Search Results (1,199)

Sediment plumes threatening benthic ecosystems are one of the environmental hazards associated with seafloor interventions such as bottom trawling, cabling, dredging, and marine mining operations. This study focuses on sediment plume release from hypothetical future deep-sea mining activities, emphasizing its interaction with turbulent ocean currents in regions characterized by complex seafloor topography. In such environments, turbulent lee waves may significantly enhance the scattering of released sediments, pointing to the clear need for appropriate impact assessment frameworks. Global-scale models are limited in their ability to resolve sufficiently high Reynolds numbers to accurately represent turbulence generated by seafloor topography. To overcome these limitations and effectively assess lee wave dynamics, models must incorporate the full physics of turbulence without simplifying the Navier–Stokes equations and must operate with significantly finer spatial discretization while maintaining a domain large enough to capture the full topographic signal. Considering a seamount in the Lofoten Basin of the Norwegian Sea as an example, we present a novel numerical analysis that explores the interplay between lee wave turbulence and sediment plume dispersion using a high-resolution Large Eddy Simulation (LES) framework. We show that the turbulence occurs within semi-horizontal channels that emerge beyond the topographic highs and extend into sheet-like tails close to the seafloor. In scenarios simulating sediment release from various sites on the seamount, our model predicts distinct behavior patterns for different particle sizes. Particles with larger settling velocities tend to deposit onto the seafloor within 50–200 m of release sites. Conversely, particles with lower settling velocities are more susceptible to turbulent transport, potentially traveling greater distances while experiencing faster dilution. Based on our scenarios, we estimate that the plume concentration may dilute below 1 ppm at about 2 km distance from the release site. Although our analysis shows that mixing with ambient seawater results in rapid dilution to low concentrations, it appears crucial to account for the effects of topographic lee wave turbulence in impact assessments related to man-made sediment plumes. Our high-resolution numerical simulations enable the identification of sediment particle size groups that are most likely affected by turbulence, providing valuable insights for developing targeted mitigation strategies. Full article

We study stochastic variants of the Kairat-II and Kairat-X equations in (3 + 1) dimensions, two canonical models in soliton theory. Random fluctuations are incorporated through a Wiener process, yielding a multiplicative stochastic embedding of the wave fields. By combining the enhanced direct algebraic technique with the new projective Riccati equation approach, we obtain closed-form stochastic soliton solutions and analyze how noise modulates their amplitude and localization. The solutions are illustrated with consistent 3D surface plots (mean field vs. sample paths) and 2D time traces to highlight wave geometry and variability. In addition, we employ the energy balance approach to separate kinetic and potential contributions and to verify an energy balance relation for the derived solutions, thereby clarifying their physical plausibility and stability under noise. The results provide exact, easily verifiable benchmarks for stochastic nonlinear wave models and a practical template for incorporating randomness into nonlinear dispersive systems. Full article

The current study examines optical soliton solutions in a complicated system of metamaterial-based optical solutions coupled with extremely dispersive couplers. The conformable fractional derivative (CFD) influences the nonlinear refractive index, which is governed by a parabolic equation. Some soliton solutions are extracted, like bright, singular solitons, and singular periodic ones; also, Weierstrass elliptic doubly periodic, and several other exact solutions are systematically revealed by the study using the modified extended direct algebraic method. The findings shed important light on the many solitons in these intricate systems and the interactions between nonlinearity, dispersion, and metamaterial properties. The findings have significance beyond advancing our theoretical understanding of soliton behavior in metamaterial-based optical couplers; they might influence the advancement and development of optical communication technologies and systems. Complementary 2D and 3D representations show how stability parameters change throughout various dynamical regimes and confirm solution consistency. In order to comprehend the complex nonlinear phenomena of this system and its possible practical applications, this paper offers a comprehensive theoretical framework. Full article

This study addresses the complete integrability of a generalized multicomponent version of the first multiplicative Bogoyavlensky lattice with branched dispersion. The analysis is performed using the Hirota bilinear formalism and the periodic reduction technique. Initially, a two-dimensional mB1 lattice is considered, for which complete integrability is established by constructing its bilinear form and general multisoliton solutions via the Hirota bilinear formalism. A periodic reduction along the discrete independent variable is then applied to derive the coupled multicomponent mB1 lattice, along with its corresponding bilinear representation and multisoliton solutions. The resulting system serves as an integrable semi-discrete generalization of the classical Volterra-type equation. These findings contribute to the broader understanding of integrable lattice systems with branched dispersion relations and provide a constructive framework for obtaining explicit soliton solutions in multicomponent systems, which exhibit rich internal symmetry structures. Full article

An extended growth curve model with fixed and random effects is considered. Under the assumption of multivariate normality, the maximum likelihood estimators of the fixed effects and the dispersion matrix are determined in a model with random nuisance parameters, both without any assumption on the covariance structure and under the assumption of compound symmetry. For this purpose, rules for differentiation of symmetric matrices are applied. Furthermore, when the experiments are designed in balanced complete blocks, particular symmetric matrices appear in the likelihood equations, allowing closed-form expressions for the estimators. It is also shown that the vector of sufficient statistics for the fixed effects extended growth curve model is also sufficient for the model with random nuisance parameters. The presented results are illustrated using a real data example. Full article

Since the early twentieth century, quantum mechanics has sought an interpretation that offers a consistent worldview. In the course of that, many proposals were advanced, but all of them introduce, at some point, interpretation elements (semantics) that find no correlate in the formalism (syntactics). This distance from semantics and syntactics is one of the major reasons for finding so abstruse and diverse interpretations of the formalism. To overcome this issue, we propose an alternative stochastic interpretation, based exclusively on the formal structure of the Schrödinger equation, without resorting to external assumptions such as the collapse of the wave function or the role of the observer. We present four (mathematically equivalent) mathematical derivations of the Schrödinger equation based on four constructs: characteristic function, Boltzmann entropy, Central Limit Theorem (CLT), and Langevin equation. All of them resort to axioms already interpreted and offer complementary perspectives to the quantum formalism. The results show the possibility of deriving the Schrödinger equation from well-defined probabilistic principles and that the wave function represents a probability amplitude in the configuration space, with dispersions linked to the CLT. It is concluded that quantum mechanics has a stochastic support, originating from the separation between particle and field subsystems, allowing an objective description of quantum behavior as a mean-field theory, analogous, but not equal, to Brownian motion, without the need for arbitrary ontological entities. Full article

This work analyzes the hydrodynamic behavior of a magnetorheological valve, considering the microscopic fluid characteristics to generate a damper force. The magnetorheological fluid is composed of ferromagnetic particles dispersed in a non-magnetic carrier fluid, whose mechanical resistance depends on the magnetic field intensity. In the absence of a magnetic field, the magnetorheological fluid behaves as a liquid whose viscosity depends on the particle volume fraction. Conversely, the presence of a magnetic field generates particle chain-like structures that inhibit fluid motion, thereby regulating flow in the control valve. The mathematical model employs the continuity and momentum equations, the Bingham model, and the boundary conditions at the solid–liquid interfaces to determine the flow field. The results show the fluid hydrodynamic response under different flow conditions depending on dimensionless parameters such as the pressure gradient, the field-independent viscosity, the yield stress, the particle volume fraction, the Bingham number, the Mason number, and the critical Mason number. For a pressure gradient of $\Gamma =-10$, the flow rate inside the valve (with particle volume fraction $\varphi =0.2$) results in ${\overline{Q}}_{T,x}=0.34$, $0.06$, and 0 when the magnetic field is 80, 120, and 160 kA m⁻¹, respectively. Likewise, when the magnetic field increases from 80 to 160 kA m⁻¹, the damping capacity increases by $88\%$ when $\varphi =0.2$ and $128\%$ when $\varphi =0.3$ compared to the Newtonian viscous damping. This work contributes to our understanding of semi-active damping devices for flow control. Full article

Thisreview provides a comprehensive synthesis of recent theoretical and experimental advances on turbulent plane jets interacting with surface waves or rigid vegetation. In wave-affected conditions, a unified mathematical framework based on velocity decomposition and the integral balances of momentum and energy reveals the fundamental scaling laws governing jet spreading and momentum exchange. The analysis demonstrates that wave-induced shear alters classical entrainment mechanisms, leading to modified power-law relationships for jet width and centerline velocity, consistent with laboratory and numerical evidence. In obstructed environments, such as canopies of rigid or flexible vegetation, distributed drag induces a transition from entrainment to detrainment. The resulting momentum loss is captured analytically by incorporating drag-induced dissipation into the Reynolds-averaged momentum equations, yielding exponential decay of jet momentum and reduced mixing efficiency. Together, these models elucidate how environmental forcing—dynamic (waves) and structural (vegetation)—controls the evolution of turbulent jets in natural and engineered aquatic systems. The review highlights key scaling relationships, theoretical developments, and experimental findings, offering a coherent basis for future studies on mixing, dispersion, and transport in complex coastal and vegetated flows. Full article

Three-wave resonant interaction equations can model nonlinear dynamics in many fields, e.g., fluids, optics, and plasma. Rogue waves, i.e., modes algebraically localized in both space and time, are obtained analytically. The aim of this paper is to study degenerate three-wave resonant interaction equations, where two out of the three interacting wave packets have identical group velocities. Physically, degenerate resonance typically occurs for dispersion relation, possessing many branches, e.g., internal waves in a continuously stratified fluid. Here, the Nth-order rogue wave solutions for this dynamical model are presented. Based on these solutions, we examine the effects of the group velocity on the width and structural profiles of the rogue waves. The width of the rogue waves exhibit a linear increase as the group velocity increases, a feature well-correlated with the prediction made using modulation instability. In terms of structural profiles, first-order rogue waves display ‘four-petal’ and ‘eye-shaped’ patterns. Second-order rogue waves can reveal intriguing configurations, e.g., ‘butterfly’ patterns and triplets. To ascertain the robustness of these modes, numerical simulations with random initial conditions were performed. Sequences of localized modes resembling these analytical rogue waves were observed. A spectral jump was observed, with the jump broadening in the case of rogue wave triplets. Furthermore, we predict new rogue waves based on information from two existing ones obtained using the deep learning technique in the context of rogue wave triplets. This predictive model holds potential applications in ocean engineering. Full article

This study investigates the dynamics of optical solitons for the variable-coefficient coupled higher-order nonlinear Schrödinger equation (VCHNLSE) enriched with $\beta$-derivatives. By employing an extended direct algebraic method (EDAM), we successfully derive explicit soliton solutions that illustrate the intricate interplay between nonlinearities and variable coefficients. Our approach facilitates the transformation of the complex NLS into a more manageable form, allowing for the systematic exploration of diverse solitonic structures, including bright, dark, and singular solitons, as well as exponential, polynomial, hyperbolic, rational, and Jacobi elliptic solutions. This diverse family of solutions substantially expands beyond the limited soliton interactions studied in conventional approaches, demonstrating the superior capability of our method in unraveling new wave phenomena. Furthermore, we rigorously demonstrate the robustness of these soliton solutions against various perturbations through comprehensive stability analysis and numerical simulations under parameter variations. The practical significance of this work lies in its potential applications in advanced optical communication systems. The derived soliton solutions and the analysis of their dynamics provide crucial insights for designing robust signal carriers in nonlinear optical media. Specifically, the management of variable coefficients and fractional-order effects can be leveraged to model and engineer sophisticated dispersion-managed optical fibers, tunable photonic devices, and ultrafast laser systems, where controlling pulse propagation and stability is paramount. The presence of $\beta$-fractional derivatives introduces additional complexity to the wave propagation behaviors, leading to novel dynamics that we analyze through numerical simulations and graphical representations. The findings highlight the potential of the proposed methodology to uncover rich patterns in soliton dynamics, offering insights into their robustness and stability under varying conditions. This work not only contributes to the theoretical foundation of nonlinear optics but also provides a framework for practical applications in optical fiber communications and other fields involving nonlinear wave phenomena. Full article

A continuum model for describing pseudo-turbulent flows of a dispersed phase is developed using a statistical approach based on the kinetic equation for the probability density of particle velocity and temperature. The introduction of the probability density function enables a statistical description of the particle ensemble through equations for the first and second moments, replacing the dynamic description of individual particles derived from Langevin-type equations of motion and heat transfer. The lack of detailed dynamic information on individual particle behavior is compensated by a richer statistical characterization of the motion and heat transfer within the particle continuum. A numerical simulation of the unsteady flow of a gas–particle suspension generated by the interaction of a shock wave with a particle cloud is performed using an interpenetrating continua model and equations for the first and second moments of both gas and particles. Numerical methods for solving the two-phase gas dynamics equations—formulated using a two-velocity and two-temperature model—are discussed. Each phase is governed by conservation equations for mass, momentum, and energy, written in a conservative hyperbolic form. These equations are solved using a high-order Godunov-type numerical method, with time discretization performed by a third-order Runge–Kutta scheme. The study analyzes the influence of two-dimensional effects on the formation of shock-wave flow structures and explores the spatial and temporal evolution of particle concentration and other flow parameters. The results enable an estimation of shock wave attenuation by a granular backfill. The extended pressure relaxation region is observed behind the cloud of particles. Full article

Maglev trains represent an advanced form of modern rail transportation. The guideway irregularity presents a common disturbance to the safe and reliable operation of the maglev train. Variations in the air gap between the train and the guideway, induced by the guideway irregularities, exert a significant influence on the train’s dynamic performance, thereby impacting both ride comfort and operational safety. Although previous studies have acknowledged the importance of guideway irregularity, the stochastic effects on the car body vibration across different speeds have not been quantitatively assessed. To fill in this gap, this paper presents a 10-degree-of-freedom maglev train model based on multibody dynamics. The guideway is modelled via the finite element method using Euler–Bernoulli beam theory, and a linearized electromagnetic force equation is employed to couple the guideway and the train dynamics. Furthermore, the measurement data of guideway irregularity from the Shanghai Maglev commercial line are incorporated to evaluate their stochastic effect. Analysis results under varying speeds and irregularity wavelengths identify a resonance speed of 127.34 km/h, attributed to the interplay between guideway periodicity and the train’s natural frequency. When the ratio of the train speed versus irregularity wavelength satisfies the train’s natural frequency, a significant resonance can be observed, leading to an increase in train vibration. Based on the Monte Carlo method, stochastic analysis is conducted using 150 simulations per speed in 200–600 km/h. The maximum vertical acceleration remains relatively stable at 200–400 km/h but increases significantly at higher speeds. When the irregularity is present, greater dispersion is observed with increasing speed, with the standard deviation at 600 km/h reaching 2.7 times that at 200 km/h. Across all tested cases, acceleration values are consistently higher than those without irregularities within the corresponding confidence intervals. Full article

In the study of linear dispersive media, it is of primary interest to gain knowledge of the impulse response of the material. The standard approach to compute the response involves a Laplace transform inversion, i.e., the solution of a Bromwich integral, which can be a notoriously troublesome problem. In this paper we propose a novel approach to the calculation of the impulse response, based on the well-assessed method of the steepest descent path, which results in the replacement of the Bromwich integral with a real line integral along the steepest descent path. In this exploratory investigation, the method is explained and applied to the case study of the Klein–Gordon equation with dissipation, for which analytical solutions of the Bromwich integral are available, so as to compare the numerical solutions obtained by the newly proposed method to exact ones. Since the newly proposed method, at its core, consists of replacing a Laplace transform inverse with a potentially much less demanding real line integral, the method presented here could be of general interest in the study of linear dispersive waves in the presence of dissipation, as well as in other fields in which Laplace transform inversion comes into play. Full article

An ambit of enhancing heat transfer throughout thermal convection in a cavity is explored numerically in this study, contemplating the heat dispersal from a segmental heat source circumscribed in a square-vented porous cavity with a moving lid. The cavity can be used as a heat sink for electronic cooling, material processing, and convective drying. Aluminum $10$ PPI metal foam saturated by aluminum oxide–water nanofluid is occupied in this lid-driven vented cavity system. The bottom cavity wall is fully and partially heated by a heat source of specific length $L_H$, and the left wall and inlet fluid are kept at the same cold temperature, while the right wall and top-driven wall are thermally insulated. Thermal dispersion and local thermal non-equilibrium effects are included in an energy equation, and continuity and Darcy–Brinkmann–Forchheimer momentum equations are implemented and resolved by utilizing the finite volume method with the aid of a vorticity–stream function approach operation. The inspirations behind pertinent parameters, including the Reynolds number ($Re=10–50$), Grashof number ($Gr={10}^3–{10}^6$), inlet and outlet ports’ aspect ratio ($D/H=0.1–0.4$), outlet port location ratio ($S/H=0.25–0.75$), and discrete partial heating ratio ($L_H/L=0.25–1$) are scrutinized. The baseline circumstance corresponds to full-length heating $L_H/L=1$ and the outlet port location ratio $S/H=0.25$. The results reveal that the fluid and heat flow domains are addressed mostly via these specification alterations. For $Gr={10}^3$, increasing $Re$ from $10$ to $40$ does not alter streamlines or the isotherm field, but when $Re=50$ it is detected that streamlines increase monotonically. Streamlines are not altered when $L_H/L$ and $S/H$ are amplified but strengthened more when the opening vent aspect ratio is increased. A greater temperature difference occurs as $L_H/L$ is raised from $0.25–0.75$ and isotherms are intensified, and the thermal boundary layer becomes more distinct when $S/H$ is augmented. The average Nusselt number rises as $Re$, $Gr$, $L_H/L$, and $D/H$ are increased by about $30\%$, $3.5\%$, $23\%$, and $19.4\%$, respectively, and it decreases with $S/H$ amplifying is increased by around $5.5\%$. Full article

We present an analytical and numerical study of nonlinear wave localization in a one-dimensional rhombic (diamond) waveguide array that combines forward- and backward-propagating channels. This mixed-index configuration, realizable through Bragg-type couplers or corrugated waveguides, produces a tunable spectral gap and supports nonlinear self-localized states in both transmission and forbidden-band regimes. Starting from the full set of coupled-mode equations, we derive the effective evolution model, identify the role of coupling asymmetry and nonlinear coefficients, and obtain explicit soliton solutions using the method of multiple scales. The resulting envelopes satisfy a nonlinear Schrödinger equation with an effective nonlinear parameter $\theta$, which determines the conditions for soliton existence ($\theta >0$) for various combinations of focusing and defocusing nonlinearities. We distinguish solitons formed outside and inside the bandgap and analyze their dependence on the dispersion curvature and nonlinear response. Direct numerical simulations confirm the analytical predictions and reveal robust propagation and interactions of counter-propagating soliton modes. Order-of-magnitude estimates show that the predicted effects are accessible in realistic integrated photonic platforms. These results provide a unified theoretical framework for soliton formation in mixed-index lattices and suggest feasible routes for realizing controllable nonlinear localization in Bragg-type photonic structures. Full article