This work provides an explicit, accurate, and physically interpretable formulation of the waveguide invariant (WI) for the shallow-water Pekeris model with a finite-impedance seabed, addressing limitations of existing approximations in the low-frequency regime. This is achieved by deriving an approximate closed-form expression for the intermodal WI based on the physically intuitive cycle-distance formula for modal group velocities. Its accuracy is established through comprehensive validation against full-wave KRAKEN simulations, showing close agreement with the benchmarks and a rapid decay of error beginning immediately above the modal cutoff. Three key analytical insights are derived. First, a rigorous lower bound-confirming that finite seabed impedance elevates the WI above its ideal baseline-is formally established and experimentally supported by large WI values from seabed-dominated, low-frequency data. Second, a compact closed-form expression is obtained for the limit as the grazing angle approaches zero, helping to explain the stability of far-field interference structures. Third, a continuous angular-dependent approximation for adjacent-mode WIs is presented. Experimental analysis further defines the framework's operational boundary, confirming its optimal use where seabed effects dominate over water-column stratification. Together, the derived formulation, analytical insights, and experimental evidence constitute a refined framework for understanding modal interference in shallow-water waveguides.

Dispersion characteristics and mode conversion of guided waves in plate-like structures with arbitrarily varying thickness.

Abstract The vibrational modes of spherical monoatomic gas phase nanoparticles are calculated by quantizing the solutions of Lamb. The mode cutoff gives the two types of modes equal weights, and rounds the high frequency, both in strong contrast to Debye model spectra. The calculated spectra agree fairly well with spectra obtained by numerical diagonalization of Hessians of large disordered Lennard–Jones (LJ) clusters. The effect of a symmetry in the atomic arrangement is demonstrated with calculations for ground state LJ clusters. Our calculations allow the specification of the angular momentum carried by the vibrational motion, for which an example is calculated.

Tilted fiber Bragg gratings (TFBGs) are highly sensitive refractometric probes, but their broad cladding-mode spectra have long been considered incompatible with wavelength-division multiplexing. As a result, TFBG refractive-index sensors are generally restricted to single-point operation, despite their inherent advantages. Here, we demonstrate for the first time that multiple bare, uncoated TFBGs (inscribed with distinct grating periods and tilt angles) can be cascaded within a single-mode fiber and independently interrogated over an 80-nm bandwidth. Although the cladding-mode spectra strongly overlap, we show that first-order derivative spectrum analysis isolates the local slope of each cut-off mode, effectively suppressing the envelope distortions typically induced by upstream gratings. This enables reliable and decoupled multipoint refractive-index sensing, with sensitivities of 52-58 nm/RIU that are fully consistent with intrinsic TFBG performance in aqueous media and remain stable after cascading. The derivative method enhances the demodulation accuracy by up to 65% and preserves linearity (R2 = 0.94-0.98) while maintaining cross-talk below 0.03 nm. These results overturn the longstanding belief that TFBG refractometers cannot be multiplexed, paving the way for compact, low-cost, and scalable quasi-distributed chemical and biological sensing networks based on TFBG arrays.

This work improves upon our previously introduced explicit dynamic modal filter (DEMF) within the framework of the discontinuous Galerkin spectral element method (DGSEM) by introducing a mechanism for self-tuning of the model parameters. The new self-tuning dynamic explicit modal filter (STDEMF) also extends the methodology for obtaining modal values from nodal values beyond Chebyshev grids and polynomials to general collocation points and orthogonal polynomial bases by leveraging orthogonality. The generated modes are used to remove the built-up energy due to unresolved sub-grid scales (SGSs) in large-eddy simulation (LES) of turbulent flows. The STDEMF improves the performance of DEMF in two ways. First, the filter kernel applied to the modes is adapted from a cutoff kernel to a hyperbolic tangent shape, which automatically adjusts the model for different polynomial orders. Second, the cutoff mode is computed dynamically for each element as a function of local flow characteristics, including the local Kolmogorov length scale and the second invariants of the strain and rotation rate tensors. The suggested formulation for the cutoff mode treats unresolved elements distinctly and improves performance by avoiding under- or over-dissipation. Moreover, the cutoff mode evolves over time within the same element as turbulent characteristics vary. The model is evaluated on three flows: homogeneous isotropic decaying, the Taylor–Green vortex, and periodic channel flow, each with distinct turbulent characteristics. Comparisons of the results show that the STDEMF model outperforms the DEMF model and the Smagorinsky eddy viscosity model.

• We investigate a classical model of coupled harmonic oscillators (CHO) as the classical counterpart of the Lee model. In this classical model, the divergence of the fundamental frequency and its renormalization precisely reproduce the divergence and renormalization of the physical mass of the particle, revealing that mass divergence in the Lee model is not solely a quantum phenomenon. • We derive the necessary conditions that any renormalization must satisfy for the two-oscillator system corresponding to the single-mode Lee model. • We examine the classical analog of the N - θ scattering process in the Lee model and demonstrate that the cutoff-dependent behavior of the scattering strength parallels the quantum scenario, indicating that the suppression of scattering also has a classical origin. Although divergence and renormalization of physical quantities are frequently encountered in quantum field theory (QFT), they are not necessarily quantum-specific characteristics. We show in this paper that there exists a classical counterpart of the Lee model which is the model of coupled harmonic oscillators (CHO). It is demonstrated that the frequency divergence in this classical model precisely replicates the phenomenon of mass divergence in the Lee model, as does the corresponding renormalization procedure. Considering the arbitrariness in renormalization schemes, we establish necessary conditions that a general renormalization must satisfy for the model of two coupled oscillators which corresponds to the single-mode Lee model. Furthermore, we analyze the classical analog of the N - θ scattering process and show that the dependence of scattering strength on the cutoff mode mirrors that of the quantum case. These findings challenge the quantum-centric view of mass renormalization in the Lee model and offer new insights into the classical-quantum correspondence in renormalization theories.

A wall-modelled large eddy simulation approach is proposed in a discontinuous Galerkin (DG) setting, building on the slip-wall concept of Bae et al. (J. Fluid Mech., vol. 859, 2019, pp. 400–432) and the universal scaling relationship by Pradhan and Duraisamy (J. Fluid Mech., vol. 955, 2023, A6). The effect of the order of the DG approximation is introduced via the length scales in the formulation. The level of under-resolution is represented by a slip Reynolds number and the model attempts to incorporate the effects of the numerical discretization and the subgrid-scale model. The dynamic part of the new model is based on a modified form of the Germano identity -- performed on the universal scaling parameter -- and is coupled with the dynamic Smagorinsky model. A sharp modal cutoff filter is used as the test filter for the dynamic procedure, and the dynamic model can be easily integrated into any DG solver. Numerical experiments on channel flows show that grid independence of the statistics is achievable and predictions for the mean velocity and Reynolds stress profiles agree well with the direct numerical simulation, even with significant under-resolution. When applied to flows with separation and reattachment, the model also consistently predicts one-point statistics in the reverse flow and post-reattachment regions in good agreement with experiments. The performance of the model in accurately predicting equilibrium and separated flows using significantly under-resolved meshes can be attributed to several aspects that work synergistically: the optimal finite-element projection framework, the interplay of the scale separation and numerical discretization within the DG framework, and the consistent dynamic procedures for subgrid and wall modelling.

This study explores the use of parabolized stability equations (PSEs) for predicting sound propagation in ducts, a novel application in computational duct acoustics. The PSE, formulated in a general duct-fitted coordinate system, was validated against several test cases, including uniform flow, axial temperature gradients, and laminar/turbulent flows, demonstrating close agreement with existing literature. This paper highlights limitations of the PSE, particularly when the local Helmholtz number decreases, potentially causing mode cutoff, and suggests remedies for mitigating phase and amplitude errors. The efficiency of the PSE is further demonstrated through a comparison with linearized Euler equations for forward fan noise propagation in a turbofan inlet, showing 75.8% reduced computational time and 98.2% reduced memory usage. These computational advantages become more significant as problem size increases, with the PSE outperforming traditional finite element and parabolic approximation methods, especially in cases involving viscous shear flow effects. This makes the PSE particularly well-suited for applications such as boundary layer shielding and liner-boundary layer interactions. The study provides a promising avenue for future acoustic research and practical engineering applications, emphasizing the efficiency and accuracy of PSE in complex duct acoustics.

A kind of compact fiber optic vector magnetic field sensor is proposed. This sensor features a highly localized eccentric point-by-point fiber Bragg grating as its core component, with a gold-coated end facet to enhance cladding mode reflection. Eccentric local modulation points disrupt the axial symmetry of the fiber core, enabling the excitation of significant higher-order cladding modes as the core mode passes through the modulation points. Among these, the cut-off mode is exceptionally sensitive to changes in the refractive index near the fiber surface, with a sensitivity of approximately 536 nm/RIU. The sensor supports vector magnetic field sensing, achieving a maximum magnetic field sensitivity of 0.24 dB/mT in the range of 0-21 mT. The sensor is characterized by rapid fabrication, high stability, and holds significant potential for applications in vector magnetic field sensing.

Plastids of diatoms and related algae with complex plastids of red algal origin are surrounded by four membranes, which also define the periplastidic compartment (PPC), the space between the second and third membranes. Metabolic reactions as well as cell biological processes take place in the PPC; however, genome-wide predictions of the proteins targeted to this compartment were so far based on manual annotation work. Using published experimental protein localizations as reference data, we developed the first automatic prediction method for PPC proteins, which we included as a new feature in an updated version of the plastid protein predictor ASAFind. With our method, at least a subset of the PPC proteins can be predicted with high specificity, with an estimate of at least 81 proteins (0.7% of the predicted proteome) targeted to the PPC in the model diatom Phaeodactylum tricornutum. The proportion of PPC proteins varies, since 180 PPC proteins (1.3% of the predicted proteome) were predicted in the genome of the diatom Thalassiosira pseudonana. The new ASAFind version can also generate a newly designed graphical output that visualizes the contribution of each position in the sequence to the score and accepts the output of the recent versions of SignalP (5.0) and TargetP (2.0) as input data. Furthermore, we release a script to calculate custom scoring matrices that can be used for predictions in a simplified score cut-off mode. This allows for adjustments of the method to other groups of algae.

Abstract Tip clearance is a critical parameter affecting fan performance and aeroelastic stability. This paper investigates the effect of tip clearance on fan aeroelasticity under different acoustic propagation characteristics through numerical simulations. Focusing on the first bending mode, which is most prone to flutter, the aeroelastic stability under various nodal diameters (ND) is studied using the energy method, with a detailed analysis of the 2 ND mode, which exhibits flutter risk. The study reveals that tip clearance does not alter the position of the most unstable nodal diameter. Under upstream and downstream cut-off mode and upstream cut-on mode, increasing tip clearance enhances aerodynamic damping, whereas under downstream cut-on mode, it reduces aerodynamic damping. The aerodynamic damping of the blade is jointly influenced by the flow field and acoustic propagation characteristics. The impact of the flow field is primarily concentrated near the leading edge of the pressure side at the blade tip, while the acoustic propagation characteristics significantly alter the phase of unsteady pressure, leading to notable changes in energy exchange characteristics. The study concludes that there is no optimal aeroelastic clearance, as the effect of clearance on aeroelasticity is closely related to acoustic propagation characteristics.

An autonomous double-scroll chaos generator was recently introduced, intentionally designed using a circuit topology that does not stem from canonical oscillators. The circuit comprises two bipolar junction transistors, one resistor, one capacitor, and two inductors. To date, the underlying operational principles of this circuit remained unclear. Here, the original circuit is initially simulated using realistic transistor models, and the key features of its dynamics are revealed. A simplified mathematical model reproducing the observed phenomena is then introduced based on an analysis of the functioning of each transistor in the circuit, which hinges on the coupling role of one of the inductors. When one transistor saturates, the other enters cut-off mode. This creates competitive dynamics, resulting in the transistors continuously switching between saturation and cut-off, eventually leading to chaotic behavior. The circuit is further analyzed in terms of two distinct components: a damped resonator and a relaxation oscillator, which consists of two transistors. A simplified switching model reproducing the double-scroll dynamics is subsequently put forward and proposed as a means of generalizing the results. It is found that, at the heart of double-scroll generation, there lies a peculiar motif of partially symmetric interconnection between the two bipolar transistors.

Abstract Large-scale and long-term two-dimensional particle-in-cell simulations of high resolution are performed for the first time to study the dynamics of electrostatic decay of upper-hybrid wave turbulence generated by electron beams into Langmuir/ Z -mode ( L Z ) waves in weakly to moderately magnetized plasmas, in conditions relevant to type III solar radio bursts. Simulations use parameters characteristic of beam–plasma interactions between ∼0.1 and 1 au. The impact of plasma magnetic field on decay is shown, and magnetic properties of L Z waves are determined. During their energy transport through k wavevector scales, waves undergo several decay cascades, acquiring increasing magnetic energy until they reach electromagnetic Z -mode dispersion below the plasma frequency. Whereas the impact of magnetic field on decaying waves of large k = ∣ k ∣ is weak, important differences with respect to the unmagnetized plasma case manifest at small k-scales, where a boundary layer delimiting a spectral domain free of L Z energy is revealed. It prevents decayed waves from reaching the Z -mode cutoff frequency and a high level of left-handed polarization, and it modifies the conditions for the appearance of modulational instabilities and strong turbulence phenomena at k ∼ 0. Ordinary O -mode waves are generated jointly with Z -mode waves at comparable energy levels, via electromagnetic decay, whereas X -mode emissions are much weaker in most cases. These results provide support for the interpretation of observations by satellites such as Parker Solar Probe and Solar Orbiter, and they supply a solid basis for tackling the more complex problem of dynamics of upper-hybrid wave turbulence in magnetized plasmas where random density fluctuations cannot be neglected.

Periodic insertion of mode scramblers can reduce the accumulation of group-delay spread and mode-dependent loss in mode-division-multiplexed links. Past effective mode scramblers, however, exhibit too much loss, owing to coupling from guided to unguided modes, specifically cutoff modes. We present a mode scrambler design based on long-period fiber Bragg gratings for links employing graded-index transmission fibers with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$D=12$</tex-math></inline-formula> guided spatial and polarization modes. In typical graded-index fibers, the guided and lowest-order cutoff modes have nearly equally spaced propagation constants. Hence, a grating will induce coupling not only between all the guided modes but also to the lowest-order cutoff modes, causing high losses. To remedy this problem, we design the mode scrambler transverse refractive index profile to yield equal spacing between the propagation constants of the guided mode groups and a different and larger propagation constant spacing between the highest-order guided modes and the lowest-order cutoff modes. We also ensure that the highest-order guided modes cannot be phase-matched to any other unguided modes by a grating. This enables a uniform grating, obtained by a grid search optimization of the grating parameters, to couple all the guided mode groups with minimal loss. We obtain a design with mode-averaged and mode-dependent loss standard deviations less than 0.027 dB and 0.011 dB, respectively, over the C-band. We perform numerical simulations to study the effect of fabrication errors and show that the choice of grating modulation depth involves a tradeoff between mode scrambler loss and sensitivity of link group-delay spread to fabrication errors.

We present a simple yet effective method for realizing compact waveguides that support efficient below-cutoff propagation with user-defined modal characteristics. The design incorporates a Huygens’ metasurface (HMS) as one of the waveguide walls, engineered to transform a cutoff mode into a propagating one by satisfying suitable boundary conditions. By tuning the metasurface’s local electric and magnetic responses, the propagation constant can also be independently controlled. We validate this concept both numerically and experimentally around 4 GHz in a waveguide of height 15 mm, well below the 10-GHz cutoff of a conventional counterpart, and show that it supports user-defined phase constants.

We propose and demonstrate a superfine multiresonant fiber grating sensor characterized by superior spectral resolution and enhanced sensing capabilities. This sensor can be easily constructed by inserting a tilted fiber Bragg grating (TFBG) probe into a silica capillary filled with a refractive index (RI) matching oil. As the fiber cladding, the RI-matching oil, and the capillary all have the same RI, the cladding modes excited by the TFBG can extend into the RI-matching oil and capillary, facilitating surface sensing outside the capillary. Our study shows that the number of cladding modes increases, and the resonance spectrum becomes denser as the outer diameter of the capillary gets larger. As a result, the detection accuracy of RI based on mode cutoff wavelength identification can be improved. Particularly, with a capillary diameter of 1 mm, the heightened spectral density enhances refractometric accuracy by nearly an order of magnitude compared to the intrinsic TFBG. The superfine multiresonant fiber grating sensor proposed here is flexible in configuration and easy to fabricate, providing a new strategy for developing new fiber sensing devices.

Abstract This work investigates the impact of acoustically treated intakes on fan flutter. The propagation of the fan acoustic perturbations is studied using a simplified model, where the frequency of the waves in the intake is the natural frequency of the fan blade in the stationary frame of reference. The model consists of a constant cross-section annular duct, where the acoustic modes are computed for hard wall and lined wall regions, assuming a uniform axial flow. The interfaces between the lined and hard wall sections are solved by doing mode matching. The acoustic reflections in the zero-thickness intake are computed using the Wiener-Hopf technique following Rienstra's model. Analytical results show that the waves propagating from the fan are reflected and scattered radially at the interfaces between the hard wall and the liner. Furthermore, the liner damps and changes the phase velocity of acoustic modes. Due to the low frequency of the flutter waves, the radial scattering can activate different cut-off modes, which need to be retained in order to make accurate predictions. The likelihood of fan flutter is estimated using the phase of the reflected cut-on waves reaching the fan. This strategy is used to assess the impact of the acoustic liners on the stability of a realistic fan. It is concluded that the impact of the phasing and reflections induced by the acoustic liners is comparable to that of the intake and can alter the flutter characteristics of the fan significantly.

High-sensitive glucose sensor based on tilted fiber Bragg gratings

In this paper, we investigate a dielectrically chiral-core fiber for the generation of orbital angular momentum (OAM) modes. We observe that the presence of chirality induces a modal index split between the same order OAM modes with opposite topological charges and arbitrary phase front rotation directions, which are originally degenerate in achiral fibers. This split indicates the existence of circular birefringence (CB) associated with a dielectric chirality. The modal cutoff splitting results in a single polarization property without the possibility of coupling between the same order modes that correspond to a single +l or −l OAM mode guiding. However, neither of the two fundamental modes guided by the chiral fiber exhibits a cutoff, despite having different modal indices due to chirality. Upon fraction of modal power cutoff, the high-order modes in the core region display different cutoff fractions of modal power between the same order modes, while the fundamental mode has no cutoff fraction of modal power. Due to CB and different fractions of modal power in the core for different handed OAM modes, dielectrically chiral fibers have potential applications in chiral sensing, circular polarization-dependent OAM mode filters, and new kinds of OAM mode generators.

There are differences between the dynamic deflection and bending moment (strain) in the same section of continuous girder bridges. However, the selection of the response for calculating dynamic amplification factors (DAFs), which are essential for bridge health monitoring and safety assessment, remains controversial. Modes may play a role in the relationship between the deflection DAF and the bending moment DAF in both numerical analysis and field tests. To investigate the distinctions between the DAFs of the deflection and bending moment in a continuous girder bridge, functional expressions of the DAFs were derived, taking into account multi-factor coupling under concentrated forces. The interaction effects of the mode and road surface condition (RSC), vehicle speed, bridge span length, and span number on the deflection DAF, the bending moment DAF, and the ratio of the deflection DAF to the bending moment DAF (RDM) of precast continuous box-girder bridges were analyzed using vehicle-bridge interaction. To ensure the accuracy of the DAF in numerical computations and experimental tests, two types of accuracy indexes and the corresponding cut-off modes were provided. Validation was conducted by performing dynamic load tests on two field bridges. The results indicate that different modes have a significant effect on the RDM of the mid-span section of a bridge. When considering multiple factors, the deflection DAF and bending moment DAF of the mid-span section increased rapidly with the considered modes and then stabilized. Statistically, the RDM of all nine bridges ranged from 1.00 to 1.12, indicating that the deflection DAF was greater than the bending moment DAF. The suggested cut-off modes can be utilized for efficient and accurate calculation of the DAF and response signal fidelity.