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Homogenization of a Hele-Shaw problem in periodic and random media
Free boundary problem Hele-Shaw equation Obstacle problem Viscosity solution Homogenization
2015/10/15
We investigate the homogenization limit of a free boundary problem with space-dependent free boundaryvelocities. The problem under consideration has a well-known obstacle problem transformation, forma...
Homogenization of one-phase Stefan-type problems in periodic and random media
one-phase Stefan-type periodic random
2015/10/15
We investigate the homogenization of Stefan-type problems with oscillating diffusion coefficients. Both cases of periodic and random (stationary ergodic) medium are considered. The proof relies on the...
Time splitting for wave equations in random media
Time splitting wave equations random media
2015/7/14
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 sp...
Wave field correlations in weakly mismatched random media
Wave field correlations weakly mismatched random media
2015/7/14
This paper concerns the derivation of a Fokker-Planck equation for the correlation of two high frequency wave fields propagating in two different random media. The mismatch between therandom media nee...
Waves in weakly random media:lecture notes for the Vienna Inverse Problems school
weakly random media Vienna Inverse Problems
2015/7/14
Wave propagation in complex media is an ubiquitous phenomenon–applications include light propagation through the atmosphere, underwater acoustic, tomography, and innumerable other ones. These problems...
Precursors for Waves in Random Media
Parabolic approximation random media precursor O’Doherty-Anstey approximation
2015/7/14
We consider scattering of a pulse propagating through a three-dimensional random media and study the shape of the pulse in the parabolic approximation. We show that, similarly to the one-dimensional O...
Spectral control of broadband light through random media by wavefront shaping
Spectral control of broadband light random media wavefront shaping Optics
2012/5/31
A random medium can serve as a controllable arbitrary spectral filter with spectral resolution determined by the inverse of the interaction time of the light in the medium. We use wavefront shaping to...
Light Transport in Random Media with ${\cal PT}$-Symmetry
Light Transport Random Media ${\cal PT}$-Symmetry Optics
2012/5/29
The scattering properties of randomly layered optical media with ${\cal PT}$-symmetric index of refraction are studied using the transfer-matrix method. We find that the transmitance decays exponentia...
We analyze the random fluctuations of several multi-scale algorithms such as the multi-scale finite element method (MsFEM) and the finite element heterogeneous multiscale method (HMM), that have been...