence reliability and computational speed, this paper proposes a novel online trajectory optimization framework based on analytical lateral planning and equivalent dynamic decoupling. First, a cubic Bézier curve is employed to parameterize the lateral ground track, enabling the rapid generation of analytical expressions for the lateral states that strictly satisfy boundary constraints. Leveraging these analytical solutions, the original six-degree-of-freedom dynamics are exactly decoupled and reduced to a lower-dimensional model governing only the longitudinal motion. To further mitigate nonlinearity, the third derivative of height with respect to range is introduced as a virtual control variable, transforming the problem into a smoother form. The resulting equivalent longitudinal optimization problem is then efficiently solved using the Gauss Pseudospectral Method. Numerical simulations demonstrate that the proposed method significantly outperforms traditional approaches in computational efficiency: it generates feasible trajectories satisfying all constraints within 0.26 s (3$\sigma$ value). Furthermore, the method exhibits remarkable insensitivity to initial guesses, achieving stable convergence even with simple linear initialization. This approach provides a robust and real-time capable solution for complex TAEM trajectory optimization problems characterized by high nonlinearity and multiple constraints. Full article

Differential operators often admit multiple algebraically equivalent symbolic formulations, yet those formulations can differ in the organization of their internal structure prior to solution analysis. A reproducible symbolic framework is introduced to compare such formulations at the level of operator expressions. Within a declared symbolic specification consisting of a fixed grammar, an admissible weight class, canonical compression rules, and an admissible family of reformulations, we define four encoding-relative structural descriptors: structural strain $\tau$, structural curvature $\kappa$, compressibility $\sigma$, and the balance ratio $\Gamma =\kappa /\tau$. Structural strain compares an encoding to a designated reference representation, while compressibility measures reduction under canonical symbolic compression. These quantities are deterministic descriptors within the declared encoding class rather than coordinate-free invariants of the underlying operator. The structural length functional underlying these descriptors is developed, canonical compression is formalized, and finite symbolic comparison is distinguished from pathwise symbolic deformation. A robustness theorem shows that, away from the threshold surface $\Gamma =\sigma$, sufficiently small admissible perturbations preserve the induced diagnostic label. A supporting weight-robustness result further shows that qualitative labels persist across a local admissible family of weight choices under corresponding nondegeneracy conditions. The framework serves as a reproducible diagnostic for operator representations alongside Lyapunov, spectral, pseudospectral, and energy-based stability theories. Examples of representative ordinary and partial differential operators illustrate how the descriptors are computed and how they behave under admissible re-expression, while the appendices provide the technical backbone of the paper: formal definitions, reproducibility protocol, extended perturbation arguments, and explicit failure-mode analysis. Additional sensitivity checks regarding encoding, weights, and threshold variation clarify the method’s scope, and explicit failure modes delineate the boundary cases in which the descriptors cease to apply. The main contribution of this study is a formally delimited and reproducible symbolic framework for comparing differential operators under a fixed, declared specification, together with robustness results and worked examples that clarify the method’s scope. Full article

This study investigates the mechanisms of nonlinear modal interactions in a circularly curved cantilever beam, utilizing the geometrically exact Timoshenko beam formulation. The governing equations take into account shear deformation, rotary inertia, and the geometric nonlinearities associated with significant deflections. A Chebyshev pseudospectral scheme is employed to achieve highly accurate linear eigenvalues, which are subsequently used in a nonlinear modal projection to develop a reduced-order model. Explicit expressions for the quadratic and cubic modal coupling coefficients are derived. The Harmonic Balance Method is then applied to explore internal resonance phenomena, frequency modulation behavior, and the transfer of energy between non-commensurate lateral and normal vibration modes. Full article

Spectral methods form a cornerstone of linear dynamics, where evolution is resolved into harmonic modes governed by eigenvalues and spectral measures of normal operators. For nonlinear dynamical systems, however, the harmonic eigenfunction paradigm typically breaks down: Koopman operators are often non-normal, may possess a continuous spectrum, and rarely admit complete eigenbases on natural observable spaces. This work develops a resolvent-centered operator-theoretic framework for generalized spectral representations of nonlinear flows through their associated Koopman $C_0$ semigroups. Rather than relying on diagonalization, we construct resolvent-generated generalized spectral operators that yield weak integral representations of the semigroup valid in non-normal and continuous-spectrum regimes. We show that, under mild polynomial resolvent growth bounds along vertical lines, these spectral distributions become finite complex Radon measures on bounded spectral regions, thereby recovering a measure-theoretic interpretation analogous to classical spectral integrals. In the normal case, the framework reduces to the standard spectral theorem. The resulting resolvent-based perspective naturally incorporates pseudospectral amplification and transient growth, providing a unified description of both asymptotic and non-modal dynamics. Full article

Heterogeneous change detection (HCD) using satellite and Unmanned Aerial Vehicle (UAV) imagery is a pivotal task in remote sensing and Earth observation. However, the effective utilization of such multi-source data is significantly hindered by extreme spatial resolution disparities and distinct radiometric characteristics. Existing deep learning methods, often based on weight-sharing Siamese architectures, struggle to bridge these domain gaps, leading to spectral pseudo-changes and blurred detection boundaries. To address these challenges, we propose a novel Dual-Branch Cross-Scale Fusion Network (DBCF-Net) specifically tailored for heterogeneous satellite–UAV change detection. We introduce a Difference-Aware Attention Module (DAAM) to explicitly align cross-modal feature spaces and suppress domain-related noise through a hybrid local–global attention mechanism. Furthermore, an Adaptive Gated Fusion Module (AGFM) is designed to dynamically weight multi-scale interactions, ensuring the preservation of high-frequency spatial details from UAV imagery while maintaining the semantic consistency of satellite data. Extensive experiments on the Heterogeneous Satellite–UAV Dataset (HSUD) demonstrate that DBCF-Net achieves state-of-the-art performance, reaching an F1-score of 88.75% and an IoU of 80.58%. This study provides a robust technical framework for heterogeneous sensor fusion and high-precision monitoring in complex remote sensing scenarios. Full article

The Korteweg–de Vries (KdV) equation is a foundational model in geophysical fluid dynamics (GFD), governing the propagation of long internal and surface gravity waves in stratified and shallow ocean environments where the interplay between nonlinear steepening and frequency-dependent dispersion gives rise to solitons. Although the analytical tractability of the KdV equation through inverse scattering is well established, systematic numerical exploration of multi-soliton interactions remains valuable for benchmarking solvers, probing conservation properties under varied oceanic initial conditions, and building intuition for more complex ocean wave phenomena. This article presents sangkuriang, an open-source Python library that solves the KdV equation using Fourier pseudo-spectral spatial discretization and adaptive eighth-order Runge–Kutta time integration. The implementation leverages just-in-time (JIT) compilation to achieve research-grade computational efficiency on standard hardware, making it readily accessible for coastal and ocean engineering applications, including idealized modeling of internal solitary waves on continental shelves, rapid parameter studies for solitary wave propagation in stratified basins, and pedagogical investigations of nonlinear dispersive wave dynamics. The solver is validated through four progressively complex idealized scenarios motivated by oceanic wave dynamics: isolated soliton propagation, symmetric interactions, overtaking collisions, and three-body interactions. High-fidelity conservation of mass, momentum, and energy is demonstrated, with relative errors remaining below $\mathcal{O}\left({10}^{-4}\right)$ across all test cases. Measured soliton velocities align with theoretical predictions within 5%, confirming the capture of the amplitude-dependent dispersion characteristic of oceanic solitary waves. Complementary diagnostics, including spectral entropy and recurrence quantification analysis (RQA), verify that the numerical solutions preserve the regular phase-space structure characteristic of integrable Hamiltonian systems. These results establish sangkuriang as a robust, lightweight platform for reproducible numerical investigation of idealized nonlinear dispersive wave dynamics relevant to coastal and ocean engineering applications. Full article

The parafoil is highly susceptible to deviations from its reference trajectory under wind disturbances. Given its constrained longitudinal control authority, it has limited capability to correct these deviations and regain the intended glide path. To overcome this limitation, we propose a dynamic planning framework based on a layered homing strategy. The airdrop mission trajectory is initially designed as a traditional multi-segment path. To approximate non-uniform glide characteristics under wind disturbances, this planning problem incorporates a predicted wind model as an external input. Node parameters of the segmented trajectory are then solved using an improved grey wolf optimizer (IGWO). By tracking this reference trajectory, the parafoil is guided into the proximity of the target. To ensure landing precision, the terminal phase is formulated and discretized using an adaptive pseudo-spectral method (APSM). The online planner computes a real-time trajectory to account for actual motion characteristics. This dynamic replanning (DRP) compensates for deviations caused by model mismatches and external disturbances. The proposed homing method is statistically verified via extensive Monte Carlo simulations under different wind conditions. Finally, the airdrop experiment is conducted to validate the DRP method. Full article