Search Results (518)

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

The Kudryashov–Sinelshchikov equation (KSE) is crucial in modeling pressure waves in liquids containing gas bubbles, capturing both nonlinear wave phenomena and dispersion effects. This article applies the reproducing kernel Hilbert space method (RKHSM) to find a numerical solution for the time-fractional KSE. We develop a numerical solution to the KSE using the RKHSM, which offers an efficient and accurate approach for solving nonlinear partial differential equations due to its smoothness and orthogonality properties. The key components of this method include the reproducing kernel (RK) theory, important Hilbert spaces, normal basis, orthogonalization, and homogenization. We construct an appropriate RK and derive an iterative solution that converges rapidly to the exact solution. The effectiveness of this approach is demonstrated through numerical simulations in which we analyze the behavior of pressure waves and compare the results with existing analytical and numerical solutions. The RKHSM consistently demonstrates highly accurate, rapid convergence, and remarkable stability across a wide range of problems. Thus, the RKHSM is a promising tool for studying wave propagation in bubbly liquids. Full article

The Kuramoto–Sivashinsky (KS) equation and its fractional form (FKS) are widely used across scientific fields, including fluid dynamics, plasma physics, and chemical processes, to model nonlinear phenomena such as shock waves. It is worth emphasizing that this contribution is part (II) of a larger, systematic research program aimed at modeling, for the first time, completely nonintegrable, nonplanar, and fractional nonplanar evolutionary wave equations. This work focuses on the nonplanar KS framework and its applications to dust–acoustic shock waves in a complex plasma composed of inertial dust grains and inertialess nonextensive ions. This study analyzes both the nonplanar integer KS and nonplanar FKS equations, accounting for geometric effects. This is because the nonplanar model is most suitable for analyzing various nonlinear phenomena (e.g., shock waves) that arise and propagate in plasma physics, fluids, and other physical and engineering systems. Since the nonplanar KS equation is a fully non-integrable problem, its analysis poses a significant challenge for studying the properties of nonplanar shock waves in plasma physics. Therefore, the primary objective of this study is to analyze the nonplanar KS equation using the Ansatz method, thereby deriving semi-analytical solutions that simulate the propagation mechanism of nonplanar shock waves in various physical systems. Following this, we investigate the effect of the fractional factor on the profiles of nonplanar dust–acoustic shock waves to elucidate their propagation mechanism and assess the impact of the memory factor on their behavior. To achieve the second goal, we face a significant challenge because the model under study does not support exact solutions and is more complex than simpler physical models. Thus, the Tantawy technique is employed to overcome this challenge and to analyze this model for generating highly accurate analytical approximations suitable for modeling nonplanar fractional shock waves in various plasma models and in other physical and engineering systems. Full article

This article covers the rarely focused-on topic of optimizing unmanned aerial vehicle (UAV) flight paths around telecommunication masts. Due to the large variety of structures, along with additional obstacles such as stiffening struts, nearby buildings, and tall vegetation, collecting object data is a complex and demanding problem. One of the main applications of small UAVs is the ability to generate a point cloud of various objects. These are generated using pictures taken by the UAV and information about its position, which are then subjected to special analysis. This article examines the development of an optimal method for conducting flights around telecommunication masts. Many additional difficulties characterize this type of object. Among them, we can include lashings, communication interference caused by wave propagation through antennas, and the high diversity of objects. Finding an optimal, general methodology for performing such flights, taking into account all the difficulties and requirements for the later-generated point cloud, becomes a very complex and complicated problem. In this work, the problems of performing optimal flights around telecommunication masts are described. Then, solutions for taking pictures and different flight paths are considered. An example application for creating flight trajectories around such masts, written in the MATLAB (ver. R2022b) environment, is also presented. Finally, the results and conclusions obtained are described. Full article

Air–ground joint jamming enables three-dimensional, distributed jamming configurations, making it effective against air–ground communication networks with complex, dynamically adjustable links. Once the jamming layout is fixed, dynamic jamming power scheduling becomes essential to conserve energy and prolong jamming duration. However, existing methods suffer from poor applicability in such scenarios, primarily due to their sparse deployment and adversarial nature. To address this limitation, this paper develops a set of mathematical models and a dedicated algorithm for air–ground communication countermeasures. Specifically, we (1) randomly select communication nodes to determine the jammer operation sequence; (2) schedule the number of active jammers by sorting transmission path losses in ascending order; and (3) estimate jamming effects using electromagnetic wave propagation characteristics to adjust jamming power dynamically. This approach formally converts the original dynamic, stochastic jamming resource scheduling problem into a static, deterministic one via cognitive certainty of dynamic parameters and deterministic modeling of stochastic factors—enabling rapid adaptation to unknown, dynamic communication power strategies and resolving the coordination challenge in air–ground joint jamming. Experimental results demonstrate that the proposed Transmission Loss Ordering Algorithm (TLOA) extends the system operating duration by up to 41.6% compared to benchmark methods (e.g., genetic algorithm). Full article

In high-frequency circuit design, parameters such as the characteristic impedance and propagation constant of transmission lines directly affect key performance metrics, including signal integrity and power transmission efficiency. To address the challenge of optimizing impedance matching for high-frequency PCB transmission lines, this study applies a hybrid deep Q-network—genetic algorithm (DQN-GA) that integrates deep reinforcement learning with a genetic algorithm (GA). Unlike existing methods that primarily focus on predictive modeling or single-algorithm optimization, the proposed approach introduces a bidirectional interaction mechanism for algorithm fusion: transmission line structures learned by the deep Q-network (DQN) are encoded as chromosomes to enhance the diversity of the genetic algorithm population; simultaneously, high-fitness individuals from the genetic algorithm are decoded and stored in the experience replay pool of the DQN to accelerate its convergence. Simulation results demonstrate that the DQN-GA algorithm significantly outperforms both unoptimized structures and standalone GA methods, achieving substantial improvements in fitness scores and S11 transmission coefficients. This algorithm effectively overcomes the limitations of conventional approaches in addressing complex reflected wave compensation problems in high-frequency applications, providing a robust solution for signal integrity optimization in high-speed circuit design. This study not only advances the field of intelligent circuit optimization but also establishes a valuable framework for the application of hybrid algorithms to complex engineering challenges. Full article

Physics–Informed Neural Networks (PINNs) have demonstrated efficacy in solving both forward and inverse problems for nonlinear partial differential equations (PDEs). However, they frequently struggle to accurately capture multiscale physical features, particularly in regions exhibiting sharp local variations such as shock waves and discontinuities, and often suffer from optimization difficulties in complex loss landscapes. To address these issues, we propose LocRes–PINN, a physics–informed neural network framework that integrates local awareness mechanisms with residual learning. This framework integrates a radial basis function (RBF) encoder to enhance the perception of local variations and embeds it within a residual backbone to facilitate stable gradient propagation. Furthermore, we incorporate a residual–based adaptive refinement strategy and an adaptive weighted loss scheme to dynamically focus training on high–error regions and balance multi–objective constraints. Numerical experiments on the Extended Korteweg–de Vries, Navier–Stokes, and Burgers equations demonstrate that LocRes–PINN reduces relative prediction errors by approximately 12% to 67% compared to standard benchmarks. The results also verify the model’s robustness in parameter identification and noise resilience. Full article

Despite existing protection limits established by different health agencies and regulatory bodies, chronic exposure to non-ionising electromagnetic field radiation (NIR) has raised concerns about its potential biological effects and its impact on human health. Exposure to NIR in urban environments is almost inevitable due to the density of devices and communication systems that emit these waves. Correctly measuring exposure levels among city residents is key to determining whether there is a relationship between these levels and potential health problems associated with NIR. Several factors, including the ubiquity of electromagnetic fields (EMFs) and people’s unawareness of their exposure, make the NIR assessment challenging. This paper proposes a standardised procedure for NIR testing and measurement for frequencies from 100 kHz to 3 GHz, designed explicitly for outdoor urban environments. The measurement procedure is intended for populated urban areas, a complex environment for signal propagation. The complete procedure, techniques, and equipment used for wideband and narrowband measurements are detailed, along with their corresponding overall uncertainty budgets. The data collected by this procedure are suitable and valuable for comparative epidemiological studies due to a systematic measurement protocol and rigorous control of measurement uncertainty. The proposed measurement procedure has been tested in two cities in central Spain, with a total population of 262,000. A total of 534 measurement points have been performed. The results can be used to verify compliance with exposure limits and to demonstrate levels below the applicable regulatory limits. Furthermore, it has been possible to test the validity of the hypothesis that urban environments can be characterised by NIR exposure, which was postulated in this work based on an ITU-R-inspired simplification that classifies urban outdoor areas into representative exposure categories. Full article

To address the fault location problem in multi-terminal hybrid overhead–cable transmission lines with multiple sections, this paper proposes a novel method combining Modified Ensemble Empirical Mode Decomposition (MEEMD) and the Teager Energy Operator (TEO). First, the MEEMD algorithm—which mitigates mode mixing—is integrated with the TEO, which captures instantaneous energy variations, to achieve accurate detection of traveling wavefronts. Considering the topological complexity of multi-terminal hybrid transmission lines, a fault branch separation and iterative judgment method is proposed. Based on the arrival time characteristics of traveling waves, two topology decoupling strategies are designed to enable branch identification through network reconstruction and iterative computation. After determining the faulted branch, the fault section is precisely localized by comparing the time difference between the arrival of traveling waves at branch terminals and T-nodes with the propagation time differences at each connection point. Finally, the dual-ended traveling wave method is applied to calculate the fault distance. The proposed method is validated through co-simulation using PSCAD 4.6.2 and MATLAB R2023b. Comparative analysis of ranging accuracy demonstrates that this approach ensures reliable fault location under varying fault positions and transition resistances. Full article