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Tidal-scale wave modulation is a critical yet complex process in macro-tidal estuaries. This study investigates semidiurnal wave modulations in the Changjiang River Estuary (CRE) using unique, long-term in situ observations and high-resolution ADCIRC–SWAN coupled simulations. Pronounced semidiurnal signals are identified in significant wave height (Hs), mean wave period, and wave direction. Observational results demonstrate that the modulation intensity is highest in Hangzhou Bay and the CRE mouth, decreasing gradually offshore. A key finding is that semidiurnal Hs maxima systematically coincide with peak flood currents and precede high water by approximately three hours. Long-term records confirm that this modulation persists year-round and intensifies during energetic events such as typhoons. The expression of the tidal signal depends on wave composition: wind-sea-dominated conditions exhibit stronger period modulation, whereas swell-dominated conditions favor coherent Hs modulation as kinematic tidal effects remain more apparent in the absence of strong local wind forcing. Numerical sensitivity experiments demonstrate that tidal currents are the primary driver of the observed wave modulation, while water-level effects are largely confined to shallow shoals. The results highlight that accurately reproducing the observed frequency–directional structure requires the inclusion of current-induced Doppler shifts and refraction. Beyond the classical following-current effects, the analysis suggests that the spatial deceleration of currents along the wave path acts as a kinematic trap that focuses wave action and sustains Hs intensification. This mechanism provides a physically plausible explanation for the observed phase relationship and points to the non-local nature of estuarine wave dynamics, where the wave state appears as an integrated response to cumulative current gradients along the propagation path. These findings emphasize the necessity of incorporating wave–current coupling in future coastal modeling and hazard forecasting.

Populations are heterogeneous, deviating in numerous ways. Phenotypic diversity refers to the range of traits or characteristics across a population, where for cells this could be the levels of signalling, movement and growth activity, etc. Clearly, the phenotypic distribution – and how this changes over time and space – could be a major determinant of population-level dynamics. For instance, across a cancerous population, variations in movement, growth, and ability to evade death may determine its growth trajectory and response to therapy. In this review, we discuss how classical partial differential equation (PDE) approaches for modelling cellular systems and collective cell migration can be extended to include phenotypic structuring. The resulting non-local models – which we refer to as phenotype-structured partial differential equations (PS-PDEs) – form a sophisticated class of models with rich dynamics. We set the scene through a brief history of structured population modelling, and then review the extension of several classic movement models – including the Fisher-KPP and Keller-Segel equations – into a PS-PDE form. We proceed with a tutorial-style section on derivation, analysis, and simulation techniques. First, we show a method to formally derive these models from underlying agent-based models. Second, we recount travelling waves in PDE models of spatial spread dynamics and concentration phenomena in non-local PDE models of evolutionary dynamics, and combine the two to deduce phenotypic structuring across travelling waves in PS-PDE models. Third, we discuss numerical methods to simulate PS-PDEs, illustrating with a simple scheme based on the method of lines and noting the finer points of consideration. We conclude with a discussion of future modelling and mathematical challenges.

The current study deals with reflected waves through a porous medium with viscoelastic properties. The considered continuum media is a semiconductor with elastic and thermal properties which varies exponentially along the depth of the medium. The thermal disturbance caused by elastic propagation is then encountered by the refined phase-lag heat conduction model. The scattering relation for the coupled waves has been computed. It is observed that the functionally graded, voids and non-local parameters reduce the amplitude ratios of reflected waves propagating through the medium. The solution in the form of amplitude ratios for reflected waves has been obtained analytically and represented graphically for a particular medium.

This study investigates the thermomechanical deformation in a homogeneous, isotropic micropolar thermo-viscoelastic solid half-space, integrating nonlocal viscoelastic effects and the hyperbolic two-temperature (HTT) theory based on the Moore–Gibson–Thompson (MGT) heat equation. The governing equations are derived and solved using Laplace and Fourier transforms, with the displacement components, stresses, thermodynamic temperature, and conductive temperature modified based on specific normal force and heat sources at the boundary surface. Key findings include the significant influence of viscosity on the deformation and thermal distribution, the modification of wave propagation and energy distribution due to nonlocal effects, and the crucial role of HTT parameters in dictating thermal relaxation and wave behavior, particularly in high-speed or short-time scenarios. Additionally, several exceptional cases are identified, demonstrating unique thermomechanical responses resulting from the interplay between viscosity, nonlocality, and HTT parameters. Numerical inversion is employed to retrieve the physical quantities, with graphical results highlighting the effects of these parameters, thereby providing valuable insights into the thermomechanical behavior of micropolar thermo-viscoelastic solids for advanced material design and applications.

We investigate a nonlinear multiphysics model motivated by ultrasound-enhanced drug delivery. The acoustic pressure field is modeled by Westervelt’s quasilinear wave equation to adequately capture the nonlinear effects in ultrasound propagation. The non-local attenuation characteristic for soft biological media is modeled by acoustic damping of the time-fractional type. Additionally, acoustic medium parameters are allowed to depend on the temperature of the medium. The wave equation is coupled to the nonlinear Pennes heat equation with a pressure-dependent source to account for ultrasound waves heating up the tissue. Finally, the drug concentration is obtained as the solution to an advection–diffusion equation with a pressure-dependent velocity. Toward gaining a rigorous understanding of this system, we set up a fixed-point argument in the analysis combined with devising energy estimates that can accommodate the time-fractional damping. The energy arguments are, in part, carried out by employing time-weighted test functions to reduce the regularity assumptions on the initial temperature. The analysis reveals that different smoothness of the initial pressure, temperature, and concentration fields is needed as well as smallness of the pressure-temperature data in order to ensure non-degeneracy of the system and establish well-posedness. Our theoretical considerations are complemented by a numerical investigation of the system under more realistic boundary conditions. The numerical experiments, performed in different computational scenarios, underline the importance of considering nonlinear effects when modeling ultrasound-targeted drug delivery.

This study analyzes a hybrid computational framework that combines peridynamics (PD) and the finite element (FE) method to model wave propagation in a one-dimensional bar, focusing on their integration for enhanced accuracy and efficiency. The analysis investigates PD’s ability to capture non-local interactions in regions near loading points, with computationally efficient coarse discretization in other areas through finite element methods. The dynamic response to symmetric and asymmetric axial loading, including loading and unloading phases, is analyzed through time-dependent external forces, solving displacement, velocity, and acceleration fields at each time step. The effects of PD-specific parameters, such as the horizon size, and the FE–PD node spacing size ratios on the performance of the hybrid model in wave propagation are investigated. Additionally, the study examines the von Neumann stability for PD to ensure stability and reliability, offering a robust framework for integrating PD and FE in dynamic analyses.

The aim of the present investigation is to examine the impacts of non-local, hyperbolic two-temperature (HTT) and impedance parameters on the propagation of plane waves in the context of the micropolar thermoelastic medium under Moore–Gibson–Thompson (MGT) heat equation. The problem is formulated for two dimensional and simplified with the aid of dimensionless quantities and potential functions. A reflection technique is used to solve the problem. The amplitude ratios of reflected waves namely longitudinal displacement wave (LD-wave), thermal wave (T-wave), coupled transverse wave (CD-I wave), and coupled micro-rotational wave (CD-II wave) are obtained against the angle of incidence by applying impedance boundary restrictions. The characteristics of non-local, HTT and impedance parameters on amplitude ratios have been depicted graphically. Some special cases are also obtained for the present study. Physical views presented in the article may be useful for the composition of new materials, geophysics, earthquake engineering, and other scientific disciplines.

This study aims to investigate the behavior of viscoelastic materials exhibiting complex mechanical behavior characterized by both elastic and viscous properties. They are widely used in various engineering applications, such as structural components, transportation systems, energy storage devices, microelectromechanical systems (MEMS), and earthquake research and detection. Accurate modeling of viscoelastic behavior is crucial for predicting its performance under dynamic loading conditions. In this study, we modify the equations governing the thermoelastic resistance to describe the thermal variables of a thermoelastic micro-beam supported by a two-parameter Pasternak viscoelastic foundation by using a fractional Moore–Gibson–Thompson (MGT) model in the context of non-locality. The temperature, bending displacement, and moment were computed and graphically displayed using the Laplace transform method. Different theoretical approaches have been compared in order to explain how the phase delay affects physical phenomena. Numerical results show that the wave fluctuations of variables in thermoelastic micro-beams are slightly smaller for the studied model and that the speed of these plane waves depends on fractional and non-local parameters.

The purpose of this study is to investigate vibrations in 2D functionally graded nanobeams (FGN) with memory-dependent derivatives. A sinusoidal variation of temperature is assumed. The dimensionless expressions for axial displacement, thermal moment, lateral deflection, strain and temperature distribution are found in the transformed domain using Laplace Transforms, and the expressions in the physical domain are derived by numerical inversion techniques. The nanobeam is simply supported at the both ends and have constant temperatures. The FGN is a non-homogenous composite structure with constant structural variations along with the layer thickness, changing from ceramic at the bottom to metal at the top. Adding non-local MDD to thermoelastic models opens up new possibilities for the study of thermal deformations in solid mechanics. The effect of different kernel functions and periodic frequency of thermal vibration is illustrated graphically for lateral deflection, axial displacement, strain, temperature, and thermal moment. Article highlights A novel model of vibrations in a functionally graded nanobeams is presented. The medium is subjected to sinusoidal variation of temperature. Dynamic response of memory dependent derivative theory of thermoelasticity and non-local parameter is investigated. The effects of kernel functions and periodic frequency of thermal vibration on all physical fields are investigated and shown graphically.

We study a nonlocal regularisation of a scalar conservation law given by a fractional derivative of order between one and two. The nonlocal operator is of Riesz–Feller type with skewness two minus its order. This equation describes the internal structure of hydraulic jumps in a shallow water model. The main purpose of the paper is the study of the vanishing viscosity limit of the Cauchy problem for this equation. First, we study the properties of the solution of the regularised problem and then we show that the difference between the regularised solution and the entropy solution of the scalar conservation law converges to zero in this limit in C([0,T];Lloc1(R)) for initial data in L∞(R) , and in C([0,T];L1(R)) for initial data in L∞(R)∩BV(R) . In order to prove these results we use weak entropy inequalities and the double scale technique of Kruzhkov. Such techniques also allow to show the L1(R) contraction of the regularised problem. For completeness, we study the behaviour in the tail of travelling wave solutions for genuinely nonlinear fluxes. These waves converge to shock waves in the vanishing viscosity limit, but decay algebraically as x-ct→∞ , rather than exponentially, the latter being a behaviour that they exhibit as x-ct→-∞ , however. Finally, we generalise the results concerning the vanishing viscosity limit to Riesz–Feller operators.