Search Results (139)

Shear-wave time-of-flight (TOF) measurement enables controlled assessment of frequency-dependent wave propagation, but its feasibility in biological tissues remains insufficiently established. This study evaluated whether a custom shear-wave TOF device could detect frequency- and direction-dependent responses in ex vivo tissues. Three porcine liver samples and three chicken breast samples were examined. Chicken breast was measured with propagation parallel and perpendicular to visible muscle fibers. One-cycle sinusoidal excitations were applied at 40–160 Hz, with 50 acquisitions ensemble-averaged per sample–frequency measurement. TOF was estimated using Tx threshold detection and cumulative-energy-based Rx onset detection, and TOF-derived apparent shear-wave propagation speed was calculated from the Tx–Rx distance and the measured TOF. Frequency-dependent data were fitted using the Kelvin–Voigt fractional derivative model to obtain model-dependent KVFD fit parameters. Signal quality was assessed, and a preliminary descriptive comparison with HISKY EQTouch UD3000 (Wuxi Hisky Medical Technologies Co., Ltd., Wuxi, China) SWE was performed. All 63 averaged sample–frequency measurements satisfied the predefined primary-detection criteria. Mean apparent shear-wave speed was 3.145 m/s in porcine liver, 6.133 m/s in chicken breast measured parallel to the fibers, and 5.914 m/s in chicken breast measured perpendicular to the fibers, giving a parallel-to-perpendicular speed ratio of 1.037. Mean post-averaging, post-processing SNR ranged from 24.47 to 31.52 dB. The UD3000 comparison showed the same tissue ranking. The device detected frequency- and direction-dependent responses in averaged ex vivo signals, supporting its feasibility as a controlled research platform. Claims of absolute stiffness accuracy and intrinsic muscle anisotropy require independent calibration and validation. Full article

Ultrasonic attenuation in particle–cementitious heterogeneous media results from the coupled effects of matrix memory dissipation and particle-induced random heterogeneity, which cannot be readily distinguished using conventional homogeneous-medium models. This study develops a unified stochastic fractional wave framework that couples Caputo fractional dissipation with a random-potential representation of spatial heterogeneity. The main contribution is an analytically tractable amplitude–phase formulation that separates the leading-order roles of the two mechanisms: fractional dissipation primarily governs exponential amplitude attenuation, with $\kappa (\omega )\propto {\omega }^{\alpha -1}$, whereas the random potential mainly modulates local phase propagation and introduces finite scattering-type amplitude corrections. By transforming the governing equation into a frequency-domain Helmholtz form and applying Wentzel–Kramers–Brillouin (WKB) asymptotic analysis, explicit scaling relations are obtained for both attenuation and phase fluctuations. Two-dimensional Helmholtz simulations support the predicted attenuation law and show that the relative $L_2$ error of the WKB phase prediction decreases from 25.23% to 5.36%, while the covariance-based fixed-receiver ensemble phase-variance prediction lies within the 95% confidence interval of 30 independent realizations. Single-frequency ultrasonic transmission experiments provide complementary trend-level evidence, showing reduced tail retention and increased descriptive tail attenuation with increasing particle volume fraction. The proposed framework provides a mechanistically interpretable basis for distinguishing dissipation-dominated and heterogeneity-induced ultrasonic responses. Full article

Landslide-induced waves are primarily controlled by granular dynamics during landslide–water impact. While particle size, velocity, and volume are recognized influences, the role of internal grain arrangement and segregation remains less clear. This study employs a coupled CFD-DEM model to investigate how vertical permutation of three fixed grain fractions and layered configurations affect surge generation and propagation. Simulations using three particle sizes (1, 3, and 5 mm) in six initial arrangements reveal that fine particles dominate leading wave formation through efficient momentum transfer, yielding an overall wave height growth of 5.22% and a maximum local growth rate of 2.42%. Grain size segregation governs deposit morphology, with larger particles migrating preferentially along the flow direction. Increasing still-water depth systematically shifts surge characteristics from strongly nonlinear, high-amplitude shallow-water waves to more linear, longer-wavelength, smaller-amplitude deep-water features. Energy dissipation, which is linked to reduced equivalent water depth, decreases wave celerity with propagation distance. The model reproduces granular collapse experiments with a relative error below 5%, confirming that granular segregation critically controls surge dynamics and providing a refined framework for simulating natural landslide-generated waves. Full article

A high-resolution unstructured-grid ocean model was used to investigate the generation, propagation, and dissipation of M₂ internal tides in the Luzon Strait and northeastern South China Sea, with the aim of clarifying how energy evolves across contrasting topographic regimes. Wave decomposition, harmonic and modal analyses, energy-budget diagnostics, and along-path tracking were applied to quantify the spatial distribution and modal evolution of internal-tide energy. The results show that the Luzon Strait double-ridge system is the primary source region, contributing approximately 4.826 GW of barotropic-to-baroclinic energy conversion, with the Lanyu Ridge (3.080 GW) exhibiting stronger conversion than the Hengchun Ridge (1.643 GW). The generated low-mode internal tides radiate mainly westward into the northeastern South China Sea, with energy progressively attenuated over the deep basin and continental slope. Energy-budget analyses indicate that the ridge region dominates generation, the Luzon Trough mainly supports transmission, and the deep basin and slope are associated with enhanced dissipation and scattering. Along-path energetic diagnostics quantitatively reveal a sequential depletion of mode 1 internal-tide energy in the vicinities of steep topography and internal-tide steepening zones, concomitant with a marked augmentation of mode 2 energy and intensified cross-frequency energy transfer. Specifically, within the deep basin of the South China Sea, the fractional contribution of mode 1 energy declines from 78.3% to 73.8% as the internal tide propagates from the abyssal to the shallower shelf-slope region, whereas that of mode 2 increases correspondingly from 18.2% to 24.3%. Moreover, pronounced internal-tide steepening is observed in the deep basin, and the spectrally integrated cross-frequency transfer coefficient reaches 0.32 in this area, substantially exceeding that in other regions. These findings suggest that topographic scattering, modal redistribution, and nonlinear interactions contribute substantially to regional internal-tide dissipation. Full article

This study investigates the propagation characteristics of Rayleigh waves in partially saturated poroviscoelastic half-spaces based on fundamental theories of elastic wave propagation. Firstly, a poroviscoelastic model tailored to unsaturated porous media is developed, integrating constitutive relations and dynamic equilibrium equations with fractional derivatives to effectively capture the complex, history-dependent viscoelastic behavior of materials. Secondly, the potential function method is employed to derive the dispersion equation for Rayleigh waves in the proposed medium. Lastly, numerical simulations are conducted to analyze the effects of liquid saturation and fractional order parameters on Rayleigh wave velocity, with results presented through graphical illustrations. The analysis reveals that both liquid saturation and fractional order significantly influence the propagation features of Rayleigh waves. This work provides valuable theoretical support for seismic exploration and related engineering applications involving unsaturated porous formations. Full article

The Aharonov–Bohm (AB) effect demonstrates that a charged particle can acquire an observable phase shift in a region where the local magnetic field identically vanishes provided the configuration space is multiply connected and the electromagnetic connection exhibits non-trivial holonomy. We present a gauge-covariant physico-mathematical framework that systematically disentangles three regimes: (i) the standard ideal AB effect governed by the holonomy of a flat but globally inexact connection on ${\mathsf{\Omega }}_R={\mathbb{R}}^2\setminus D_R$ with $D_R=\{r\le R\}$; (ii) the path-integral decomposition into homotopy sectors indexed by the winding number, which is constructed on the universal cover; and (iii) non-topological corrections arising from evanescent wave-function penetration when the solenoid is modeled as a finite radial barrier. The ideal AB phase is taken as the reference topological holonomy, while the finite-barrier extension developed here separates the measured phase, under explicit weak-penetration assumptions, as $\Delta {\phi }_{\mathrm{total}}=\Delta {\phi }_{\mathrm{AB}}^{\mathrm{hol}}+\delta {\phi }_{\mathrm{finite}}+\mathcal{O}\left(T_{\mathrm{eff}}^2\right)$. Here, $\Delta {\phi }_{\mathrm{AB}}^{\mathrm{hol}}=q\mathsf{\Phi }/\mathit{ħ}$ is the standard topological holonomy, whereas $\delta {\phi }_{\mathrm{finite}}=\mathcal{O}\left(e^{-2\kappa {\mathsf{\ell }}_b}\right)$ is a small dynamical, microphysics-dependent correction controlled by the barrier height, particle energy, and effective forbidden length ${\mathsf{\ell }}_b$. Within Laskin’s fractional quantum mechanics, we use the fractional extension as a diagnostic test: the topological AB phase is independent of the Lévy index $\alpha$, whereas the finite-barrier correction acquires an anomalous, $\alpha$-dependent penetration length. The numerical material provides gauge-covariant diagnostics: a Peierls-substituted split-operator scheme, a sector-resolved Monte Carlo path integral benchmarked against the exact Aharonov–Bohm propagator of Gerry and Singh, a WKB/transfer-matrix finite-barrier estimate tracking $\delta {\phi }_{\mathrm{finite}}\to 0$, and Berry-phase computations used as consistency checks. Full article

The fractional Whitham–Broer–Kaup model governs nonlinear wave propagation in memory-dependent media, including porous structures, viscoelastic fluids, and irregular seabeds, yet the full dynamical spectrum from quasi-periodicity to deterministic chaos, the role of stochastic forcing, and reliable identification from noisy data remains insufficiently explored, particularly how the fractional order $\beta$ influences these regimes. This study addresses these gaps through a comprehensive, multi-method dynamical analysis of a representative nonlinear oscillator embodying key FWBK features. Three-dimensional attractor visualizations, return maps, and surrogate data tests demonstrate a transition from quasi-periodic toroidal attractors to fully developed chaos via torus breakdown, confirming that observed complexity originates from deterministic nonlinearity. Poincaré sections reveal multistability and KAM-type structures, where coexisting attractors depend on initial conditions, while increasing noise progressively disrupts coherent dynamics. The OGY control method effectively stabilizes unstable periodic orbits across chaotic regimes with minimal perturbation, and Lyapunov analysis indicates that stochastic forcing attenuates chaos while enhancing dissipation. The Fokker–Planck framework shows that noise reshapes probability landscapes, driving transitions from unimodal to bimodal distributions. Comparative analysis of SINDy, JMAP and VBA highlights trade-offs in interpretability, computational efficiency, and uncertainty quantification, while an integrated Bayesian–PCE–Sobol approach quantifies parametric uncertainty and reveals time-dependent sensitivity variations. Additionally, the overlapping of soliton solutions extracted via the enhanced modified Sardar sub-equation method reveals structural relationships among soliton families and their stability under interaction. Soliton branches that maintain high overlap under noise correspond to stable regimes, while those losing coherence indicate the onset of chaos. Furthermore, while the reduced dynamics in $\eta$-space are independent of $\beta$, the fractional order controls spatial compression and temporal scaling in physical coordinates, directly influencing observable wave localization. These results imply that fractional effects can modify chaos transitions, support controllability through OGY, and influence noise–instability interactions depending on $\beta$. This framework provides a robust, transferable methodology for analyzing and controlling nonlinear oscillatory systems under deterministic and stochastic conditions, with direct applications to FWBK-based models in coastal engineering, fiber optics, and quantum interference systems. Full article

In this study, a detailed analytical-numerical study of the complex modified Korteweg–De Vries (mKdV) model with truncated M-fractional derivative is carried out to investigate the effects of the fractional order on nonlinear wave propagation. The fractional partial differential equation is solved by an appropriate fractional traveling wave transformation, which transforms it into a nonlinear ordinary differential equation. Two very powerful analytical methods are then used: the modified sub-equation method and the Kumar–Malik method, which give the exact closed-form solutions. The obtained semi-analytical numerical approximations are then obtained from the Differential Transformation Method (DTM). Bright and dark solitons, kink-type waves, periodic and rational solutions, exponential solutions, and Jacobi elliptic functions are found for a variety of parametric regimes. Explicit compatibility conditions and parametric constraints, which control the amplitude, width, and propagation, are derived. The DTM approximations are found to converge to the exact solutions with good accuracy, and the absolute errors are almost negligible, which validates the accuracy of the approximations and reliability of the solution. The three-dimensional visualizations of surface plots, two-dimensional profiles, and contour visualization further illustrate the dispersive dynamics and stability properties. Significance: This study shows that the truncated M-fractional derivative is a good operator to model memory-dependent nonlinear wave propagation. A new precise solution and reliable validation methods have been obtained for high-dimensional fractional nonlinear evolution equations in the hybrid analytical-numerical framework, which can be useful in plasma physics, nonlinear optics, and complex media. The present study contains restrictions for constant coefficients, a specific parametric regime, one fractional derivative definition, and experimental validation is not included. Future directions are limitations on constant coefficients, specific parametric regimes, one fractional derivative definition, and experimental validation is not included. The approach is to be extended in the future to variable coefficients, other fractional operators (Caputo, Riemann–Liouville), and to higher-order nonlinearities, and then to be experimentally tested in optical or plasma systems. Full article

This study investigates a 2D fractional order generalized thermoelastic problem in a homogeneous and isotropic thermoelastic hollow sphere. The sphere is exposed to a decaying heat source, and the governing equations are derived using a refined fractional-order Lord–Shulman (LS) model of generalized thermoelasticity. The Laplace transform technique is used to convert time-dependent PDEs into simpler ODEs in the Laplace domain. Its numerical inversion method is used to revert to the time domain. Numerical simulations are carried out to investigate the distributions of temperature, displacement, and stress fields within the hollow sphere. The obtained results reveal that both the fractional-order parameter and the variable thermal conductivity strongly affect the thermoelastic response, particularly the propagation characteristics of thermal waves, stress intensity, and relaxation behavior. In addition, the curvature of the hollow geometry plays an important role in modifying the radial and circumferential stress distributions and their attenuation throughout the medium. Full article

We propose an exploratory framework for a Bohmian model of quantum matter propagating on a classical curved spacetime background. The gravitational sector is governed by classical Einstein field equations throughout; no quantisation of spacetime is attempted. The wave function emerges as the scalar contraction $\mathrm{\Psi }={\psi }_{\nu }{\psi }^{\nu }\in \mathbb{C}$ of a complex-valued tensorial field ${\psi }^{\mu }$, encoding quantum dynamics in a geometric object. The wave tensor interacts with spacetime via the stress–energy tensor $T_{\mu \nu }$, mediated by a real scalar field a of dimension volume, so that $a{T}_{\mu \nu }{\psi }^{\mu }{\psi }^{\nu }$ yields the correct potential energy. We derive a covariant Adapted Schrödinger Equation as the unique minimal covariant lift of the standard equation, justify it from four guiding principles, and verify three internal consistency checks. Under seven explicit approximations the framework reproduces the Schrödinger equation with Coulomb potential for the hydrogen atom. We also derive a dynamical equation for ${\psi }^{\mu }$ that entails the Adapted Schrödinger Equation by contraction. Two open problems are then resolved. First, a complete Lagrangian formulation is provided: a real-valued action for $\mathrm{\Psi }$ yields the Adapted Schrödinger Equation via the Euler–Lagrange equations; a separate action for ${\psi }^{\mu }$, extended by a non-polynomial term, yields the full dynamical equation variationally. Second, two experimental predictions are derived. Expanding to first post-Newtonian order, the perturbation Hamiltonian has coefficients $(3, 1)$ on the kinetic and potential operators; via the virial theorem these produce a coordinate-time blueshift, which after photon propagation yields the universal Einstein gravitational redshift $\delta \nu /\nu =\mathrm{\Phi }/c^2$, confirming consistency with the equivalence principle. The same kinetic coefficient independently predicts that free quantum wave packets spread more slowly by the fractional amount $3\left|\mathrm{\Phi }\right|/c^2$, a correction absent in standard non-relativistic quantum mechanics. Full article

Hereditary damping and fractional attenuation are widely used to model wave propagation in complex media, but the variational and spectral origin of the corresponding nonlocal-in-time operators is often left implicit. In this work, we derive such operators from a minimal conservative field–reservoir model. A real scalar field is coupled locally to a continuum of harmonic reservoir modes, which are then eliminated exactly. The resulting reduced dynamics is a causal wave equation with a memory-friction term acting on the field velocity. The memory kernel is generated by the reservoir coupling spectrum through a cosine-transform relation, establishing a direct spectrum-to-kernel correspondence. This relation provides both a physical interpretation of hereditary damping and a practical admissibility criterion: macroscopic attenuation and dispersion arise from the delayed back-action of unresolved internal modes, while physically admissible kernels are constrained by the non-negativity of the underlying spectral density. The framework unifies several standard damping regimes. A broadband reservoir recovers the Markovian locally damped wave equation, reservoirs with a finite characteristic time generate finite-memory relaxation and frequency-dependent dispersion, and scale-free reservoir spectra produce power-law memory kernels. In the latter case, the hereditary damping operator reduces to a Caputo-type fractional derivative, showing that fractional wave attenuation can emerge as an effective reduced dynamics rather than being postulated phenomenologically. We further analyze dispersion, attenuation, causality, stability, and admissibility conditions in terms of the reservoir spectrum. The main contribution of the work is therefore to provide a variational and spectral derivation of hereditary and fractional wave damping, linking the structure of unresolved reservoir modes to macroscopic nonlocal wave dynamics. Full article

Ion-acoustic waves in dense quantum plasmas are strongly influenced by Fermi degeneracy, Landau quantization, and finite-temperature effects, and in many relevant environments, they also experience memory and nonlocal transport processes that cannot be captured within the planar integer Korteweg-de Vries (KdV) paradigm. In the present work, we revisit this problem by considering a two-fluid, partially degenerate electron-ion plasma in which electron trapping in the presence of a quantizing field and finite temperature is taken into account. Starting from the normalized fluid-Poisson system appropriate for such magnetized quantum plasmas, the reductive perturbation technique is used to derive the planar integer KdV equation for weakly nonlinear ion-acoustic disturbances. Within this integer-order KdV framework, we recast the evolution equation as a planar dynamical system, construct the associated Hamiltonian and effective Sagdeev-like potential, and demonstrate the existence of compressive solitary waves and nonlinear periodic modes via homoclinic and periodic phase-space orbits. Exact multi-soliton solutions and interaction states are then obtained by combining Hirota’s direct bilinear method with generalized Wronskian representations, allowing us to describe not only standard one-, two-, and three-soliton profiles but also positon-negaton interactions relevant to magnetized, partially degenerate plasmas. To incorporate hereditary and history-dependent effects that arise from anomalous transport and nonlocal temporal response in dense environments, we extend the model by introducing a Caputo time-fractional derivative, thereby obtaining a time-fractional KdV (FKdV) equation that continuously connects the classical KdV limit to fractional dynamics. The FKdV equation is analyzed using the Tantawy technique. This semi-analytical iterative scheme yields rapidly convergent series approximations for the fractional ion-acoustic soliton and provides explicit control of the approximation error. The fractional solutions show that varying the order of the Caputo derivative modifies the amplitude, width, and temporal relaxation of the solitary structures and can even split the pulse into two distinct lobes, in contrast with the nearly rigid propagation predicted by the integer-order KdV equation. Taken together, these results clarify how Landau quantization, finite electron temperature, and fractional-order memory jointly shape the morphology, robustness, and interaction properties of ion-acoustic structures in strongly magnetized quantum plasmas of astrophysical and high-energy-density laboratory interest. Full article

Fractional derivatives introduce an effective mathematical structure to describe memory effects, long-range interactions, and anomalous transport processes that are not well represented by the traditional integer-order models. This paper presents the unidirectional fractional longitudinal wave equation as a governing equation where a model is proposed to explain the steady wave propagation of solitary waves in a magneto-electro-elastic circular rod. Magneto-electro-elastic substances are a groundbreaking category of advanced functional materials with tremendous nanotechnology and biomedical engineering prospects because of their effective multi-field energy conversion and temperature responsiveness. In order to solve this complicated fractional nonlinear equation, we introduce a new computation-analysis approach: the Riccati subequation neural network method. This hybrid solution is a synergistic combination of an analytical solution structure and a neural network structure consisting of input, hidden, and output layers, with interconnection between neurons through weighted connections and activation functions. It is important to note that every neuron in the first hidden layer is coupled to the solutions of the Riccati equation, and this allows the systematic use of the new trial functions. With the suggested method, analytical solutions are obtained for the spacetime fractional partial differential equations of the unidirectional fractional longitudinal wave equation in the exact form of trigonometric, hyperbolic, and rational functions. This paper is the first attempt to combine the Riccati subequation method with a neural network model, which has given rise to new types of solitary wave solutions. The three-dimensional, two-dimensional, and contour plots are used to visualize the dynamic nature of these solutions and to display the rich nonlinear wave behavior. The effectiveness and the robustness of the implemented technique is not only proven through our findings but also provides more profound information about the nonlinear wave phenomena in the advanced multifunctional materials, which can inform future developments in energy harvesting and the design of biomedical devices. Full article

This paper probes into the propagation characteristics of Rayleigh waves in a partially saturated, porous, thermo-viscoelastic half-space, with full consideration of the fractional viscoelastic effect and thermal coupling effect. A fractional Zener model is introduced to depict the thermo-viscoelastic mechanical behavior of the solid skeleton by constructing a complete set of governing equations that include mass balance, generalized Darcy’s law, momentum balance, and generalized heat conduction. Field equations are derived by means of Helmholtz vector decomposition, and the dispersion equation, and the phase velocity expression of Rayleigh waves are obtained by combining the traction-free and adiabatic boundary conditions of the medium. The impacts of key material properties, such as medium saturation, intrinsic permeability, medium viscoelasticity, and thermal expansion coefficient, on the dispersion feature of Rayleigh waves are discussed in detail. Numerical analysis results show that an increase in the thermal expansion coefficient will lead to a rise in Rayleigh wave phase velocity, in which the increase in P1 compressional wave velocity plays a dominant role among the velocities of various types of waves. Meanwhile, the attenuation coefficient of Rayleigh waves presents a decreasing trend and gradually tends to be stable with the growth of the thermal expansion coefficient. Similarly, the phase velocity of Rayleigh waves also increases with the rise in fractional order index, which is jointly dominated by the velocity enhancement of P1 waves and S waves. In addition, the attenuation coefficient of Rayleigh waves increases first and then decreases with the increase in fractional order index and reaches the peak value when the fractional order index is about 0.4. The research results reveal the influence of laws of thermal expansion characteristics and viscoelasticity on Rayleigh wave propagation and provide theoretical support for the analysis of wave propagation characteristics in porous media in relevant engineering applications. Full article

Pneumatic transmission lines play a critical role in the dynamic performance of soft robotic actuation systems, yet their behaviour is difficult to capture using conventional integer-order (IO) models. In long, slender pipelines, compressibility, viscothermal losses, and wave propagation give rise to distributed damping and non-exponential relaxation dynamics that are not well represented by finite-dimensional models. This paper presents a control-oriented, experimentally validated fractional-order (FO) modelling framework for pneumatic pipeline dynamics under closed-end boundary conditions. Models are calibrated using measured step-response data from a 13.2 m pipeline, with all parameters—including the fractional order—identified through a unified optimisation procedure. In addition to global fitting accuracy, model performance is evaluated using control-relevant metrics, including effective delay, initial slope and early transient behaviour, and early-time error. The results show that FO models provide a more compact and structurally consistent representation of long-memory dynamics while improving the accuracy of control-relevant features compared to their IO counterparts. These findings demonstrate that fractional dynamics offer a physically meaningful and practically useful framework for modelling pneumatic transmission lines, with direct implications for high-performance control design in soft robotic systems. Full article