Search Results (248)

Energy generation from renewable sources has increased exponentially worldwide, particularly wind energy, which is converted into electricity through wind turbines. The growing demand for renewable energy has driven the development of horizontal-axis wind turbines with larger dimensions, as the energy captured is proportional to the area swept by the rotor blades. In this context, the dynamic loads typically observed in wind turbine towers include vibrations caused by rotating blades at the top of the tower, wind pressure, and earthquakes (less common). In offshore wind farms, wind turbine towers are also subjected to dynamic loads from waves and ocean currents. Vortex-induced vibration can be an undesirable phenomenon, as it may lead to significant adverse effects on wind turbine structures. This study presents a two-dimensional transient model for a rigid body anchored by a torsional spring subjected to a constant velocity flow. We applied a coupling of the Fourier pseudospectral method (FPM) and immersed boundary method (IBM), referred to in this study as IMERSPEC, for a two-dimensional, incompressible, and isothermal flow with constant properties—the FPM to solve the Navier–Stokes equations, and IBM to represent the geometries. Computational simulations, solved at an aspect ratio of $\varphi =4.0$, were analyzed, considering Reynolds numbers ranging from $Re=150$ to Re = 1000 when the cylinder is stationary, and $Re=250$ when the cylinder is in motion. In addition to evaluating vortex shedding and Strouhal number, the study focuses on the characterization of space–time symmetry during the galloping response. The results show a spatial symmetry breaking in the flow patterns, while the oscillatory motion of the rigid body preserves temporal symmetry. The numerical accuracy suggested that the IMERSPEC methodology can effectively solve complex problems. Moreover, the proposed IMERSPEC approach demonstrates notable advantages over conventional techniques, particularly in terms of spectral accuracy, low numerical diffusion, and ease of implementation for moving boundaries. These features make the model especially efficient and suitable for capturing intricate fluid–structure interactions, offering a promising tool for analyzing wind turbine dynamics and other similar systems. Full article

We advance a mathematical framework for collective conviction by deriving a continuum theory from the network-based model introduced by us recently. The resulting equation governs the evolution of belief through a degenerate anisotropic logistic–diffusion process, where diffusion slows as conviction saturates. In one spatial dimension, we prove global well-posedness, demonstrate spectral front pinning that arrests the spread of influence at finite depth, and construct explicit traveling-wave solutions. In two dimensions, we uncover a geometric mechanism of curvature–induced quenching, where belief propagation halts along regions of low effective mobility and curvature. Building on this insight, we formulate a variational principle for optimal control under resource constraints. The derived feedback law prescribes how to spatially allocate repression effort to maximize inhibition of front motion, concentrating resources along high-curvature, low-mobility arcs. Numerical simulations validate the theory, illustrating how localized suppression dramatically reduces transverse spread without affecting fast axes. These results bridge analytical modeling with societal phenomena such as protest diffusion, misinformation spread, and institutional resistance, offering a principled foundation for selective intervention policies in structured populations. Full article

This work examines the fractional Sawada–Kotera and Korteweg–de Vries (KdV)–Burgers equations, which are essential models of nonlinear wave phenomena in many scientific domains. The homotopy perturbation transform method (HPTM) and the Yang transform decomposition method (YTDM) are two sophisticated techniques employed to derive analytical solutions. The proposed methods are novel and remarkable hybrid integral transform schemes that effectively incorporate the Adomian decomposition method, homotopy perturbation method, and Yang transform method. They efficiently yield rapidly convergent series-type solutions through an iterative process that requires fewer computations. The Caputo operator, used to express the fractional derivatives in the equations, provides a robust framework for analyzing the behavior of non-integer-order systems. To validate the accuracy and reliability of the obtained solutions, numerical simulations and graphical representations are presented. Furthermore, the results are compared with exact solutions using various tables and graphs, illustrating the effectiveness and ease of implementation of the proposed approaches for various fractional partial differential equations. The influence of the non-integer parameter on the solutions behavior is specifically examined, highlighting its function in regulating wave propagation and diffusion. In addition, a comparison with the natural transform iterative method and optimal auxiliary function method demonstrates that the proposed methods are more accurate than these alternative approaches. The results highlight the potential of YTDM and HPTM as reliable tools for solving nonlinear fractional differential equations and affirm their relevance in wave mechanics, fluid dynamics, and other fields where fractional-order models are applied. Full article

This study examines the behavior of Rayleigh waves propagating through a homogeneous, isotropic material, analyzed using a three-phase-lag thermoelastic diffusion framework enhanced by modified couple stress theory. The mathematical model integrates coupled thermoelastic and diffusive effects, incorporating phase-lags associated with (1) temperature gradients, (2) heat flux, and (3) thermal displacement gradients. By solving the derived governing equations analytically subject to stress-free, thermally insulated, and impermeable boundary conditions, we obtain the characteristic secular equation for Rayleigh wave propagation. Numerical simulations conducted on a copper medium evaluate how the secular equation’s determinant, wave velocity, and attenuation coefficient vary with angular frequency. The analysis focuses particularly on the influence of phase-lag parameters, including thermal and diffusion gradients and relaxation times. Results demonstrated that increasing the displacement gradient phase-lag elevated the secular determinant but reduced wave velocity and attenuation, while temperature gradient phase-lags exhibited the opposite trend. The study highlights the sensitivity of Rayleigh wave propagation to thermo-diffusive coupling and microstructural effects, offering insights applicable to seismic wave analysis, geophysical exploration, and material processing. Comparisons with prior theories underscore the model’s advancement in capturing size-dependent and memory-dependent phenomena. Full article

The Holby–Morgan model of electrochemical degradation in platinum on a carbon catalyst is studied with respect to the impact of particle size distribution on aging in polymer electrolyte membrane fuel cells. The European Union harmonized protocol for testing by non-symmetric square-wave voltage is applied for accelerated stress cycling. The log-normal distribution is estimated using finite size groups which are defined by two parameters of the median and standard deviation. In the non-diffusive model, the first integral of the system is obtained which reduces the number of differential equations. Without ion diffusion, it allows to simulate platinum particles shrank through platinum dissolution and growth by platinum ion deposition. Numerical tests of catalyst degradation in the diffusion model demonstrate the following changes in platinum particle size distribution: broadening for small and shrinking for large medians with tailing towards large particles; the possibility of probability decrease as well as increase for each size group; and overall, a drop in the platinum particle size takes place, which is faster for the small median owing to the Gibbs–Thompson effect. Full article

Gravity water waves in the shallow-ocean scenario described by generalized Boussinesq–Broer–Kaup–Whitham (gBBKW) equations are discussed. The residual symmetry and Bäcklund transformation associated with the gBBKW equations are systematically constructed. The time and space evolution of wave velocity and height are explored. Additionally, it is demonstrated that the gBBKW equations are solvable through the consistent Riccati expansion method. Leveraging this property, a novel Bäcklund transformation, solitary wave solution, and soliton–cnoidal wave solution are derived. Furthermore, miscellaneous novel solutions of gBBKW equations are obtained using the modified Sardar sub-equation method. The impact of variations in the diffusion power parameter on wave velocity and height is quantitatively analyzed. The exact solutions of gBBKW equations provide precise description of propagation characteristics for a deeper understanding and the prediction of some ocean wave phenomena. Full article

This study sought to deepen our understanding of the dynamical properties of the newly extended $(3+1)$-dimensional integrable Kadomtsev–Petviashvili (KP) equation, which models the behavior of ion acoustic waves in plasmas and nonlinear optics. This paper aimed to perform Lie symmetry analysis and derive lump, breather, and soliton solutions using the extended hyperbolic function method and the generalized logistic equation method. It also analyzed the dynamical system using chaos detection techniques such as the Lyapunov exponent, return maps, and the fractal dimension. Initially, we focused on constructing lump and breather soliton solutions by employing Hirota’s bilinear method. Secondly, employing Lie symmetry analysis, symmetry generators were utilized to satisfy the Lie invariance conditions. This approach revealed a seven-dimensional Lie algebra for the extended $(3+1)$-dimensional integrable KP equation, incorporating translational symmetry (including dilation or scaling) as well as translations in space and time, which were linked to the conservation of energy. The analysis demonstrated that this formed an optimal sub-algebraic system via similarity reductions. Subsequently, a wave transformation method was applied to reduce the governing system to ordinary differential equations, yielding a wide array of exact solitary wave solutions. The extended hyperbolic function method and the generalized logistic equation method were employed to solve the ordinary differential equations and explore closed-form analytical solitary wave solutions for the diffusive system under consideration. Among the results obtained were various soliton solutions. When plotting the results of all the solutions, we obtained bright, dark, kink, anti-kink, peak, and periodic wave structures. The outcomes are illustrated using 2D, 3D, and contour plots. Finally, upon introducing the perturbation term, the system’s behavior was analyzed using chaos detection techniques such as the Lyapunov exponent, return maps, and the fractal dimension. The results contribute to a deeper understanding of the dynamic properties of the extended KP equation in fluid mechanics. Full article

In this article, novel methods of analysis to solve the (3+1)-dimensional generalized fractional Kadomtsev–Petviashvili equation, which plays a crucial role in the modelling of fluid dynamics, particularly wave propagation in complicated media, are presented. The fractional KP equation, a well-established mathematical model, uses fractional derivatives to more adequately describe more general types of nonlinear wave phenomena, with a richer and improved understanding of the dynamics of fluids with non-classical characteristics, such as anomalous diffusion or long-range interactions. Two efficient methods, the exponential rational function technique (ERFT) and the generalized Kudryashov technique (GKT), have been applied to find exact travelling solutions describing soliton behaviour. Solitons, localized waveforms that do not deform during propagation, are central to the dynamics of waves in fluid systems. The characteristics of the obtained results are explored in depth and presented both by three-dimensional plots and by two-dimensional contour plots. Plots provide an explicit picture of how the solitons evolve in space and time and provide insight into the underlying physical phenomena. We also added modulation instability. Our analysis of modulation instability further underscores the robustness and physical relevance of the obtained solutions, bridging theoretical advancements with observable phenomena. Full article

In this paper, the inverse problem of identifying the source term of the time fractional diffusion-wave equation is studied. This problem is ill-posed, i.e., the solution (if it exists) does not depend on the measurable data. Under the priori bound condition, the condition stable result and the optimal error bound are all obtained. The fractional Landweber iterative regularization method is used to solve this inverse problem. Based on the priori regularization parameter selection rule and the posteriori regularization parameter selection rule, the error estimation between the regularization solution and the exact solution is obtained. Moreover, the error estimations are all order optimal. At the end, three numerical examples are given to prove the effectiveness and stability of this regularization method. Full article

This paper mainly consists of two parts: (i) We study the uniqueness, existence, and stability of a new fractional nonlinear partial integro-differential equation in ${\mathbb{R}}^n$ with three-point conditions and variable coefficients in a Banach space using inverse operators containing multi-variable functions, a generalized Mittag-Leffler function, as well as a few popular fixed-point theorems. These studies have good applications in general since uniqueness, existence and stability are key and important topics in many fields. Several examples are presented to demonstrate applications of results obtained by computing approximate values of the generalized Mittag-Leffler functions. (ii) We use the inverse operator method and newly established spaces to find analytic solutions to a number of notable partial differential equations, such as a multi-term time-fractional convection problem and a generalized time-fractional diffusion-wave equation in ${\mathbb{R}}^n$ with initial conditions only, which have never been previously considered according to the best of our knowledge. In particular, we deduce the uniform solution to the non-homogeneous wave equation in n dimensions for all $n\ge 1$, which coincides with classical results such as d’Alembert and Kirchoff’s formulas but is much easier in the computation of finding solutions without any complicated integrals on balls or spheres. Full article

On steep-sloped watersheds, high-intensity, short-duration rainfall events are the leading causes of flash floods. Typical overland flow analysis assumes sheet-like flow with a shallow water depth. However, the natural creek beds in steep watersheds produce complex and intense flows with a shallow depth and high velocity. According to the hydrodynamical modeling processes for open channel turbulent flow, calculating rainfall-induced overland flow becomes a complex task. Steep topography requires a highly refined numerical mesh, which demands a more complex simulation process. Depth-integrated models with distributed parameters provide useful methods to capture the behavior of steep watersheds. This study investigates the watershed’s overland flow behavior by varying turbulent flow parameters and monitoring possible model errors. The refined modeling places a heavy demand on numerical solvers used for simulating the overland flow motion. This paper examines different depth-integrated model solvers applied to artificial watersheds and compares results produced by the different solver types. This study found that the Shallow Water Equation solutions produced the most consistent and stable results, with the Local Inertia Approximation solutions performing adequately. Adding Large Eddy Simulation to these solutions tended to overcomplicate Shallow Water solutions but generally improved Large Eddy solutions. The Diffuse Wave Equation solutions produced erratic results, losing stability and accuracy as watershed slopes steepened and flow paths became complex. Full article

In this study, we propose a generalized framework based on the Simple Equations Method (SEsM) for finding exact solutions to systems of fractional nonlinear partial differential equations (FNPDEs). The key developments over the original SEsM in the proposed analytical framework include the following: (1) an extension of the original SEsM by constructing the solutions of the studied FNPDEs as complex composite functions which combine two single composite functions, comprising the power series of the solutions of two simple equations or two special functions with different independent variables (different wave coordinates); (2) an extension of the scope of fractional wave transformations used to reduce the studied FNPDEs to different types of ODEs, depending on the physical nature of the studied FNPDEs and the type of selected simple equations. One variant of the proposed generalized SEsM is applied to a mathematical generalization inspired by the classical Boussinesq model. The studied time-fractional Boussinesq-like system describes more intricate or multiphase environments, where classical assumptions (such as constant wave speed and energy conservation) are no longer applicable. Based on the applied SEsM variant, we assume that each system variable in the studied model supports multi-wave dynamics, which involves combined propagation of two distinct waves traveling at different wave speeds. As a result, numerous new multi-wave solutions including combinations of different hyperbolic, elliptic, and trigonometric functions are derived. To visualize the wave dynamics and validate the theoretical results, some of the obtained analytical solutions are numerically simulated. The new analytical solutions obtained in this study can contribute to the prediction and control of more specific physical processes, including diffusion in porous media, nanofluid dynamics, ocean current modeling, multiphase fluid dynamics, as well as several geophysical phenomena. Full article

In this study, we sought numerical solutions for three-dimensional coupled Burgers’ equations. Burgers’ equations are fundamental partial differential equations in fluid mechanics. They integrate the characteristics of both the first-order wave equation and the heat conduction equation, serving as crucial tools for modeling the interaction between convection and diffusion. First, the fractional step method was applied to decompose the equations into one-dimensional forms. Then, implicit finite difference approximations were used to solve the resulting one-dimensional equations. To assess the accuracy of the proposed approach, we tested it on two benchmark problems and compared the results with existing methods in the literature. Additionally, the symmetry of the solution graphs was analyzed to gain deeper insight into the results. Stability analysis using the von Neumann method confirmed that the proposed approach is unconditionally stable. The results obtained in this study strongly support the effectiveness and reliability of the proposed method in solving three-dimensional coupled Burgers’ equations. Full article

The acoustic emissions of ventilation systems and their subcomponents contribute to the perceived overall comfort in indoor environments and are, therefore, the subject of research. In contrast to fans, there is little research on the aeroacoustic properties of air diffusers (often referred to as outlets). This study investigates a commercially available ceiling swirl diffuser. Using a hybrid approach, a detailed three-dimensional large-eddy simulation is coupled with a perturbed wave equation to capture the aeroacoustic processes within the diffuser. The flow model is validated for the investigated operating point of 470 m³/h using laser-optical and acoustic measurements. To identify the noise sources, the acoustic pressure is sampled with various receivers and on cut sections to evaluate the cross-power spectral density, and the sound-pressure level distribution on cut sections is evaluated. It is found that the plenum attenuates the noise near its acoustic eigenmodes and thus dominates other noise sources by several orders of magnitude. By implementing the plenum walls as sound-absorbing, the overall sound-pressure level is predicted to decrease by nearly 10 dB/Hz. Other relevant geometric features are the mounting beam and the guide elements, which are responsible for flow-borne noise emissions near 698 Hz and 2699 Hz, respectively. Full article

The purpose of this study is to investigate a series of novel exact closed form traveling wave solutions for the TFSMCH equation and (1 + 1) dimensional TFDMBBM equation using the EMSE technique. The considered FONLEEs are used to delineate the characteristic of diffusion in the creation of shapes in liquid beads arising in plasma physics and fluid flow and to estimate the external long waves in nonlinear dispersive media. These equations are also used to characterize various types of waves, such as hydromagnetic waves, acoustic waves, and acoustic gravity waves. Here, we utilize the Caputo-type fractional order derivative to fractionalize the considered FONLEEs. Some trigonometric and hyperbolic trigonometric functions have been used to represent the obtained closed form traveling wave solutions. Furthermore, here, we reveal that the EMSE technique is a suitable, significant, and dominant mathematical tool for finding the exact traveling wave solutions for various FONLEEs in mathematical physics. We draw some 3D, 2D, and contour plots to describe the various wave behaviors and analyze the physical consequence of the attained solutions. Finally, we make a numerical comparison of our obtained solutions and other analogous solutions obtained using various techniques. Full article