WAVES IN RANDOM MEDIA

"
focusing

Focusing waves through a randomly scattering medium in the
whitenoise paraxial regime.
[.pdf,]
J. Garnier and K. Solna, SIAM Journal of Applied Mathematics,
77:2, pp. 500519, 2 DOI:10.1137/16M1087266, 2017.

"
turbulent waveguide

Wave Propagation in Random Waveguides with LongRange Correlations.
[.pdf,]
C. Gomez and K. Solna,
Accepted Communication in Mathematical Sciences 2017.

"
turbulent media

On effective attenuation in multiscale composite media
[.pdf,]
J. Garnier and K. Solna, Waves
in Random and Complex Media, 25:5, 2015. 
"
elastic waves

Apparent attenuation of shear waves propagating through a randomly stratied anisotropic medium.
[.pdf,]
J. Garnier and K. Solna, Stochastic and Dynamics, 16, 2016. 
"
scintillation

Fourthmoment Analysis for Wave Propagation in the WhiteNoise Paraxial
Regime.
[.pdf,]
J. Garnier and K. Solna, Arch. Rat. Mech. Anal., 220, 3781, 2016.

"
time varying media

Pulse propagation in time dependent randomly layered media.
[.pdf,]
L. Borcea and K. Solna,
SIAM J. Multiscale Model. Simul., 14:1, 265300, 2016. 
"
hyperbolic system

WhiteNoise Paraxial Approximation for a General Random Hyperbolic
System.
[.pdf,]
J. Garnier and K. Solna, SIAM J. Multiscale Model. Simul., 13:3, 10221060, 2015.

"
Brewster angle

Transmission and Reflection of Electromagnetic Waves in Randomly Layered Media,
[.pdf,]
J. Garnier and K. Solna.
Commun. Math. Sci., 13, 707728, 2015.

"
backscatter

Wave backscattering by point scatterers in the random paraxial regime
[.pdf,]
J. Garnier and K. Solna.
SIAM J. Multiscale Model. Simul., 3, 13091334, 2014.

"
precursor

Precursors for Waves in Random Media.
[.pdf,]
G. Bal, O. Pinaud, L. Ryzhik and K. Solna.
Wave Motion, 51, 12371253, 2014.

"
scintillation

Scintillation in the WhiteNoise Paraxial Regime.
[.pdf,]
J. Garnier and K. Solna.
Communications in PDE, 39, 626650, 2014.

"
wide angle

Coupled wideangle wave approximations.
[.pdf,]
J. Garnier and K. Solna.
SIAM Multiscale Model. Simul., 10:1, 217244, 2012.

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weak localization

Enhanced and Specular Backscattering in Random Media,
[.pdf,]
M.V. de Hoop, J. Garnier and K. Solna.
Waves in Random and Complex Media, 22:4, 505530,
2012.

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longrange

A general framework for waves in random media with longrange correlations,
[.pdf,]
R. Marty and K. S\o lna,
Ann. Applied Probability, 21, 115139, 2011.

"
pressure release

Wave transmission through random layering with pressure release boundary conditions,
[.pdf,]
J. Garnier and K. S\o lna,
SIAM J. on Multiscale Modeling and Simulation, 8, 912943,
2010.

"
precursor

Fractional precursors in random media,
[.pdf,]
J. Garnier and K. S\o lna,
Waves in Random and Complex Meida, 20, 122155, 2010.

"
fractional equation

Effective fractional acoustic wave equations in random multiscale media,
[.pdf,]
J. Garnier and K. S\o lna,
J. Acoust. Soc. Am., 127, 6772, 2010.

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enhanced backscattering

Scaling limits for wave pulse transmission and reflection operators,
[.pdf,]
J. Garnier and K. S\o lna,
Wave Motion, 2, 122143, 2009.

"
elastic waves

Parabolic and whitenoise approximations for elastic waves in random media,
[.pdf,]
J. Garnier and K. S\o lna,
Wave Motion,
46, 237254, 2009.

"
el mag

Paraxial Coupling of Electromagnetic Waves in Random Media,
[.pdf,]
J. Garnier and K. S\o lna,
SIAM J. on Multiscale Modeling and Simulation,
7, 19281955, 2009.

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long range

Acoustic Waves in Long Range Random Media,
[.pdf,]
R. Marty and K. S\o lna,
SIAM J. on Applied Math., 69, 10651083, 2009.

"
long range

Pulse propagation in random media with longrange correlation,
[.pdf,]
J. Garnier and K. S\o lna,
SIAM J. on Multiscale Modeling and Simulation, 7,
13021324, 2009.

"
coupled paraxial

Random backscattering in the parabolic scaling,
[.pdf,]
J. Garnier and K. S\o lna,
J. Stat. Phys., 131, 445486, 2008.

"
waveguide

Effective transport equations and enhanced backscattering in random
waveguides.
[.pdf,]
J. Garnier and K. S\o lna,
SIAM J. Appl. Math., 68, 15741599, 2008.

"
paraxial

Coupled paraxial wave equation in random media in the
whitenoise regime.
[.pdf,]
J. Garnier and K. Solna.
Annals of Applied Probability, 19, 318346, 2009.

"
selfaveraging

Selfaveraging from lateral diversity in the ItoSchrodinger equation,
[.pdf,]
G. Papanicolaou, L. Ryzhik and K. Solna.
SIAM Journal on
Multiscale Modeling and Simulation, To appear 2007.

"
medium perturbations

Time Reversal of Waves in a Perturbed Random Medium,
[.pdf,]
Daniel V. Alfaro and K. Solna.
Communications in Mathematical Sciences, 6, 331360, 2008.

"
twofrequency

Time reversal of Parabolic Waves and TwoFrequency Wigner Distribution
[.pdf,]
A. Fannjiang and K. Solna.
Discrete and Continuous Dynamical Systems, 6, 4, 783802, 2006.

"
superresolution

Superresolution and Duality for Timereversal of Waves in
Random Media,
[.pdf,]
A. Fannjiang and K. Solna.
Physics Letters A, V 352, 12, 2229, 2005.

"
timereversal

Propagation and timereversal of wave beams in atmospheric
turbulence,
[.pdf,]
A. Fannjiang and K. Solna,
SIAM Journal on Multiscale Modeling and Simulation, 3, 3, 522558, 2005.

"
timereversal

Time Reversal Super Resolution in Randomly Layered Media.
[.pdf,]
J.P. Fouque, J. Garnier and K. Solna.
Wave Motion, 42,238260,2006.

"
timereversal

Time Reversal Refocusing for Point Source in Randomly
Layered Media.
[.pdf,]
J.P. Fouque, J. Garnier A. Nachbin and K. Solna.
Wave Motion 42:3, 191288, 2005.

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timereversal

Focusing of timereversed reflections.
[.pdf,]
K. Solna.
Waves in Random Media, 12, 121, 2002.

"
timereversal

The parabolic wave approximation and time reversal.
[.ps, .pdf, ]
G. Papanicolaou, L. Ryzhik and K. Solna.
Matematica Contemporanea, V 23, 139160, 2002.

"
timereversal

Statistical stability in time reversal.
[.ps, .pdf, ]
G. Papanicolaou, L. Ryzhik and K. Solna.
SIAM Journal of Applied Mathematics, V 64, 11331155, 2004.

"
timereversal

Timereversal aperture enhancement.
[.ps, .pdf, ]
J. P. Fouque and K. Solna.
SIAM Journal on
Multiscale Modeling and Simulation, V 1, 4, 609629, 2003.

"
shallow water

Apparent pulse diffusion due to disordered microstructure.
[.ps, .pdf, .ps.gz]
A. Nachbin and K. Solna.
Proceeding, XX CILAMCE, Sao Paulo, 1999.

"
shallow water

Apparent diffusion due to mountain microstructure
in shallow waters.
[.ps, .pdf, .ps.gz]
A. Nachbin and K. Solna.
Physics of Fluids, V 15, 1, 6677, 2003.

"
multiscale

Scaling limits for wave beams in atmospheric turbulence.
[.pdf]
A. Fannjiang and K. Solna.
Stochastics and Dynamics, V 4, 1, 135151, 2004.

"
multiscale

Acoustic pulse spreading in a random fractal.
[.ps, .pdf, ]
K. Solna.
SIAM Journal of Applied
Mathematics, V 63, 5, 17641788, 2003.

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local layering

Ray Theory for a Locally Layered Medium.
[.pdf,]
K. Solna and G. C. Papanicolaou.
Waves in Random Media, V 10, 151  198, 2000.

IMAGING

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SAR

Resolution analysis of passive synthetic aperture imaging of fast moving objects.
[.pdf,]
L. Borcea, J. Garier, G. Papanicolaou
K. Solna and C. Tsogka,
SIAM Journal on Imaging Sciences 10:2, 665710, 2017.

"
daylight imaging

Global acoustic daylight imaging in a stratified Earthlike model.
[.pdf,]
M.V. de Hoop, J. Garnier and K. Solna,
Inverse Problems, Accepted, 2017.

"
superresolution

Medium induced resolution enhancement for
broadband imaging,
[.pdf,]
H. Ammari, J. Garnier, J. de Rosny, and K. Solna, Inverse Problems, 30:8, 085006, 2014.

"
RMT

Applications of random matrix theory for sensor array
imaging with measurement noise
[.pdf,]
J. Garnier and K. Solna.
Random Matrices MSRI Publications, 65, 223246, 2014.

"
SAR

A Multiscale Approach to Synthetic Aperture Radar in Random Media
[.pdf,]
J. Garnier and K. Solna.
Inverse Problems, 5, 29, 054006, 2013.

"
partial aperture

Partial Data Resolving Power of Conductivity Imaging from Boundary Measurements
[.pdf,]
H. Ammari, J. Garnier and K. Solna.
SIAM Journal on Mathematical Analysis, 45:3, 1704722, 2013.

"
noise blending

Imaging with Noise Blending
[.pdf,]
M. de Hoop, E. Fedrizzi, J. Garnier and K. Solna.
In
``MultiScale and HighContrast PDE: From Modelling, to Mathematical Analysis, to Inversion'', Proceedings of the AMS, Editors H. Ammari, Y. Capdeboscq and H. Kang,
105124, 2012.

"
conductivity

Resolution and stability analysis in fullaperture linearized conductivity and wave imaging
[.pdf,]
H. Ammari, J. Garnier and K. Solna.
Proceedings of the AMS, 141, 34313446, 2013.

"
cross correlations

Retrival of a Greens function with reflections from partly
coherent waves generated by wave packets using cross correlations.
[.pdf,]
M.V. de Hoop, J. Garnier, S.F. Holman and K. Solna.
SIAM J. App. Math., 73:1, 493522, 2013.

"
cross correlations

Scattering enabled retrieval of Green's functions from remotely incident
wave packets using cross correlations
[.pdf,]
M.V. de Hoop, J. Garnier, S.F. Holman and K. Solna.
Comptes Rendus Geoscience, 343:89, 526532, 2011.

"
Extended targets

Multistatic imaging of extended targets,
[.pdf,]
H. Ammari, J. Garnier, H. Kang, M. Lim and K. S\o lna,
Submitted SIAM J. Imaging Science, 2011.

"
Passive Kirchhoff

Filtered Kirchhoff migration of crosscorrelations of ambient noise signals,
[.pdf,]
J. Garnier and K. S\o lna,
Inverse Problems, 2011.

"
passive imaging

Background velocity estimation by cross correlations of ambient noise
signals,
[.pdf,]
J. Garnier and K. S\o lna,
Comm. Math. Sci., 2011.

"
detection

A statistical approach to target detection and localization in the prescence of noise,
[.pdf,]
H. Ammari, J. Garnier and K. S\o lna,
Waves in Random and Complex Media, 2011.

"
detection

Imaging Schemes for perfectly conducting cracks,
[.pdf,]
H. Ammari, J. Garnier, H. Kang, W.K. Park and K. S\o lna,
SIAM Journal on Applied mathematics, 71 6819, 2011.

"
passive imaging

Passive imaging and detection in cluttered media,
[.pdf,]
J. Garnier and K. S\o lna,
PROCEEDINGS of The Third International
Workshop on Computational Advances in MultiSensor Adaptive
Processing,
edited by IEEE, 225228, December 2009.

"
detection

Time reversal for inclusion detection in randomly layered media,
[.pdf,]
D. Alfaro Vigo and K. S\o lna,
Cont. Math. AMS, 2011.

"
passive imaging

Cross correlation and deconvolution of noise signals in randomly layered media,
[.pdf,]
J. Garnier and K. S\o lna,
SIAM J. Imaging Sci., 3, 809139, 2010.

"
velocity estimation

Background velocity estimation with cross correlations
of incoherent waves in the parabolic scaling,
[.pdf,]
J. Garnier and K. S\o lna,
Inverse Problems, 25, 045005, 2009.

"
segmentation

ExpectationMaximization Algorithm with Local Adaptivity,
[.pdf,]
Shingyu Leung, Gang Liang, Knut S\o lna and Hongkai Zhao,
Siam Journal on Imaging Sciences, 2 [3], 834857, 2009.

"
multitone

A phase and space coherent direct imaging algorithm,
[.pdf,]
S. Hou, K. Huang, K. Solna and H. Zhao,
J. of Acoustic Society of America, 125, 227238, 2009.

"
SAR

Synthetic Aperture Imaging of Multiple Point Targets in Rician
Fading Media,
[.pdf,]
A.C. Fannjiang, K. Solna and P. Yan,
SIAM J. Imaging Sci., 2, 344, 2009.

"
passive imaging

Estimating a Green's function from ``fieldfield'' correlations in a random medium,
[.pdf,]
M. de Hoop and K. S\o lna,
SIAM J. Appl. Math., 69, 909932, 2009.

"
SAR

Coherent Interferometric Imaging for Synthetic
Aperture Radar in the Presence of Noise,
[.pdf,]
J. Garnier and K. S\o lna,
Inverse Problems, 24, 055001, 2008.

"
resolution

Broadband Resolution Analysis for Imaging with Measurement Noise.
[.pdf,]
A. Fannjiang and K. Solna.
Journal of the Optical Society of America A, 24, 6,
16231632, 2007.

"
incoherent

Imaging of a Dissipative layer in a random Medium Using a
Timereversal Method.
[.pdf,]
J.P. Fouque, J. Garnier A. Nachbin and K. Solna.
Proceedings MC2QMC, JuanlesPins, 2004.

"
farfield

A Direct Imaging Method Using Far Field Data.
[.pdf,]
S. Hou, K. Solna and H. Zhao.
Inverse Problems, 22, 4, 11511178, 2006.

"
SVD

A Direct Imaging Algorithm for Extended Targets.
[.pdf,]
S. Hou, K. Solna and H. Zhao.
Inverse Problems, 22,4, 11511178, 2006.

"
level set method

Imaging of location and geometry for extended targets using
the response matrix.
[.pdf,]
S. Hou, K. Solna and H. Zhao.
Journal of Comp. Physics, 199:1, 317338, 2004.

MATHEMATICAL FINANCE

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turbulent markets

Option pricing under fastvarying and rough stochastic volatility.
[.pdf,]
J. Garnier and K. Solna,
submitted , 2017.

"
turbulent markets

Option pricing under fastvarying longmemory stochastic volatility.
[.pdf,]
J. Garnier and K. Solna,
submitted , 2017.

"
turbulent markets

Correction to BlackScholes formula due to fractional stochastic volatility.
[.pdf,]
J. Garnier and K. Solna,
SIAM J. Finan. Math., 8:1, 560588, 2017.

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portfolio

Three l1 based nonconvex methods in constructing
sparse mean reverting portfolios.
[.pdf,]
X. Long, K. Solna and J. Xin,
Accepted Journal of Scientific Computing, 2017.

"
credit

Multiname and Multiscale Default Modeling,
[.pdf,]
J.P. Fouque, R. Sircar and K. S\o lna,
SIAM J. on Multiscale Modeling and Simulation,
7, 19561978, 2009.

"
fixedincome

Bond markets with stochastic volatility,
[.pdf,]
R. DeSantiago, J. P. Fouque and K. Solna.
In Advances in Econometrics: Econometrics of Risk Managemen,
T. F. Fomby, J.P. Fouque and K. S\o lna, editors,
Emerald Group Publishing, 215242, 2008.

"
creditrisk

Stochastic Volatility Effects on Defaultable Bonds,
[.pdf,]
J. P. Fouque, K. R. Sircar and K. Solna.
Applied Mathematical Finance, 13, 3, 215244, 2006.

"
multiscale

Maturity Cycles in Implied Volatility.
[.ps, .pdf,]
J. P. Fouque, G. Papanicolaou, K. R. Sircar and K. Solna.
Finance and Stochastics, V 8, 4, 451477, 2004.

"
multiscale

Multiscale Stochastic Volatility Asymptotics.
[.ps, .pdf,]
J. P. Fouque, G. Papanicolaou, K. R. Sircar and K. Solna.
SIAM Journal for Multiscale
Modeling and Simulation, V 2, 1, 2242, 2003.

"
estimation

Short timescale in S&P500 volatility.
[.ps, .pdf,]
J. P. Fouque, G. Papanicolaou, K. R. Sircar and K. Solna.
Journal of Computational
Finance, V 6, 4, 124, 2003.

"
stochastic volatility

Singular perturbations in option pricing.
[.ps, .pdf,]
J. P. Fouque, G. Papanicolaou, K. R. Sircar and K. Solna.
SIAM Journal of Applied Mathematics, V 63, 5, 16481665, 2003.

"
multiscale

Timing the smile.
[.pdf,]
J. P. Fouque, G. Papanicolaou, K. R. Sircar and K. Solna.
The Wilmott Magazine, March 2004.

COMPOSITES/COMPLEX MEDIA

"
escape problem

The mean escape time for a narrow escape problem with
multiple switching gates,
[.pdf,
]
H. Ammari, J. Garnier, H. Kang, H. Lee and K. Solna.
SIAM Multiscale Model. Simiul., 2011.

"
group velocity

Bounds for the group velocity of electromagnetic signals
in two phase materials.
[.ps, .pdf, .ps.gz]
K. Solna and G. Milton. Physica B, V 279, 1, 912, 2000.

"
group velocity

Can mixing materials make electromagnetic signals travel faster?
[.pdf]
K. Solna and G. Milton.
SIAM Journal of Applied
Mathematics, V 62, 6, 20642091, 2002.

ESTIMATION

"
local turbulence

Characterization of local turbulence in
magnetic confinement devices,
[.pdf,]
M. Rajkovic, M. Skoric, K. S\o lna and G. Antar,
Nucl. Fusion}, 48, 024016, 2008.

"
geophysics

Estimation of pulse shaping for welllogs.
[.ps, .pdf, .ps.gz]
K. Solna. Geophysics, V 66, 16051611, 2001.

"
turbulence

Wavelet based estimation of Kolmogorov turbulence.
[.ps, .pdf, .ps.gz]
G. Papanicolaou and K. Solna.
In: Longrange Dependence: Theory and Applications.
Editors P. Doukhan, G. Oppenmeim and M. S. Taqqu, 2002.

NUMERICAL ANALYSIS

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Foldy Lax

A generalized FoldyLax formulation,
[.pdf,]
K. Huang, K. S\o lna and H. Zhao,
J. of Computational Physics, 229, 45444553, 2010.

"
paraxial backscattering

A Twoway Paraxial System for Simulation of Wave Backscattering by a Random Medium,
[.pdf,]
J. Garnier and K. S\o lna,
J. of Computational Physics, 20, 33073325, 2009.

"
wave propagation

Analysis of wave propagation in 1D inhomogeneous media.
[.pdf,]
P. Guidotti, J. Lambers and K.
Numerical Functional Analysis and Optimization,
27, 1, 2555, 2006.

"
wave propagation

Efficient Numerical Simulation for Long Range Wave Propagation.
[.pdf,]
K. Huang, G. Papanicolaou, K. Solna, C. Tsogka and H. Zhao,
Journal of Computational Physics, 215, 2, 448464, 2006.

"
wave propagation

Coupled Parabolic Equations for Wave Propagation.
[.pdf,]
K. Huang, K. Solna and H. Zhao, Methods and
Applications of Analysis, 11, 3, 399412, 2004.

"
generalized SVD

Computing the SVD of a general matrix product/quotient.
[.ps, .pdf,]
G. Golub, K. Solna and P. Van Dooren.
SIAM Journal on Matrix Analysis
and Applications, V22, 1, 119, 2001.
