Sparse Plane Wave Approximation of Acoustic Modes to Address Basis Mismatch

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.

Wave packet approach to quantum correlations in neutrino oscillations

Quantum correlations provide a fertile testing ground for investigating fundamental aspects of quantum physics in various systems, especially in the case of relativistic (elementary) particle systems as neutrinos. In a recent paper, Ming et al. (Eur Phys J C 80:275, 2020), in connection with results of Daya-Bay and MINOS experiments, have studied the quantumness in neutrino oscillations in the framework of plane-wave approximation. We extend their treatment by adopting the wave packet approach that accounts for effects due to localization and decoherence. This leads to a better agreement with experimental results, in particular for the case of MINOS experiment.

Understanding the interaction of the fundamental Lamb-wave modes with material discontinuity: finite element analysis and experimental validation

The interaction of guided waves with a material discontinuity is not well understood. This study investigates the propagation behavior of the fundamental Lamb-wave modes, the symmetric mode ( S0) and the anti-symmetric mode ( A0), upon interaction with welded joints of dissimilar materials. A plate with an intact AA6061-T6/AZ31B dissimilar joint was employed, and the interaction of the propagating wave with the material interface was scrutinized numerically and validated experimentally. Plane-wave approximation was also adopted to investigate the behavior of the symmetric modes, and its performance was compared to the numerical and experimental results. The effect of the angle of incidence on the reflection, transmission, and mode conversion of the incident modes was analyzed. The study was conducted as the excited Lamb wave propagated from AA6061-T6 to AZ31B (forward), and when the propagation direction was reversed (backward). Different techniques were developed to identify the in-plane and out-of-plane modes from the three-dimensional measurements and to separate wave reflections and transmissions of the joint. The fundamental shear-horizontal guided-wave mode ( SH0 mode) has evolved upon the interaction of the obliquely-incident Lamb-wave S0 mode with the interface. While the reflection of the SH0 mode from the joint was found to be well-pronounced, its transmission to the other material is extremely weak. The analytical solution, using plane-wave approximation, was accurate for predicting the behavior of the in-plane modes ( S0 and S0– SH0 modes). Despite the peaks appearing at the critical angle, the absolute values of the reflection coefficients of the studied modes have shown similar trends between the forward and the backward propagation directions. The total reflection of the excited wave, from the material interface, was not observed in any condition. The transmission coefficients of the S0 and A0 modes are almost constant until reaching very steep incidence angles [Formula: see text]. The results were experimentally validated on an intact AA6061-T6/AZ31B friction-stir-welded joint using an excitation frequency of 200 kHz. Measurements along the transmission and reflection directions were conducted using a three-dimensional scanning laser vibrometer. Experimental results showed very good agreement with both the analytical and the numerical ones.

Post-processing of the plane-wave approximation of Schrödinger equations. Part II: Kohn–Sham models

In this article, we provide a priori estimates for a perturbation-based post-processing method of the plane-wave approximation of nonlinear Kohn–Sham local density approximation (LDA) models with pseudopotentials, relying on Cancès et al. (2020, Post-processing of the plane-wave approximation of Schrödinger equations. Part I: linear operators. IMA Journal of Numerical Analysis, draa044) for the proofs of such estimates in the case of linear Schrödinger equations. As in Cancès et al. (2016, A perturbation-method-based post-processing for the plane-wave discretization of Kohn–Sham models. J. Comput. Phys., 307, 446–459), where these a priori results were announced and tested numerically, we use a periodic setting and the problem is discretized with plane waves (Fourier series). This post-processing method consists of performing a full computation in a coarse plane-wave basis and then to compute corrections based on the first-order perturbation theory in a fine basis, which numerically only requires the computation of the residuals of the ground-state orbitals in the fine basis. We show that this procedure asymptotically improves the accuracy of two quantities of interest: the ground-state density matrix, i.e. the orthogonal projector on the lowest $N$ eigenvectors, and the ground-state energy.

A variant of the plane wave least squares method for the time-harmonic Maxwell’s equations

In this paper we are concerned with the plane wave method for the discretization of time-harmonic Maxwell’s equations in three dimensions. As pointed out in Hiptmair et al. (Math. Comput. 82 (2013) 247–268), it is difficult to derive a satisfactory L2 error estimate of the standard plane wave approximation of the time-harmonic Maxwell’s equations. We propose a variant of the plane wave least squares (PWLS) method and show that the new plane wave approximations yield the desired L2 error estimate. Moreover, the numerical results indicate that the new approximations have sightly smaller L2 errors than the standard plane wave approximations. More importantly, the results are derived for more general models in inhomogeneous media.

THERMAL EFFECTS IN THE EYE-SAFE RING OPTICAL PARAMETRIC OSCILLATOR BASED ON KTiOPO4 CRYSTALS

For an eye-safe optical parametric oscillator (OPO) built on the basis of a three-mirror ring cavity, each section of which (the space between adjacent plane mirrors) contains a x-cut KTiOPO4 (KТР) crystal having a size of 15(х) × 7(y) × 7(z) mm3, the thermal effects due to idler wave absorption in KTP crystals were investigated. These thermal effects were evaluated by means of experimental measurement of the change in the OPO performance (divergence of the output beam and pulse energy) when transferring the OPO from the mode of generation of occasional single pulses to the mo de of generation of periodically repetitive pulses. It was found when the eye-safe OPO pumped by multimode YAG: Nd laser radiation generates 8-ns pulses with a repetition rate of 10 Hz and an energy of 30–35 mJ, thermal distortions of KTP crystals placed in metal holders at their natural air-cooling, are moderate. The total effect of positive thermolenses induced in nonlinear crystals leads to an increase in the divergence of the beam of the eye-safe OPO by 10 % and to a decrease in the efficiency of the OPO by 0.76 %, by virtue of fact that the induced thermal lenses are not ideal and thereby introduce additional aberration losses into the OPO cavity. The theoretical simulation of the OPO operation in the plane-wave approximation with the use of a system of three coupled first-order abridged differential equations showed that among three KTP crystals the KTP crystal placed first in the path of pump radiation in the OPO is the largest thermal load and the action of the most intense beams.