Search Results (526)

This paper discusses the influence of the periodicity of finite-element (FE) discrete models and its influence on solutions to the one-dimensional (1-D) wave equation. Numerical solutions to wave-propagation problems obtained via the displacement-based formulations of the finite-element method (FEM) often exhibit high-frequency behavior, which is frequently dismissed in the literature as undesired, spurious, and/or having no physical meaning. In this paper, we verify this notion by demonstrating that this behavior is not merely a computational anomaly but is due to the inherent periodic properties of discrete numerical models. Using Bloch’s theorem, we reveal and demonstrate how, at high frequencies, the discrete nature of FEM numerical models leads to the prevailing behavior governed by the periodic nature of the computational models. In order to illustrate this phenomenon, we investigate 1-D wave propagation in rods, leveraging the non-dispersive nature of the governing equation as a benchmark. In addition to the classical and specialized FEM, we analyze two alternative formulations: the time-domain spectral finite-element method (TD-SFEM) and a novel spline-based finite-element method (spFEM) proposed by the authors. The results obtained and presented explain qualitatively the origins of these numerical anomalies and suggest strategies to mitigate their effects, effectively shifting the periodicity-induced behavior beyond the range of physically relevant frequencies by appropriate selection of approximation polynomials. The authors demonstrate that this can be fully achieved only in the case of spFEM, for which the usable percentage of the available spectra of eigenfrequencies reaches 67%, while in the case of other FEM approaches discussed is significantly smaller as determined by numerical dispersion and the presence of frequency band gaps. Full article

This paper develops an analytical treatment of vibro-acoustic wave propagation in a cylindrical waveguide containing two clamped elastic membranes and a central flexible-shell segment. The acoustic field obeys the time-harmonic Helmholtz equation, the shell motion is described by Donnell–Mushtari thin-shell theory under axisymmetric loading, and the membrane response is governed by classical membrane theory and incorporated through a tailored Galerkin scheme. The resulting coupled fluid–structure boundary-value problem is solved by the Mode-Matching Method: the acoustic potentials are expanded in orthogonal radial eigenfunctions within each subregion, and continuity of pressure, normal velocity, and structural displacement are enforced at every interface. The mirror symmetry of the configuration is exploited by an exact decomposition into symmetric and anti-symmetric sub-problems, each of which reduces to a truncated linear algebraic system of dimension $4N+4$ for the unknown modal amplitudes. Acoustic power-balance identities provide a quantitative consistency check on the numerical implementation and diagnose convergence with respect to the truncation order; structural damping is accommodated through complex-modulus substitutions for the shell and the membrane tension without altering the algebraic structure of the system. The numerical results demonstrate that the dual-membrane configuration delivers transmission-loss values exceeding $25\mathrm{dB}$ across the low-frequency band relevant to HVAC and automotive applications, with a representative plateau near $13\mathrm{dB}$ at the reference geometry, through resonance-driven modal coupling between the acoustic field and the compliant interfaces. Parametric studies identify the excitation frequency, the inner-membrane radius, the shell radius, and the chamber length as effective design parameters for tuning the attenuation. The formulation furnishes a unified and computationally efficient analytical tool for predicting and optimising noise attenuation in flexibly coupled cylindrical duct systems. Full article

The quantum motion of a photon in an arbitrary medium was considered within the framework of the gauge symmetry group $SU\left(2\right)\otimes U\left(1\right)$ using the Yang–Mills (Y-M) equations for Abelian fields. A system of second-order partial differential equations (PDEs) for the vector wave function of a photon is derived using the first-order Y-M equations as identities. The full wave function of a photon was defined as the arithmetic mean of the components of the wave function. In a particular case, an equation is obtained for its full wave function, taking into account the structure of space-time in a plane perpendicular to the direction of propagation of the photon. The quantum state of a photon in a nanowaveguide was investigated, and it is shown that under certain conditions, it is reduced to the problem of two coupled 1D quantum harmonic oscillators (QHO) with variable frequencies. An explicit expression is obtained for the wave function of a photon, which is characterized by two vibrational quantum numbers. A quantum theory of a photon for a dissipative medium has been developed taking into account the processes of absorption and emission of photons. The mathematical expectation (ME) of the photon wave function is constructed as the product of two 2D integral representations in which the integrand is the solution of a system of two coupled second-order PDEs. The ME of the probability amplitude of the transition of a single-photon state into one of the two-photon entangled Bell states is constructed. Finally, it was proven that, in addition to frequency, spin, momentum and polarization, the photon also has a spatial structure responsible for the cross sections of processes in which this massless fundamental particle participates. Full article

High-speed train aerodynamics have mainly been improved by passive design methods, such as streamlined noses, local fairings, and surface smoothing. These methods have achieved clear benefits, but several important aerodynamic problems remain difficult to solve by geometry optimization alone. Open-air drag is still affected by tail flow separation, base-pressure recovery, and disturbances around bogies and the underbody; crosswind safety is influenced by unsteady leeward-side separation and wake asymmetry; slipstream behavior depends on wake vortices, boundary-layer development, and complex near-ground underbody flow; and tunnel-related pressure transients arise from compression-wave generation, propagation, and reflection. These coupled effects mean that one fixed train shape cannot perform optimally in all operating conditions. For this reason, this review proposes that active flow control (AFC) should not be regarded only as a drag-reduction or stability-improvement technique for high-speed trains. Instead, it should be understood as a mission-adaptive aerodynamic control framework, in which different control actions are used for different operating scenarios. This paper first clarifies that passive optimization is increasingly subject to diminishing returns under multi-objective and engineering constraints. It then reviews AFC studies on drag reduction, base-pressure recovery, wake and slipstream control, underbody flow conditioning, crosswind mitigation, and tunnel pressure-wave suppression. Related AFC studies on bluff bodies, road vehicles, and other separated flows are included only when their physical relevance to trains is clear. The review further distinguishes gross aerodynamic improvement from net energy gain and identifies actuator power, durability, maintainability, acoustic impact, validation level, and full-scale transferability as decisive feasibility factors. Current research is still dominated by open-loop numerical studies with simplified actuation. Future work should therefore move toward multi-objective, closed-loop, energy-aware, sensor–actuator-integrated, and explainable machine-learning-assisted AFC. The main message is that the next step in train aerodynamics is not simply a better fixed shape, but a control-enabled train that can selectively redistribute aerodynamic authority across its mission profile. Full article

Stock price prediction is a challenging problem in quantitative investment, as financial markets generate complex, noisy, and dynamic time series containing heterogeneous signals. Short-term fluctuations usually exhibit greater uncertainty and stronger local variation, whereas long-term trends convey relatively stable and persistent information shaped by market and macroeconomic conditions. However, most existing methods struggle to distinguish these two components effectively, often leading to interference between short-term fluctuations and longer-term trends. In addition, they fail to capture dynamic temporal dependencies and cross-stock information propagation while preserving the causal structure of financial time series. To tackle these issues, we propose the Wavelet-Decoupled Spatiotemporal Network (WaveDSTN). It leverages wavelet transformation to decompose stock returns into high-frequency and low-frequency information, corresponding to short-term fluctuations and long-term trends, respectively. This decomposition enables the model to learn complementary predictive patterns more effectively. Furthermore, WaveDSTN incorporates a Dual-Path Spatiotemporal Encoder to capture complex temporal dependencies and evolving cross-stock information propagation while preserving temporal order and causal consistency. Extensive experiments demonstrate that WaveDSTN achieves significant improvements over existing methods, showing that explicitly modeling trend and fluctuation components can enhance predictive accuracy and reduce uncertainty in stock return forecasting. Full article

An integrated numerical method is proposed for analyzing the nonlinear seismic response of near-fault building clusters, comprising three algorithms: (1) a structural investigated lump algorithm for elastoplastic dynamic response of structure; (2) a connecting investigated lump algorithm for bidirectional wave propagation between the site and elastoplastic building clusters; (3) a geomedia investigated lump algorithm for seismic wave propagation with an improved viscoelastic constitutive model, which allows independent definition of P/S-wave quality factors to characterize geomedia attenuation. Validated for its capability in simulating site-city dynamic interaction problems via a shaking table test, the method is applied to study the seismic response of near-fault building clusters in Xichang City under a hypothetical M_w6.8 earthquake. It is shown that irrespective of whether shallow geological structures are considered, clusters (c2–c4) situated in rupture-forward surface area within ~1.5 km of the fault trace entered the elastoplastic stage, while others (c1, c5) remained elastic. Shallow geological structures may reverse locally hanging-wall/footwall effects of both near-fault structural seismic response and ground motion. A notable seismic-response characteristic of near-fault structures undergoing the elastoplastic stage is that the permanent structural motion displacement (PSMD) at the slab of a specific floor incorporates not only the non-zero permanent ground motion displacement (PGMD) but also the non-zero final structural residual displacement (FSRD) relative to the supporting ground. The developed method could provide support for seismic damage assessment, site selection, and structural optimization design of near-fault building clusters. Full article

This paper presents a theoretical analysis of frequency shifts in broadband acoustic field interference structures caused by an internal soliton wave in shallow water. It analyzes the spectral signature of interference-maxima frequency shifts within a coupled-mode framework that describes the scattering of acoustic normal modes under soliton-induced perturbations. Using the weak coupling approximation, analytical expressions are obtained for modal phase variations and the spectral peak frequency associated with the temporal evolution of frequency shifts induced by internal soliton waves. The analytical estimates obtained in the weak coupling approximation are extensively validated using numerical simulations under realistic ocean conditions without invoking it. This paper’s theoretical analysis demonstrates that internal soliton wave-induced mode coupling produces frequency shift spectrum signatures that strongly depend on soliton parameters. These results suggest that it is potentially feasible to estimate key soliton parameters, such as propagation direction, velocity, and effective amplitude, from measured frequency shifts. Numerical simulations demonstrate the feasibility of solving this inverse problem. These findings highlight the potential of frequency shift analysis as a practical, robust tool for remote sensing of internal wave dynamics in ocean acoustics. Full article

A nonlinear ultrasonic time-domain identification method based on chaos sensitivity was proposed in this study. The Duffing chaotic system was introduced into the weak second harmonic identification to realize early detection and quantitative evaluation of fatigue damage in U71Mn steel. First, to ensure the reliability of nonlinear ultrasonic testing, a probe-pressure monitoring device was designed. Through pressure-stability experiments, 16 N was determined as the optimal pressure, which effectively suppresses contact nonlinearity interference and ensures coupling stability. Subsequently, the Duffing chaos detection system was established. The signal-system frequency-matching problem was resolved through time-scale transformation. Simultaneously, the issue of unknown initial phases was resolved using phase traversal compensation. Based on the chaotic system’s sensitivity to specific frequency signals and immunity to noise, the amplitudes of the fundamental wave and second harmonics in the target signals were quantified to calculate the nonlinear coefficient. Experimental results demonstrate that the proposed method can extract these amplitudes directly in the time domain, thereby effectively overcoming the spectral leakage inherent in traditional frequency-domain methods. The nonlinear coefficient of U71Mn steel exhibits a “double-peak” characteristic as fatigue damage increases. Specifically, the first peak appears at approximately 50% of fatigue life, while the second occurs at approximately 80%. This phenomenon is closely correlated with the distinct stages of internal fatigue crack propagation, reflecting a complex damage-evolution mechanism. This study not only provides a novel method for the precise extraction of weak nonlinear signals but also establishes a critical theoretical and experimental foundation for accurate fatigue life prediction for U71Mn rail steel. Full article

In this study, the nonlocal theory of peridynamics (PD) is adopted to simulate elastic wave propagation in an infinite plate. To realistically represent an unbounded domain and suppress artificial wave reflections at computational boundaries, the perfectly matched layer (PML) technique is incorporated into the peridynamic framework. A refined non-ordinary state-based peridynamic (RNOSB-PD) formulation is developed in which the peridynamic differential operator is employed to accurately capture wave kinematics and stress responses. The proposed model is validated through numerical simulations of wave propagation, where displacement field is examined within both the physical domain and the absorbing layers. The results demonstrate that the peridynamic PML effectively attenuates outgoing waves without generating spurious reflections, leading to responses that closely replicate those of an infinite plate. This study confirms the robustness and accuracy of the RNOSB-PD–PML approach and highlights its potential for simulating wave phenomena in unbounded or large-scale solid mechanics problems involving nonlocal effects. Full article

Cardiovascular disease has become the leading cause of death worldwide, underscoring the urgent need for widespread cardiac monitoring, while the Electrocardiogram (ECG) remains the diagnostic gold standard, the complexity of its acquisition limits its long-term feasibility. In contrast, Photoplethysmography (PPG), ubiquitous in wearable devices, is increasingly adopted due to its accessibility. However, synthesizing ECG from PPG poses an intrinsically ill-posed inverse problem. Existing purely data-driven paradigms often neglect underlying biophysical mechanisms, resulting in a lack of physical constraints and interpretability, which renders them prone to generating non-physiological hallucinations. To address this, we propose PhysDiff-LBM, a novel physics-aware framework that incorporates Lattice Boltzmann hemodynamic constraints into a conditional diffusion model. Employing a dual-stream architecture, our framework captures high-frequency morphological details via a cross-attention-guided diffusion model with region-wise adaptability. Synergistically, we physically regularize the ECG synthesis by leveraging the mesoscopic streaming and collision operators of LBM. By forcing the synthesized waveform gradients to evolve consistently with hemodynamic momentum, this mechanism constrains the model to strictly adhere to the fluid dynamic conservation laws governing pulse wave propagation. Experimental results demonstrate that our method achieves superior signal fidelity and exhibits significant advantages in downstream clinical applications. Full article

This paper deals with several equations of mathematical physics written in explicit form with their solutions. In Theorem 1, an oblique derivative problem for the string equation is studied. More precisely, the initial-boundary value problem for the string equation is investigated. The corresponding vector field on the boundary is non-vanishing and does not have a characteristic direction, but can be tangential to some part of the boundary, and it is allowed to change sign. A classical solution exists with suitable compatibility conditions at the corner points. The picture changes significantly in the case of the wave equation with several (say two: 2D) space variables in a circular cylinder. The initial-boundary value problem turns out to be underdetermined with an infinite-dimensional kernel if the boundary vector field is orthogonal to the time axis. By prescribing extra conditions on the generatrices of the cylinder where the vector field is tangential to the cylinder, we obtain a unique classical solution. In Theorem 2, we consider the Cauchy problem in the interior of the parabola of the Lorentzian-type eikonal equation and find its unique classical solution in $\{0\le x_2\le 1/2\}\cap \{x_2\ge {\displaystyle \frac{x_1^2}{2}}\}$. Propagation of singularities for the D and 3 D hyperbolic (Klein–Gordon) equations in ${\mathbf{R}}^4$, ${\mathbf{R}}^8$ is studied in Theorem 3. In the double characteristic points, the wave front propagates either along the surface of the characteristic cone, or in the solid cone starting from $(t_0,x_0)$. Full article

The coupled nonlinear system of fractional Boussinesq–Burger equations that may be utilized to model the propagation of shallow water waves is solved in this study using a novel numerical approach. The fractional derivatives in Caputo–Fabrizio and Atangana–Baleanu manner are executed in the system under consideration. The exact solutions of the proposed nonlinear fractional system are shown in the classical scenario of fractional order at $\mathrm{ß}=1$, whereas the approximate solutions are derived using the natural decomposition method. The series solution is generated such that it is simple to compute. Our results are compared with the exact results which clearly show that the suggested approach solutions quickly converge to the known accurate results. We acquire some analysis of the absolute error by comparing the approximate values with their corresponding precise solutions throughout the provided computations. Numerical and graphical simulations are used to confirm the usefulness of the suggested approach, and the outcomes are compared with well-known methods like the fractional decomposition method (FDM) and Laplace residual power series method (LRPSM). It is evident from the comparison that our approach offers better outcomes compared to other approaches. The results of the suggested method are very accurate and give helpful details on the real dynamics of the proposed system. The obtained outcomes ensure that the suggested approach is more effective and examines the highly nonlinear problems arising in engineering and science. Full article

Electromagnetic imaging in a slab medium presents significant challenges due to complex wave reflections and refractions at the interfaces of different layers. Multiple scattering and interference increase ill-posedness and nonlinearity, degrading reconstruction accuracy and stability. Under transverse magnetic (TM) and transverse electric (TE) excitations, we compare the CNN-refined reconstructions based on the Back Propagation Scheme (BPS) and the Dominant Current Scheme (DCS) to solve the Electromagnetic Inverse Scattering (EMIS) problem. Numerical results demonstrate that our proposed method can accurately reconstruct buried objects of various sizes and positions, even in the presence of noise. In particular, the DCS-CNN framework yields superior reconstruction performance compared to the BPS-CNN approach, highlighting the advantage of integrating the DCS with DL for imaging in a slab medium. Overall, this work validates the feasibility and effectiveness of combining preliminary imaging with DL, offering practical potential for solving complex inverse scattering problems. Full article

Multiple-Input–Multiple-Output Ground-Penetrating Radar (MIMO-GPR), collecting multiview–multistatic data, is now becoming an assessed diagnostic tool, enabling enhanced reconstruction accuracy and subsurface target detection due to the exploitation of multiple Tx/Rx channels. In this context, the present work deals with a 2D radar imaging approach for contactless MIMO GPR based on the equivalent permittivity concept. The imaging problem is formulated as a linearized inverse scattering problem under Born approximation, and a ray propagation model, based on equivalent permittivity spatially varying along depth, is adopted to account for the wave propagation through the air–soil interface. The resulting linear inverse problem is solved by means of an adjoint inversion, enabling reliable target reconstruction. Despite the approximation introduced by the present formulation, numerical simulations show that the proposed imaging strategy is sufficiently accurate from an engineering viewpoint and is computationally efficient. Full article

The Stueckelberg wave equation is transformed into a quantum telegraph equation and a set of stationary states is obtained as unitary solutions. As it has been shown previously that this PDE relates to the Dirac operator, and on the other hand it is a linearized Hamilton–Jacobi–Bellman PDE, from which the Schrödinger equation can be deduced in a nonrelativistic limit, it is clear that it is the key equation in relativistic quantum mechanics. We give a Bayesian interpretation for the measurement problem. The stationary solution is understood as a maximum entropy prior distribution and measurement is understood as a Bayesian update. We discuss the interpretation of the single electron experiments in the light of finite speed propagation of the transition probability field and how it relates to the interpretation of quantum mechanics more broadly. Full article