Acoustic wave equation

In physics, the acoustic wave equation governs the propagation of acoustic waves through a material medium resp. a standing wavefield. The form of the equation is a second order partial differential equation. The equation describes the evolution of acoustic pressure p or particle velocity u as a function of position x and time t. A simplified (scalar) form of the equation describes acoustic waves in only one spatial dimension, while a more general form describes waves in three dimensions. Propagating waves in a pre-defined direction can also be calculated using first order one-way wave equation. For lossy media, more intricate models need to be applied in order to take into account frequency-dependent attenuation and phase speed. Such models include acoustic wave equations that incorporate fractional derivative terms, see also the acoustic attenuation article or the survey paper. In one dimension Equation The wave equation desc

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Acoustique

L’acoustique est la science du son. La discipline a étendu son domaine à l'étude de toute onde mécanique dans tout fluide, où un ébranlement se propage presque exclusivement en onde longitudinale ;

Dynamique des fluides

La dynamique des fluides (hydrodynamique ou aérodynamique), est l'étude des mouvements des fluides, qu'ils soient liquides ou gazeux. Elle fait partie de la mécanique des fluides avec l'hydrostatiqu

Partial discharge localization in power transformers using acoustic time reversal

Florent Quentin Aviolat, Mohammad Azadifar, Hamidreza Karami, Marcos Rubinstein

The localization of partial discharges (PD) is important to monitor the conditioning of high voltage insulator materials. One of the key components in power grids is the high power transformer. Localization of PDs in these pieces of equipment can increase the reliability of power networks. One of the most commonly used methods to localize PDs is the time difference of arrival (TDoA) technique. Recently, time reversal (TR) techniques in the electromagnetic regime have been proposed to localize PD sources with a lower number of needed sensors compared to the TDoA technique. Contrary to TDoA, TR-based techniques do not need line-of-sight wave propagation from PD sources to the sensor(s). In this study, we extend the TR technique to localize PD sources in the acoustic regime for three-dimensional structures. Similar to the electromagnetic TR methods, a typical time reversal process includes three steps: 1) record the acoustic fields caused by a PD source using at least one sensor, 2) time reverse and back inject into the medium the recorded acoustic signal(s), 3) use a proper criterion to obtain the focusing point associated with the location of the PD source. The acoustic TR technique presented in this paper uses only one sensor. Numerical simulations are used to evaluate the performance of the acoustic TR technique for three-dimensional power transformer models. To do this, an open source MATLAB toolbox is used to solve the acoustic wave equation. The numerical results show that the TR technique can accurately localize the PD sources in three-dimensional power transformer models. Our analysis shows that the presence of windings inside the transformer tank does not degrade the efficiency of the acoustic TR technique.

Elsevier2022

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A mathematical and numerical framework for magnetoacoustic tomography with magnetic induction

Pierre Robert Maurice Millien

We provide a mathematical analysis and a numerical framework for magnetoacoustic tomography with magnetic induction. The imaging problem is to reconstruct the conductivity distribution of biological tissue from measurements of the Lorentz force induced tissue vibration. We begin with reconstructing from the acoustic measurements the divergence of the Lorentz force, which is acting as the source term in the acoustic wave equation. Then we recover the electric current density from the divergence of the Lorentz force. To solve the nonlinear inverse conductivity problem, we introduce an optimal control method for reconstructing the conductivity from the electric current density. We prove its convergence and stability. We also present a point fixed approach and prove its convergence to the true solution. A new direct reconstruction scheme involving a partial differential equation is then proposed based on viscosity-type regularization to a transport equation satisfied by the electric current density field. We prove that solving such an equation yields the true conductivity distribution as the regularization parameter approaches zero. Finally, we test the three schemes numerically in the presence of measurement noise, quantify their stability and resolution, and compare their performance. © 2015 Elsevier Inc.

Elsevier2015

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Deep-learning projector for optical diffraction tomography

Harshit Gupta, Thanh-An Michel Pham, Michaël Unser, Fangshu Yang

Optical diffraction tomography is an effective tool to estimate the refractive indices of unknown objects. It proceeds by solving an ill-posed inverse problem for which the wave equation governs the scattering events. The solution has traditionally been derived by the minimization of an objective function in which the data-fidelity term encourages measurement consistency while the regularization term enforces prior constraints. In this work, we propose to train a convolutional neural network (CNN) as the projector in a projected-gradient-descent method. We iteratively produce high-quality estimates and ensure measurement consistency, thus keeping the best of CNN-based and regularization-based worlds. Our experiments on two-dimensional-simulated and real data show an improvement over other conventional or deep-learning-based methods. Furthermore, our trained CNN projector is general enough to accommodate various forward models for the handling of multiple-scattering events. (C) 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

OPTICAL SOC AMER2020

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MICRO-426: Laser fundamentals and applications for engineers

The course will cover the fundamentals of lasers and focus on selected practical applications using lasers in engineering. The course is divided approximately as 1/3 theory and 2/3 covering selected applications.

PHYS-201(d): General physics: electromagnetism

The topics covered by the course are concepts of fluid mechanics, waves, and electromagnetism.

EE-348: Electroacoustics

Ce cours a pour objectif de former les étudiants de section Génie Electrique et Electronique à la conception de systèmes acoustiques, à l'aide d'un formalisme basé sur l'électrotechnique. A la fin du semestre, les étudiants seront capables de dimensionner, entre autres, des filtres acoustiques.