Search Results (194)

CFRP laminates are widely adopted for the strengthening of steel structures and the debonding damage poses a severe threat to the integrity of CFRP-reinforced structures. However, as the early stage of debonding damage, kissing bond detection in these structures using the conventional ultrasonic guided waves method is a significant challenge due to the imperceptibility of microscale damage and the complexity of the wave properties at the interface. To address this problem, mixed-frequency ultrasonic guided waves with nonlinear characteristics are proposed to identify and evaluate kissing bond damage with different damage sizes in CFRP-reinforced steel structures. A finite element model is developed to simulate a kissing bond in a CFRP-reinforced steel plate and is utilized to investigate the interaction between mixed-frequency guided waves and the interface. Experimental tests are also carried out to verify the kissing bond detection method. Nonlinear parameters calculated based on the damage-induced sum and difference frequency components are employed to quantitatively evaluate the kissing bond damage. In addition, excitations with different wave modes are used in damage detection to compare their sensitivities to kissing bond damage. Both the simulation and experimental results reveal that the nonlinear parameter rises as the length of the kissing bond increases, reflecting the effectiveness of mixed-frequency ultrasonic guided wave for the identification and evaluation of kissing bond damage in CFRP-bonded structures. Full article

This paper proposes an advanced all-optical de-aggregation scheme based on cascaded phase-sensitive amplification (PSA) for high-fidelity hierarchical information extraction from circular-32QAM signals. The proposed architecture systematically decomposes complex high-order modulation into three fundamental components: PAM4, QPSK, and BPSK. The first PSA stage performs amplitude normalization to equalize power fluctuations, followed by quadrant phase classification through phase-dependent gain mapping, and final intra-quadrant phase resolution via a cascaded dual-PSA configuration with a 90° phase offset. Through meticulous numerical simulations, we demonstrate that the optimized normalization depth effectively suppresses both amplitude and phase noise. Results indicate a high quadrant classification accuracy of 92%, which leads to a significant cumulative error reduction from 22% to 8% across the PSA chain. These findings demonstrate the theoretical feasibility of the proposed scheme in processing complex modulation formats entirely in the optical domain, which offers a potential framework for future high-capacity optical networks. Full article

Semiconductor optical amplifiers (SOAs) are central to the development of ultrafast, low-power all-optical signal processing systems. Their strong nonlinear response, compact size, and compatibility with photonic integration platforms make them key enablers for implementing all-optical logic functions beyond the limitations of electronic switching. This review offers a comprehensive analysis of the principal SOA technologies used in all-optical logic gate implementations, including conventional bulk and quantum well SOAs, quantum dot SOAs (QD-SOAs), photonic crystal SOAs (PhC-SOAs), reflective SOAs (RSOAs), and carrier reservoir SOAs (CR-SOAs). For each architecture, we examine the carrier dynamics, gain recovery mechanisms, saturation behavior, and fabrication considerations, together with their associated nonlinear effects such as cross-gain modulation, cross-phase modulation, and four-wave mixing. We further evaluate reported implementations of key logic operations—AND, NAND, OR, NOR, XOR, and XNOR—highlighting performance trade-offs in terms of speed, extinction ratio, operational power, integration complexity, and scalability. The review concludes with current challenges and emerging research directions aimed at realizing fully integrated, high-speed, and energy-efficient all-optical logic systems based on next-generation SOA technologies. Full article

In this contribution, we propose and study long-time behaviors of a new class of N-dimensional delayed Kirchhoff–Carrier-type problems with variable transfer coefficients involving a logarithmic nonlinearity. We take into account the dependence of diffusion and damping coefficients on the position and direction, as well as the presence of different types of delays. This class of nonlocal anisotropic and nonlinear wave-type equations with multiple time-varying mixed delays and dampings, of a fairly general form, containing several arbitrary functions and free parameters, is of the following form: ${\displaystyle \frac{{\partial }^{2}u}{\partial t^2}-{div(\mathcal{K}(\Vert \sigma \nabla u\Vert }_{L^2(\Omega )}^2)A_{\sigma }{(\mathbf{x})\nabla u)+\mathcal{M}(\Vert u\Vert }_{L^2(\Omega )}^2)u-div(\zeta (t)A_{\sigma }(\mathbf{x})\nabla \frac{\partial u}{\partial t})+d_0(t)\frac{\partial u}{\partial t}+{\mathbb{D}}_r(\mathbf{x},t;\frac{\partial u}{\partial t})=\mathbb{G}(u),}$ where $u(\mathbf{x},t)$ is the state function, $\mathcal{M}$ and $\mathcal{K}$ are the nonlocal Kirchhoff operators and the nonlinear operator $\mathbb{G}(u)$ corresponds to a logarithmic source term. The symmetric tensor $A_{\sigma }$ describes the anisotropic behavior and processes of the system, and the operator ${\mathbb{D}}_r$ represents the multiple time-varying mixed delays related to velocity ${\displaystyle \frac{\partial u}{\partial t}}$. Our problem, which encompasses numerous equations already studied in the literature, is relevant to a wide range of practical and concrete applications. It not only considers anisotropy in diffusion, but it also assumes that the strong damping can be totally anisotropic (a phenomenon that has received very little mathematical attention in the literature). We begin with the reformulation of the problem into a nonlinear system coupling a nonlocal wave-type equation with ordinary differential equations, with the help of auxiliary functions. Afterward, we study the local existence and some necessary regularity results of the solutions by using the Faedo–Galerkin approximation, combining some energy estimates and the logarithmic Sobolev inequality. Next, by virtue of the potential well method combined with the Nehari manifold, conditions for global in-time existence are given. Finally, subject to certain conditions, the exponential decay of global solutions is established by applying a perturbed energy method. Many of the obtained results can be extended to the case of other nonlinear source terms. Full article

In this study, a comprehensive numerical investigation of amplitude-driven flow dynamics in shocked heavy-fluid layers is presented to focus on the evolution of the Richtmyer–Meshkov instability (RMI). A high-order mixed local discontinuous Galerkin scheme is employed to resolve the complex interactions between shock waves and perturbed interfaces within a compressible viscous flow framework. Impacts of the initial interface amplitudes are systematically examined through a series of single-mode configurations with amplitude–wavelength ratios ranging from $a_0/\lambda =0.025$ to $0.4$. The simulations capture the complete transition from early linear growth to nonlinear roll-up and subsequent mixing. This investigation illustrates that increasing the initial perturbation amplitude enhances baroclinic vorticity generation, intensifies interfacial deformation, and accelerates the onset of secondary instabilities. Low-amplitude interfaces maintain nearly symmetric deformation with delayed nonlinear transition, whereas high-amplitude cases exhibit pronounced spike–bubble asymmetry, stronger curvature, and rapid Kelvin–Helmholtz roll-ups. Quantitative diagnostics of the circulation, enstrophy, and kinetic energy demonstrate that both baroclinic torque and mixing intensity scale directly with the initial perturbation amplitude. This study offers new physical insight into amplitude-dependent shock–interface interactions and elucidates the mechanisms governing vorticity amplification and energy redistribution in RMI flows. Full article

This paper experimentally investigates the resonant behavior of the one-way Lamb and SH (shear horizontal) mixing method in composite laminates with inherent quadratic nonlinearity, delamination damage and impact damage. When the fundamental S₀-mode Lamb waves and SH₀ waves mix in the damage regions of composite laminates, experimental results demonstrate the generation of the resonant SH₀ waves with the resonance condition. Meanwhile, the damage localization method in composite laminates is experimentally verified by the time-domain signal of resonant waves. Furthermore, it is found that the one-way Lamb and SH mixing method is sensitive to inherent quadratic nonlinearity and impact damage but insensitive to delamination damage. Full article

This paper studies a mixed PDE containing the second time derivative and a quadratic nonlinearity of the Monge–Ampère type in two spatial variables, which is encountered in geophysical fluid dynamics. The Lie group symmetry analysis of this highly nonlinear PDE is performed for the first time. An invariant point transformation is found that depends on fourteen arbitrary constants and preserves the form of the equation under consideration. One-dimensional symmetry reductions leading to self-similar and some other invariant solutions that described by single ODEs are considered. Using the methods of generalized and functional separation of variables, as well as the principle of structural analogy of solutions, a large number of new non-invariant closed-form solutions are obtained. In general, the extensive list of all exact solutions found includes more than thirty solutions that are expressed in terms of elementary functions. Most of the obtained solutions contain a number of arbitrary constants, and several solutions additionally include two arbitrary functions. Two-dimensional reductions are considered that reduce the original PDE in three independent variables to a single simpler PDE in two independent variables (including linear wave equations, the Laplace equation, the Tricomi equation, and the Guderley equation) or to a system of such PDEs. A number of specific examples demonstrate that the type of the mixed, highly nonlinear PDE under consideration, depending on the choice of its specific solutions, can be either hyperbolic or elliptic. To analyze the equation and construct exact solutions and reductions, in addition to Cartesian coordinates, polar, generalized polar, and special Lorentz coordinates are also used. In conclusion, possible promising directions for further research of the highly nonlinear PDE under consideration and related PDEs are formulated. It should be noted that the described symmetries, transformations, reductions, and solutions can be utilized to determine the error and estimate the limits of applicability of numerical and approximate analytical methods for solving complex problems of mathematical physics with highly nonlinear PDEs. Full article

Generation of idler pulses via the four-wave mixing (FWM) effect in a nonlinear optical ring resonator (NORR) was investigated numerically. It was found that the relative delay $\tau$ between input pump pulses significantly affects both the energy and temporal–spectral characteristics of generated idler pulses. Specifically, idler pulse energy decreases with increasing $\tau$ due to phase-matching conditions in FWM. Maximum energy transfer occurs for $\tau$ = 0, where optimal phase alignment among pump, signal, and idler waves is achieved. Temporal and spectral analysis at different relative delays reveals a change from a symmetric, multi-subpulse structure with a comb-like spectrum (for $\tau$ = 0) to a near-single-pulse form with a single-comb-line spectrum (for $\tau$ = 9 ps). These findings demonstrate the critical dependence of FWM efficiency on pump pulse synchronization. Therefore, precise control of the relative delay is essential for optimizing idler pulse generation in NORRs. Full article

Shock–accelerated interfaces between fluids of different densities are prone to Richtmyer–Meshkov-type instabilities, whose evolution is strongly influenced by the incident shock Mach number. In this study, we present a systematic numerical investigation of the Mach number effect on the instability growth at a light–heavy fluid layer. The governing dynamics are modeled using the compressible multi-species Euler equations, and the simulations are performed with a high-order modal discontinuous Galerkin method. This approach provides accurate resolution of sharp interfaces, shock waves, and small-scale vortical structures. A series of two-dimensional simulations is carried out for a range of shock Mach numbers impinging on a sinusoidally perturbed light–heavy fluid interface. The results highlight the distinct stages of instability evolution, from shock–interface interaction and baroclinic vorticity deposition to nonlinear roll-up and interface deformation. Quantitative diagnostics—including circulation, enstrophy, vorticity extrema, and mixing width—are employed to characterize the instability dynamics and to isolate the role of Mach number in enhancing or suppressing growth. Particular attention is given to the mechanisms of vorticity generation through baroclinic torque and compressibility effects. Moreover, the analysis of controlling parameters, including Atwood number, layer thickness, and initial perturbation amplitude, broadens the parametric understanding of shock-driven instabilities. The results reveal that increasing shock Mach number markedly enhances vorticity generation and accelerates interface growth, while the resulting nonlinear morphology remains strongly sensitive to variations in Atwood number and perturbation amplitude. 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

The four buckets phase demodulation method is a widely used sinusoidal modulation and demodulation technique in interferometry. Strict calibration is essential to minimize nonlinear errors in subsequent measurements. The core of the algorithm calibration lies in determining the initial phase value of the modulation signal that matches the modulation depth while overcoming the influence of system phase delay. Currently, there are few systematic calibration methods specifically designed for optical fiber interferometry. This paper proposes a self-calibration method based on triangular wave mixing for four buckets phase demodulation in fiber optic interferometric probes, which efficiently achieves self-calibration of the phase demodulation while the measured object remains stationary. Simulations and experimental validations were conducted, demonstrating that the optimal initial phase value of 0.62 rad during phase demodulation can be accurately identified under static conditions. The calibrated phase value was then applied to the displacement measurement, where the target displacement was effectively detected, resulting in a root mean square (RMS) error of 3.0337 nm and an average error of 2.4479 nm. Full article

Internal waves play a critical role in material transport, vertical mixing, and energy dissipation within stratified aquatic systems. Their dynamics are strongly modulated by thermal stratification and surface meteorological forcing. This study examines the influence of interannual meteorological variability from 1980 to 2010 on internal wave behavior using a series of numerical simulations in Lake Biwa in Japan. In each simulation, air temperature, wind speed, or precipitation was perturbed by ±2 standard deviations relative to the climatological mean. Power spectral analysis of simulated velocity fields was conducted for the surface, thermocline, and bottom layers, focusing on super-inertial (6–16 h), near-inertial (~16–30 h), and sub-inertial (>30 h) frequency bands. The results show that higher air temperatures intensify stratification and enhance near-inertial internal waves, particularly within the thermocline, whereas cooler conditions favor sub-inertial wave dominance. Increased wind speeds amplify internal wave energy across all layers, with the strongest effect occurring in the high-frequency band due to intensified wind stress and vertical shear, while weaker winds suppress wave activity. Precipitation variability primarily affects surface stratification, exerting more localized and weaker impacts. These findings highlight the non-linear, depth-dependent responses of internal waves to atmospheric drivers and improve understanding of the coupling between climate variability and internal wave energetics. The insights gained provide a basis for more accurate predictions and sustainable management of stratified aquatic ecosystems under future climate scenarios. Full article

Non-perturbative approaches to linear and nonlinear responses (NLR) of atoms, molecules, and molecular aggregates are reviewed in relation to low and high harmonic generations (HG) by laser fields. These response properties are effective for the generation of entangled light pairs for quantum information processing by spontaneous parametric downconversion (SPDC) and stimulated four-wave mixing (SFWM). Quasi-energy derivative (QED) methods, such as QED Møller–Plesset (MP) perturbation, are reviewed as time-dependent variational methods (TDVP), providing analytical expressions of time-dependent linear and nonlinear responses of open-shell atoms, molecules, and molecular aggregates. Numerical Liouville methods for the low HG (LHG) and high HG (HHG) regimes are reviewed to elucidate the NLR of molecules in both LHG and HHG regimes. Three-step models for the generation of HHG in the latter regime are reviewed in relation to developments of attosecond science and spectroscopy. Orbital tomography is also reviewed in relation to the theoretical and experimental studies of the amplitudes and phases of wave functions of open-shell atoms and molecules, such as molecular oxygen, providing the Dyson orbital explanation. Interactions between quantum lights and molecules are theoretically examined in relation to derivations of several distribution functions for quantum information processing, quantum dynamics of molecular aggregates, and future developments of quantum molecular devices such as measurement-based quantum computation (MBQC). Quantum dynamics for energy transfer in dendrimer and related light-harvesting antenna systems are reviewed to examine the classical and quantum dynamics behaviors of photosynthesis. It is shown that quantum coherence plays an important role in the well-organized arrays of chromophores. Finally, applications of quantum optics to molecular quantum information and quantum biology are examined in relation to emerging interdisciplinary frontiers. Full article

This study examines the soliton dynamics in the time-fractional cubic–quintic nonlinear non-paraxial propagation model, applicable to optical signal processing, nonlinear optics, fiber-optic communication, and biomedical laser–tissue interactions. The fractional framework exhibits a wide range of nonlinear effects, such as self-phase modulation, wave mixing, and self-focusing, arising from the balance between cubic and quintic nonlinearities. By employing the Multivariate Generalized Exponential Rational Integral Function (MGERIF) method, we derive an extensive catalog of analytic solutions, multi-peakon structures, lump solitons, kinks, and bright and dark solitary waves, while periodic and singular solutions emerge as special cases. These outcomes are systematically constructed within a single framework and visualized through 2D, 3D, and contour plots under both anomalous and normal dispersion regimes. The analysis also addresses modulation instability (MI), interpreted as a sideband amplification of continuous-wave backgrounds that generates pulse trains and breather-type structures. Our results demonstrate that cubic–quintic contributions substantially affect MI gain spectrum, broadening instability bands and permitting MI beyond the anomalous-dispersion regime. These findings directly connect the obtained solution classes to experimentally observed routes for solitary wave shaping, pulse propagation, and instability and instability-driven waveform formation in optical communication devices, photonic platforms, and laser technologies. Full article

The convective Cahn–Hilliard–Oono equation is analyzed under the conditions ${\mu }_1\ge 0$ and ${\mu }_3+{\mu }_4\le 0$. The Lie invariance criteria are examined through symmetry generators, leading to the identification of Lie algebra, where translation symmetries exist in both space and time variables. By employing Lie group methods, the equation is transformed into a system of highly nonlinear ordinary differential equations using appropriate similarity transformations. The extended direct algebraic method are utilized to derive various soliton solutions, including kink, anti-kink, singular soliton, bright, dark, periodic, mixed periodic, mixed trigonometric, trigonometric, peakon soliton, anti-peaked with decay, shock, mixed shock-singular, mixed singular, complex solitary shock, singular, and shock wave solutions. The characteristics of selected solutions are illustrated in 3D, 2D, and contour plots for specific wave number effects. Additionally, the model’s stability is examined. These results contribute to advancing research by deepening the understanding of nonlinear wave structures and broadening the scope of knowledge in the field. Full article