scholarly journals Low Frequency Sound Field Reproduction within a Cylindrical Cavity Using Higher Order Ambisonics

2018 ◽  
Vol 36 (4) ◽  
pp. 649-655
Author(s):  
Yan Wang ◽  
Kean Chen ◽  
Jian Xu
Keyword(s):  
Green Function ◽  
Spherical Harmonics ◽  
Cylindrical Cavity ◽  
Microphone Array ◽  
Low Frequency ◽  
Sound Field ◽  
High Order ◽  
Acoustic Modes ◽  
The Green Function ◽  
Order Components

Sound field reproduction of the aircraft and submarine within a cabin mock-up using a loudspeaker array is of great importance to the active noise control technology.The conventional method is to calculate the driving functions of the secondary sources by solving an acoustic inverse problem in a least square sense, which requires a large number of microphones and only the sound field near the microphone array can be reproduced accurately.In order to overcome these drawbacks, higher order ambisonics (HOA) method which is widely used in spatial sound field synthesis for a large room is introduced to reproduce a low frequency sound field within a cylindrical cavity.Due to the different sound propagation characteristics within the cavity compared with a free field and a diffuse field, the Green function spectrum in spherical harmonics domain which is modeled as a superposition of the acoustic modes and the reproduction formulas are deduced.Reproduction characteristics are investigated by numerical simulations.Results show that for a small, the Green function spectrum in spherical harmonics domain is mainly concentrated on low orders and contributed by the low order acoustic modes, with the increase of, high order components of the Green function arise and the contributions of high order acoustic modes increase.In the reproduction process, the high order components of the pressure spectrum over the sphere in harmonics domain will be greatly amplified by the reproduction filter.Finally, HOA method is compared with the acoustic inversion method in terms of the microphone array system, the impact factors on the reproductions and the reproduction accuracy, and validated through experiments.Results show that HOA can better reproduce the entire sound field within the cylindrical cavity and the reproduction accuracy is improved.

Wave propagation for the compressible Navier–Stokes equations

2015 ◽  
Vol 12 (02) ◽  
pp. 385-445 ◽  
Author(s):  
Tai-Ping Liu ◽  
Se Eun Noh
Keyword(s):  
Green Function ◽  
Stokes Equations ◽  
Low Frequency ◽  
Explicit Construction ◽  
Large Time Behavior ◽  
Energy Estimates ◽  
Navier Stokes ◽  
Time Behavior ◽  
Navier Stokes Equations ◽  
The Green Function

We establish the pointwise description of solutions to the isentropic Navier–Stokes equations for compressible fluids in three spatial dimensions. First, we give an explicit construction of the Green function for the linearized system. The Green function consists of singular waves, which dominate the short-time behavior, while the low frequency waves, the dissipative Huygens, diffusion and Riesz waves representing the large-time behavior. The nonlinear terms are treated by a suitable combination of energy estimates and pointwise estimates using the Duhamel's principle for the Green function.

scholarly journals Sparse Plane Wave Approximation of Acoustic Modes to Address Basis Mismatch

2022 ◽  
Vol 12 (2) ◽  
pp. 837
Author(s):  
Jian Xu ◽  
Kean Chen ◽  
Lei Wang ◽  
Jiangong Zhang
Keyword(s):  
Plane Wave ◽  
Bayesian Learning ◽  
Computational Cost ◽  
Low Frequency ◽  
Sound Field ◽  
Approximation Accuracy ◽  
Acoustic Modes ◽  
Wave Approximation ◽  
Basis Mismatch ◽  
Plane Wave Approximation

Low-frequency sound field reconstruction in an enclosed space has many applications where the plane wave approximation of acoustic modes plays a crucial role. However, the basis mismatch of the plane wave directions degrades the approximation accuracy. In this study, a two-stage method combining ℓ1-norm relaxation and parametric sparse Bayesian learning is proposed to address this problem. This method involves selecting sparse dominant plane wave directions from pre-discretized directions and constructing a parameterized dictionary of low dimensionality. This dictionary is used to re-estimate the plane wave complex amplitudes and directions based on the sparse Bayesian framework using the variational Bayesian expectation and maximization method. Numerical simulations show that the proposed method can efficiently optimize the plane wave directions to reduce the basis mismatch and improve acoustic mode approximation accuracy. The proposed method involves slightly increased computational cost but obtains a higher reconstruction accuracy at extrapolated field points and is more robust under low signal-to-noise ratios compared with conventional methods.

scholarly journals Spectra of Collective Excitations and Low-Frequency Asymptotics of Green’s Functions in Uniaxial and Biaxial Ferrimagnetics

2019 ◽  
Keyword(s):  
Asymptotic Behavior ◽  
Green Function ◽  
Wave Vector ◽  
Easy Axis ◽  
Green’S Functions ◽  
Low Frequency ◽  
Easy Plane ◽  
Collective Excitations ◽  
Green Functions ◽  
The Green Function

The paper studies the dynamic description of uniaxial and biaxial ferrimagnetics with spin s=1/2 in alternative external field. The nonlinear dynamic equations with sources are obtained, on basis on which low-frequency asymptotics of two-time Green functions in the uniaxial and biaxial cases of the ferrimagnet are obtained. Energy models are constructed that are specific functions of Casimir invariants of the algebra of Poisson brackets for magnetic degrees of freedom. On their basis, the question of the stable magnetic states has been solved for the considered systems. These equations were linearized, an explicit form of the collective excitations spectra was found, and their character was analyzed. The article studies the uniaxial case of a ferrimagnet, as well as biaxial cases of an antiferromagnet, easy-axis and easy-plane ferrimagnets. It is shown that for a uniaxial antiferromagnet the spectrum of magnetic excitations has a Goldstone character. For biaxial ferrimagnetic materials, it was found that the spectrum has either a quadratic character or a more complex dependence on the wave vector. It is shown that in the uniaxial case of an antiferromagnet the Green function of the type Gsα,sβ(k,0), Gsα,nβ(k,0) and Gsα,sβ(0,ω) have regular asymptotic behavior, and the Green function of type Gnα,nβ(k,0)≈1/k2 and Gsα,nβ(0,ω)≈1/ω, Gnα,nβ(0,ω)≈1/ω2 have a pole feature in the wave vector and frequency. Biaxial ferrimagnetic states have another type of the features of low-frequency asymptotics of the Green's functions. In the case of a ferrimagnet, the “easy-axis” of the asymptotic behavior of the Green functions Gsα,sβ(0,ω), Gsα,nβ(0,ω), Gnα,nβ(0,ω), Gsα,sβ(k,0), Gsα,nβ(k,0), Gnα,nβ(k,0) have a pole character. For the case of the “easy-plane” type ferrimagnet, the asymptotics of the Green functions Gsα,nβ(0,ω), Gnα,nβ(0,ω), Gsα,nβ(k,0), Gnα,nβ(k,0), have a pole character, and the Green function Gsα,sβ(k,ω) contains both the pole component and the regular part. A comparative analysis of the low-frequency asymptotics of Green functions shows that the nature of magnetic anisotropy significantly effects the structure of low-frequency asymptotics for uniaxial and biaxial cases of ferrimagnet. Separately, we note the non-Bogolyubov character of the Green function asymptotics for ferrimagnet with biaxial anisotropy Gnα,nβ(k,0)≈1/k4.

Exponentially Convergent Approximation to the Elliptic Solution Operator

2006 ◽  
Vol 6 (4) ◽  
pp. 386-404 ◽  
Author(s):  
Ivan. P. Gavrilyuk ◽  
V.L. Makarov ◽  
V.B. Vasylyk
Keyword(s):  
Green Function ◽  
Boundary Value Problem ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Solution Operator ◽  
Hyperbolic Operator ◽  
Elliptic Solution ◽  
Elliptic Boundary Value ◽  
Sine Family ◽  
The Green Function

AbstractWe develop an accurate approximation of the normalized hyperbolic operator sine family generated by a strongly positive operator A in a Banach space X which represents the solution operator for the elliptic boundary value problem. The solution of the corresponding inhomogeneous boundary value problem is found through the solution operator and the Green function. Starting with the Dunford — Cauchy representation for the normalized hyperbolic operator sine family and for the Green function, we then discretize the integrals involved by the exponentially convergent Sinc quadratures involving a short sum of resolvents of A. Our algorithm inherits a two-level parallelism with respect to both the computation of resolvents and the treatment of different values of the spatial variable x ∈ [0, 1].

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