Search Results (506)

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

We establish a rigorous kinetic-theoretical framework to analyze causal propagation in thermal transport phenomena within relativistic ideal fluids, building a more rigorous framework based on the kinetic theory of gases. Specifically, we provide a refined derivation of the wave equation governing thermal and density fluctuations, clarifying its hyperbolic nature and the associated characteristic propagation speeds. The analysis confirms that thermal fluctuations in a simple non-degenerate relativistic fluid satisfy a causal wave equation in the Euler regime, and it recovers the classical expression for the speed of sound in the non-relativistic limit. This work offers enhanced mathematical and physical insights, reinforcing the validity of the hyperbolic description and suggesting a foundation for future studies in dissipative relativistic hydrodynamics. Full article

This study explores the (1+1)-dimensional Klein–Fock–Gordon equation, a distinct third-order nonlinear differential equation of significant theoretical interest. The Klein–Fock–Gordon equation (KFGE) plays a pivotal role in theoretical physics, modeling high-energy particles and providing a fundamental framework for simulating relativistic wave phenomena. To find the exact solution of the proposed model, for this purpose, we utilized two effective techniques, including the sine-Gordon equation method and a new extended direct algebraic method. The novelty of these approaches lies in the form of different solutions such as hyperbolic, trigonometric, and rational functions, and their graphical representations demonstrate the different form of solitons like kink solitons, bright solitons, dark solitons, and periodic waves. To illustrate the characteristics of these solutions, we provide two-dimensional, three-dimensional, and contour plots that visualize the magnitude of the (1+1)-dimensional Klein–Fock–Gordon equation. By selecting suitable values for physical parameters, we demonstrate the diversity of soliton structures and their behaviors. The results highlighted the effectiveness and versatility of the sine-Gordon equation method and a new extended direct algebraic method, providing analytical solutions that deepen our insight into the dynamics of nonlinear models. These results contribute to the advancement of soliton theory in nonlinear optics and mathematical physics. Full article

This study focuses on the analysis of soliton solutions within the framework of the time-fractional cubic–quintic nonlinear Schrödinger equation (TFCQ-NLSE), a powerful model with broad applications in complex physical phenomena such as fiber optic communications, nonlinear optics, optical signal processing, and laser–tissue interactions in medical science. The nonlinear effects exhibited by the model—such as self-focusing, self-phase modulation, and wave mixing—are influenced by the combined impact of the cubic and quintic nonlinear terms. To explore the dynamics of this model, we apply a robust analytical technique known as the sub-ODE method, which reveals a diverse range of soliton structures and offers deep insight into laser pulse interactions. The investigation yields a rich set of explicit soliton solutions, including hyperbolic, rational, singular, bright, Jacobian elliptic, Weierstrass elliptic, and periodic solutions. These waveforms have significant real-world relevance: bright solitons are employed in fiber optic communications for distortion-free long-distance data transmission, while both bright and dark solitons are used in nonlinear optics to study light behavior in media with intensity-dependent refractive indices. Solitons also contribute to advancements in quantum technologies, precision measurement, and fiber laser systems, where hyperbolic and periodic solitons facilitate stable, high-intensity pulse generation. Additionally, in nonlinear acoustics, solitons describe wave propagation in media where amplitude influences wave speed. Overall, this work highlights the theoretical depth and practical utility of soliton dynamics in fractional nonlinear systems. Full article

This study presents a hyperbolic three-dimensional telegraph interface model with regular interfaces, numerically solved using a hybrid scheme that integrates Haar wavelets and the finite difference method. Spatial derivatives are approximated via a truncated Haar wavelet series, while temporal derivatives are discretized using the finite difference method. For linear problems, the resulting algebraic system is solved using Gauss elimination; for nonlinear problems, Newton’s quasi-linearization technique is applied. The method’s accuracy and stability are evaluated through key performance metrics, including the maximum absolute error, root mean square error, and the computational convergence rate $R_c\left(M\right)$, across various collocation point configurations. The numerical results confirm the proposed method’s efficiency, robustness, and capability to resolve sharp gradients and discontinuities with high precision. Full article

For a significant fluid model and the truncated M-fractional (1 + 1)-dimensional nonlinear generalized water wave equation, distinct types of truncated M-fractional wave solitons are obtained. Ocean waves, tidal waves, weather simulations, river and irrigation flows, tsunami predictions, and more are all explained by this model. We use the improved $(G^{\prime }/G)$ expansion technique and a modified extended direct algebraic technique to obtain these solutions. Results for trigonometry, hyperbolic, and rational functions are obtained. The impact of the fractional-order derivative is also covered. We use Mathematica software to verify our findings. Furthermore, we use contour graphs in two and three dimensions to illustrate some wave solitons that are obtained. The results obtained have applications in ocean engineering, fluid dynamics, and other fields. The stability analysis of the considered equation is also performed. Moreover, the stationary solutions of the concerning equation are studied through modulation instability. Furthermore, the used methods are useful for other nonlinear fractional partial differential equations in different areas of applied science and engineering. Full article

The objective of the present study is to detect chirped optical solitons of the perturbed Chen–Lee–Liu equation with full nonlinearity. By virtue of the traveling wave hypothesis, the discussed model is reduced to a simple form known as an elliptic equation. The latter equation, which is a second-order ordinary differential equation, is handled by the undetermined coefficient method of two forms expressed in terms of the hyperbolic secant and tangent functions. Additionally, the auxiliary equation method is applied to derive several miscellaneous solutions. Various types of chirped solitons are revealed such as W-shaped, bright, dark, gray, kink and anti-kink waves. Taking into consideration the existence conditions, the dynamical behaviors of optical solitons and their corresponding chirp are illustrated. The modulation instability of the perturbed CLL equation is examined by means of the linear stability analysis. It is found that all solutions are stable against small perturbations. These entirely new results, compared to previous works, can be employed to understand pulse propagation in optical fiber mediums and dynamic characteristics of waves in plasma. Full article

This study presents a theoretical model for the thermoelastic response in transmission-mode photoacoustic systems that feature a two-layer structure. The model incorporates volumetric optical absorption in both layers and is based on classical heat conduction theory, hyperbolic generalized heat conduction theory, and fractional heat conduction models including inertial memory in Generalizations of the Cattaneo Equation (GCEI, GCEII, and GCEIII). To validate the model, comparisons were made with the existing literature models. Using the proposed model, the thermoelastic photoacoustic response of a two-layer system composed of a 3D-printed porous polyamide (PA12) substrate coated with a thin, highly absorptive protective dye layer is analyzed. We obtain that the thickness and thermal conduction in properties of the coating are very important in influencing the thermoelastic component and should not be overlooked. Furthermore, the thermoelastic component is affected by the selected fractional model—whether it is subdiffusion or superdiffusion—along with the value of the order of the fractional derivative, as well as the optical absorption coefficient of the layer being investigated. Additionally, it is concluded that the phase has a greater impact than the amplitude when selecting the appropriate theoretical heat conduction model. 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

In this study, we investigate the fractional Tzitzéica equation, a nonlinear evolution equation known for modeling complex phenomena in various scientific domains such as solid-state physics, crystal dislocation, electromagnetic waves, chemical kinetics, quantum field theory, and nonlinear optics. Using the (G′/G, 1/G)-expansion approach, we derive different categories of exact solutions, like hyperbolic, trigonometric, and rational functions. The beta fractional derivative is used here to generalize the classical idea of the derivative, which preserves important principles. The derived solutions with broader nonlinear wave structures are periodic waves, breathers, peakons, W-shaped solitons, and singular solitons, which enhance our understanding of nonlinear wave dynamics. In relation to these results, the findings are described by showing the solitons’ physical behaviors, their stabilities, and dispersions under fractional parameters in the form of contour plots and 2D and 3D graphs. Comparisons with earlier studies underscore the originality and consistency of the (G′/G, 1/G)-expansion approach in addressing fractional-order evolution equations. It contributes new solutions to analytical problems of fractional nonlinear integrable systems and helps understand the systems’ dynamic behavior in a wider scope of applications. Full article

This paper investigates an integrable spin system known as the Myrzakulov-XIII (M-XIII) equation through geometric and gauge-theoretic methods. The M-XIII equation, which describes dispersionless dynamics with curvature-induced interactions, is shown to admit a geometric interpretation via curve flows in three-dimensional space. We establish its gauge equivalence with the complex coupled dispersionless (CCD) system and construct the corresponding Lax pair. Using the Sym–Tafel formula, we derive exact soliton surfaces associated with the integrable evolution of curves and surfaces. A key focus is placed on the role of geometric and gauge symmetry in the integrability structure and solution construction. The main contributions of this work include: (i) a commutative diagram illustrating the connections between the M-XIII, CCD, and surface deformation models; (ii) the derivation of new exact solutions for a fractional extension of the M-XIII equation using the Kudryashov method; and (iii) the classification of these solutions into trigonometric, hyperbolic, and exponential types. These findings deepen the interplay between symmetry, geometry, and soliton theory in nonlinear spin systems. 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

In this article, we present the extended simple equations method (SEsM) for finding exact solutions to systems of fractional nonlinear partial differential equations (FNPDEs). The expansions made to the original SEsM algorithm are implemented in several directions: (1) In constructing analytical solutions: exact solutions to FNPDE systems are presented by simple or complex composite functions, including combinations of solutions to two or more different simple equations with distinct independent variables (corresponding to different wave velocities); (2) in selecting appropriate fractional derivatives and appropriate wave transformations: the choice of the type of fractional derivatives for each system of FNPDEs depends on the physical nature of the modeled real process. Based on this choice, the range of applicable wave transformations that are used to reduce FNPDEs to nonlinear ODEs has been expanded. It includes not only various forms of fractional traveling wave transformations but also standard traveling wave transformations. Based on these methodological enhancements, a generalized SEsM algorithm has been developed to derive exact solutions of systems of FNPDEs. This algorithm provides multiple options at each step, enabling the user to select the most appropriate variant depending on the expected wave dynamics in the modeled physical context. Two specific variants of the generalized SEsM algorithm have been applied to obtain exact solutions to two time-fractional shallow-water-like systems. For generating these exact solutions, it is assumed that each system variable in the studied models exhibits multi-wave behavior, which is expressed as a superposition of two waves propagating at different velocities. As a result, numerous novel multi-wave solutions are derived, involving combinations of hyperbolic-like, elliptic-like, and trigonometric-like functions. The obtained analytical solutions can provide valuable qualitative insights into complex wave dynamics in generalized spatio-temporal dynamical systems, with relevance to areas such as ocean current modeling, multiphase fluid dynamics and geophysical fluid modeling. Full article

The objective of this work is to investigate the global existence, general decay and blow-up results for a class of p-Biharmonic-type hyperbolic equations with delay and acoustic boundary conditions. The global existence of solutions has been obtained by potential well theory and the general decay result of energy has been established, in which the exponential decay and polynomial decay are only special cases, by using the multiplier techniques combined with a nonlinear integral inequality given by Komornik. Finally, the blow-up of solutions is established with positive initial energy. To our knowledge, the global existence, general decay, and blow-up result of solutions to p-Biharmonic-type hyperbolic equations with delay and acoustic boundary conditions has not been studied. Full article

Conventional designs of pile foundations for houses on expansive soils adopt conservative approaches by using swelling pressure measured in oedometer tests to compute pile uplift force. However, in practice, piles are often installed in unsaturated soils, where changes in moisture content influence soil behavior. Increasing moisture in expansive soils reduces matric suction, increases soil volume, and induces swelling pressure, all of which affect uplift shear stress. This study investigates the impact of varying degrees of saturation on pile uplift force through a series of laboratory tests on single-pile models. The results of the experimental investigation indicate that uplift force developed along the pile shaft due to the wetting of expansive soils exhibits a hyperbolic trend. A significant portion of the uplift force developed during the early stage of the heaving process. Back-calculation analyses using theoretical equations reveal that the coefficient of uplift, α, and the swelling pressure ratio, β, increases as the initial degree of saturation of soil specimens increases, with a change of less than 10% within the tested range. These findings suggest that constant values of the α and β parameters can be used for pile design in expansive soils, even under unsaturated conditions. Nonetheless, the influence of other factors, such as pile dimensions, pile materials, and soil properties, on the α and β values should be investigated to improve the accuracy of pile design in expansive soil conditions. Full article