Search Results (22)

Landau–Zener–Stückelberg–Majorana (LZSM) interference describes the coherent superposition of nonadiabatic transitions when a quantum system is driven through an avoided crossing, but its classical optical analog remains largely unexplored. This work establishes an optical-resonator-based platform for exploring LZSM interference in atomic polarization dynamics using temporal coupled-mode theory. By exploiting the formal correspondence between the cavity mode and atomic polarization in a weakly driven two-level system (TLS), exact analytical solutions are derived for linear frequency sweeps and sinusoidal modulation. The results reveal that the Landau–Zener transition of atomic polarization occurs even when the input frequency transiently sweeps across resonance. The finite temporal memory inherent in the cavity response gives rise to Stückelberg interference, manifesting as oscillations in transmission and cavity energy. The dependence of the interference pattern on sweep rate, linewidth, and modulation is systematically analyzed, and a non-monotonic behavior of oscillation amplitude versus the cavity linewidth is identified. Furthermore, the conventional critical coupling concept is reexamined in the nonadiabatic regime, where counterintuitively the deepest transmission dip occurs under over-coupling rather than critical coupling. Finally, an inverse-design approach engineering both the amplitude and frequency of the input frequency is introduced to tailor the LZSM interference pattern. Our results provide a new platform to all-optical simulation of complex quantum interference. Full article

To address three major industry pain points—the lack of quantified profit-sharing standards in the two-stage pricing under the separation model of military research and production, the absence of stable Nash equilibrium in single-layer synchronous optimization, and insufficient incentives for full-cycle process optimization in design units—this paper constructs a two-level Stackelberg leader–follower game model with the general contracting unit as the leader and design and general contracting units as followers. This aligns with current prototype incentives and phased pricing policies for production rewards and penalties. At the theoretical level, it improves the complete proof system for the two-stage concave profit two-level Stackelberg Nash equilibrium, distinguishes the mathematical differences in equilibrium existence between sequential decision-making and synchronous optimization, and extracts general rules for phased differentiated profit sharing: high-innovation segments should be allocated more profit weight; simply maximizing total alliance profit may cause imbalanced interests, while introducing a minimum net profit-weighted objective can achieve Pareto improvements without profit loss. This conclusion can be applied to multi-stage general contracting scenarios across industries, such as EPC and military–civil collaborative innovation, enriching the basic theory of profit sharing and hierarchical games. Theoretically, the existence of the lower-level Nash equilibrium is proven using Brouwer’s fixed-point theorem, and combining it with the strictly monotonically decreasing feature of the best response function, uniqueness of the equilibrium is derived. Multiple sets of differentiated initial values are simulated to rule out multi-equilibrium bifurcation risk. The model incorporates the military’s reward and penalty policies as rigid exogenous constraints, sets dual individual rationality constraints of ‘cooperative profit greater than baseline profit with no allocation, and both parties’ net profit non-negative,’ and introduces differentiated cost-reduction efficiency and quadratic increasing effort costs to characterize the heterogeneous input of the two types of development entities. For models with piecewise nonlinearity and multi-constraint nonconvex structures, this paper modifies the standard PSO into a Bi-PSO solving framework through hierarchical temporal adaptation. It does not innovate the underlying particle update mechanism and is only used to match the sequential decision order of the leader–follower game. By comparing five algorithms—IPM, GA, SA, DE, and adaptive PSO—through 20 repeated simulations: gradient-based interior point methods easily get stuck in locally invalid solutions that violate cooperation thresholds; differential evolution has the best numerical global search performance, but all general evolutionary algorithms optimize allocation and effort variables simultaneously, disrupting the Stackelberg hierarchical timing. Only Bi-PSO maintains consistent game logic. Using a pricing case for a certain type of equipment and jointly calibrating all parameters with policy documents, three simulation scenarios were set up: no allocation, equal 50/50 split, and single-layer profit maximization. Under the no-allocation mode, R&D investment from the design unit drops to zero and alliance benefits plummet; a blanket equal split ignores differences in technical contributions across two stages, leading to clear efficiency losses; single-layer optimization only pursues total profit maximization, causing a severe imbalance in profit distribution. The two-layer basic framework can achieve the upper limit of alliance benefits, and by adding a weighted optimization goal that considers both total profit and cooperation fairness, it can achieve equal net profits for both parties without reducing overall profit. Through single-parameter sweeps and two-factor heatmap simulations, the study further revealed the coupled effects of main party efficiency and mass production rewards and penalties on equilibrium input and optimal sharing ranges. A robust check was performed by replacing the logarithmic concave output function, producing a standardized allocation range resilient to parameter perturbations: optimal split for the prototype stage is 0.4–0.6 for the design unit, and for mass production stage 0.7–0.9. The findings suggest that high-contribution stages in multi-phase collaboration contracts should receive more benefits, and a weighted fairness objective can achieve Pareto improvements. These conclusions can extend to multi-stage collaboration scenarios such as EPC and military–civilian cooperation. Theoretically, this research further completes the equilibrium proof system for two-party concave payoff two-layer games, providing a new reference for the theory of phased differentiated benefit-sharing contracts in the military sector. Methodologically, it proposes a two-layer intelligent solving tool adapted to leader–follower sequential decisions, effectively mitigating issues where single-layer model equilibria fail or analytical algorithms struggle with multi-constraint nonconvex games. The results can provide quantitative support for the military, general contracting unit, and design unit in drafting equipment incentive pricing contracts and managing full-cycle cost collaboration. Full article

The study is driven by its importance in modern material processing and precision engineering, where understanding and controlling interfacial stability is crucial in maintaining reliable performance across various operating conditions. The interplay between the tangential magnetic field and temporal periodicity generates additional mechanisms of mode coupling and amplifies instability. These observations address critical shortcomings in nonlinear stability theory and suggest practical uses in flow regulation and the control of conductive fluids. The fluids are assumed as Eyring–Powell non-Newtonian and flow with uniform velocities through porous media. The analysis is conducted using a non-perturbative method that relies mainly on He’s frequency formulation. To facilitate the mathematical treatment, viscous potential theory is adopted. The governing linear partial differential equations describing the flow are then solved under nonlinear boundary conditions, resulting in a nonlinear characteristic equation that represents the displacement of the interface. A non-dimensional procedure is then applied to extract the key dimensionless physical parameters influencing the system behavior. A set of graphical results is provided to demonstrate how the system’s stability behavior is influenced by changes in the key dimensionless physical parameters. The validation of the innovative process is achieved using Mathematica Software. The study considers both uniform and periodically varying magnetic fields, and the associated stability conditions are evaluated for each case, where the impacts of various non-dimensional attributes are assessed. As density ratio increases, it stabilizes periodic magnetic fields while destabilizing uniform ones. A stronger MF enhances magnetic damping, reducing instability regions and promoting stable periodic interfacial motion. Enhanced conductivity improves Magnetohydrodynamic interactions, resulting in greater energy dissipation and stability. Full article

We propose a loss-managed BIC-derived GSST metasurface for robust phase-change-tunable mid-infrared transmission suppression. The metasurface consists of a SiO₂ substrate, a Si grating layer, and an upper Si/Ge₂Sb₂Se₄Te₁ (GSST)/Si trilayer with an off-centered air slot. The slot plays a dual role: it breaks the mirror symmetry of the unit cell to convert a symmetry-protected bound state in the continuum into an externally accessible high-Q resonance, while reducing the effective GSST filling region to limit material-loss participation. Lossless eigenmode analysis confirms the BIC-derived origin of the resonance, with the quality factor following $Q\propto x_{\mathrm{disp}}^{-1.993}$. A crystalline-state loss-channel analysis further identifies $x_{\mathrm{disp}}=40\mathrm{nm}$ as a finite-coupling operating point that preserves good up/down radiation balance, a large resonant amplitude factor, and a moderate-high quality factor under the fully crystalline GSST condition. Full-wave simulations show that the transmission-dip wavelength shifts from about $3.9568\mathsf{\mu }\mathrm{m}$ to about $3.9740\mathsf{\mu }\mathrm{m}$ as GSST evolves from the amorphous to the crystalline state, while the extracted quality factor remains in the range of 483–780 and the transmission minimum stays deeply suppressed throughout the phase-change trajectory. A two-port temporal coupled-mode theory analysis reveals that this persistent low-transmission state originates from destructive interference between the resonant and background transmission channels. Fabrication tolerance analysis shows that $\pm 5\%$ variations in GSST thickness and slot width, as well as moderate variations in the slot displacement, preserve the deep transmission suppression across GSST phase states, although the absolute resonance wavelength shifts with geometry. These results provide a practical strategy for balancing radiative coupling and material-loss participation in phase-change high-Q metasurfaces. Full article

Modeling forced nonlinear multivariable dynamical systems remains challenging, particularly when first-principles models are unavailable or strong nonlinear couplings are present. In recent years, data-driven approaches grounded in the Koopman operator theory have gained attention for their ability to represent nonlinear dynamics via linear evolution in appropriately lifted spaces. This work presents a data-driven modeling framework for forced nonlinear multiple-input multiple-output (MIMO) systems based on Hankel Dynamic Mode Decomposition with control and lifting functions (HDMDc+Lift). The proposed methodology exploits Hankel matrices to encode temporal correlations and employs lifting functions to approximate the Koopman operator’s action on observable functions. As a result, an augmented-order linear state-space model is identified exclusively from input–output data, without relying on explicit knowledge of the system’s governing equations. The effectiveness of the proposed approach is demonstrated using operational data from a real multivariable tank system that was not used during the identification stage. The identified model achieves a coefficient of determination exceeding 0.87 in multi-step prediction tasks. Furthermore, spectral analysis of the resulting linear operator reveals that the dominant dynamical modes of the physical system are accurately captured. At the same time, additional modes associated with nonlinear interactions are also identified. These results highlight the HDMDc+Lift framework’s ability to provide accurate and interpretable linear representations of forced nonlinear MIMO dynamics. Full article

This paper presents an analytical model for the hereditary vibrations of a coupled circular plate system interconnected by viscoelastic creep layers. The system is represented as a discrete-continuous chain of thin, isotropic plates with time-dependent material properties. Based on the theory of hereditary viscoelasticity and D’Alembert’s principle, a system of partial integro-differential equations is derived and reduced to ordinary integro-differential equations using Bernoulli’s method and Laplace transforms. Analytical expressions for natural frequencies, mode shapes, and time-dependent response functions are obtained. The results reveal the emergence of multi-frequency vibration regimes, with modal families remaining temporally uncoupled. This enables the identification of resonance conditions and dynamic absorption phenomena. The fractional parameter serves as a tunable damping factor: lower values result in prolonged oscillations, while higher values cause rapid decay. Increasing the kinetic stiffness of the coupling layers raises vibration frequencies and enhances sensitivity to hereditary effects. This interplay provides deeper insight into dynamic behavior control. The model is applicable to multilayered structures in aerospace, civil engineering, and microsystems, where long-term loading and time-dependent material behavior are critical. The proposed framework offers a powerful tool for designing systems with tailored dynamic responses and improved stability. Full article

Robust control over the coupling and propagation of surface plasmon polaritons (SPPs) is essential for advancing various plasmonic applications. Traditional planar structures, commonly used to design SPP directional couplers, face limitations such as low extinction ratios and design complexities. These issues frequently hinder the dense integration and miniaturisation of photonic systems. Recently, exceptional points (EPs)—unique degeneracies within the parameter space of non-Hermitian systems—have garnered significant attention for enabling a range of counterintuitive phenomena in non-conservative photonic systems, including the non-trivial control of light propagation. In this work, we develop a rigorous temporal coupled-mode theory (TCMT) description of a non-Hermitian metagrating composed of alternating silicon–germanium nanostrips and use it to explore the unidirectional excitation of SPPs at EPs in the visible spectrum. Within this framework, EPs, typically associated with the coalescence of eigenvalues and eigenstates, are leveraged to manipulate light propagation in nonconservative photonic systems, facilitating the refined control of SPPs. By spatially modulating the permittivity profile at a dielectric–metal interface, we induce a passive parity–time ($\mathcal{PT}$)-symmetry, which allows for refined tuning of the SPPs’ directional propagation by optimising the structure to operate at EPs. At these EPs, a unidirectional excitation of SPPs with a directional intensity extinction ratio as high as 40 dB between the left and right excited SPP modes can be reached, with potential applications in integrated optical circuits, visible communication technologies, and optical routing, where robust and flexible control of light at the nanoscale is crucial. Full article

This paper presents a triple-ring optical filter designed through direct binary search inverse design, comprising three cascaded rings in an add–drop configuration. We established a physical model using temporal coupled-mode theory to derive theoretical spectra and analyze key transmission parameters. Subsequently, we encoded the target transmission performance into a figure of merit to optimize the coupling coefficients between ring resonators and waveguides. We verify the theoretical parameters using three-dimensional finite-difference time-domain simulations. The optimized filter achieves a free spectral range of 86 nm, an insertion loss of 0.4 dB, an extinction ratio of 20 dB, and a narrow spectral linewidth of 0.2 nm within a compact footprint of $29 \mathsf{\mu }\mathrm{m}\times 46.5 \mathsf{\mu }\mathrm{m}$. This device demonstrates significant application potential, particularly in laser external cavities, dense wavelength division multiplexing systems, and sensing applications. Furthermore, this work provides a systematic design framework for the precision design of photonic devices. Full article

This study aims to investigate the spatiotemporal evolution of cavitating flow and the associated acoustic responses around a NACA0015 hydrofoil. A coupled fluid–acoustic interaction model is developed by integrating a nonlinear cavitation model with vortex–sound coupling theory. Numerical simulations are conducted within a computational domain established for the hydrofoil to capture the interactions between cavitation dynamics and acoustic radiation. The results indicate that the temporal variations in cavity evolution and pressure fluctuations agree well with experimental observations. The simulations predict a dominant pressure fluctuation frequency of 30.15 Hz, consistent with the cavitation shedding frequency, revealing that the evolution of leading-edge vortex structures governs the periodic variations in the lift-to-drag ratio. Cavitation significantly modifies the development of vortex structures, with vortex stretching effects mainly concentrated near cavitation regions. The dilation–contraction term is closely associated with cavity formation, while the pressure–torque tilting term predominantly affects cloud cavitation collapse. Dynamic mode decomposition (DMD) shows that the coherent structures of the leading modes exhibit morphological similarity to multiscale cavitation and vortex structures. Furthermore, hydrofoil cavitation noise consists mainly of loading noise and cavitation-induced pulsating radiation noise, with surface acoustic sources concentrated in cloud cavitation shedding regions. The dominant frequency of cavitation-induced radiation noise is highly consistent with experimental measurements. Full article

We propose a dual-ring optical filter based on direct binary search inverse design. The proposed device comprises two cascaded rings in an add–drop configuration. A physical model was established using temporal coupled mode theory to derive theoretical spectra and analyze key parameters governing transmission performance. Based on theoretical results, a direct binary search algorithm was implemented. The parameters of the proposed device were calculated using a three-dimensional finite-difference time-domain method for verification. The numerical results demonstrate a free spectral range of 86 nm, with insertion loss and extinction ratios of 0.3 dB and 22 dB, respectively. The proposed device has a narrow spectral linewidth of 0.3 nm within a compact footprint of $24 \mathsf{\mu }\mathrm{m}\times 25.5 \mathsf{\mu }\mathrm{m}$. The device shows significant application potential in laser external cavities and dense wavelength division multiplexing systems. Moreover, this work provides a novel methodology for precision design of photonic devices. Full article

A real-time tunable planar plasmonic waveguide based on a voltage-adjustable ferroelectric resonator is designed and investigated. The laminated ferroelectric compound resonator is composed of a ferroelectric Ba_0.85Ca_0.15Zr_0.9Ti_0.1O₃ (BCZT) layer, a PCB layer, as well as a localized spoof plasmonic metal layer, where the BCZT layer is beneficial for enhancing the voltage tunability in the spoof surface plasmon polariton (SSPP) waveguide. The simulated results show that the tuning range of the notch in the transmission curve, generated by the coupling between the ferroelectric compound resonator and the plasmonic waveguide, can achieve a variation of up to 8.8% thanks to the large tunability value in the BCZT ferroelectric layer. In addition, the notches consist of Fano resonant frequencies, the generation mechanism of which is elaborately discussed in terms of the temporal coupled mode theory. Full article

This paper presents a quaternion-based robust sliding-mode controller for quadrotors operating under significant wind disturbances. The proposed control method improves the reliability and efficiency of quadrotor control by eliminating the singularity problem inherent in the Euler angle method. The quadrotor dynamics and wind environment are modeled, and dynamic analysis is performed via numerical simulation. A realistic wind model is used, similar to a combination of deterministic and statistical models. The Lyapunov stability theory is utilized to prove the convergence and stability of the proposed control system. The simulation results demonstrate that the quaternion-based controller enables the quadrotor to follow the desired path and remain stable, even under external wind disturbances. Specifically, both position and attitude converge to the desired values within 10 s, demonstrating stable performance despite the challenging wind disturbances in both scenarios. Scenario 1 features turbulence with an average wind speed of 12 m/s and changing wind directions, while Scenario 2 models an environment with wind speeds that change abruptly and discretely over time, coupled with temporal variations in wind direction. Additionally, a comparative analysis with the conventional PD controller highlights the superior performance of the proposed RSMC controller in terms of trajectory tracking, stability, and energy efficiency. The rotor speeds remain within a reasonable and hardware-feasible range, ensuring practical applicability. Full article

We develop a 4 × 4-matrix model based on temporal coupled mode theory (TCMT) to elucidate the intricate energy exchange within a non-Hermitian, resonant photonic structure, based on the recently described infinity-loop micro-resonator (ILMR). We consider the structure to consist of four coupled resonant modes, with clockwise and counterclockwise propagating optical fields, the interplay between which gives rise to a rich spectral form with both overlapping and non-overlapping resonances within a single free spectral range (FSR). Our model clarifies the precise conditions for exceptional points (EPs) in this system by examining neighboring resonances over the device free spectral range (FSR). We find that the system is robust to the conditions for observing an EP, despite the presence of non-zero coupling of signals, or crosstalk, between the resonant modes. Full article

The quest for the physical mechanisms underlying turbulent high-speed jet flows is underpinned by the extraction of spatio-temporal coherent structures from their flow fields. Experimental measurements to enable data decomposition need to comprise time-resolved velocity fields with a high-spatial resolution—qualities which current particle image velocimetry hardware are incapable of providing. This paper demonstrates a novel approach that addresses this challenge through the implementation of an experimental high-spatial resolution dual-particle image velocimetry methodology coupled with dynamic mode decomposition. This new approach is exemplified by its application in studying the dynamics of the near-field region of a turbulent high-speed jet, enabling the spatio-temporal structure to be investigated by the identification of the spatial structure of the dominant dynamic modes and their temporal dynamics. The spatial amplification of these modes is compared with that predicted by classical linear stability theory, showing close agreement, which demonstrates the powerful capability of this technique to identify the dominant frequencies and their associated spatial structures in high-speed turbulent flows. Full article

In this paper, we combine the dielectric metasurface with monolayer graphene to realize a high quality(Q)-factor quasi-BIC-based optical modulator, and the corresponding modulation performances are investigated by using the finite-difference time-domain (FDTD) method, which can be well fitting by the Fano formula based on the temporal couple-mode theory. The results demonstrate that bound states in the continuum (BIC) will turn into the quasi-BIC with high Q-factor by breaking the symmetry of every unit of the metasurface. Meanwhile, the amplitude and bandwidth of transmission based on the quasi-BIC mode can be efficiently adjusted by changing the Fermi energy (E_F) of monolayer graphene, and the maximum difference in transmission up to 0.92 is achieved. Moreover, we also discuss the influence of the asymmetry degree to further investigate the modulation effect of graphene on the quasi-BIC mode. Full article