Related papers: A posteriori error estimates for Webster's equatio…
The diffusive viscous wave equation describes wave propagation in diffusive and viscous media. Examples include seismic waves traveling through the Earth's crust, taking into account of both the elastic properties of rocks and the…
The Gaussian theory of errors has been generalized to situations, where the Gaussian distribution and, hence, the Gaussian rules of error propagation are inadequate. The generalizations are based on Bayes' theorem and a suitable measure.…
This work studies a posteriori error estimates and their use for time-dependent acoustic scattering problems, formulated as a time-dependent boundary integral equation based on a single-layer ansatz. The integral equation is discretized by…
Acoustic wave propagation in a one-dimensional waveguide connected with Helmholtz resonators is studied numerically. Finite amplitude waves and viscous boundary layers are considered. The model consists of two coupled evolution equations: a…
In order to improve the frequency dispersion effects of irrotational shallow water models in coastal oceanography, several full dispersion versions of classical models were formally derived in the literature. The idea, coming from G.…
We describe propagation of torsional elastic waves in cylindrical waveguide with wedge dislocation in the framework of geometric theory of defects. The defect changes the dispersion relation. For positive deficit angles, it increases the…
The mechanism of acoustic wave propagation in supercooled liquids is not yet fully understood since the vibrational dynamics of supercooled liquids are strongly affected by their amorphous inherent structures. In this paper, the acoustic…
We compare two high order finite-difference methods that solve the elastic wave equation in two dimensional domains with curved boundaries and material discontinuities. Two numerical experiments are designed with focus on wave boundary…
The procedure of evaluating of the spectrum for discrete periodic operators perturbed by operators of smaller dimensions is obtained. This result allows to obtain propagative, guided, localised spectra for different kind of physical…
We postulate that validity of the Backus (1962) average, whose weights are layer thicknesses, is limited to waves whose incidence is nearly vertical. The accuracy of this average decreases with the increase of the source-receiver offset.…
Westervelt's equation is a nonlinear wave equation that is widely used to model the propagation of sound waves in a compressible medium, with one important application being ultra-sound in human tissue. Two fundamental aspects of this…
Some iterative techniques are defined to solve reversible inverse problems and a common formulation is explained. Numerical improvements are suggested and tests validate the methods.
In this paper we propose an objective Bayesian estimation approach for the parameters of the generalized gamma distribution. Various reference priors are obtained, but showing that they lead to improper posterior distributions. We overcome…
In this paper we show a general Strichartz estimate for certain perturbed wave equation, and here we can drop the nontrapping hypothesis and handle trapping obstacles with some loss of derivatives for data in the local energy decay…
We consider an undetermined coefficient inverse problem for a nonlinear partial differential equation describing high intensity ultrasound propagation as widely used in medical imaging and therapy. The usual nonlinear term in the standard…
The problem of propagating nonlinear acoustic waves is considered; the solution to which, both with and without damping, having been obtained to-date starting from the Navier-Stokes-Duhem equations together with the continuity and thermal…
We study the propagation of acoustic waves in a fluid that is contained in a thin two-dimensional tube, and that it is moving with a velocity profile that only depends on the transversal coordinate of the tube. The governing equations are…
A modelling of low-frequency sound propagation in slowly varying ducts with smoothly varying lining is proposed leading to an acoustic mild-slope equation analogue to the with mild-slope equation for water waves. This simple 1D Mild Slope…
In this paper we consider a sub-diffusion problem where the fractional time derivative is approximated either by the L1 scheme or by Convolution Quadrature. We propose new interpretations of the numerical schemes which lead to a posteriori…
We study a linear model for the propagation of hydro-acoustic waves and tsunami in a stratified free-surface ocean. A formulation was previously obtained by linearizing the compressible Euler equations. The new formulation is obtained by…