# On the Self-Averaging of Wave Energy in Random Media

@article{Bal2004OnTS, title={On the Self-Averaging of Wave Energy in Random Media}, author={Guillaume Bal}, journal={Multiscale Model. Simul.}, year={2004}, volume={2}, pages={398-420} }

We consider the stabilization (self-averaging) and destabilization of the energy of waves propagating in random media. Propagation is modeled here by an Ito--Schrodinger equation. The explicit structure of the resulting transport equations for arbitrary statistical moments of the wave field is used to show that wave energy density may be stable in the high frequency regime, in the sense that it depends only on the statistics of the random medium and not on the specific realization. Stability is…

## 33 Citations

Self-averaging of kinetic models for waves in random media

- Physics
- 2007

Kinetic equations are often appropriate to model the energy density
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The limitations of the kinetic model are quantified by the…

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- Physics, MathematicsMultiscale Model. Simul.
- 2007

The Wigner transform of the wave field is used and it is shown that it becomes deterministic in the large diversity limit when integrated against test functions and also shows that the limit is deterministic when the support of the test functions tends to zero but is large compared to the correlation length.

Fourth-Moment Analysis for Wave Propagation in the White-Noise Paraxial Regime

- Physics
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In this paper we consider the Itô–Schrödinger model for wave propagation in random media in the paraxial regime. We solve the equation for the fourth-order moment of the field in the regime where the…

White-Noise Paraxial Approximation for a General Random Hyperbolic System

- MathematicsMultiscale Model. Simul.
- 2015

A general hyperbolic system subject to random perturbations which models wave propagation in random media and shows how to derive the system of Itoź--Schroźdinger equations driven by Brownian fields that govern the wave propagation.

Dynamics of Wave Scintillation in Random Media

- Mathematics
- 2010

This paper concerns the asymptotic structure of the scintillation function in the simplified setting of wave propagation modeled by an Itô–Schrödinger equation. We show that the size of the…

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- Computer Science, Physics
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It is shown that capturing macroscopic quantities of the wave field, such as the wave energy density, is achievable with much coarser discretizations, using a time splitting algorithm that solves separately and successively propagation and scattering in the simplified regime of the parabolic wave equation in a random medium.

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- Mathematics
- 2016

We consider wave propagation in random media in the paraxial regime. We show how to solve the equations for the secondand fourth-order moment of the field in the regime where the correlation length…

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- PhysicsProceedings of the International Congress of Mathematicians (ICM 2018)
- 2019

Wave propagation in random media can be studied by multiscale and stochastic analysis. We review some recent advances and their applications. In particular, in a physically relevant regime of…

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Single scattering estimates for the scintillation function of waves in random media

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- 2010

The energy density of high frequency waves propagating in highly oscillatory random media is well approximated by solutions of deterministic kinetic models. The scintillation function determines the…

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