Existing theoretical analyses on the Faraday instability in Hele-Shaw cells typically adopt gap-averaged governing equations and rely on Hamraoui’s model coming from molecular kinetics theory, thereby oversimplifying essential transverse information, such as contact line velocity and capillary hysteresis, and conflicting with the unsteady meniscus dynamics. In this paper, a gap-resolved approach is developed by directly modelling the transverse gap flow and the contact angle dynamics, which overcomes the aforementioned limitations, ultimately yielding a modified damping with respect to the static contact angle and hysteresis range. A novel amplitude equation for linear Faraday instability is derived that combines this damping and the gap-averaged counterpart based on the oscillatory Stokes boundary layer, with the viscous dissipation preserved. By means of Lyapunov’s first method, an explicit analytical expression for the critical stability boundary is established. Two series of laboratory experiments are performed that focus, respectively, on evolutions of the lateral meniscus and the longitudinal free surface near the Faraday onset, from which key parameters relevant to the theory are precisely measured. Based on the experimental data, the validity of the proposed mathematical model for addressing the Faraday instability problem in Hele-Shaw cells is confirmed, and the generation and development mechanisms of the onset are clarified. In the asymptotic analysis, the inclusion of contact angle dynamics increases the overall damping and thus partially compensates for the frequency detuning introduced by oscillatory Stokes flow approximation.

In the circular restricted three-body problem (CRTBP), periodic orbits in the vicinity of collinear libration points not only exhibit profound nonlinear dynamical characteristics but also serve as critical orbital resources for deep-space exploration mission design. In this study, we introduce a systematic analytical framework based on the Homotopy Analysis Method (HAM) to construct high-order series solutions for Lyapunov and Halo orbits near the libration points. The convergence behavior of the series solutions is thoroughly investigated, and their accuracy is validated through comparison with high-precision numerical integration results. The results indicate that the HAM-based solutions exhibit good agreement with the numerical results. Consequently, the initial conditions derived from the HAM series solutions provide enhanced accuracy and reliability for the practical computation of periodic orbits in mission design and trajectory analysis.

This study investigates the coupled dynamics of liquid sloshing with covered elastic plates in a rectangular tank, examining the effects of material properties, plate thickness, and boundary conditions on natural frequencies and damping characteristics. Three materials with distinct mechanical properties including polyvinyl chloride (PVC), high-density polyethylene (HDPE), and silicone gel (SG) were tested under fully clamped (CCCC) and mixed free-clamped (FCFC) boundary configurations across varying liquid depths. Results demonstrate that natural sloshing frequencies exhibit weak dependence on plate thickness but strong sensitivity to material stiffness and boundary conditions, with PVC plates producing frequency enhancements exceeding 60% compared to clean tank baselines. Damping characteristics reveal complex interactions between material compliance, boundary configuration, and liquid depth. Under CCCC conditions, stiffer materials achieve superior damping at large depths through enhanced boundary layer dissipation, while compliant materials dominate at shallow depths via viscoelastic energy absorption. The FCFC configuration activates additional dissipation pathways: stiff plates generate strong velocity gradients near edge transition zones, whereas compliant plates exploit large-amplitude flexural deformation at free edges. Notably, intermediate-stiffness materials perform optimally at moderate depths but lose their advantage under extreme loading conditions, where systems favor either high stiffness or high compliance. These findings provide guidance for designing passive sloshing suppression systems through strategic selection of plate material and edge constraints.

Accurate and real-time prediction of ocean waves is paramount for marine engineering, ship design, and offshore operations. While traditional physical models like Linear Wave Theory (LWT) fail to capture complex nonlinear interactions, high-fidelity numerical simulations such as the High-Order Spectral (HOS) method are prohibitively expensive for real-time applications. To bridge this gap, this study introduces a hybrid deep learning architecture that combines Convolutional Neural Networks (CNNs) for spatial feature extraction and Bidirectional Long Short-Term Memory (BiLSTM) networks for temporal sequence modeling. Trained on a comprehensive dataset generated by the HOS method across diverse sea states, the model’s performance was optimized through a systematic investigation of key hyperparameters, including sampling intervals, sequence lengths, and activation functions. The results demonstrate that the CNN-BiLSTM model substantially surpasses both LWT and individual network architectures (e.g., standalone CNN or BiLSTM) in prediction accuracy and robustness, particularly under highly nonlinear and irregular wave conditions. Consequently, the CNN-BiLSTM framework offers a computationally efficient yet highly accurate surrogate model which presents a viable solution for real-time operational wave forecasting in ocean engineering.

Rogue waves, commonly defined as waves whose heights exceed twice the significant wave height, are among the most hazardous ocean phenomena and pose serious risks to offshore structures and marine operations. Over the past decades, advances in observational technologies have provided unprecedented in-situ evidence of their occurrence across diverse ocean environments. This review synthesizes these measurement-based findings to clarify the statistical characteristics, physical mechanisms, and predictive potential of rogue waves under realistic sea states.Field observations consistently show that rogue wave occurrence often exceeds predictions from classical linear Gaussian theory and exhibits pronounced spatial and temporal clustering, particularly in energetic conditions influenced by storms, crossing seas, strong currents, and wind forcing. Measurements further reveal that rogue waves rarely occur as isolated crests but are typically embedded within energetic wave groups, highlighting the central role of group-scale energy focusing. Under broadband ocean spectra, transient linear focusing and weakly nonlinear interactions account for a substantial proportion of observed events, whereas modulational instability appears less dominant. Although deterministic forecasting shows promising capability, predictive skill remains fundamentally constrained by intrinsic limits of nonlinear ocean wave dynamics.These insights provide an observationally grounded framework for improving hazard assessment and forecasting in offshore engineering.

This study investigates the global families of periodic orbits in the planar circular restricted three-body problem (CRTBP) with two equal-mass primaries. A numerical approach integrating a grid-search scheme and the Newton-Raphson correction method is employed to compute periodic solutions. Unlike conventional searches over a two-parameter space that impose symmetry constraints, the proposed approach performs a threedimensional exploration of the parameter space. This extension effectively removes symmetry restrictions and enables the discovery of a wide variety of asymmetric planar periodic orbits that are inaccessible to classical methods. The numerical periodic orbits are classified using a topological coding method, which provides an unambiguous description of their geometric structure. A total of 142 fully asymmetric periodic-orbit families are identified, and their linear stability is analyzed using Floquet theory. The asymmetric orbits uncovered in this study substantially enrich the global catalog of planar CRTBP solutions and offer valuable orbit candidates for mission design in equal-mass binary systems.

An experimental investigation on the effect of the baffle crossing the width of an annular cell is conducted to determine if its existence can alter the Faraday instability and characteristics. The results indicate that while the baffle introduces additional viscous dissipation, raising the instability threshold, it also generates dominant perturbations that reduce the energy barrier for wave formation. The relationship between wavenumber and angular frequency agrees well with theoretical predictions accounting for surface tension. The presence of the baffle slightly increases the wavenumber with respect to forcing acceleration but has no significant impact on wave steepness. Measurements of wave crest positions reveal that for the annular cell with a baffle, the crests remain nearly unchanged, while they do not align for a clean annular cell. This suggests that the meniscus induced by the baffle crossing the width of the cell plays a more significant role in Faraday instability than the influence of the inner circular wall, which lies along the wavelength direction.

The three-body problem is ubiquitous in various physical systems. Thousands of periodic orbits for the three-body problem with zero angular momentum were obtained in recent years. In this paper, we present a numerical scheme to obtain periodic orbits for the three-body problem with finite angular momentum. The proposed approach combines a continuation method and the Newton-Raphson method, which are implemented using Clean Numerical Simulation (CNS) for the integration of the equations of motion. The figure-eight periodic orbit and another newly found periodic orbit are taken to generate periodic orbits by continuously varying the angular momentum. The linear stability of these periodic orbits are investigated through Floquet theory. It is suggested that angular momentum plays a significant role in influencing the linear instability of periodic orbits. Our proposed numerical approach inspires the further research in the intricate dependence of the periodic orbits on the angular momentum, providing a powerful tool for investigating the nonlinear dynamics of the three-body problem.

Steady-state acoustic-gravity wave systems are investigated using the homotopy analysis method (HAM) to examine the effects of compressibility on the generation mechanism of acoustic-gravity waves under nonresonant, near-resonant, and exactly resonant conditions. In the nonresonant state, the acoustic-gravity wave system resembles a pure gravity wave system without compressibility effects, while exact resonance involves energy exchanges between the hydroacoustic wave and primary gravity waves, and near resonance, lying between these two states, may exhibit either stronger or weaker nonlinearity than exact resonance. For different wave frequency ω3 values, steady-state acoustic-gravity wave systems are obtained with appropriate auxiliary linear operators and initial guesses in the HAM framework. It is found that when exact resonance occurs, the amplitudes of the two primary gravity waves and the resonant hydroacoustic wave are nearly equal, with energy distributed almost uniformly. As ω3 deviates from the exact resonance point and decreases, the system transitions from exact resonance to near resonance and eventually to nonresonance, simplifying to a gravity wave system without compressibility. Conversely, when ω3 increases, the system transitions to near resonance with rising nonlinearity, leading to a bifurcation into a nonresonant state. The dynamic pressure on the seabed produced by different steady-state acoustic-gravity wave systems is analyzed, and the effect of water depth changes on the exactly resonant systems is examined, revealing that shallower water enhances the nonlinearity of the wave system.

We present an experimental study on the natural sloshing frequencies and damping ratios of a liquid-elastic plate coupled system. Two types of edges including complete clamped edges and combined edges (two free and two clamped) are examined. The natural sloshing frequencies measured experimentally agree well with the theoretical predictions. Our findings indicate that the natural frequencies tend to increase with the number of clamped edges with other parameters fixed, while the damping ratio exhibits an opposite trend. Despite the general agreement, there are still minor deviations between analytical solutions and experimental measurements. For combined edges, these deviations increase with liquid depth, whereas for complete clamped edges, they decrease. We attribute these discrepancies primarily to the theoretical assumption that the surface elevation is equal to plate deflection across the entire plate, which is inconsistent with the experimental observation. Furthermore, the rapid decay of the coupled system may also introduce additional measurement errors.

The triple collision represents a fundamental singularity in the equations of motion for the three-body problem. Building upon previously identified triple collision orbits with equal masses, we employ the Clean Numerical Simulation (CNS) and the numerical continuation method to compute triple collision orbits for the free-fall three-body system with unequal masses. We first identify triple collision orbits for the three-body system where two bodies have unit mass, while the third body has various masses. Additionally, we extend our computation to obtain the triple collision orbits for the three-body problem with different masses. Numerical evidence is presented to demonstrate the asymptotic behavior of triple collision orbits with unequal masses. Our findings have potential inspiration for the study of the dynamical characteristic around the singularity of three-body systems.

We present experimental results of a group of focused waves propagating over a submerged barrier positioned in various locations on the bottom of a flume. The study investigates the effect of the relative distance between the fixed focusing position and different barrier installation positions on the characteristics of the wave group. The surface elevation and skewness are observed to approach a crest just on top of the barrier's rear. It can be also suggested that the presence of the barrier may affect the evolution of the wave group for approximately two times of the barrier length, as indicated by the frequency component distribution. In the time domain, a small tail with mildly higher energy is generally observed when the gauge is fixed at the front surface of the barrier. It suggests that long waves at lower frequencies propagate at higher speeds, while short waves at higher frequencies are intercepted due to the barrier.

This study numerically investigates the effects of damping ratios on flow-induced vibration (FIV) of two-degree-of-freedom elastically mounted tandem cylinders. By setting the tandem spacing between cylinder centers to four cylinder diameters, the FIV problem was solved using the two-dimensional unsteady Reynolds-averaged Navier–Stokes equations and the shear stress transport k−ω turbulence model. Four typical damping ratios of 0.0036, 0.036, 0.198, and 0.36 are employed to explore the effects of damping ratios on the FIV response. Simulation results show that the peak transverse amplitudes and the fluid force coefficients of cylinders generally decrease with increasing damping ratios. Owing to the presence of lock-in region in the streamwise vibration of the downstream cylinder for ζ=0.36, its streamwise vibration amplitude is larger than those for the damping ratio ζ=0.198 when the reduced velocity Ur≥8. With the increase in damping ratios, trajectories of the downstream cylinder become more regular. It is found that the damping ratio has little impact on the frequency capture phenomenon in the cross-flow direction, while the frequency capture phenomenon is first discovered in the in-line direction, which depends on the damping ratio. A transition in the vortex shedding mode is observed as the damping ratio increases. The increase in damping ratio contributes to the stabilization of energy transfer. It is suggested that damping ratios play a significant role in the FIV responses of tandem cylinders.

This is a response to the comment cited as PoF2023,35:029101. We show that the depth will have an impact on the wave height and the scaling law we obtained before is more feasible to use as a prior to give an initial guess of the wave height without any experimental information. This response strongly supports our previous work and the capability of the scaling law.

A numerical study on the two-layer liquid sloshing with a free surface in a rectangular tank under horizontal sinusoidal excitation is investigated in this work. It is observed that the interface displacement is mainly influenced by the lower liquid depth, while the free surface displacement primarily depends on the total liquid depth. Using dimensional analysis of the numerical results, we obtained a fitting curve in the S-model expression, which relates the displacements of both liquids to the forcing amplitude, forcing frequency and liquid depth. Furthermore, distinct from the phenomena for a single-layer liquid, we find that the sum and difference frequencies play significant roles in the power spectral density curves. There are similar power spectral density curve shapes and energy concentration locations with a fixed type of excitation independent of the liquid filling depth and layer depths ratio.

Understanding the determinants of transfer ridership is important for providing insights into improving the attractiveness of transit systems and building reliable and resilient metro stations. This study focuses on the transfer ridership between bus and metro systems under different dates and severe weather conditions to quantify the impacts of various attributes on the transfer ridership of different transfer modes (metro-to-bus and bus-to-metro). A multivariate generalized Poisson regression (GPR) model is applied to investigate the effects of critical factors on the transfer ridership of different transfer modes on weekdays, holidays, and typhoon days, respectively. The results indicate that the transfer-related variables, real-time weather, socioeconomic characteristics, and built environment significantly affect the transfer ridership. Concretely, the influence of socioeconomic and demographic factors on transfer ridership is the most significant on different types of dates, which is approximately 1.19 to 9.28 times that of the other variables. Weather variables have little effect on transfer ridership on weekdays, but they have a more significant impact on the transfer ridership on holidays and typhoon days. Specifically, during typhoons, transfer ridership is more affected by the weather factors: the coefficients are about 2.36 to 4.74 times higher than that in the other periods. Moreover, under strong wind speed, heavy rain, and high-temperature conditions, transfer ridership of the metro-to-bus mode significantly increases. In contrast, transfer ridership of the bus-to-metro mode rapidly decreases. Additionally, the peak hours have a strong positive influence on the transfer ridership, and the average hourly transfer ridership during peak hours is 1.16 to 4.02 times higher than that during the other periods. These findings indicate that the effect of each factor on transfer ridership varies with dates and transfer modes. This can also provide support for improving metro stations and increasing the attractiveness of public transport.

Despite the extensive efforts, accurate traffic time series forecasting remains challenging. By taking into account the non-linear nature of traffic in-depth, we propose a novel ST-CRMF model consisting of the Compensated Residual Matrix Factorization with Spatial-Temporal regularization for graph-based traffic time series forecasting. Our model inherits the benefits of MF and regularizer optimization and further carries out the compensatory modeling of the spatial-temporal correlations through a well-designed bi-directional residual structure. Of particular concern is that MF modeling and later residual learning share and synchronize iterative updates as equal training parameters, which considerably alleviates the error propagation problem that associates with rolling forecasting. Besides, most of the existing prediction models have neglected the difficult-to-avoid issue of missing traffic data; the ST-CRMF model can repair the possible missing value while fulfilling the forecasting tasks. After testing the effects of key parameters on model performance, the numerous experimental results confirm that our ST-CRMF model can efficiently capture the comprehensive spatial-temporal dependencies and significantly outperform those state-of-the-art models in the short-to-long terms (5-/15-/30-/60-min) traffic forecasting tasks on the open Seattle-Loop and METR-LA traffic datasets.

The hydrodynamic performance of short-crested wave diffraction by bottom-mounted V-shaped and arc-shaped breakwaters was examined based on the linear wave theory and the eigenfunction expansion method, respectively. Both types of breakwaters are assumed to be thin, impermeable, vertical, and rigidly embedded in the seabed. With the help of a virtual interface, the fluid domains were subdivided into subdomains and the velocity potential in each subdomain was described by eigenfunctions. The linear algebraic equations that determine the unknown coefficients can be obtained using the boundary and matching conditions. The analytical models fully agree with previous predictions. The major factors including wave propagation direction, opening angle, and water depth that affect wave forces and run-ups were explored. The results showed that the wave patterns of short-crested waves near breakwaters were quite different from those of long-crested waves, and using the long-crested wave model can overestimate the wave-defending effects of the breakwaters in a short-crested sea. An analogous wave attenuation effect was observed for breakwaters with comparable structures, which means that engineering practice has a certain degree of substitutability between them.

We report a numerical study of the contact-line effect on the Faraday instability. A momentum balance model is implemented to simulate the hysteresis of the meniscus. By using this model, a stick-slip-motion of the contact line happens on the lateral wall when a vertical vibration is exerted to the container. The numerical result further supports that the contact-line hysteresis can increase the natural frequency by inference. Besides, it can largely delay the timing of the onset because of an extra dissipation provided by the capillary effect. The growth rate can also be affected by the meniscus but the impact of the hysteresis seems limited. The presence of the meniscus is the reason why Faraday instability occurs without any artificial disturbance. Finally, a linear relation between the contact-angle range and the contact-line position is observed from our computation.

We numerically investigate triple collision orbits of the free-fall three-body system which has no double collisions before three bodies collide. Triple collision is an important property of the three-body system. Tanikawa, Saito, Mikkola (Celest Mech Dyn Astron 131(6):24, 2019) obtained 11 triple collision orbits without double collision for the free-fall three-body problem. In this paper, we present 1658 triple collision orbits including the Lagrange's homothetic solution, 11 ones found by Tanikawa et al. (2019) and 1646 new triple collision orbits. The symbol sequences of these 1646 new triple collision orbits have digits that range between 1 and 120. With our high-precision results, numerical evidences of the asymptotic property of triple collision orbits are given.