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

@article{Bal2010SingleSE,
  title={Single scattering estimates for the scintillation function of waves in random media},
  author={Guillaume Bal and Ian Langmore and Olivier Pinaud},
  journal={Journal of Mathematical Physics},
  year={2010},
  volume={51},
  pages={022903}
}
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 statistical instability of the kinetic solution. This paper analyzes the single scattering term in the scintillation function. This is the term of the scintillation function that is linear in the power spectrum of the random fluctuations. We show that the structure of the scintillation function is… 
Analysis of the Double Scattering Scintillation of Waves in Random Media
High frequency waves propagating in highly oscillatory media are often modeled by radiative transfer equations that describes the propagation of the energy density of the waves. When the medium is
IMAGING USING TRANSPORT MODELS FOR WAVE–WAVE CORRELATIONS
We consider the imaging of objects buried in unknown heterogeneous media. The medium is probed by using classical (e.g. acoustic or electromagnetic) waves. When heterogeneities in the medium become
On the stability of some imaging functionals
This work is devoted to the stability/resolution analysis of several imaging functionals in complex environments. We consider both linear functionals in the wavefield as well as quadratic functionals
Uncertainty Modeling and Propagation in Linear Kinetic Equations
This paper reviews recent work in two complementary aspects of uncertainty quantification of linear kinetic models. First, we review the modeling of uncertainties in linear kinetic equations as high
A Complete Bibliography of Publications in the Journal of Mathematical Physics: 2005{2009
(2 < p < 4) [200]. (Uq(∫u(1, 1)), oq1/2(2n)) [92]. 1 [273, 79, 304, 119]. 1 + 1 [252]. 2 [352, 318, 226, 40, 233, 157, 299, 60]. 2× 2 [185]. 3 [456, 363, 58, 18, 351]. ∗ [238]. 2 [277]. 3 [350]. p

References

SHOWING 1-10 OF 28 REFERENCES
Dynamics of Wave Scintillation in Random Media
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
Self-averaging of kinetic models for waves in random media
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
On the Self-Averaging of Wave Energy in Random Media
  • G. Bal
  • Mathematics
    Multiscale Model. Simul.
  • 2004
TLDR
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.
Kinetics of scalar wave fields in random media
Self-Averaging of Wigner Transforms in Random Media
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
Power statistics for wave propagation in one-dimension and comparison with radiative transport theory. II
We consider a one‐dimensional medium with random index of refraction or a transmission line with random capacitance per unit length, allowing for impedance mismatch at the load and generator. We
Self-Averaging from Lateral Diversity in the Itô-Schrödinger Equation
TLDR
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.
SELF-AVERAGING IN TIME REVERSAL FOR THE PARABOLIC WAVE EQUATION
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
...
...