Low-frequency Approximation Research Articles

Linear-acoustic effects of asymmetrical undercutting of toneholes of woodwind instruments.

The influence of the presence and magnitude of asymmetrical undercutting of the toneholes of woodwind instruments on the change in their effective radius and the corresponding shift of the eigenfrequencies of the air duct is considered. Within the framework of the electro-acoustic analogy, a tonehole with an asymmetrical undercutting along the axis of the main bore is presented as a cascade connection of two holes with different radii (undercutting and not undercutting parts of the hole), and with a sideway undercutting-in the form of a parallel connection. Formulas for numerical calculations are given that make it possible to determine the effective radius of such holes for the open state in the low-frequency approximation. Based on the obtained dependencies, using the transmission-matrix method, the eigenfrequencies of an air duct with one hole were calculated and compared with the results of computer modeling in the COMSOL Multiphysics 5.6 program. It is shown that increasing the degree and angle of undercutting leads to an increase in the effective radius, a displacement of the "center of gravity" of the sound hole along the main bore axis, and has effect on the shift of resonant frequency.

Multi-scale transformer network for super-resolution of visible and thermal air images

Reference image-based Super-Resolution (RefSR) is introduced to improve the quality of a Low-resolution (LR) input image by leveraging the additional information provided by a High-Resolution (HR) reference image (Ref). While existing RefSR methods focus on thermal or visible flows separately, they often struggle to enhance the resolution of small objects such as Mini/Micro UAVs (Unmanned Aerial Vehicle) due to the resolution disparities between the input and reference images. To cope with these challenges when dealing with UAV early detection in context of video surveillance, we propose ThermoVisSR, a multiscale texture transformer for enhancing the Super-Resolution (SR) of visible and thermal images of Mini/Micro UAVs. Our approach tries to reconstruct the fine details of these objects while preserving their approximation (the body form and color of the different scene objects) already contained in the LR image. Hence, our model is divided up into two streams dealing separately with approximation and detail reconstruction. In the first one, we introduce a Convolution Neural Network (CNN) fusion backbone to extract the Low-Frequency (LF) approximation from the original LR image pairs. In the second one and to extract the details from the Ref image, our approach involves blending features from both visible and thermal sources to make the most of what each offer. Subsequently, we introduce the High-Frequency Texture Transformer (HFTT) across various resolutions of the merged features to ensure an accurate correspondence matching and significant transfer of High-Frequency (HF) patches from Ref to LR images. Moreover, to adapt the injection to the different bands well, we incorporate the separable software decoder (SSD) into the HFTT allowing to capture channel-specific details during the reconstruction phase. We validated our approach using a newly created dataset of Air images of Mini/Micro UAVs. Experimental results demonstrate that the proposed model consistently outperforms the state-of-the-art approaches on both qualitative and quantitative assessments.

Low-frequency approximations to the finite-length Warburg diffusion impedance: The reflexive case

A study on the influence of the characteristic parameters of the finite-length diffusion processes on the galvanostatic dynamic response of electrochemical systems described by the reflexive Warburg impedance, is presented. The characteristic frequencies of the reflexive diffusion impedance, originally including those of the purely diffusive behaviour, are identified. The galvanostatic charge/discharge cycle is interpreted from the truncated series obtained from the development into partial fractions of the impedance. The low-frequency behaviour is also compared to the impedance obtained from the development into continued fractions with an only characteristic frequency. Interesting results associated to the transition between the capacitive and diffusive behaviours, emerge from the use of a hybrid methodology dealing with frequency and time domains. A simple electric circuit physically based on the series developments of the reflexive Warburg impedance with an only relaxation time, is used to interpret the galvanostatic charge curve of a commercial supercapacitor and to validate the theoretical study.

On the sound field of an oscillating elliptical disk in free space with an open and closed back.

An oscillating elliptical disk in free space has a uniform surface velocity distribution and is therefore a rigid sound radiator. The radiated sound also represents that scattered from a stationary disk in the presence of a normal plane wave. Using the Fourier (Hankel) Green's function in cylindrical coordinates, together with the monopole Kirchhoff-Helmholtz boundary integral, rigorous analytical formulas are derived for calculating the surface pressure distribution, radiation impedance, on-axis pressure, and, directivity pattern of an elliptical open-back disk in free space, and these are plotted over a range of normalized frequencies. The directivity is compared with that of a rigid circular disk in free space, and asymptotic low-frequency approximations are derived for the radiation impedance and on-axis pressure. Using the Gutin concept, the radiated sound is combined with that from a rigid elliptical disk in an infinite baffle to obtain the radiation impedance, on-axis pressure, and, directivity pattern of a closed-back elliptical disk in free space. The latter has a uniform velocity distribution on the front surface and zero velocity over the entire back surface.

Analysis and verification of vibration isolation performance of engine mount based on low-frequency approximation method

At present, most of the turbofan engine use the articulated link mount to connect the engine to the wing. The mechanical modeling, analysis and experimental research of articulated link mount are important means in the development of engine mount. In this paper, multibody dynamics method is used to establish the dynamic theory equation for a certain type of turbofan engine mount, and the low-frequency approximation method of the MNF file is proposed, which greatly improves the calculation speed on the basis of ensuring the calculation accuracy. In addition, a full-scale engine mounting system vibration isolation performance test platform was developed, and the vibration isolation efficiency of a certain type of engine mount at the high and low pressure rotor frequency was obtained. The results show that the simulation and test results agree well, the error is within 15% at the low-frequency, and 5% at the high-frequency. This work provides theoretical method and test evaluation means for the design and improvement of large passenger aircraft engine installation devices.

On the sound field of a resilient elliptical disk in an infinite baffle.

A resilient elliptical disk has zero mass and stiffness and is driven by a uniform pressure distribution rather than uniform velocity as would be the case for a rigid disk. It can represent the diffraction of a plane wave through an elliptical aperture in an infinite rigid screen of zero thickness as well as provide an idealized model of a loudspeaker of the electrostatic or planar magnetic type. Using the Fourier (Hankel) Green's function in cylindrical coordinates, together with the monopole Kirchhoff-Helmholtz boundary integral, rigorous analytical formulas are derived for calculating the surface velocity distribution, radiation admittance, on-axis pressure, and directivity pattern of an elliptical resilient disk in an infinite baffle and these are plotted over a range of normalized frequencies. The directivity is compared with that of a resilient circular disk and asymptotic low-frequency approximations are derived for the radiation resistance, reactance, and on-axis pressure.

Maxwell’s True Current

Maxwell defined a ‘true’ or ‘total’ current in a way not widely used today. He said that “… true electric current … is not the same thing as the current of conduction but that the time-variation of the electric displacement must be taken into account in estimating the total movement of electricity”. We show that the true or total current is a universal property of electrodynamics independent of the properties of matter. We use mathematics without the approximation of a dielectric constant. The resulting Maxwell current law is a generalization of the Kirchhoff law of current used in circuit analysis, that also includes the displacement current. The generalization is not a long-time low-frequency approximation in contrast to the traditional presentation of Kirchhoff’s law.

Mass-spring model for acoustic metamaterials consisting of a compact linear periodic array of dead-end resonators.

This paper presents a mass-spring model to predict the normal incidence acoustic response of a metamaterial composed of a compact linear periodic array of dead-end resonators. The dead-end resonators considered are ring-shaped Helmholtz resonators. The model is based on a mass-spring analogy and considers the thermoviscous losses in the metamaterial following an effective fluid approach. A matrix equation of acoustic motion is derived for the finite case of N-periodic arrays. Under external excitation, its direct solution predicts the sound absorption coefficient and transmission loss. Under the homogeneous case, the solution of its associated eigenvalue problem predicts the acoustic eigenfrequencies and mode shapes. The dispersion relation is also solved to predict the beginning of the first stopband, and a low frequency approximation allows development of a formula to estimate the first eigenfrequency. The results show that the system with N degrees of freedom has three stopbands over the frequency range studied, with zero sound absorption and transmission. The model also helps to understand how the acoustic dissipation, at a given resonant frequency, is affected by the position of the acoustic velocity nodes (eigenmodes) in the geometry of the metamaterial. Prototypes are designed, manufactured, and tested in an impedance tube to validate the model.

Effect of the Oersted field on the dynamics of magnetic drop solitons formed at a nanocontact

The magnon drop soliton is a non-topological structure formed at a nanocontact, and it is referred to as a dynamic soliton since it is stabilized by uniform precession of the magnetization. Because of magnetization precession there is a time dependent interaction between the magnetization and the magnetic field produced by the nanocontact current (referred to as the Oersted field). At a particular instant of precession the Oersted field forces the soliton off-center, but owing to precession this force will average to zero over one precession period. However, when the soliton orbits the nanocontact center at a period equal to the precession period, this force will become constant forcing the soliton off-center. This lowers the Oersted energy with an increase in the soliton orbital kinetic energy. A balance is attained with the soliton undergoing circular orbital motion about the nanocontact, and the orbit radius is determined by minimization of these energies. Previous low frequency approximations are used semi-analytically obtain these energies as well as the orbit radius.

Investigation of second-order low-frequency wave forces approximations for moored floating structures

Floating structures are widely used in both shallow and deep waters in industries such as offshore oil, gas, and wind. However, the safety of floating structures subject to long-crested irregular waves is threatened by slowly varying wave drift forces. In this study, the mesh-convergence laws for a panel model, which is used to calculate second-order potentials using a near-field approach, are investigated using a semi-submersible platform as an example. The effect of the relative-wave-height component of low-frequency (LF) wave forces is sensitive to the mesh near the waterline; therefore, it should be fully refined. The key difference-frequency band of the quadratic transfer function (QTF) matrix is investigated using time-domain-coupled dynamic analysis with a truncated QTF matrix. The results show that a difference-frequency limit of 0.4 rad/s is sufficient to calculate the slow drift and mooring tension. Based on prior approximations of the second-order LF wave force, a new hybrid approximation method is proposed. The discrepancies between the approximations and the full-QTF method are investigated in the time domain. This shows that the approximations are greatly affected by the water depth and the spectral peak period. This is because shallow-water mooring systems are more rigid than deep-water mooring systems; thus, the structural response is strongly dependent on a wider difference frequency and the off-diagonal elements in the QTF matrix (with a bigger difference frequency), which contain more errors. In approximations, the mooring-tension error is more sensitive to the water depth than the slow drift owing to the effects of heave and pitch. If the maximum values of the drift offset and mooring tension are considered, the approximation without the free-surface integral and the proposed “WN + Newman” hybrid approximation are recommended for use in shallow water.

Centrifugal instability in a weakly magnetized rotating plasma column

A two-fluid model is developed to study the stability of weakly magnetized rotating plasma columns. Previous works have shown that rotating plasma columns are prone to centrifugal flute modes. Most of these models are based on the low-frequency assumption which is valid when the instability frequency and the plasma azimuthal frequency are small compared with the ion cyclotron frequency. This assumption is challenged in many laboratory plasma devices, including weakly magnetized plasma columns. A radially global dispersion relation relaxing the low-frequency approximation and applicable in these devices is derived. The validity domain of the low-frequency approximation is discussed. In addition, the impact of the radial boundary on the linear stability is investigated and comparison with results obtained in the radially local approximation are performed.

Impact of combinations of time-delay interferometry channels on stochastic gravitational wave background detection

The method of time-delay interferometry (TDI) is proposed to cancel the laser noise in space-borne gravitational-wave detectors. Among all different TDI combinations, the most commonly used ones are the orthogonal channels A, E, and T, where A and E are signal-sensitive and T is signal-insensitive. Meanwhile, for the detection of stochastic gravitational-wave background, one needs to introduce the overlap reduction function to characterize the correlation between channels. For the calculation of overlap reduction function, it is often convenient to work in the low-frequency approximation, and assuming the equal-arm Michelson channels. However, if one wishes to work on the overlap reduction function of $\mathrm{A}/\mathrm{E}$ channels, then the low-frequency approximation fails. We derive the exact form of overlap reduction function for $\mathrm{A}/\mathrm{E}$ channels. Based on the overlap reduction function, we calculate the sensitivity curves of TianQin, TianQin $\mathrm{I}+\mathrm{II}$, and $\mathrm{TianQin}+\text{LISA}$. We conclude that the detection sensitivity calculated with $\mathrm{A}/\mathrm{E}$ channels is mostly consistent with that obtained from the equal-arm Michelson channels.

IVOMFuse: An image fusion method based on infrared-to-visible object mapping

Due to the significant difference in the structure of infrared and visible images, most of the existing algorithms use globally consistent strategy, which may weaken the contrast of the target region. To solve this problem, we propose an infrared and visible image fusion method based on infrared-to-visible object mapping (IVOMFuse) First of all, we use the probability induced intuitionistic fuzzy C-means algorithm (PIIFCM) to process the infrared image, and extract the target region of the infrared image according to the image structure features. However, because of the poor contrast of the target of the visible image, it can not be segmented directly. For this reason, we map the infrared target region to the visible image, and the target region with the same coordinates of the two images can be obtained very quickly. Secondly, due to the significant differences in image structure, we set a hybrid fusion strategies for different regions. We use the fusion strategy based on the Expectation-Maximization (EM) algorithm to iterate and optimize the probability model for the target region. The fourth-order partial differential equation (FPDE) is used for the background region to decompose the source image into high-frequency texture and low-frequency approximation images respectively. Then, the principal component analysis (PCA) and the average fusion strategy are used to obtain the fused image. Finally, we evaluated our algorithm with fourteen other state-of-the-art image fusion methods on three commonly used datasets, namely TNO, CVC14, and RoadScene. Among the ten evaluation metrics, our algorithm achieved the best six times.

A Low-Frequency Approximation PEEC Model for Thin-Wire Grounding Systems in Half-Space

This paper presents a PEEC model of thin-wire structures for lightning grounding analysis based on low-frequency approximation of dyadic Green's functions. To avoid the time-consuming numerical Sommerfeld integrals, the primary and quasi-dynamic terms are extracted from the spectral-domain Green's function and used as the low-frequency approximation closed-form of the full-wave solution, which is appropriate in the near-field region. The corresponding equivalent circuit is constructed with this closed-form approximated Green's function and the formulas for the partial inductance and coefficient of potential is given. Comparison in terms of the Green's function and circuit parameters between the proposed method and the conventional modified-image method is made. The validity of the proposed method is confirmed with experimental results gathered from published literature and MOM-calculated results from other researchers. A systematic parametric analysis is conducted to evaluate the accuracy and applicability of the different approximate models, which clearly shows the superiority of the proposed method over the traditional modified-image method.

Photon emission in the graphene under the action of a quasiconstant external electric field

Following a nonperturbative formulation of strong-field QED developed in our earlier works, and using the Dirac model of the graphene, we construct a reduced QED_{3,2} to describe one species of the Dirac fermions in the graphene interacting with an external electric field and photons. On this base, we consider the photon emission in this model and construct closed formulas for the total probabilities. Using the derived formulas, we study probabilities for the photon emission by an electron and for the photon emission accompanying the vacuum instability in the quasiconstant electric field that acts in the graphene plane during the time interval T. We study angular and polarization distribution of the emission as well as emission characteristics in a high frequency and low frequency approximations. We analyze the applicability of the presented calculations to the graphene physics in laboratory conditions. In fact, we are talking about a possible observation of the Schwinger effect in these conditions.

Long-Wave Anti-Plane Motion in a Pre-Stressed Compressible Elastic Laminate with One Fixed and One Free Face

In this paper, long-wave anti-plane shear motion in a multilayered laminate composed of pre-stressed compressible elastic layers is investigated. The layers of the laminate are perfectly bonded, while a fixed-free boundary condition is prescribed on the outer faces of the laminate. The solution of the model is determined analytically via the propagator matrix and numerically through the asymptotic approach. Moreover, the numerical results featuring harmonic curves are presented graphically, together with an asymptotic long-wave analysis of the vibration modes. As a special case of materials, linear isotropic with one shear modulus is considered. A polynomial long-wave low-frequency approximation of the related dispersion relation is also studied. It governs dispersion curves including the lowest harmonic. It is revealed that a low-frequency mode exists in both the two- and three-layered laminates, which are taken as prototypical structures. Lastly, comparisons between the exact and approximate asymptotic results are presented, and excellent agreement is observed.

Low-frequency amplification of propeller tonal noise due to the scattering by a compact rigid cylinder

The present work addresses the scattering of the tonal noise of a low-speed propeller by a rigid cylinder, as a generic configuration representative of installed marine propellers. Both propeller and cylinder axes are parallel to each other. The diameters of the propeller and of the cylinder are much smaller than the acoustic wavelengths, as well as the propeller-cylinder distance. This corresponds to a compact regime of diffraction. Only the hydrodynamic tonal noise of the propeller at the first multiples of the blade-passing frequency is considered, assuming rigid blades, in a two-dimensional formulation. The direct and scattered sound fields are expressed in terms of spinning modes, with respect to the propeller and cylinder axes, respectively. Use is made of the exact Green’s function of the cylinder for the Helmholtz equation. The modes of orders ±1 are found the only efficient ones in the direct field, whereas higher-order modes rapidly decay. Yet, in the presence of the cylinder, higher-order modes are scattered into the contra-rotating mode of order 1 in the reference frame of the cylinder, with a strong amplification. A simple experiment, performed in air but with Helmholtz numbers typical of marine applications, confirms these results as key features of the asymptotic Green’s function of the cylinder. The same modal behavior is reproduced as closed-form simple expressions from a low-frequency approximation of the Green’s function. The results show that the installation effect is crucial for the tonal noise of marine propellers at very low frequencies.

Excitation of a layered sphere by 𝑁 acoustic sources: Exact solutions, low-frequency approximations, and inverse problems

Acoustic excitation of a layered sphere by N N external and internal point sources is considered. The direct problem is solved by developing a T-Matrix method leading to the analytical determination of all the involved acoustic fields. Low-frequency far-field approximations are derived for different source distributions and scatterer’s characteristics. The behaviour of the scattering cross sections is investigated. Several inverse problems are formulated and solved analytically; thus the respective unknown quantities are recovered explicitly. These problems include localization of the sources, determination of their number, identification of the core’s type and extraction of the parameters of the scatterer’s layers.

An explicit predictor/multicorrector time marching with automatic adaptivity for finite-strain elastodynamics

We propose a time-adaptive predictor/multi-corrector method to solve hyperbolic partial differential equations, based on the generalized-α scheme that provides user-control on the numerical dissipation and second-order accuracy in time. Our time adaptivity uses an error estimation that exploits the recursive structure of the variable updates. The predictor/multicorrector method explicitly updates the equation system but computes the residual of the system implicitly. We analyze the method's stability and describe how to determine the parameters that ensure high-frequency dissipation and accurate low-frequency approximation. Subsequently, we solve a linear wave equation, followed by non-linear finite strain deformation problems with different boundary conditions. Thus, our method is a straightforward, stable and computationally efficient approach to simulate real-world engineering problems. Finally, to show the performance of our method, we provide several numerical examples in two and three dimensions. These challenging tests demonstrate that our predictor/multicorrector scheme dynamically adapts to sudden energy releases in the system, capturing impacts and boundary shocks. The method efficiently and stably solves dynamic equations with consistent and under-integrated mass matrices conserving the linear and angular momenta as well as the system's energy for long-integration times.

Low-frequency development approximations to the transmissive Warburg diffusion impedance

A study of the behaviour of the low-frequency development approximations to the transmissive Warburg diffusion impedance in both the frequency and time domains is presented. Simple low-frequency electric circuits have been derived from the Weierstrass products expansion and the equivalent ladder networks based on Foster, Maxwell and Cauer series. An original comparative study of the different low-frequency approximated impedances, including the characteristic frequencies, and those of the transmissive Warburg element is reported. The galvanostatic small-signal dynamic responses involving current steps and ramps have been compared by using exact numerical solutions and the approximated solutions at low frequencies derived from the different electric circuits. This study allows the dynamic response of electrochemical energy devices, such as fuel cells or rechargeable batteries, to be physically interpreted on the basis of an only relaxation time by means of the charging/discharging process of a capacitor through one or two resistors.