Related papers: A posteriori error estimates for Webster's equatio…
Gravitational-wave astronomers often wish to characterize the expected parameter-estimation accuracy of future observations. The Fisher matrix provides a lower bound on the spread of the maximum-likelihood estimator across noise…
We propose a mathematical formalisation of the ``wave model'' originally developed in historical linguistics but with further applications in human sciences. This model assumes new traits appear in a population and spread to nearby…
We interpret the forward Maxwell equation with up to third order induced polarizations and get so called nonlinear wave equation in frequency domain (NWEF), which is based on Maxwell wave equation and using slowly varying spectral amplitude…
In a posteriori error analysis, the relationship between error and estimator is usually spoiled by so-called oscillation terms, which cannot be bounded by the error. In order to remedy, we devise a new approach where the oscillation has the…
The distributions of the angular transmission coefficient and of the total transmission are calculated for multiple scattered waves. The calculation is based on a mapping to the distribution of eigenvalues of the transmission matrix. The…
For over 70 years it has been assumed that scalar wave propagation in (ensemble-averaged) random particulate materials can be characterised by a single effective wavenumber. Here, however, we show that there exist many effective…
This expository note gives a digest version of Hormander's propagation of singularities theorem for the wave equation.
Recently, the Wasserstein loss function has been proven to be effective when applied to deterministic full-waveform inversion (FWI) problems. We consider the application of this loss function in Bayesian FWI so that the uncertainty can be…
We describe a novel approach for computing wave correlation functions inside finite spatial domains driven by complex and statistical sources. By exploiting semiclassical approximations, we provide explicit algorithms to calculate the local…
We derive a posteriori error estimators for an optimal control problem governed by a convection-reaction-diffusion equation; control constraints are also considered. We consider a family of low-order stabilized finite element methods to…
A theory of the propagation of acoustic waves in a porous medium filled with superfluid solution is developed. The elastic coefficients in the system of equations are expressed in terms of physically measurable quantities. The equations…
Motivated by stochastic convection-diffusion problems we derive a posteriori error estimates for non-stationary non-linear convection-diffusion equations acting as a deterministic paradigm. The problem considered here neither fits into the…
We discuss the generalisation of the so-called traditional approximation, well known in geophysics, to general relativity. We show that the approximation is applicable for rotating relativistic stars provided that one focuses on relatively…
The probability distribution of the total transmission is studied for waves multiple scattered from a random, static configuration of scatterers. A theoretical study of the second and third cumulant of this distribution is presented. Within…
We study long range propagation of electromagnetic waves in random waveguides with rectangular cross-section and perfectly conducting boundaries. The waveguide is filled with an isotropic linear dielectric material, with randomly…
The propagation of high-frequency gravitational waves can be analyzed using the geometrical optics approximation. In the case of large but finite frequencies, the geometrical optics approximation is no longer accurate, and…
A posteriori estimates for mixed finite element discretizations of the Navier-Stokes equations are derived. We show that the task of estimating the error in the evolutionary Navier-Stokes equations can be reduced to the estimation of the…
The propagation of terahertz waves in a dust acoustic wave is investigated numerically. By assuming a sinus profile of the dust number density in the dust acoustic waves, the transmission properties are calculated using finite difference…
We propose a new technique for a-posteriori diffusion analysis of numerical schemes. The scalar linear advection equation with a broadband signal as initial conditions is numerically solved to simulate a traveling linear wave. A diffusion…
An averaging method is applied to derive effective approximation to the following singularly perturbed nonlinear stochastic damped wave equation \nu u_{tt}+u_t=\D u+f(u)+\nu^\alpha\dot{W} on an open bounded domain $D\subset\R^n$\,, $1\leq…