# Self-averaging of kinetic models for waves in random media

@article{Bal2007SelfaveragingOK,
title={Self-averaging of kinetic models for waves in random media},
author={Guillaume Bal and Olivier Pinaud},
journal={Kinetic and Related Models},
year={2007},
volume={1},
pages={85-100}
}
• Published 25 November 2007
• Physics
• Kinetic and Related Models
Kinetic equations are often appropriate to model the energy density of high frequency waves propagating in highly heterogeneous media. The limitations of the kinetic model are quantified by the statistical instability of the wave energy density, i.e., by its sensitivity to changes in the realization of the underlying heterogeneous medium modeled as a random medium. In the simplified Ito-Schrodinger regime of wave propagation, we obtain optimal estimates for the statistical…
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## References

SHOWING 1-10 OF 27 REFERENCES
On the Self-Averaging of Wave Energy in Random Media
• G. Bal
• Mathematics
Multiscale Model. Simul.
• 2004
It is shown that wave energy is not stable, and instead scintillation is created by the wave dynamics, when the initial energy distribution is sufficiently singular.
Kinetic Models for Imaging in Random Media
• Physics
Multiscale Model. Simul.
• 2007
This work quantifies the influence of small objects on (i) the energy density measured at an array of detectors and (ii) the correlation between the wave field measured in the absence of the object and theWave field measuredIn the presence of the objects.
Self-Averaging from Lateral Diversity in the Itô-Schrödinger Equation
• Physics, Mathematics
Multiscale 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.
Parabolic and Gaussian White Noise Approximation for Wave Propagation in Random Media
• Mathematics
SIAM J. Appl. Math.
• 1996
The parabolic or forward scattering approximation has been used extensively in the study of wave propagation and the validity of this approximation is proved for stratified weakly fluctuating random media in the high-frequencies regime.
SELF-AVERAGING IN TIME REVERSAL FOR THE PARABOLIC WAVE EQUATION
• Mathematics
• 2002
We analyze the self-averaging properties of time-reversed solutions of the paraxial wave equation with random coefficients, which we take to be Markovian in the direction of propagation. This allows
Self-Averaging of Wigner Transforms in Random Media
• Mathematics
• 2003
AbstractWe establish the self-averaging properties of the Wigner transform of a mixture of states in the regime when the correlation length of the random medium is much longer than the wave length
Kinetic Limit for Wave Propagation in a Random Medium
• Mathematics
• 2006
We study crystal dynamics in the harmonic approximation. The atomic masses are weakly disordered, in the sense that their deviation from uniformity is of the order $$\sqrt{\epsilon}$$. The dispersion