Search Results (28)

Diffraction-based velocity analysis is a key data interpretation technique in geophysical exploration, typically relying on the geometric characteristics, energy distribution, or propagation paths of diffraction waves. The hyperbola-based method is a classical strategy in this category, which extracts depth-dependent velocity (or dielectric properties) by correlating the hyperbolic shape of diffraction events with subsurface parameters for characterizing subsurface structures and material compositions. In this study, we propose a layer-stripping velocity analysis method applicable to ground-penetrating radar (GPR) and lunar-penetrating radar (LPR) data, with two main innovations: (1) replacing traditional local optimization algorithms with an intuitive parallelism check scheme, eliminating the need for complex nonlinear iterations; (2) performing depth-progressive velocity scanning of radargram diffraction signals, where shallow-layer velocity analysis constrains deeper-layer calculations. This strategy avoids misinterpretations of deep geological objects’ burial depth, morphology, and physical properties caused by a single average velocity or independent deep-layer velocity assumptions. The workflow of the proposed method is first demonstrated using a synthetic rock-fragment layered model, then applied to derive the near-surface dielectric constant distribution (down to 27 m) at the Chang’e-4 landing site. The estimated values range from 2.55 to 6, with the depth-dependent profile revealing lunar regolith stratification and interlayer material property variations. Consistent with previously reported results for the Chang’e-4 region, our findings confirm the method’s applicability to LPR data, providing a new technical framework for high-resolution subsurface structure reconstruction. Full article

This paper investigates the reverse space-time nonlocal nonlinear Schrödinger (NNLS) equation, which arises in nonlinear optics, Bose–Einstein condensation, integrable systems, and plasma physics. Several classes of exact solutions are constructed using multiple analytical techniques. First, traveling wave solutions of Jacobi elliptic, hyperbolic, and trigonometric function types are ultimately obtained by employing a traveling wave transformation combined with a Weierstrass-type Riccati equation expansion method. Second, Lie symmetry analysis is applied to the NNLS equation, and the corresponding infinitesimal generators are determined. Using these generators, the original equation is reduced to local and nonlocal ordinary differential equations (ODEs), whose invariant solutions are subsequently obtained through integration. Finally, the NNLS equation is generalized to a multi-component system, for which the general form of the infinitesimal symmetries is derived. Symmetry reductions of the extended system yield further classes of reduced ODEs. In particular, the general form of the multi-component solutions is derived. Full article

Reclaimed coastal areas are highly susceptible to uneven subsidence caused by the consolidation of soft marine deposits, which can induce differential settlement, structural deterioration, and systemic risks to urban infrastructure. Further, engineering activities, such as construction and loadings, exacerbate subsidence, impacting infrastructure stability. Therefore, monitoring the integrity and vulnerability of linear urban infrastructure after construction on reclaimed land is critical for understanding settlement dynamics, ensuring safe and reliable operation and minimizing cascading hazards. Subsequently, in the present study, to monitor deformation of the linear infrastructure constructed over decades-old reclaimed land in Mokpo city, South Korea (where 70% of urban and port infrastructure is built on reclaimed land), we analyzed 79 Sentinel-1A SLC ascending-orbit datasets (2017–2023) using the Persistent Scatterer Interferometry (PSInSAR) technique to quantify vertical land motion (VLM). Results reveal settlement rates ranging from −12.36 to 4.44 mm/year, with an average of −1.50 mm/year across 1869 persistent scatterers located along major roads and railways. To interpret the underlying causes of this deformation, Casagrande plasticity analysis of subsurface materials revealed that deep marine clays beneath the reclaimed zones have low permeability and high compressibility, leading to slow pore-pressure dissipation and prolonged consolidation under sustained loading. This geotechnical behavior accounts for the persistent and spatially variable subsidence observed through PSInSAR. Spatial pattern analysis using Anselin Local Moran’s I further identified statistically significant clusters and outliers of VLM, delineating critical infrastructure segments where concentrated settlement poses heightened risks to transportation stability. A hyperbolic settlement model was also applied to anticipate nonlinear consolidation trends at vulnerable sites, predicting persistent subsidence through 2030. Proxy-based validation, integrating long-term groundwater variations, lithostratigraphy, effective shear-wave velocity (V_s³⁰), and geomorphological conditions, exhibited the reliability of the InSAR-derived deformation fields. The findings highlight that Mokpo’s decades-old reclamation fills remain geotechnically unstable, highlighting the urgent need for proactive monitoring, targeted soil improvement, structural reinforcement, and integrated InSAR-GNSS monitoring frameworks to ensure the structural integrity of road and railway infrastructure and to support sustainable urban development in reclaimed coastal cities worldwide. Full article

Because artificially cemented granular (ACG) materials employ diverse combinations of aggregates and binders—including cemented soil, low-cement-content cemented sand and gravel (LCSG), and concrete—their stress–strain responses vary widely. In LCSG, the binder dosage is typically limited to 40–80 kg/m³ and the sand–gravel skeleton is often obtained directly from on-site or nearby excavation spoil, endowing the material with a markedly lower embodied carbon footprint and strong alignment with current low-carbon, green-construction objectives. Yet, such heterogeneity makes a single material-specific constitutive model inadequate for predicting the mechanical behavior of other ACG variants, thereby constraining broader applications in dam construction and foundation reinforcement. This study systematically summarizes and analyzes the stress–strain and volumetric strain–axial strain characteristics of ACG materials under conventional triaxial conditions. Generalized hyperbolic and parabolic equations are employed to describe these two families of curves, and closed-form expressions are proposed for key mechanical indices—peak strength, elastic modulus, and shear dilation behavior. Building on generalized plasticity theory, we derive the plastic flow direction vector, loading direction vector, and plastic modulus, and develop a concise, transferable elastoplastic model suitable for the full spectrum of ACG materials. Validation against triaxial data for rock-fill materials, LCSG, and cemented coal–gangue backfill shows that the model reproduces the stress and deformation paths of each material class with high accuracy. Quantitative evaluation of the peak values indicates that the proposed constitutive model predicts peak deviatoric stress with an error of 1.36% and peak volumetric strain with an error of 3.78%. The corresponding coefficients of determination R² between the predicted and measured values are 0.997 for peak stress and 0.987 for peak volumetric strain, demonstrating the excellent engineering accuracy of the proposed model. The results provide a unified theoretical basis for deploying ACG—particularly its low-cement, locally sourced variants—in low-carbon dam construction, foundation rehabilitation, and other sustainable civil engineering projects. Full article

This manuscript aims to explore localized waves for the nonlinear partial differential equation referred to as the $(1+1)$-dimensional generalized Kundu–Eckhaus equation with an additional dispersion term that describes the propagation of the ultra-short femtosecond pulses in an optical fiber. This research delves deep into the characteristics, behaviors, and localized waves of the $(1+1)$-dimensional generalized Kundu–Eckhaus equation. We utilize the multivariate generalized exponential rational integral function method (MGERIFM) to derive localized waves, examining their properties, including propagation behaviors and interactions. Motivated by the generalized exponential rational integral function method, it proves to be a powerful tool for finding solutions involving the exponential, trigonometric, and hyperbolic functions. The solutions we found using the MGERIF method have important applications in different scientific domains, including nonlinear optics, plasma physics, fluid dynamics, mathematical physics, and condensed matter physics. We apply the three-dimensional (3D) and contour plots to illuminate the physical significance of the derived solution, exploring the various parameter choices. The proposed approaches are significant and applicable to various nonlinear evolutionary equations used to model nonlinear physical systems in the field of nonlinear sciences. Full article

This work presents a comprehensive mathematical framework for symmetrized neural network operators operating under the paradigm of fractional calculus. By introducing a perturbed hyperbolic tangent activation, we construct a family of localized, symmetric, and positive kernel-like densities, which form the analytical backbone for three classes of multivariate operators: quasi-interpolation, Kantorovich-type, and quadrature-type. A central theoretical contribution is the derivation of the Voronovskaya–Santos–Sales Theorem, which extends classical asymptotic expansions to the fractional domain, providing rigorous error bounds and normalized remainder terms governed by Caputo derivatives. The operators exhibit key properties such as partition of unity, exponential decay, and scaling invariance, which are essential for stable and accurate approximations in high-dimensional settings and systems governed by nonlocal dynamics. The theoretical framework is thoroughly validated through applications in signal processing and fractional fluid dynamics, including the formulation of nonlocal viscous models and fractional Navier–Stokes equations with memory effects. Numerical experiments demonstrate a relative error reduction of up to 92.5% when compared to classical quasi-interpolation operators, with observed convergence rates reaching $\mathcal{O}\left(n^{-1.5}\right)$ under Caputo derivatives, using parameters $\lambda =3.5$, $q=1.8$, and $n=100$. This synergy between neural operator theory, asymptotic analysis, and fractional calculus not only advances the theoretical landscape of function approximation but also provides practical computational tools for addressing complex physical systems characterized by long-range interactions and anomalous diffusion. Full article

Conventional integer-order models fail to adequately capture non-local memory effects and constrained nonlinear interactions in emotional dynamics. To address these limitations, we propose a coupled framework that integrates Caputo fractional derivatives with hyperbolic tangent–based interaction functions. The fractional-order term quantifies power-law memory decay in affective states, while the nonlinear component regulates connection strength through emotional difference thresholds. Mathematical analysis establishes the existence and uniqueness of solutions with continuous dependence on initial conditions and proves the local asymptotic stability of network equilibria ($W_{ij}^{*}={\displaystyle \frac{1}{\delta }}{\sec \mathrm{h}}^2(\parallel {\mathrm{E}}_i-{\mathrm{E}}_j\parallel )$, e.g., $W^{*}\approx 1.40$ under typical parameters $\eta =0.5$, $\delta =0.3$). We further derive closed-form expressions for the steady-state variance under stochastic perturbations ($\mathrm{Var}\left(W_{ij}\right)={\displaystyle \frac{{\sigma }_{\zeta }^2}{2\eta \delta }}$) and demonstrate a less than 6% deviation between simulated and theoretical values when ${\sigma }_{\zeta }=0.1$. Numerical experiments using the Euler–Maruyama method validate the convergence of connection weights toward the predicted equilibrium, reveal Gaussian features in the stationary distributions, and confirm power-law scaling between noise intensity and variance. The numerical accuracy of the fractional system is further verified through L1 discretization, with observed error convergence consistent with theoretical expectations for $\mu =0.5$. This framework advances the mechanistic understanding of co-evolutionary dynamics in emotion-modulated social networks, supporting applications in clinical intervention design, collective sentiment modeling, and psychophysiological coupling research. Full article

As a range-free localization algorithm, DV-Hop has gained widespread attention due to its advantages of simplicity and ease of implementation. However, this algorithm also has some defects, such as poor localization accuracy and vulnerability to network topology. This paper presents a comprehensive analysis of the factors contributing to the inaccuracy of the DV-Hop algorithm. An improved proportional integral derivative (PID) search algorithm (PSA) DV-Hop hybrid localization algorithm based on weighted hyperbola (IPSA-DV-Hop) is proposed. Firstly, the first hop distance refinement is employed to rectify the received signal strength indicator (RSSI). In order to replace the original least squares solution, a weighted hyperbolic algorithm based on the degree of covariance is adopted. Secondly, the localization error is further reduced by employing the improved PSA. In addition, the selection process of the node set is optimized using progressive sample consensus (PROSAC) followed by a 3D hyperbolic algorithm based on coplanarity. This approach effectively reduces the computational error associated with the hopping distance of the beacon nodes in the 3D scenarios. Finally, the simulation experiments demonstrate that the proposed algorithm can markedly enhance the localization precision in both isotropic and anisotropic networks and reduce the localization error by a minimum of 30% in comparison to the classical DV-Hop. Additionally, it also exhibits stability under the influence of a radio irregular model (RIM). Full article

In this article, we propose a new path-conservative discontinuous Galerkin (DG) method to solve non-conservative hyperbolic partial differential equations (PDEs). In particular, the method here applies the one-stage ADER (Arbitrary DERivatives in space and time) approach to fulfill the temporal discretization. In addition, this method uses the differential transformation (DT) procedure rather than the traditional Cauchy–Kowalewski (CK) procedure to achieve the local temporal evolution. Compared with the classical ADER methods, the current method is free of solving generalized Riemann problems at inter-cells. In comparison with the Runge–Kutta DG (RKDG) methods, the proposed method needs less computer storage, thanks to the absence of intermediate stages. In brief, this current method is one-step, one-stage, and fully-discrete. Moreover, this method can easily obtain arbitrary high-order accuracy both in space and in time. Numerical results for one- and two-dimensional shallow water equations (SWEs) show that the method enjoys high-order accuracy and keeps good resolution for discontinuous solutions. Full article

The relaxation spectrum is a fundamental viscoelastic characteristic from which other material functions used to describe the rheological properties of polymers can be determined. The spectrum is recovered from relaxation stress or oscillatory shear data. Since the problem of the relaxation spectrum identification is ill-posed, in the known methods, different mechanisms are built-in to obtain a smooth enough and noise-robust relaxation spectrum model. The regularization of the original problem and/or limit of the set of admissible solutions are the most commonly used remedies. Here, the problem of determining an optimally smoothed continuous relaxation time spectrum is directly stated and solved for the first time, assuming that discrete-time noise-corrupted measurements of a relaxation modulus obtained in the stress relaxation experiment are available for identification. The relaxation time spectrum model that reproduces the relaxation modulus measurements and is the best smoothed in the class of continuous square-integrable functions is sought. Based on the Hilbert projection theorem, the best-smoothed relaxation spectrum model is found to be described by a finite sum of specific exponential–hyperbolic basis functions. For noise-corrupted measurements, a quadratic with respect to the Lagrange multipliers term is introduced into the Lagrangian functional of the model’s best smoothing problem. As a result, a small model error of the relaxation modulus model is obtained, which increases the model’s robustness. The necessary and sufficient optimality conditions are derived whose unique solution yields a direct analytical formula of the best-smoothed relaxation spectrum model. The related model of the relaxation modulus is given. A computational identification algorithm using the singular value decomposition is presented, which can be easily implemented in any computing environment. The approximation error, model smoothness, noise robustness, and identifiability of the polymer real spectrum are studied analytically. It is demonstrated by numerical studies that the algorithm proposed can be successfully applied for the identification of one- and two-mode Gaussian-like relaxation spectra. The applicability of this approach to determining the Baumgaertel, Schausberger, and Winter spectrum is also examined, and it is shown that it is well approximated for higher frequencies and, in particular, in the neighborhood of the local maximum. However, the comparison of the asymptotic properties of the best-smoothed spectrum model and the BSW model a priori excludes a good approximation of the spectrum in the close neighborhood of zero-relaxation time. Full article

Solitary waves, inherent in nonlinear wave equations, manifest across various physical systems like water waves, optical fibers, and plasma waves. In this study, we present this type of wave solution within the integrable Mikhailov–Novikov–Wang (MNW) equation, an integrable system known for representing localized disturbances that persist without dispersing, retaining their form and coherence over extended distances, thereby playing a pivotal role in understanding nonlinear dynamics and wave phenomena. Beyond this innovative work, we examine the stability and modulation instability of its gained solutions. These new solitary wave solutions have potential applications in telecommunications, spectroscopy, imaging, signal processing, and pulse modeling, as well as in economic systems and markets. To derive these solitary wave solutions, we employ two effective methods: the improved Sardar subequation method and the (℧′/℧, 1/℧) method. Through these methods, we develop a diverse array of waveforms, including hyperbolic, trigonometric, and rational functions. We thoroughly validated our results using Mathematica software to ensure their accuracy. Vigorous graphical representations showcase a variety of soliton patterns, including dark, singular, kink, anti-kink, and hyperbolic-shaped patterns. These findings highlight the effectiveness of these methods in showing novel solutions. The utilization of these methods significantly contributes to the derivation of novel soliton solutions for the MNW equation, holding promise for diverse applications throughout different scientific domains. Full article

Nematicons upgrade the recognition of light localization in the reorientation of non-local media. the current research employs a powerful integral scheme using a different procedure, namely, the modified simple equation method (MSEM), to analyze nematicons in liquid crystals from the controlling model. The expanded MSEM is investigated to enlarge the applicability of the standard one. The suggested expansion depends on merging the MSEM and the ansatz method. The new generalized nonlinear n-times quadruple power law is included. With the aid of the symbolic computational package Mathematica, new explicit complex hyperbolic, periodic, and more exact spatial soliton solutions are derived. Moreover, the related existence constraints are obtained. To show the dynamical properties of some of the obtained nematicons, three-dimensional profiles with corresponding contours are depicted with the choice of appropriate values of arbitrary parameters. The fractional impacts in various applicable senses are analyzed to investigate the generality of the considered model. Full article

The time-fractional nonlinear Drinfeld–Sokolov–Wilson system, which has significance in the study of traveling waves, shallow water waves, water dispersion, and fluid mechanics, is examined in the presented work. Analytic exact solutions of the system are produced using the modified auxiliary equation method. The fractional implications on the model are examined under $\beta$-fractional derivative and a new fractional local derivative. Extracted solutions include rational, trigonometric, and hyperbolic functions with dark, periodic, and kink solitons. Additionally, by specifying values for fractional parameters, graphs are utilized to comprehend the fractional effects on the obtained solutions. Full article

A generalization of the time-delayed Burgers–Fisher equation is studied. This partial differential equation appears in many physical and biological problems describing the interaction between reaction, diffusion, and convection. New travelling wave solutions are obtained. The solutions are derived in a systematic way by applying the multi-reduction method to the symmetry-invariant conservation laws. The translation-invariant conservation law yields a first integral, which is a first-order Chini equation. Under certain conditions on the coefficients of the equation, the Chini type equation obtained can be solved, yielding travelling wave solutions expressed in terms of the Lerch transcendent function. For a special case, the first integral becomes a Riccati equation, whose solutions are given in terms of Bessel functions, and for a special case of the parameters, the solutions are given in terms of exponential, trigonometric, and hyperbolic functions. Furthermore, a complete classification of the zeroth-order local conservation laws is obtained. To the best of our knowledge, our results include new solutions that have not been previously reported in the literature. Full article

In this paper, we compare three energy harvesting systems in which we introduce additional bumpers whose mathematical model is mapped with a non-linear characteristic based on the hyperbolic sine Fibonacci function. For the analysis, we construct non-linear two-well, three-well and four-well systems with a cantilever beam and permanent magnets. In order to compare the effectiveness of the systems, we assume comparable distances between local minima of external wells and the maximum heights of potential barriers. Based on the derived dimensionless models of the systems, we perform simulations of non-linear dynamics in a wide spectrum of frequencies to search for chaotic and periodic motion zones of the systems. We present the issue of the occurrence of transient chaos in the analyzed systems. In the second part of this work, we determine and compare the effectiveness of the tested structures depending on the characteristics of the bumpers and an external excitation whose dynamics are described by the harmonic function, and find the best solutions from the point view of energy harvesting. The most effective impact of the use of bumpers can be observed when dealing with systems described by potential with deep external wells. In addition, the use of the Fibonacci hyperbolic sine is a simple and effective numerical tool for mapping non-linear properties of such motion limiters in energy harvesting systems. Full article