Impedance Boundary Condition Research Articles

Shape reconstruction of a cavity with impedance boundary condition via the reciprocity gap method

We consider an interior inverse scattering problem of reconstructing the shape of a cavity with impedance boundary condition from measured Cauchy data of the total field. The incident point sources and the measurements are distributed on two different manifolds inside the cavity. We first prove that the boundary of the cavity and the surface impedance can be uniquely determined by the scattered field data on the measurement manifold. Then we develop a reciprocity gap (RG) method to reconstruct the cavity. The theoretical analysis shows the uniquely solvability and existence of the approximate solution for the linear integral equation constructed in the RG method. We also prove that the shape of the cavity can be characterized by the blow-up property of the approximate solution of the proposed integral equation. Numerical examples are presented to verify the feasibility of the RG method.

Mesh registration-based boundary element method of head-related transfer function: unification of hair impedance boundary conditions

In the calculation of Head-Related Transfer Functions (HRTFs) using the Boundary Element Method (BEM), the head surface of a subject needs to be discretized into boundary elements with specific impedance. To simplify HRTF calculation, a method for coupling Mesh Registration and BEM (MR-BEM) is proposed in this work, which means that a template mesh for calculation is established to register and generate the calculation mesh of a new head model, to replace the tedious operations of boundary conditions configuration. To validate the proposed method, the widely-used KEMAR artificial head model was adopted to compare the HRTFs of two groups of calculation meshes manually assigned and automatically registered impedance boundary conditions, respectively. Based on the inherent similarities in head shape and hair regions across individuals, the non-rigid impedance was set only for the hair region. Although the reflections from the non-rigid impedance of hair and clothes were shielded by pinnae in practice, this work just aims to validate the feasibility of the MR-BEM, which is significant for the simplification of BEM-based HRTF calculation.

Accurate computation of scattering poles of acoustic obstacles with impedance boundary conditions

We propose a computation method for scattering poles of impedance obstacles. Boundary integral equations are used to formulate the problem. It is shown that the scattering poles are the eigenvalues of some integral operator. Then we employ the Nyström method to discretize the integral operator and obtain a nonlinear matrix eigenvalue problem. The eigenvalues are computed using a multistep parallel spectral indicator method. Numerical examples demonstrate the high accuracy of the proposed method and can serve as the benchmarks. Our study provides a practical approach and can be extended to other scattering problems. This paper continues our previous study on the computation method for scattering poles of sound-soft obstacles.

Effect of Circadian Rhythm Modulated Blood Flow on Nanoparticle based Targeted Drug Delivery in Virtual In Vivo Arterial Geometries.

A novel integration of nanoparticle-based drug delivery framework with shear-rate dependent blood flow model is presented. The framework is comprised of a unique combination of mechanics-based dispersion model, an asperity model for endothelium surface roughness, and a stochastic nanoparticle-endothelial cell adhesion model. Simulations of MRI based in vivo carotid artery system showcase the effects of vessel geometry on nanoparticle adhesion and retention at the targeted site. Vessel geometry and target site location impact nanoparticle adhesion; curved and bifurcating regions favor local accumulation of drug. It is also shown that aligning drug administration with circadian rhythm and sleep cycle can enhance the efficacy of drug delivery processes. These simulations highlight the potential of the computational modeling for exploring circadian rhythm modulated blood flow for targeted drug delivery while minimizing the in vivo experimentation.

Rayleigh Waves Propagation in a Micropolar Viscothermoelastic Half-Space with Impedance Boundary Conditions

Rayleigh Waves Propagation in a Micropolar Viscothermoelastic Half-Space with Impedance Boundary Conditions

Resolvent Analysis for Subsonic Compressor With Impedance Boundary Condition Casing Treatment

Abstract A resolvent analysis framework for the axial compressor is established, and the impedance optimization is achieved based on the resolvent analysis framework for the impedance boundary condition casing treatment. This framework is derived by treating the nonlinearity in the perturbation equations as an unknown forcing, the linear relationship between wall impedance and energy gains is obtained. The validity of this framework is confirmed through experiments on rotating inlet distortion, which captures the most susceptible frequency for the stall points of the compressor. The resolvent analysis framework further confirms that the first-order circumferential mode exhibits the highest energy in the given cases. Subsequently, the proposed impedance optimization method is tested under throttling operating conditions, especially focusing on the first-order circumferential mode. The introduction of a favorable impedance boundary condition notably reduces energy gain within the low-order circumferential mode and in the range of the rotor rotating frequency, particularly in near-stall operating conditions. The energy suppression mechanism of the impedance boundary condition casing treatment is investigated, demonstrating that the impedance boundary condition, with an optimal impedance value, significantly suppresses perturbations compared to the case with the solid wall boundary condition. Lastly, a design method for the impedance boundary condition casing treatment is discussed, offering a reliable theoretical design tool for enhancing the stall margin of axial compressors.

Применение модифицированного метода дискретных источников в задаче дифракции импульсной волны на подповерхностном импедансном цилиндре

In contrast to the classical method of auxiliary sources (MAS) with the location of discrete sources (DS) on a closed additional contour, this article investigates the use of a complete system of functions for describing DS fields localized on an open curve in a modified MAS (MMAS). The MMAS was applied to solve a two-dimensional diffraction problem of a broadband electromagnetic impulse on an impedance cylinder located in free space and in the subsurface. The electric thread was a source of external current, excited by an impulse of 1.6 ns duration with a spectrum width from 122 MHz to 726 MHz (at the level of -6 dB). In various combinations, fresh water, thawed and frozen soil, air, and ice were used as the filling medium of the cylinder and the dielectric half-space. The complete system of functions for describing the fields of DS was constructed based on the Hankel functions of the first kind of zero order, the corresponding Green's function for the layered medium problem, and their derivatives in the direction of normal to the curve on which the DS was placed. When compared with the finite difference time domain method (FDTD), it is shown that the MMAS, using Leontovich impedance boundary conditions, can describe impulse fields, scattered by a dielectric cylinder with practically significant accuracy. It has been established that in the case of an elliptical cylinder, the MMAS requires approximately half as many auxiliary DSs compared to the classical MAS while achieving the same accuracy of the solution. In general, this article confirms the possibility of using a complete system of functions to describe the fields of DSs, localized on an open curve for the solving of impulse diffraction problems on subsurface impedance cylinders.

On plane wave scattering at the piezothermoelastic half-space with impedance boundary condition

On plane wave scattering at the piezothermoelastic half-space with impedance boundary condition

On the existence of Rayleigh waves with full impedance boundary condition

The existence of Rayleigh waves (propagating in isotropic elastic half-spaces) with the tangential and normal impedance boundary conditions was investigated. It has been shown that for the tangential impedance boundary condition (TIBC), there always exists a unique Rayleigh wave, while for the normal impedance boundary condition (NIBC), there exists a domain (of impedance and material parameters) in which exactly one Rayleigh wave is possible and outside this domain a Rayleigh wave is impossible. In this paper, we consider the existence of Rayleigh waves with the full impedance boundary condition (FIBC) that contains both TIBC and NIBC. It is shown that the existence picture of Rayleigh waves for this general case is more complicated. It contains domain for which exactly one Rayleigh wave exists, domain where a Rayleigh wave is impossible, and domain for which all three possibilities may occur: two Rayleigh waves exist, one Rayleigh wave exists, and no Rayleigh wave exists at all. The obtained existence results recover the existence results established previously for the cases of TIBC and NIBC. The formulas for the Rayleigh wave velocity are derived. As these formulas are totally explicit, they are very useful in various practical applications, especially in the non-destructive evaluation of the mechanical properties of structures. In order to establish the existence results and derive formulas for the Rayleigh wave velocity, the complex function method, which is based on the Cauchy-type integrals, is employed.

Evaluating impedance boundary conditions to model interfacial dynamics in acoustofluidics

We present a numerical study to investigate the efficacy of impedance boundary conditions in capturing the interfacial dynamics of a particle subjected to an acoustic field and study the concomitant time-averaged acoustic streaming and radiation force fields. While impedance boundary conditions have been utilized to represent fluid–solid interface in acoustofluidics, such models assume the solid material to be locally reactive to the acoustic waves. However, there is a limited understanding of when this assumption holds true, raising concerns about the suitability of impedance boundary conditions. Here, we systematically investigate the applicability of impedance boundary conditions by comparing the predictions of an impedance boundary approach against a fully coupled fluid–solid model. We contrast the oscillation profiles of the fluid–solid interface predicted by the two models. We consider different scatterer materials to identify the extent to which the differences in interfacial dynamics impact the time-averaged fields and highlight the divergence within the predictions of the two models. Our findings indicate that, although impedance boundary conditions can yield qualitatively similar results to the full model in certain situations, the predictions from the two models generally differ both qualitatively and quantitatively. These results underscore the importance of exercising caution when applying these boundary conditions to model general acoustofluidic systems.

RCS Estimation of Objects with Impedance Boundary Condition Using PO and ITD

RCS Estimation of Objects with Impedance Boundary Condition Using PO and ITD

Reconstructing the shape and material parameters of dissipative obstacles using an impedance model

In inverse scattering problems, a model that allows for the simultaneous recovery of both the domain shape and an impedance boundary condition covers a wide range of problems with impenetrable domains, including recovering the shape of sound-hard and sound-soft obstacles and obstacles with thin coatings. This work develops an optimization framework for recovering the shape and material parameters of a penetrable, dissipative obstacle in the multifrequency setting, using a constrained class of curvature-dependent impedance function models proposed by Antoine et al (2001 Asymptotic Anal. 26 257–83). We find that in certain regimes this constrained model improves the robustness of the recovery problem, compared to more general models, and provides meaningfully better obstacle recovery than simpler models. We explore the effectiveness of the model for varying levels of dissipation, for noise-corrupted data, and for limited aperture data in the numerical examples.

Bayesian Parameter Identification in Impedance Boundary Conditions for Helmholtz Problems

Bayesian Parameter Identification in Impedance Boundary Conditions for Helmholtz Problems

Analysis of two-dimensional planar gratings and metasurfaces in the quasi-static approximation

Currently, composite materials based on metal gratings with a period D much smaller than the wavelength l are widely used. With the use of such materials, it is possible to control the amplitude, phase and polarization of an electromagnetic wave, which opens wide possibilities for the creation of new types of antennas, radio-absorbing coatings, etc. This paper considers gratings of metallic strip or patches on the surface of a thin metal-backed dielectric slab to control the phase of the reflected wave. In the quasi-static approximation, the input impedance of such materials can be calculated using simple analytical formulas. This paper investigates the accuracy of the quasi-static approximation at different angles of incidence of the electromagnetic wave on two-dimensional gratings. Using the equivalent circuits method, analytical expressions for the input impedance of metasurfaces are obtained. The dispersion properties of composite materials “inductive or capacitive grating on the surface of a thin metal-backed dielectric slab” are investigated, and a technique for determining the resonant frequency, which corresponds to the maximum of the input impedance of the metasurface, is presented. The obtained results show that at any angle of incidence, it is possible to evaluate the condition of the quasi-static approximation applicability for two-dimensional gratings and for metasurfaces based on such gratings. If this condition is satisfied, that simple analytical expressions can be used to calculate the input impedance. The use of these expressions allows us to determine the frequency at which the input impedance reaches its maximum. It is established that for inductive and capacitive gratings the impedance boundary condition of M.A. Leontovich is equivalent to the averaged boundary condition of M.I. Kontorovich. It is obtained that for grating in free space, quasi-static approximation corresponds to the M.A. Leontovich impedance condition. The dispersion properties of composite materials “inductive or capacitive grating on a thin metal-backed dielectric slab” are investigated. It is shown that the phase transition of the reflection coefficient through zero occurs at maximum values of the input impedance. Using the considered method of equivalent circuits, the presented results can be easily generalized to any type of multilayer metasurfaces.

Longitudinal plane wave amplitude in N-type semiconductors with inviscid liquid loading and impedance boundary

The present analytical investigation focuses on longitudinal quasi-plane (qP) waves scattering in N-type piezoelectric semiconductor (PSC) halfspace, generating four reflected waves: qP, qSV, electro-acoustic, and carrier plane. It analyzes wave amplitudes under two conditions: inviscid liquid loading and impedance boundary conditions, deriving a secular equation and determining reflection/transmission coefficients. These calculations rely on 3D constitutive relations and equilibrium equations. Furthermore, the study also extends to the calculation of bulk energy flux. The outcomes of the study may provide insights into the applications of piezoelectric semiconductors in underwater navigation or detection systems and electromagnetic transducers.

Heuristic solution to the problem of diffraction of a TE-polarized electromagnetic field on a half-plane with generalized two-sided impedance boundary conditions

Employing the method of fundamental components, heuristic formulas are constructed for solving the problem of diffraction on a half-plane with non-ideal boundary conditions. The problem of diffraction of a TE-polarized wave on a half-plane with generalized two-sided impedance boundary conditions was chosen as a verification solution. The accuracy was increased by two types of adjustment functions. The effectiveness of the applied technique is proven by quantification of accuracy. This approach represents a new way to obtain high-accuracy heuristic formulas and allows one to create solvers that simultaneously have both high accuracy and high performance. The main result is the development and description of adjustment methods for increasing the accuracy of heuristic formulas.

Non-linear impedance boundary condition from linear piecewise B-H curve applied to induction heating systems

Purpose This paper aims to apply the non-linear impedance boundary condition (IBC) for a linear piecewise B–H curve in frequency domain simulations to find the equivalent impedance of a simple induction heating system model. Design/methodology/approach An electromagnetic description of the inductor system is performed to substitute the effects of the induction load, for a mathematical condition, the so-called IBC. This is suitable to be used in electromagnetic systems involving high conductive materials at medium frequencies, as it occurs in an induction heating system. Findings A reduction of the computational cost of electromagnetic simulation through the application of the IBC. The model based on linear piecewise B–H curve simplifies the electromagnetic description, and it can facilitate the identification of the induction load characteristics from experimental measurements. Practical implications This work is performed to assess the feasibility of using the non-linear boundary impedance condition of materials with linear piecewise B–H curve to simulate in the frequency domain with a reduced computational cost compared to time domain simulations. Originality/value In this paper, the use of the non-linear boundary impedance condition to describe materials with B–H curve by segments, which can approximate any dependence without hysteresis, has been studied. The results are compared with computationally more expensive time domain simulations.

Numerical Calculation and Direct Measurement of Local Hot Spot Temperatures in Transformer Clamping Plates

A verified multiphysics model is developed to simulate local hot spot temperatures in clamping structures. Stray field losses in clamping plates are obtained with the use of nonlinear impedance boundary condition through finite element method (FEM) while hot spot temperatures are simulated with the use of computational fluid dynamics (CFD). This multiphysics coupling is validated through direct measurements of local hot spot temperatures that were carried out with fiber optic temperature probes in real transformer. The local hot spot temperatures obtained with the simulations were in good agreement with the measured values, thus verifying overall approach and indirectly the calculation of local stray field losses.

On the Regularity of Time-Harmonic Maxwell Equations with Impedance Boundary Conditions

On the Regularity of Time-Harmonic Maxwell Equations with Impedance Boundary Conditions

Optimizing the noise control in a two-layer conduit

In the modern world, noise pollution is a major concern due to its prevalence. This work focuses on optimizing noise control in a two-layer conduit. A conduit comprises an inlet and double-outlet zones (DOZ). The upper walls of the DOZ are lined with perforated absorbent material while the lower walls are layered with fibrous. Mathematically, the physical problem is formulated with a field wave equation together with rigid and impedance boundary conditions in the respective zones. Such governing boundary value problem (BVP) leads to the Sturm-Liouville (SL) category in which standard orthogonality relations (OR) are indispensable. The system of the linear equations of the BVP is acquired with semi-analytical Mode-Matching (MM) approach by implementing the continuity conditions of sound pressures and velocities at the matching junction with the aid of OR. These systems are truncated and solved numerically with computation learning to obtain the reflected and transmitted modal amplitudes in respective zones. Due to the lining's perforated upper walls, fibrous lower walls, and reversal in the DOZ, the analysis of the reflected and transmitted powers versus frequencies is significantly observed and is shown in graphical findings. The algebraic derivation is validated by satisfying the conservation law of power flux and matching continuity conditions for impedance, perforated, and fibrous lined boundaries.