Displaying similar documents to “Multiscale analysis of wave propagation in random media. Application to correlation-based imaging”

Multi-scaled diffusion-approximation. Applications to wave propagation in random media.

Josselin Garnier (2010)

ESAIM: Probability and Statistics

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In this paper a multi-scaled diffusion-approximation theorem is proved so as to unify various applications in wave propagation in random media: transmission of optical modes through random planar waveguides; time delay in scattering for the linear wave equation; decay of the transmission coefficient for large lengths with fixed output and phase difference in weakly nonlinear random media.

Time splitting for wave equations in random media

Guillaume Bal, Lenya Ryzhik (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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Numerical simulation of high frequency waves in highly heterogeneous media is a challenging problem. Resolving the fine structure of the wave field typically requires extremely small time steps and spatial meshes. We show that capturing macroscopic quantities of the wave field, such as the wave energy density, is achievable with much coarser discretizations. We obtain such a result using a time splitting algorithm that solves separately and successively propagation and scattering...

Time splitting for wave equations in random media

Guillaume Bal, Lenya Ryzhik (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Numerical simulation of high frequency waves in highly heterogeneous media is a challenging problem. Resolving the fine structure of the wave field typically requires extremely small time steps and spatial meshes. We show that capturing macroscopic quantities of the wave field, such as the wave energy density, is achievable with much coarser discretizations. We obtain such a result using a time splitting algorithm that solves separately and successively propagation and scattering in...

Scattering Matrix for the Reflection-Transmission Problem in a Viscoelastic Medium

Alessia Berti (2007)

Bollettino dell'Unione Matematica Italiana

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The reflection-transmission problem of time-harmonic waves in a viscoelastic, anisotropic and stratified solid is examined. The medium is supposed to occupy the whole space. The waves are sent either from upwards or downwards with oblique incidence. The scattering matrix is defined by generalizing the procedure followed in the scalar case, namely, when the solid is isotropic and the wave incidence is normal. Existence, uniqueness and properties of the scattering matrix are discussed. ...

Wave Operators for Defocusing Matrix Zakharov-Shabat Systems with Pnonvanishing at Infinity

Demontis, Francesco, der Mee, Cornelis van (2010)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: Primary: 34L25; secondary: 47A40, 81Q10. In this article we prove that the wave operators describing the direct scattering of the defocusing matrix Zakharov-Shabat system with potentials having distinct nonzero values with the same modulus at ± ∞ exist, are asymptotically complete, and lead to a unitary scattering operator. We also prove that the free Hamiltonian operator is absolutely continuous.

Identification of Green’s Functions Singularities by Cross Correlation of Ambient Noise Signals

Josselin Garnier (2011-2012)

Séminaire Laurent Schwartz — EDP et applications

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In this paper we consider the problem of estimating the singular support of the Green’s function of the wave equation by using ambient noise signals recorded by passive sensors. We assume that noise sources emit stationary random signals into the medium which are recorded by sensors. We explain how the cross correlation of the signals recorded by two sensors is related to the Green’s function between the sensors. By looking at the singular support of the cross correlation we can obtain...

Invisible obstacles

A. G. Ramm (2007)

Annales Polonici Mathematici

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It is proved that one can choose a control function on an arbitrarilly small open subset of the boundary of an obstacle so that the total radiation from this obstacle for a fixed direction of the incident plane wave and for a fixed wave number will be as small as one wishes. The obstacle is called "invisible" in this case.

Scattering theory for a nonlinear system of wave equations with critical growth

Changxing Miao, Youbin Zhu (2006)

Colloquium Mathematicae

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We consider scattering properties of the critical nonlinear system of wave equations with Hamilton structure ⎧uₜₜ - Δu = -F₁(|u|²,|v|²)u, ⎨ ⎩vₜₜ - Δv = -F₂(|u|²,|v|²)v, for which there exists a function F(λ,μ) such that ∂F(λ,μ)/∂λ = F₁(λ,μ), ∂F(λ,μ)/∂μ = F₂(λ,μ). By using the energy-conservation law over the exterior of a truncated forward light cone and a dilation identity, we get a decay estimate for...