ABSTRACT The novelty of this letter lies in preliminarily analysis of the wave mapping mechanism using Gaofen-3 (GF-3) acquired in extended wide (EW) mode at low incidence angle of 10–20°. In total, 35 Chinese GF-3 images in vertical-vertical (VV) were collocated with hindcasted wave spectra from the numeric model WAVEWATCH-III (WW3). Validation of WW3-simulated significant wave heights (SWHs) against the Haiyang-2 (HY-2) altimeter wave products yields a root mean squared error (RMSE) of 0.44 m with a correlation coefficient (r) of 0.94 and a scatter index (SI) of 0.19, confirming the reliability of the WW3 simulations for this study. Subsequently, the synthetic aperture radar (SAR) intensity spectrum is simulated by multiplying the hindcasted wave spectrum by three modulation transfer functions (MTFs), i.e. tilt, hydrodynamic modulation, and velocity bunching. Based on experimental results, the spectrum correlation coefficient (Cor) and the spectrum squared error (E) of total energy between SAR intensity spectra and simulations using three MTFs are 0.94 and 7.79, respectively. These values represent significant large compared to other MTF combinations, which yield higher errors (approximately 6 E) and lower correlations (around 0.91 Cor). Therefore, it is concluded that velocity bunching has less influence on SAR mapping mechanism at low incidence angle, which is further supported by the Shapley Additive exPlanations (SHAP) analysis performed using eXtreme Gradient Boosting (XGBoost). This study establishes the foundation of wave retrieval from SAR image at low incidence angle.

A multiscale peridynamic model for surface acoustic wave-defect interactions.

Steady hydroelastic cnoidal wave on a thin flexural plate floating on a shallow water surface

Amplitude and phase modulation of SH waves by resonant scattering at PZT-5A/BaTiO3 imperfect boundary.

Conflicts, strategies, and prospects in the design of cross-spectrum compatible stealth materials: Toward synergistic electromagnetic–mechanical wave dissipation

• A rich hierarchy of topological states is achieved in fractal mechanical lattices • Knowledge of fractal topological states in mechanical structures is established • A nested fractal metamaterial enables exotic elastic wave control capabilities • Experimental realization of topological states in fractal mechanical systems • Fractal states have superb confinement, scalable quantities, and flexible locations Topological metamaterials facilitate the defect-immune manipulation of elastic waves in mechanical systems. Thus far, research on topological metamaterials has concentrated on confining elastic waves at the boundaries and interfaces of mechanical lattices with integer-dimensional periodicity. On the other hand, topological metamaterial architectures with fractal dimensionality represent an uncharted domain that has the potential to unlock elastic wave phenomena not attainable in periodic mechanical lattices. In this work, we introduce a topological elastic metamaterial that harnesses the complex boundaries and interfaces of nested fractal mechanical lattices to enable a rich collection of higher-order topological states. Theoretical modeling of a spring-mass lattice patterned into a Sierpiński carpet is utilized to establish a deep understanding of topological corner and edge states in fractal mechanical systems. A systematic design framework is pioneered that facilitates the efficient realization of fractal topological states in discrete mechanical lattices. This framework is extended to continuous structures by creating a fractal topological metamaterial composed of a thin plate with nested fractal lattices of embedded mechanical resonators. Numerical and experimental investigations of the proposed metamaterial uncover an abundance of well-confined fractal topological states that have predictable frequencies, scalable quantities, and flexible spatial locations. The presented outcomes broaden the design space for topological metamaterials, paving the way for mechanical wave control devices with unprecedented functionalities.

Quasiresonant amplification (QRA) of quasistationary Rossby waves is a mechanism for mid-latitude extreme weather that has been repeatedly proposed but subjected to only limited testing. Here, we test QRA theory by attempting to create quasiresonant Rossby waves in an idealized general circulation model, in which we identify mean flow states expected to be suitable (and unsuitable) for the existence of quasiresonant Rossby waves and quantify the associated wave amplitudes. For mean flow conditions thought to be suitable for QRA, waves of the relevant wave number are instead found to be weaker than under conditions ostensibly unsuitable for QRA. This situation cannot robustly be changed by altering the definition of a QRA-suitable mean flow. These findings cast doubt on the value of QRA theory in its current form as an interpretive tool and more generally warrant caution in the use of purely two-dimensional theories and/or zonally averaged flows to explain tropospheric extreme event dynamics.

Abstract In power cable ducts, complex environmental conditions can accelerate the insulation aging of power cables, potentially triggering serious accidents. Thus, there is an urgent demand for real-time monitoring of the internal state of power cable ducts. To address the failure of traditional wireless communication caused by shielding from metal manhole covers and the ground in power cable duct monitoring, this paper systematically investigates a through-the-earth data transmission method using a rotating permanent magnet mechanical antenna. A finite element model incorporating the well shaft, manhole covers, and soil medium was established to analyze the propagation mechanisms of electromagnetic waves in through-the-earth communication and diffraction paths. This study reveals the ‘gain’ effect of the stratum and manhole covers on low-frequency magnetic fields, as well as their role in suppressing signal attenuation. Experimental results demonstrate that the proposed mechanical antenna system achieves 5 bps 2FSK-encoded data transmission at 15 m through cast iron manhole covers. This research verifies the feasibility of the rotating permanent magnet mechanical antenna for reliable cross-medium communication in complex underground environments, and is expected to provide an effective wireless transmission solution for intelligent monitoring and fault early warning of power pipe wells.

ABSTRACT Environmentally adaptive multi‐band electromagnetic response materials, encompassing microwave absorption and infrared stealth, hold significant potential for military and civilian applications. However, developing such multifunctional materials remains challenging due to the distinct response mechanisms of electromagnetic waves across different frequency bands. Herein, we report a porous foam composed of 1D porous carbon fiber anchored with Fe─Ni heteronuclear diatomic sites and organic polyurethane, which exhibits outstanding microwave absorption and infrared stealth properties as well as environmental adaptability. The foam achieves an efficient microwave absorption bandwidth of 8.32 GHz, and a low thermal conductivity of 0.36 W m −1 K −1 , surpassing most reported absorbers. Experimental and theoretical analyses demonstrate that synergistic enhancements of conductive and polarization losses by Fe─Ni diatomic sites contribute to the microwave absorption performance, while infrared stealth originates from the low inherent thermal conductivity of the polyurethane matrix and porous structure within the foam. The foam also displays excellent mechanical strength, compression resilience, hydrophobicity, and salt corrosion resistance, thereby broadening its applicability. This work provides a viable approach for developing new‐generation, environmentally adaptive, wide‐band electromagnetic protection materials through cross‐scale precision design and multi‐functional synergistic integration.

Abstract This study presents a mechanistic framework for evaluating the service life of asphalt pavements with integrated heating using mineral-impregnated carbon fiber (MCF) grids. The proposed methodology combines a thermal model based on the finite difference method with a mechanical wave propagation model. The thermal model captures the effects of MCF-induced heating on in-pavement temperature distributions. Meanwhile, the mechanical model incorporates the viscoelastic response of the asphalt layer where the grid is embedded, the dynamics of the moving traffic load, and the localized reinforcement provided by the grid. A case study compares the performance of a conventional reference pavement to that of a pavement reinforced with an MCF grid. Two scenarios are analyzed: a fully bonded configuration, representing standard design conditions, and a debonded interface condition, simulating an off-design scenario. The results indicate that the grid significantly improves fatigue performance when it is positioned within the critical tensile strain zone, substantially extending the pavement’s service life. In contrast, when the grid is located far from this critical zone, its structural contribution becomes negligible. Additionally, the heating capability of the MCF grid proves effective in eliminating surface freezing temperatures. These findings serve as a proof-of-concept for the dual functionality of MCF grids, demonstrating their potential to enhance both pavement durability and winter performance.

Complex numbers are part of the standard Tanzanian mathematics curriculum for secondary schools. The integration of complex numbers into interdisciplinary teaching offers significant opportunities such as solving electrical problems to enhance conceptual understanding and problem-solving skills in Tanzanian secondary schools. This study explores how complex numbers are conceptualized, taught, and received across subject disciplines. Through a qualitative analysis of data collected through interviews, curriculum analysis and classroom observations, the research highlights how complex numbers can bridge abstract mathematical theory with real-world applications, such as electrical engineering, wave mechanics, and computer simulations. The findings in this study are based on connections between mathematics and science subjects, conceptual understanding of complex numbers, classroom practices and student engagement, and cultural contextualization strategies. The findings suggest that effective interdisciplinary instruction involving complex numbers promotes critical thinking, fosters learner curiosity, and aligns with the goals of competence-based curricula. However, challenges such as limited teaching resources, insufficient teacher training, and rigid syllabus design hinder the full realization of these benefits. The study recommends targeted professional development for educators, updated teaching materials, and revised policies that encourage interdisciplinary approaches.

The rapid expansion of the Internet of Things (IoT) and wearable electronics necessitates sustainable power sources to replace the limited electrochemical battery. While mechanical energy harvesting offers a promising solution, traditional harvesters face challenges of irregular and low-frequency environmental sources. This review presents the hybridized electromagnetic-triboelectric nanogenerator (HE-TENG) as an effective strategy to overcome individual limitations of the electromagnetic generator (EMG) and triboelectric nanogenerator (TENG). By integrating the high-current characteristics of the EMG with the high-voltage, low-frequency efficiency of the TENG, the HE-TENG achieves a complementary broadband frequency response and enhanced energy conversion efficiency. The fundamental working principles, theoretical models, and impedance matching requirements of both mechanisms are analyzed to elucidate their synergistic coupling. Furthermore, recent advances in structural design are categorized based on diverse mechanical energy sources, including wind, water waves, and hydrokinetic flows. The analysis highlights specific hybridization strategies, such as bio-inspired mechanisms and variable transmission systems, to optimize performance under stochastic environmental conditions.

ABSTRACT Gabions are one of the important slope protection forms for reinforced soil slopes. However, the seismic performance of this type of reinforced soil slope has not been clearly investigated. In this study, a scaled shaking table test was conducted on a reinforced soil slope model with gabions as surface protection under different seismic waves. The acceleration response, slope deformation, earth pressure, and tensile force distribution in the geogrid of the slope model were systematically studied to evaluate its performance under seismic action. The results showed that under the action of Wenchuan (WC) and EI Centro (EI) waves, the height-dependent amplification and surface-amplification phenomena coexisted in the reinforced soil slope, while the WC wave exerted a stronger influence on the acceleration response. Both peak and residual horizontal displacements of the slope surface increased with rising input peak ground acceleration (PGA) and elevation. Larger displacements accompanied by a relatively weaker recovery capability were observed in the slope under the WC wave compared to the EI wave. The slope crest settlement exhibited nonlinear dynamic responses with four distinct stages. The final slope top contour line presented an arc-shaped distribution and the EI wave-induced settlement trends aligned with WC wave behaviors. The dynamic vertical earth pressure responses across the slope exhibited a consistent pattern as the input PGA and seismic waves changed. The tensile force growth trend across geogrid positions displayed three stages based on the input PGA. Additionally, the tensile force induced by the WC wave exceeded that induced by the EI wave.

Abstract In this paper, a generalized (3+1)-dimension variable-coefficient nonlinear evolution equation is investigated, which serves as a model for describing nonlinear wave behaviors in shallow water, ion-acoustic wave fluid mechanics and plasma physics. The Painlevé integrability is tested by the (WTC) method with the simplified form of Krustal. The bilinear form of the equation is derived through the application of the Hirota bilinear method. Building on the bilinear equation, a broad range of analytical solution is then obtained, including X-shaped and Y-shaped soliton solutions, lump solution, breather solution, and interaction solutions. In addition, another type of soliton solution, periodic solution, and ratio of trigonometric functions are derived.

ABSTRACT Louis-Victor de Broglie secured his place in the history of quantum physics by proposing the existence of matter waves. Following the concept accepted early in the twentieth century that light waves could display properties characteristic of particles (photons), de Broglie suggested the complementary principle that particles could display properties characteristic of waves. Within a few years, this far-reaching proposal was experimentally verified. The well-known formula for the wavelength λ of the wave associated with a particle of momentum p , namely λ = h / p , does not appear in de Broglie’s original paper, which was published in this journal in 1924. What is derived from the starting assumption that the frequency of the wave is the rest energy of the particle divided by Planck’s constant h , is the wave's velocity, which turns out to be c 2/v, where v is the particle’s velocity. This velocity, being superluminal, means that the wave cannot transport energy. De Broglie called it a phase wave and postulated a group of such waves having virtually, but not exactly, the same velocity and wavelength. The group velocity of such a large number of almost identical phase waves is then shown, very satisfactorily, to be equal to the velocity of the particle. The proposal by de Broglie inspired Schrödinger to develop the mathematical foundations of wave mechanics. Whereas in conventional quantum theory, phase waves are considered fictional, de Broglie considered them to have a certain physical reality, renaming them pilot or guiding waves – a concept developed later by Bohm in 1952.

Abstract While General Fractional Calculus has successfully expanded the scope of memory operators beyond power-laws, standard formulations remain predominantly restricted to the half-line via Riemann-Liouville or Caputo definitions. This constraint artificially truncates the system's history, limiting the thermodynamic consistency required for modeling processes on unbounded domains. To overcome these barriers, we construct the Weighted Weyl-Sonine Framework, a generalized formalism that extends non-local theory to the entire real line without history truncation.Unlike recent algebraic approaches based on conjugation for finite intervals, we develop a rigorous harmonic analysis framework. Our central contribution is the Generalized Spectral Mapping Theorem, which establishes the Weighted Fourier Transform as a unitary diagonalization map for these operators. This result allows us to rigorously classify and solve distinct physical regimes under a single algebraic structure. We explicitly derive exact solutions for diffusive relaxation (governed by Complete Bernstein Functions), inertial wave propagation (exhibiting oscillatory dynamics), and retarded aging (via distributed order), proving that our framework unifies the description of anomalous transport and wave mechanics in complex, time-deformed media.

The interaction mechanism of oblique detonation wave (ODW) with centered Prandtl–Meyer expansion wave around the corner of a wedge is numerically studied. The governing equations are two-dimensional conservative Euler equations with a one-step global detonation model. The convective flux analysis methodology is used to analyze the movement of transverse waves. The numerical results show that the ODW is composed of either downstream-propagating transverse waves (DTWs) under lower activation energy or upstream-propagating transverse waves (UTWs) under higher activation energy. The interaction mechanism of expansion wave with these two kinds of transverse waves becomes complex. The interaction of expansion wave with DTWs cannot make the ODW decoupled directly because it cannot prevent the generation of new transverse waves. In contrast, UTWs are generated downstream via autoignition. The expansion wave can inhibit the generation of new transverse waves by extending the ignition delay time. Accordingly, the ODW is decoupled and quenched under the influence of expansion wave.

Abstract This work hypothesizes that the Madden–Julian oscillation (MJO) alters the vertical structure of synoptic convectively coupled Kelvin waves in a manner that allows nonlinear advection by the altered Kelvin waves to feed back onto the MJO. Through wavelet decomposition and linear regression, this work extracts the winds, specific humidity, and temperature signals associated with a Kelvin wave of phase speed 9 m s −1 and wavenumber 6 over the east Indian Ocean during the locally enhanced and suppressed convective phases of the MJO. Results support the idea of a feedback cycle, suggesting that the MJO modifies the background state of the Kelvin wave, altering its vertical structure. In turn, Kelvin wave nonlinear advection 1) accelerates MJO westerlies and decelerates MJO easterlies; 2) moistens the MJO in the midtroposphere but dries the MJO in the lower troposphere; and 3) warms the MJO in the lower and upper troposphere but cools the MJO in the midtroposphere by about 10%. We expect this percent contribution to increase when looking at a wider range of slow-moving Kelvin wave frequencies. This work establishes strong interactions between the MJO and slow-moving embedded Kelvin waves, which calls attention for future works on Kelvin wave behavior in the previously ignored spectral region traditionally separating synoptic Kelvin waves from the MJO.

Abstract Viscoelastic materials in engineering and biomechanics require dynamic response control, yet conventional constant-order fractional models inadequately describe elastic-to-viscoelastic state transitions. This study investigates the viscoelastic wave equation with variable-order analyzing how the variable-order fractional derivative α ( t ) and damping coefficient k ( t ) influence wave characteristics and viscoelastic phenomena. Numerical results show that α ( t ) effectively regulates the crossover transition between elastic and viscoelastic states. Notably, numerical experiments indicate that α ( t ) and k ( t ) may have similar effects on wave behavior. In particular, the wave behavior of the variable-order viscoelastic wave equation could be accurately recovered by selecting an appropriate variable coefficient in a constant-order viscoelastic wave equation. This research presents the possibility of replacing the variable-order model with a more convenient alternative for numerical treatment or theoretical study. It also offers a preliminary investigation of α ( t ) and k ( t ).

Non-destructive characterization of mechanical properties using magnetostrictive magnetoacoustic conversion: Theory and experiment.