Search Results (614)

This study aims to address the acoustic resonance control problem of a three-dimensional nose landing gear (NLG) cavity. We propose a refined numerical approach based on an eigenvalue solver for the Helmholtz equation. A high-order finite element method (FEM) combined with perfectly matched layer (PML) boundary conditions was employed to accurately capture complex eigenmodes. The radiation damping characteristics of the system were then quantitatively characterized using the quality factor (Q-factor) and resonance frequency. Results indicate that the Helmholtz-type (0,0,0) mode dominates the cavity’s resonance response, with its frequency coinciding with the shear layer-driven Rossiter mode. This study reveals a strong coupling mechanism with the shear-layer-driven Rossiter mode at Mach 0.57, confirming that this interaction is the primary driver of cavity aeroacoustic tonal noise. Taking radiation damping as the core design parameter, a systematic sensitivity analysis was conducted on geometric modifications: aft door length, front door angle, cavity volume, and the introduction of a longitudinal gap. Key findings: shortening the aft door reduces the resonance peak by 8.5 dB; introducing a longitudinal gap with a 10% width reduces the Q-factor by approximately 50%; a combined control strategy (2.5% gap width and 6% cavity volume reduction) achieves 4.9 dB of noise attenuation. Finally, this study establishes a validated acoustic-damping control framework, providing quantitative design criteria and technical guidance for aeroacoustic noise control of NLG cavities. Full article

Frequency-selective attenuation is widely needed in integrated analog front-ends, yet conventional on-chip RC low-pass filters occupy unfeasibly large silicon areas for low-frequency cutoffs and inherently introduce cumulative phase lag. Motivated by the nonlinear, frequency-dependent state evolution of memristive devices, this work experimentally demonstrates a highly compact, capacitor-free memristor–resistor network that functions as a variable-cutoff, zero-phase-lag resistive attenuator. An Au/HfO₂/Au memristor (15 µm × 15 µm) is connected in series with a load resistor and characterized over a wide frequency range. By leveraging the finite time constant of internal ionic drift, the attenuation bandwidth is strictly programmable via the device’s initial resistance. Cutoff frequencies of approximately 10 Hz, 1 kHz, and 10 kHz are achieved for initial resistances of 400 k$\Omega \pm$30 k$\Omega$, 300 k$\Omega \pm$30 k$\Omega$, and 200 k$\Omega \pm$30 k$\Omega$, respectively. Remarkably, the nonlinear state-switching mechanism enables a steep post-cutoff attenuation rate approaching −60 dB/dec—equivalent to a cascaded third-order RC network—using only a single nanoscale device. Rather than functioning as a strictly linear time-invariant (LTI) filter, the proposed circuit operates as a state-adaptive edge-processor. Its inherent amplitude-dependent dynamics and total absence of reactive poles make it exceptionally suited for highly specialized, area-constrained applications, including zero-phase closed-loop noise suppression, frequency-to-amplitude conversion, and amplitude-aware event-driven sensory preprocessing. Full article

Recently, the adaptive regularized proximal quasi-Newton (ARPQN) method has demonstrated a strong performance in solving composite optimization problems over the Stiefel manifold. However, its reliance on first-order information limits its applicability to scenarios where gradient and Hessian evaluations are unavailable or costly. In this paper, we propose a zeroth-order adaptive regularized proximal quasi-Newton method (ZO-ARPQN) for black-box composite optimization over Riemannian manifolds, particularly the Stiefel and symmetric positive definite (SPD) manifolds. The proposed method estimates the Riemannian gradient and curvature information through randomized one-point finite-difference approximations and adaptively updates a regularized quasi-Newton matrix to capture the local manifold geometry. Theoretically, we established global convergence and complex analyses under mild assumptions. More importantly, by incorporating curvature-aware regularization and random perturbations in the proximal quasi-Newton framework, we proved that ZO-ARPQN can escape strict saddle points with a high probability. This guarantees convergence to a stationary point, even in the absence of explicit gradients. Extensive numerical experiments were conducted on manifold-constrained problems, including sparse PCA and robot stiffness tuning. These demonstrated that ZO-ARPQN shows a competitive convergence behavior compared with other state-of-the-art Riemannian optimization methods, while requiring only function evaluations. Full article

Time-fractional interface problems, found in heat transfer with discontinuous conductivities and fluid flows with surface tension forces, are challenging due to irregular interfaces and the history-dependent nature of fractional derivatives. This paper presents two numerical methods for simulating time-fractional double interface problems. The first method uses the Haar wavelet collocation technique, while the second relies on a meshless approach with radial basis functions. The fractional derivatives are replaced with the Caputo sense, the resulting first-order time derivatives are handled using the finite difference method, and the spatial operator is approximated using the two proposed methods. Gauss elimination is used to solve linear problems. Quasi-Newton linearization method is used for nonlinear problems. Both methods accommodate constant and variable coefficients, handling discontinuities and singularities in both solutions and coefficients. To evaluate the effectiveness of the proposed methods, numerical experiments are carried out. The accuracy of each method is quantified using the $L_{\infty }$ error norm, and a comparative analysis highlights the validity and advantages of the approaches. Moreover, the proposed schemes are rigorously analyzed to establish their stability, and the existence and uniqueness of the solutions. Full article

We consider two steady-state heat conduction systems called, S and $S_{\alpha }$, in a multidimensional bounded domain D for the Poisson equation with source energy g. In one system, we impose mixed boundary conditions (temperature b on the boundary ${\mathsf{\Gamma }}_1$, heat flux q on ${\mathsf{\Gamma }}_2$ and an adiabatic condition on ${\mathsf{\Gamma }}_3$). In the other system, the condition on ${\mathsf{\Gamma }}_1$ is replaced by a convective heat flux condition with coefficient $\alpha$. For each of these systems, we consider three associated optimization problems $\left(P_i\right)$ and $\left(P_{i\alpha }\right)$, $i=1,2,3$, where the variable is the source energy g, the heat flux q and the environmental temperature b, respectively. In the particular case where D is a rectangle, the explicit continuous optimization variables and the corresponding state of the systems are known. In the present work, by using a finite difference scheme, we obtain the discrete systems $\left(S^h\right)$ and $\left(S_{\alpha }^h\right)$ and discrete optimization problems $\left(P_i^h\right)$ and $\left(P_{i\alpha }^h\right)$, $i=1,2,3$, where h is the space step in the discretization. Explicit discrete solutions are found, and convergence and estimation errors results are proved when h goes to zero and when $\alpha$ goes to infinity. Moreover, some numerical simulations are provided in order to test theoretical results. Finally, we note that the use of a three-point finite-difference approximation for the Neumann or Robin boundary condition at the boundary improves the global order of convergence from $O\left(h\right)$ to $O\left(h^2\right)$. Full article

Microplastics (MP) are transported through rivers, acting as major conduits to oceans, yet standard transport models often fail to capture polymer-specific dynamics like settling and removal. This study proposes two novel analytical frameworks to address this: a modified Advection–Dispersion Equation (ADE) incorporating first-order sinking and removal, and a multi-phase model accounting for hydrodynamic–particle coupling. We derived exact closed-form solutions for a finite pulse input and validated the baseline model against established results. Our results demonstrate that the conventional ADE significantly overestimates peak MP concentrations, while the modified ADE reveals a “stretching” effect that extends the duration of ecosystem exposure. Our analysis indicates that sinking is the primary driver of mass loss to sediments, with higher sinking rates reducing aqueous concentrations by approximately 50% compared to non-settling scenarios. However, removal employs negligible influence during the initial pulse phase but shows cumulative impact over long transport distances. The study highlights the critical need to incorporate sediment accumulation terms into risk assessments, as ignoring sinking leads to underestimating benthic pollution and overestimating marine flux. Additionally, the multi-phase formulation provides a theoretical basis for modeling dense plastic spills where particles alter flow momentum. Full article

Periodic supercell lattice structures with elements of random polydispersity disorder were created to simulate the effect of randomization on photonic crystals using finite-difference time domain (FDTD) methods. As a key exemplar system, a three-dimensional “inverse opal” structure of a face-centered cubic lattice with air spheres in a silicon dielectric was simulated, with sphere radii within supercells following a randomized Gaussian distribution, with characteristic standard deviation and mean. A corresponding ordered lattice with a bandgap with magnitude 3.5% of the normalized frequency range was used as a direct control, with sphere radius 0.34 times the lattice constant a. For a range of standard deviations, up to 5.9% of the 0.34a mean, a Monte Carlo-style approach was adopted, with photonic band properties analyzed over a large number of repeat simulations to ensure statistical significance. The corresponding Gaussian distribution in the resultant photonic bandgap magnitudes is broadened with increasing polydispersity such that an evolving fraction of simulations no longer exhibits a non-zero bandgap. A characteristic pseudo-transition occurs at a standard deviation of approximately 4.1% of the 0.34a mean, above where the frequency of simulations still returning a finite bandgap rapidly diminishes. Some isolated configurations, with a high degree of uniqueness, can exhibit enhanced bandgap properties (greater than the 3.5% benchmark) despite considerable polydisperse disordering; we envisage that these findings point towards the use of engineered randomness in supercell systems to create desired photonic crystal properties and functionality, such as localization and photonic bandgaps. Full article

Standard numerical methods such as Runge–Kutta and Euler methods have been widely used to approximate solutions to nonlinear systems. These methods converge to the solution only for small step sizes; for larger time steps, they generally generate spurious or chaotic solutions. In this paper, we consider a malaria propagation model with control for which we construct a second-order nonstandard finite difference scheme that preserves the important mathematical properties of the continuous model, which are positivity, boundedness, and stability of solutions irrespective of the step size. Moreover, we show that the equilibrium points of the discrete model are the same as those of the continuous model. By applying the double mesh principle, we provide evidence that the second-order NSFD scheme approximates the true solution with small errors. Theoretical assertions and numerical results show the advantages of the developed second-order nonstandard finite difference method. Full article

Cantilevered unstable rock masses constitute a prevalent geological hazard, with their stability intrinsically governed by the depth of trailing edge cracks. Traditional stability assessment methods, which largely rely on static calculations or displacement monitoring, often suffer from poor timeliness and insufficient early warning capabilities. To address these limitations, this study employs the Extended Finite Element Method (XFEM) to simulate the natural crack propagation trajectory and investigate the associated dynamic response characteristics under loading. The simulation results demonstrate that XFEM effectively captures the natural “vertical-to-oblique” fracture morphology, overcoming the limitations of pre-defined crack models. A critical correlation is established between crack evolution and natural frequency: the first-order natural frequency exhibits a staged decline, characterized by a precipitous drop of approximately 7 Hz during the late stage of fracture development (80–97% depth). Consequently, a “crack evolution–frequency response” model is proposed. This model confirms that natural frequency is a significantly more sensitive indicator of internal damage than displacement, providing a novel theoretical foundation and technical pathway for the early identification and dynamic evaluation of rock mass stability. Full article

The inevitable pore defects generated in the preparation process have a great impact on the mechanical properties of the ceramic matrix composites. However, the pore defects on the composites were ignored to a large extent in models established in the previous research. In this study, in order to investigate the bending damage behaviors of SiC_f/SiC (SiC fiber-reinforced SiC matrix) angle-interlock (2.5D) woven composites prepared by the precursor immersion pyrolysis (PIP) method, a more precise full-scale model of composites was established by finite element (FE) method with taking into account of random pore defects generated by Monte Carlo algorithm. Micro-computed tomography (Micro-CT) was employed to acquire the statistical data of the yarns and pores of SiC_f/SiC 2.5D woven composites. A bending test was conducted to study the damage behaviors of the composite and compared with the prediction of the FE model. The result shows that the proposed model with random pores can predict the mechanical damage behavior of SiC_f/SiC 2.5D woven composites effectively under three-point bending. The simulated bending strength shows a good agreement with the experimental data, with a relative error of approximately 4.6%. Full article

Historic buildings exhibit coupled response characteristics during long-term service, characterized by slowly varying global inclination evolution superimposed with local component-level deformation. Meanwhile, multi-source measurements are susceptible to environmental noise and structural non-integrality, which poses challenges to obtaining stable and physically interpretable inclination measurements. To address these issues, this study proposes a multi-source fusion monitoring method for global inclination and local deformation of historic buildings using an extended Kalman filter with fractional-order state modeling (FEKF). A state-space model incorporating global inclination, local component-level additional deformation, and their projection relationships is established, in which global inclination information derived from Global Navigation Satellite System (GNSS) and local observations obtained from inclinometers are formulated within a unified measurement framework. Fractional-order dynamics are introduced into the state evolution model to represent the long-memory and non-stationary characteristics of structural responses in historic buildings. By adopting a finite-memory approximation, the fractional-order model is embedded into the extended Kalman filtering framework, enabling joint estimation and physical decoupling of multi-source measurements. Numerical simulation results demonstrate that the proposed method can stably separate global inclination and local deformation components under noisy conditions, while improving the stability of global inclination estimation. Further validation using measured data from a historic building shows that the fusion results effectively suppress high-frequency disturbances in GNSS measurements and allow reliable reconstruction of local component-level inclination responses, indicating good stability and practical applicability. These results demonstrate that the proposed approach provides a physically consistent and robust solution for long-term posture and deformation monitoring of historic buildings. Full article

We investigate the discrete energy behavior and long-time stability of a second-order Crank–Nicolson mixed finite element discretization for the shallow water equations with nonlinear bottom friction. The method combines a compatible ${\mathrm{BDM}}_1$–${\mathrm{DG}}_0$ spatial approximation with a skew-symmetric formulation of the advective terms and a midpoint treatment of dissipative source terms. At the fully discrete level, we derive a precise mechanical energy identity showing that the scheme is energy-consistent;the discrete energy satisfies a balance law consisting of a nonnegative frictional dissipation term and a higher-order midpoint defect of the order $\mathcal{O}(\Delta t^3)$. Although the method is not unconditionally energy-dissipative, we prove that strict Lyapunov decay holds under a mild CFL-type restriction on the time step. Furthermore, we establish uniform long-time boundedness of the discrete energy and asymptotic recovery of the continuous dissipation law as $\Delta t\to 0$. We also analyze the interaction between nonlinear solver tolerances and energy diagnostics, showing that the observed positive energy increments are controlled, non-accumulating, and intrinsic to the midpoint quadrature structure rather than solver artifacts. The scheme is proven to be precisely well balanced for lake-at-rest equilibria, including nonlinear bottom friction. Comprehensive numerical experiments confirm second-order temporal accuracy, robustness under friction, asymptotic monotonicity under time step refinement, and strict equilibrium preservation. The results provide a rigorous energy-diagnostic framework clarifying when Crank–Nicolson schemes are physically reliable despite the absence of unconditional discrete dissipation. Full article

An integrated nonlinear dynamic model was developed to investigate resonance in a four-cylinder engine mounted on a viscoelastic foundation. A coupled lumped-parameter formulation captures vertical and torsional responses under unbalanced inertial forces, combustion torque, and stochastic base excitation. Time-domain simulations show that at low rotational speeds the vertical displacement reaches transient amplitudes before converging to periodic oscillations, whereas higher excitation speeds reduce steady-state amplitudes. Torsional motion exhibits initial angles near 0.05 rad that decay below 0.01 rad in steady state, with further reduction at higher speeds. Frequency-domain analysis indicates that vibration energy is concentrated in engine-order harmonics between approximately 8 and 50 Hz, while components above 60 Hz are strongly attenuated, yielding a dynamic range exceeding 50 dB. Finite element modal analysis identifies the first four structural modes between 18 Hz and 666 Hz, revealing an increasingly dominant overall translational mode and a localized directional behavior at higher frequencies. A high-dimensional kernel density spectrogram integrates modal and spectral features to map resonance regions. Results indicate that increasing rotational excitation enhances inertial stiffening, systematically reduces displacement amplitudes, and preserves bounded periodic dynamics without instability. Full article

This study proposes a three-dimensional forward modeling framework for geoelectric current distribution under high-voltage direct current (HVDC) monopolar operation. The proposed approach is based on a multi-resolution resistor network (MR-RN) discretization, in which gradient fusion interpolation is employed to suppress flux discontinuities at coarse–fine interfaces, and exterior equivalent boundary resistors are introduced to approximate open boundaries, enabling efficient and stable large-scale three-dimensional forward modeling. Compared with the traditional structured grid and finite element method (FEM), the proposed MR-RN achieves comparable accuracy while reducing computation time by up to 96% and the number of degrees of freedom by two orders of magnitude. Case studies on layered Earth, boundary extension, and substation–field coupling demonstrate that the MR-RN model maintains errors within 1–3%, confirming its suitability for large-scale HVDC ground return simulations and geoelectric safety assessment. Full article

The Burgers–Huxley equation is a nonlinear partial differential equation that incorporates convective, diffusive and reactive effects and arises in various reaction–diffusion and fluid flow models. In this paper, a numerical method based on the method of lines is proposed for its solution. The spatial derivatives are approximated using a third-order finite difference scheme, which converts the governing partial differential equation into a system of ordinary differential equations. The resulting semi-discrete system is solved in time using the classical fourth-order Runge–Kutta method. The stability and convergence properties of the proposed scheme are analyzed to establish its numerical reliability. Several numerical experiments are presented to illustrate the accuracy and efficiency of the method. The computed results confirm that the proposed approach provides accurate and stable solutions for the Burgers–Huxley equation. Full article