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Search Results (621)

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Keywords = wave-damping

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24 pages, 5313 KiB  
Article
The Influence of Gravity Gradient on the Inertialess Stratified Flow and Vortex Structure over an Obstacle in a Narrow Channel
by Karanvir Singh Grewal, Roger E. Khayat and Kelly A. Ogden
Fluids 2025, 10(8), 195; https://doi.org/10.3390/fluids10080195 - 29 Jul 2025
Viewed by 205
Abstract
The current study examines the influence of a varying gravity field and its interaction with density stratification. This represents a novel area in baroclinic flow analysis. The classical vortex and internal wave structures in stratified flows are shown to be significantly modified when [...] Read more.
The current study examines the influence of a varying gravity field and its interaction with density stratification. This represents a novel area in baroclinic flow analysis. The classical vortex and internal wave structures in stratified flows are shown to be significantly modified when gravity varies with height. Vortices may shift, stretch, or weaken depending on the direction and strength of gravity variation, and internal waves develop asymmetries or damping that are not present under constant gravity. We examine the influence of gravity variation on the flow of both homogeneous and density-stratified fluids in a channel with topography consisting of a Gaussian obstacle lying at the bottom of the channel. The flow is without inertia, induced by the translation of the top plate. Both the density and gravity are assumed to vary linearly with height, with the minimum density at the moving top plate. The narrow-gap approach is used to generate the flow field in terms of the pressure gradient along the top plate, which, in turn, is obtained in terms of the bottom topography and the three parameters of the problem, namely, the Froude number and the density and gravity gradients. The resulting stream function is a fifth-order polynomial in the vertical coordinate. In the absence of stratification, the flow is smooth, affected rather slightly by the variable topography, with an essentially linear drop in the pressure induced by the contraction. For a weak stratified fluid, the streamlines become distorted in the form of standing gravity waves. For a stronger stratification, separation occurs, and a pair of vortices generally appears on the two sides of the obstacle, the size of which depends strongly on the flow parameters. The influence of gravity stratification is closely coupled to that of density. We examine conditions where the coupling impacts the pressure and the velocity fields, particularly the onset of gravity waves and vortex flow. Only a mild density gradient is needed for flow separation to occur. The influence of the amplitude and width of the obstacle is also investigated. Full article
(This article belongs to the Section Geophysical and Environmental Fluid Mechanics)
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20 pages, 3560 KiB  
Article
Study on Vibration Effects and Optimal Delay Time for Tunnel Cut-Blasting Beneath Existing Railways
by Ruifeng Huang, Wenqing Li, Yongxiang Zheng and Zhong Li
Appl. Sci. 2025, 15(15), 8365; https://doi.org/10.3390/app15158365 - 28 Jul 2025
Viewed by 174
Abstract
With the development of underground space in urban areas, the demand for tunneling through existing railways is increasing. The adverse effects of cut-blasting during the construction of tunnels under crossing existing railways are investigated. Combined with the principle of blasting seismic wave superposition, [...] Read more.
With the development of underground space in urban areas, the demand for tunneling through existing railways is increasing. The adverse effects of cut-blasting during the construction of tunnels under crossing existing railways are investigated. Combined with the principle of blasting seismic wave superposition, LS-DYNA numerical simulation is used to analyze the seismic wave superposition law under different superposition methods. This study also investigates the vibration reduction effect of millisecond blasting for cut-blasting under the different classes of surrounding rocks. The results show that the vibration reduction forms of millisecond blasting can be divided into separation and interference of waveform. Based on the principle of superposition of blasting seismic waves, vibration reduction through wave interference is further divided. At the same time, a new vibration reduction mode is proposed. This vibration reduction mode can significantly improve construction efficiency while improving damping efficiency. The new vibration reduction mode can increase the vibration reduction to 80% while improving construction efficiency. Additionally, there is a significant difference in the damping effect of different classes of surrounding rock on the blasting seismic wave. Poor-quality surrounding rock enhances the attenuation of seismic wave velocity and peak stress in the surrounding rock. In the Zhongliangshan Tunnel, a tunnel cut-blasting construction at a depth of 42 m, the best vibration reduction plan of Class III is 3 ms millisecond blasting, in which the surface points achieve separation vibration reduction. The best vibration reduction plan of Class V is 1 ms millisecond blasting, in which the surface points achieve a new vibration reduction mode. During the tunnel blasting construction process, electronic detonators are used for millisecond blasting of the cut-blasting. This method can reduce the vibration effects generated by blasting. The stability of the existing railway is ultimately guaranteed. This can improve construction efficiency while ensuring construction safety. This study can provide significant guidance for the blasting construction of the tunnel through the railway. Full article
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17 pages, 5504 KiB  
Article
Multi-Objective Optimization of Acoustic Black Hole Plate Attached to Electric Automotive Steering Machine for Maximizing Vibration Attenuation Performance
by Xiaofei Du, Weilong Li, Fei Hao and Qidi Fu
Machines 2025, 13(8), 647; https://doi.org/10.3390/machines13080647 - 24 Jul 2025
Viewed by 315
Abstract
This research introduces an innovative passive vibration control methodology employing acoustic black hole (ABH) structures to mitigate vibration transmission in electric automotive steering machines—a prevalent issue adversely affecting driving comfort and vehicle safety. Leveraging the inherent bending wave manipulation properties of ABH configurations, [...] Read more.
This research introduces an innovative passive vibration control methodology employing acoustic black hole (ABH) structures to mitigate vibration transmission in electric automotive steering machines—a prevalent issue adversely affecting driving comfort and vehicle safety. Leveraging the inherent bending wave manipulation properties of ABH configurations, we conceive an integrated vibration suppression framework synergizing advanced computational modeling with intelligent optimization algorithms. A high-fidelity finite element (FEM) model integrating ABH-attached steering machine system was developed and subjected to experimental validation via rigorous modal testing. To address computational challenges in design optimization, a hybrid modeling strategy integrating parametric design (using Latin Hypercube Sampling, LHS) with Kriging surrogate modeling is proposed. Systematic parameterization of ABH geometry and damping layer dimensions generated 40 training datasets and 12 validation datasets. Surrogate model verification confirms the model’s precise mapping of vibration characteristics across the design space. Subsequent multi-objective genetic algorithm optimization targeting RMS velocity suppression achieved substantial vibration attenuation (29.2%) compared to baseline parameters. The developed methodology provides automotive researchers and engineers with an efficient suitable design tool for vibration-sensitive automotive component design. Full article
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21 pages, 4524 KiB  
Article
Rotational Influence on Wave Propagation in Semiconductor Nanostructure Thermoelastic Solid with Ramp-Type Heat Source and Two-Temperature Theory
by Sayed M. Abo-Dahab, Emad K. Jaradat, Hanan S. Gafel and Eslam S. Elidy
Axioms 2025, 14(8), 560; https://doi.org/10.3390/axioms14080560 - 24 Jul 2025
Viewed by 264
Abstract
This study investigates the influence of rotation on wave propagation in a semiconducting nanostructure thermoelastic solid subjected to a ramp-type heat source within a two-temperature model. The thermoelastic interactions are modeled using the two-temperature theory, which distinguishes between conductive and thermodynamic temperatures, providing [...] Read more.
This study investigates the influence of rotation on wave propagation in a semiconducting nanostructure thermoelastic solid subjected to a ramp-type heat source within a two-temperature model. The thermoelastic interactions are modeled using the two-temperature theory, which distinguishes between conductive and thermodynamic temperatures, providing a more accurate description of thermal and mechanical responses in semiconductor materials. The effects of rotation, ramp-type heating, and semiconductor properties on elastic wave propagation are analyzed theoretically. Governing equations are formulated and solved analytically, with numerical simulations illustrating the variations in thermal and elastic wave behavior. The key findings highlight the significant impact of rotation, nonlocal parameters e0a, and time derivative fractional order (FO) α on physical quantities, offering insights into the thermoelastic performance of semiconductor nanostructures under dynamic thermal loads. A comparison is made with the previous results to show the impact of the external parameters on the propagation phenomenon. The numerical results show that increasing the rotation rate Ω=5 causes a phase lag of approximately 22% in thermal and elastic wave peaks. When the thermoelectric coupling parameter ε3 is increased from 0.8×1042 to 1.2×1042. The temperature amplitude rises by 17%, while the carrier density peak increases by over 25%. For nonlocal parameter values ε=0.30.6, high-frequency stress oscillations are damped by more than 35%. The results contribute to the understanding of wave propagation in advanced semiconductor materials, with potential applications in microelectronics, optoelectronics, and nanoscale thermal management. Full article
(This article belongs to the Section Mathematical Physics)
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23 pages, 9795 KiB  
Article
Evaluation of Viscoelastic and Rotational Friction Dampers for Coupled Shear Wall System
by Zafira Nur Ezzati Mustafa, Ryo Majima and Taiki Saito
Appl. Sci. 2025, 15(15), 8185; https://doi.org/10.3390/app15158185 - 23 Jul 2025
Viewed by 146
Abstract
This research experimentally and numerically evaluates the effectiveness of viscoelastic (VE) and rotational friction (RF) dampers in enhancing the seismic performance of coupled shear wall (CSW) systems. This study consists of two phases: (1) element testing to characterize the hysteretic behavior and energy [...] Read more.
This research experimentally and numerically evaluates the effectiveness of viscoelastic (VE) and rotational friction (RF) dampers in enhancing the seismic performance of coupled shear wall (CSW) systems. This study consists of two phases: (1) element testing to characterize the hysteretic behavior and energy dissipation capacity of VE and RF dampers, and (2) shake table testing of a large-scale CSW structure equipped with these dampers under the white noise, sinusoidal and Kokuji waves. The experimental results are validated through numerical analysis using STERA 3D (version 11.5), a nonlinear finite element software, to simulate the dynamic response of the damped CSW system. Key performance indicators, including inter-story drift, base shear, and energy dissipation, are compared between experimental and numerical results, demonstrating strong correlation. The findings reveal that VE dampers effectively control high-frequency vibrations, while RF dampers provide stable energy dissipation across varying displacement amplitudes. The validated numerical model facilitates the optimization of damper configurations for performance-based seismic design. This study provides valuable insights into the selection and implementation of supplemental damping systems for CSW structures, contributing to improved seismic resilience in buildings. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Vibration)
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24 pages, 11580 KiB  
Article
GS24b and GS24bc Ground Motion Models for Active Crustal Regions Based on a Non-Traditional Modeling Approach
by Vladimir Graizer and Scott Stovall
Geosciences 2025, 15(8), 277; https://doi.org/10.3390/geosciences15080277 - 23 Jul 2025
Viewed by 241
Abstract
An expanded Pacific Earthquake Engineering Research (PEER) Center Next Generation Attenuation Phase 2 (NGA-West2) ground motion database, compiled using shallow crustal earthquakes in active crustal regions (ACRs), was used to develop the closed-form GS24b backbone ground motion model (GMM) for the RotD50 horizontal [...] Read more.
An expanded Pacific Earthquake Engineering Research (PEER) Center Next Generation Attenuation Phase 2 (NGA-West2) ground motion database, compiled using shallow crustal earthquakes in active crustal regions (ACRs), was used to develop the closed-form GS24b backbone ground motion model (GMM) for the RotD50 horizontal components of peak ground acceleration (PGA), peak ground velocity (PGV), and 5% damped elastic pseudo-absolute response spectral accelerations (SA). The GS24b model is applicable to earthquakes with moment magnitudes of 4.0 ≤ M ≤ 8.5, at rupture distances of 0 ≤ Rrup ≤ 400 km, with time-averaged S-wave velocity in the upper 30 m of the profile at 150 ≤ VS30 ≤ 1500 m/s, and for periods of 0.01 ≤ T ≤ 10 s. The new backbone model includes VS30 site correction developed based on multiple representative S-wave velocity profiles. For crustal wave attenuation, we used the apparent anelastic attenuation of SA—QSA (f, M). In contrast to the GK17, the GS24b backbone is a generic ACR model designed specifically to be adjusted to any ACRs. The GS24bc is an example of a partially non-ergodic model created by adjusting the backbone GS24b model for magnitude M, S-wave velocity VS30, and fault rupture distance residuals. Full article
(This article belongs to the Section Geophysics)
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26 pages, 4382 KiB  
Article
Effect of Biological Fouling on the Dynamic Responses of Integrated Foundation Structure of Floating Wind Turbine and Net Cage
by Yu Hu, Hao Liu, Yingyao Cheng, Jichao Lei and Junxin Liu
J. Mar. Sci. Eng. 2025, 13(7), 1372; https://doi.org/10.3390/jmse13071372 - 18 Jul 2025
Viewed by 280
Abstract
This paper proposes a novel integrated foundation structure of floating wind turbine and net cage by combining large capacity semi-submersible wind turbines with aquaculture cages. The research mainly focuses on the effect of biological fouling on net cage structures and safety performance of [...] Read more.
This paper proposes a novel integrated foundation structure of floating wind turbine and net cage by combining large capacity semi-submersible wind turbines with aquaculture cages. The research mainly focuses on the effect of biological fouling on net cage structures and safety performance of mooring systems. The study firstly validates the simplified model of net cage through comparing with results of existing scaled experimental models. Then, a hydrodynamic analysis is conducted on the net cage model to obtain the RAOs of motion response of the structure under frequency-domain analysis, and damping correction is also carried out on the structure. Finally, time-domain analyses under irregular wave conditions are conducted to evaluate the effects of biofouling fouling on motion responses of net cage foundation and tensions of mooring lines. Full article
(This article belongs to the Section Ocean Engineering)
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11 pages, 3627 KiB  
Article
The Influence of Traps on the Self-Heating Effect and THz Response of GaN HEMTs
by Huichuan Fan, Xiaoyun Wang, Xiaofang Wang and Lin Wang
Photonics 2025, 12(7), 719; https://doi.org/10.3390/photonics12070719 - 16 Jul 2025
Viewed by 253
Abstract
This study systematically investigates the effects of trap concentration on self-heating and terahertz (THz) responses in GaN HEMTs using Sentaurus TCAD. Traps, inherently unavoidable in semiconductors, can be strategically introduced to engineer specific energy levels that establish competitive dynamics between the electron momentum [...] Read more.
This study systematically investigates the effects of trap concentration on self-heating and terahertz (THz) responses in GaN HEMTs using Sentaurus TCAD. Traps, inherently unavoidable in semiconductors, can be strategically introduced to engineer specific energy levels that establish competitive dynamics between the electron momentum relaxation time and the carrier lifetime. A simulation-based exploration of this mechanism provides significant scientific value for enhancing device performance through self-heating mitigation and THz response optimization. An AlGaN/GaN heterojunction HEMT model was established, with trap concentrations ranging from 0 to 5×1017 cm3. The analysis reveals that traps significantly enhance channel current (achieving 3× gain at 1×1017 cm3) via new energy levels that prolong carrier lifetime. However, elevated trap concentrations (>1×1016 cm3) exacerbate self-heating-induced current collapse, reducing the min-to-max current ratio to 0.9158. In THz response characterization, devices exhibit a distinct DC component (Udc) under non-resonant detection (ωτ1). At a trap concentration of 1×1015 cm3, Udc peaks at 0.12 V when VgDC=7.8 V. Compared to trap-free devices, a maximum response attenuation of 64.89% occurs at VgDC=4.9 V. Furthermore, Udc demonstrates non-monotonic behavior with concentration, showing local maxima at 4×1015 cm3 and 7×1015 cm3, attributed to plasma wave damping and temperature-gradient-induced electric field variations. This research establishes trap engineering guidelines for GaN HEMTs: a concentration of 4×1015 cm3 optimally enhances conductivity while minimizing adverse impacts on both self-heating and the THz response, making it particularly suitable for high-sensitivity terahertz detectors. Full article
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31 pages, 3523 KiB  
Article
Sustainable Tunable Anisotropic Ultrasound Medical Phantoms for Skin, Skeletal Muscle, and Other Fibrous Biological Tissues Using Natural Fibers and a Bio-Elastomeric Matrix
by Nuno A. T. C. Fernandes, Diana I. Alves, Diana P. Ferreira, Maria Monteiro, Ana Arieira, Filipe Silva, Betina Hinckel, Ana Leal and Óscar Carvalho
J. Compos. Sci. 2025, 9(7), 370; https://doi.org/10.3390/jcs9070370 - 16 Jul 2025
Viewed by 482
Abstract
Medical phantoms are essential to imaging calibration, clinician training, and the validation of therapeutic procedures. However, most ultrasound phantoms prioritize acoustic realism while neglecting the viscoelastic and anisotropic properties of fibrous soft tissues. This gap limits their effectiveness in modeling realistic biomechanical behavior, [...] Read more.
Medical phantoms are essential to imaging calibration, clinician training, and the validation of therapeutic procedures. However, most ultrasound phantoms prioritize acoustic realism while neglecting the viscoelastic and anisotropic properties of fibrous soft tissues. This gap limits their effectiveness in modeling realistic biomechanical behavior, especially in wave-based diagnostics and therapeutic ultrasound. Current materials like gelatine and agarose fall short in reproducing the complex interplay between the solid and fluid components found in biological tissues. To address this, we developed a soft, anisotropic composite whose dynamic mechanical properties resemble fibrous biological tissues such as skin and skeletal muscle. This material enables wave propagation and vibration studies in controllably anisotropic media, which are rare and highly valuable. We demonstrate the tunability of damping and stiffness aligned with fiber orientation, providing a versatile platform for modeling soft-tissue dynamics and validating biomechanical simulations. The phantoms achieved Young’s moduli of 7.16–11.04 MPa for skin and 0.494–1.743 MPa for muscles, shear wave speeds of 1.51–5.93 m/s, longitudinal wave speeds of 1086–1127 m/s, and sound absorption coefficients of 0.13–0.76 dB/cm/MHz, with storage, loss, and complex moduli reaching 1.035–6.652 kPa, 0.1831–0.8546 kPa, and 2.138–10.82 kPa. These values reveal anisotropic response patterns analogous to native tissues. This novel natural fibrous composite system affords sustainable, low-cost ultrasound phantoms that support both mechanical fidelity and acoustic realism. Our approach offers a route to next-gen tissue-mimicking phantoms for elastography, wave propagation studies, and dynamic calibration across diverse clinical and research applications. Full article
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24 pages, 3945 KiB  
Article
A Parameter Sensitivity Analysis of Two-Body Wave Energy Converters Using the Monte Carlo Parametric Simulations Through Efficient Hydrodynamic Analytical Model
by Elie Al Shami and Xu Wang
Vibration 2025, 8(3), 39; https://doi.org/10.3390/vibration8030039 - 7 Jul 2025
Viewed by 279
Abstract
This paper introduces a novel approach by employing a Monte Carlo simulation to investigate the impact of various design parameters on the performance of two-body wave energy converters. The study uses a simplified analytical model that eliminates the need for complex simulations such [...] Read more.
This paper introduces a novel approach by employing a Monte Carlo simulation to investigate the impact of various design parameters on the performance of two-body wave energy converters. The study uses a simplified analytical model that eliminates the need for complex simulations such as boundary elements or computational fluid dynamics methods. Instead, this model offers an efficient means of predicting and calculating converter performance output. Rigorous validation has been conducted through ANSYS AQWA simulations, affirming the accuracy of the proposed analytical model. The parametric investigation reveals new insights into design optimization. These findings serve as a valuable guide for optimizing the design of two-body point absorbers based on specific performance requirements and prevailing sea state conditions. The results show that in the early design stages, device dimensions and hydrodynamics affect performance more than the PTO’s stiffness and damping. Furthermore, for lower frequencies, adjustments to the buoy’s height emerge as a favorable strategy, whereas augmenting the buoy radius proves more advantageous for enhancing performance at higher frequencies. Full article
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24 pages, 3084 KiB  
Article
Overall Design and Performance Analysis of the Semi-Submersible Platform for a 10 MW Vertical-Axis Wind Turbine
by Qun Cao, Xinyu Zhang, Ying Chen, Xinxin Wu, Kai Zhang and Can Zhang
Energies 2025, 18(13), 3488; https://doi.org/10.3390/en18133488 - 2 Jul 2025
Viewed by 379
Abstract
This study presents a novel semi-submersible platform design for 10 MW vertical-axis wind turbines (VAWTs), specifically engineered to address the compounded challenges of China’s intermediate-depth (40 m), typhoon-prone maritime environment. Unlike conventional horizontal-axis configurations, VAWTs impose unique demands due to omnidirectional wind reception, [...] Read more.
This study presents a novel semi-submersible platform design for 10 MW vertical-axis wind turbines (VAWTs), specifically engineered to address the compounded challenges of China’s intermediate-depth (40 m), typhoon-prone maritime environment. Unlike conventional horizontal-axis configurations, VAWTs impose unique demands due to omnidirectional wind reception, high aerodynamic load fluctuations, and substantial self-weight—factors exacerbated by short installation windows and complex hydrodynamic interactions. Through systematic scheme demonstration, we establish the optimal four-column configuration, resolving critical limitations of existing concepts in terms of water depth adaptability, stability, and fabrication economics. The integrated design features central turbine mounting, hexagonal pontoons for enhanced damping, and optimized ballast distribution, achieving a 3400-tonne steel mass (29% reduction vs. benchmarks). Comprehensive performance validation confirms exceptional survivability under 50-year typhoon conditions (Hs = 4.42 m, Uw = 54 m/s), limiting platform tilt to 8.02° (53% of allowable) and nacelle accelerations to 0.10 g (17% of structural limit). Hydrodynamic analysis reveals heave/pitch natural periods > 20 s, avoiding wave resonance (Tp = 7.64 s), while comparative assessment demonstrates 33% lower pitch RAOs than leading horizontal-axis platforms. The design achieves unprecedented synergy of typhoon resilience, motion performance, and cost-efficiency—validated by 29% steel savings—providing a technically and economically viable solution for megawatt-scale VAWT deployment in challenging seas. Full article
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26 pages, 5306 KiB  
Article
Non-Hermitian Control of Tri-Photon and Quad-Photon Using Parallel Multi-Dressing Quantization
by Haitian Tang, Rui Zhuang, Jiaxuan Wei, Qingyu Chen, Sinong Liu, Guobin Liu, Zhou Feng and Yanpeng Zhang
Photonics 2025, 12(7), 653; https://doi.org/10.3390/photonics12070653 - 27 Jun 2025
Viewed by 187
Abstract
The fifth-order nonlinear polarizability has been extensively studied in the field of quantum communication due to its ease of manipulation. By adjusting the relative size of the Rabi frequency and dephasing rate of the dressing field, natural non-Hermitian exceptional points can be generated, [...] Read more.
The fifth-order nonlinear polarizability has been extensively studied in the field of quantum communication due to its ease of manipulation. By adjusting the relative size of the Rabi frequency and dephasing rate of the dressing field, natural non-Hermitian exceptional points can be generated, and further evolution can be achieved by varying the types of dressing fields. However, as the demand for information capacity in quantum communication continues to increase, research on the higher-order seventh-order nonlinear polarizability, based on four-photon states, and the number of coherent channels and resonance positions has gradually come to the forefront. This paper focuses on the simultaneous generation of a seventh-order nonlinear polarizability through a spontaneous eight-wave mixing (SEWM) process in an atomic medium involving four photons. Compared to the fifth-order nonlinear polarizability, the seventh-order polarizability shows an exponential increase in coherent channels and resonance positions due to its strong dressing effect. Additionally, the interaction between the four photons is stronger than that between three photons, making it possible for even the difficult-to-dress eigenvalues to be influenced by the dressing field and dephasing rate, resulting in more complex coherent channels. These are manifested as more complex, damped Rabi oscillations, with periods that can be controlled by the dressing field. These findings may contribute to a promising new method for quantum communication. Full article
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21 pages, 6378 KiB  
Article
Regular Wave Effects on the Hydrodynamic Performance of Fine-Mesh Nettings in Sampling Nets
by Zhiqiang Liu, Fuxiang Hu, Rong Wan, Shaojian Guo, Yucheng Wang and Cheng Zhou
Appl. Sci. 2025, 15(13), 7229; https://doi.org/10.3390/app15137229 - 27 Jun 2025
Viewed by 299
Abstract
Fine-mesh netting, with mesh dimensions of the order of a few millimeters, is widely used in sampling nets for the collection of larval and juvenile fishes. The wave force characteristics of fine-mesh netting significantly affect the operational performance of these nets. This study [...] Read more.
Fine-mesh netting, with mesh dimensions of the order of a few millimeters, is widely used in sampling nets for the collection of larval and juvenile fishes. The wave force characteristics of fine-mesh netting significantly affect the operational performance of these nets. This study employed both wave tank experiments and numerical simulations to analyze the hydrodynamic performance of fine-mesh netting under varying wave conditions. A series of numerical simulations and particle image velocimetry (PIV) experiments were conducted to investigate the damping effects of fine-mesh netting on wave propagation. The results revealed that horizontal wave forces increased with both the wave period and wave height. When the wave period was held constant, the drag and inertial coefficients of the netting generally decreased as the Reynolds number and the Keulegan–Carpenter (KC) number increased. The wave transmission coefficients of the netting decreased as the wave height increased for the same wave period. However, at a constant wave height, the transmission coefficients initially increased and then decreased with the increasing wave period. The water particle velocity was significantly affected by the netting, with a notable reduction in velocity downstream of the netting at both the wave crest and trough phases. The simulation results and PIV measurements of the water particle velocity field distribution were in good agreement. This study provides important insights for the design and optimization of sampling nets. Full article
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21 pages, 333 KiB  
Article
Existence of Blow-Up Solution to the Cauchy Problem of Inhomogeneous Damped Wave Equation
by Sen Ming, Jiayi Du and Bo Du
Symmetry 2025, 17(7), 1009; https://doi.org/10.3390/sym17071009 - 26 Jun 2025
Viewed by 357
Abstract
This paper is concerned with the non-existence of a global solution to the initial value problem of the inhomogeneous damped wave equation with a nonlinear memory term and a nonlinear gradient term. The critical exponent and formation of singularity of solution are closely [...] Read more.
This paper is concerned with the non-existence of a global solution to the initial value problem of the inhomogeneous damped wave equation with a nonlinear memory term and a nonlinear gradient term. The critical exponent and formation of singularity of solution are closely related to symmetry in the study of blow-up dynamics for nonlinear wave equations, which provides a profound mathematical tool for analyzing the explosion of solutions within finite time. The proofs of blow-up results of solutions are based on the test function method, where the test function is variable separated. The influences of two types of damping terms, two types of nonlinearities, and an inhomogeneous term on exponents of the problem in blow-up cases are explained. It is worth pointing out that the inhomogeneous term in the problem is discussed with respect to the exponent σ in three cases (namely, σ=0, 1<σ<0, and σ>0). As far as we know, the results in Theorems 1–4 are new. Full article
(This article belongs to the Section Mathematics)
19 pages, 646 KiB  
Article
Asymptotic Stability of a Finite Difference Scheme for a Wave Equation with Delayed Damping
by Manal Alotaibi
Axioms 2025, 14(7), 497; https://doi.org/10.3390/axioms14070497 - 26 Jun 2025
Viewed by 294
Abstract
In this paper, we propose an implicit finite difference scheme for a wave equation with strong damping and a discrete delay term. Although the scheme is implicit, the use of second-order finite difference approximations for the strong damping term in both space and [...] Read more.
In this paper, we propose an implicit finite difference scheme for a wave equation with strong damping and a discrete delay term. Although the scheme is implicit, the use of second-order finite difference approximations for the strong damping term in both space and time prevents it from being unconditionally stable. A sufficient condition for the asymptotic stability of the scheme is established by applying the Jury stability criterion to show that all roots of the characteristic polynomial associated with the resulting linear recurrence lie strictly inside the unit disk. This stability condition is derived under an appropriate constraint that links the time and space discretization steps with the damping and delay parameters. A numerical example is provided to illustrate the decay behavior of the scheme and confirm the theoretical findings. Full article
(This article belongs to the Special Issue Mathematical Models and Simulations, 2nd Edition)
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