Publications:

WAVES IN RANDOM MEDIA
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turbulent waveguide
Wave Propagation in Random Waveguides with Long-Range Correlations. [.pdf,]
C. Gomez and K. Solna, preprint, 2015.
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turbulent media
On effective attenuation in multiscale composite media [.pdf,]
J. Garnier and K. Solna, to appear in Waves in Random and Complex Media, 2015.
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elastic waves
Apparent attenuation of shear waves propagating through a randomly stratied anisotropic medium. [.pdf,]
J. Garnier and K. Solna, to appear in Stochastic and Dynamics 2015.
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scintillation
Fourth-moment Analysis for Wave Propagation in the White-Noise Paraxial Regime. [.pdf,]
J. Garnier and K. Solna, accepted Arch. Rat. Mech. Anal., 2015.
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time varying media
Pulse propagation in time dependent randomly layered media. [.pdf,]
L. Borcea and K. Solna, Submitted, SIAM J. Multiscale Model. Simul., 2015.
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hyperbolic system
White-Noise Paraxial Approximation for a General Random Hyperbolic System. [.pdf,]
J. Garnier and K. Solna, Accepted for publication SIAM J. Multiscale Model. Simul., 2015.

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Brewster angle
Transmission and Reflection of Electromagnetic Waves in Randomly Layered Media, [.pdf,]
J. Garnier and K. Solna. Commun. Math. Sci., 13, 707-728, 2015.

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backscatter
Wave backscattering by point scatterers in the random paraxial regime [.pdf,]
J. Garnier and K. Solna. SIAM J. Multiscale Model. Simul., 3, 1309-1334, 2014.

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precursor
Precursors for Waves in Random Media. [.pdf,]
G. Bal, O. Pinaud, L. Ryzhik and K. Solna. Wave Motion, 51, 1237-1253, 2014.

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scintillation
Scintillation in the White-Noise Paraxial Regime. [.pdf,]
J. Garnier and K. Solna. Communications in PDE, 39, 626-650, 2014.

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wide angle
Coupled wideangle wave approximations. [.pdf,]
J. Garnier and K. Solna. SIAM Multiscale Model. Simul., 10:1, 217-244, 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, 505-530, 2012.

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long-range
A general framework for waves in random media with long-range correlations, [.pdf,]
R. Marty and K. S\o lna, Ann. Applied Probability, 21, 115-139, 2011.

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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, 912-943, 2010.

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precursor
Fractional precursors in random media, [.pdf,]
J. Garnier and K. S\o lna, Waves in Random and Complex Meida, 20, 122-155, 2010.

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fractional equation
Effective fractional acoustic wave equations in random multiscale media, [.pdf,]
J. Garnier and K. S\o lna, J. Acoust. Soc. Am., 127, 67-72, 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, 122-143, 2009.

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elastic waves
Parabolic and white-noise approximations for elastic waves in random media, [.pdf,]
J. Garnier and K. S\o lna, Wave Motion, 46, 237-254, 2009.

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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, 1928-1955, 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, 1065-1083, 2009.

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long range
Pulse propagation in random media with long-range correlation, [.pdf,]
J. Garnier and K. S\o lna, SIAM J. on Multiscale Modeling and Simulation, 7, 1302-1324, 2009.

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coupled paraxial
Random backscattering in the parabolic scaling, [.pdf,]
J. Garnier and K. S\o lna, J. Stat. Phys., 131, 445-486, 2008.

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waveguide
Effective transport equations and enhanced backscattering in random waveguides. [.pdf,]
J. Garnier and K. S\o lna, SIAM J. Appl. Math., 68, 1574-1599, 2008.

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paraxial
Coupled paraxial wave equation in random media in the white-noise regime. [.pdf,]
J. Garnier and K. Solna. Annals of Applied Probability, 19, 318-346, 2009.

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self-averaging
Self-averaging from lateral diversity in the Ito-Schrodinger equation, [.pdf,]
G. Papanicolaou, L. Ryzhik and K. Solna. SIAM Journal on Multiscale Modeling and Simulation, To appear 2007.

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medium perturbations
Time Reversal of Waves in a Perturbed Random Medium, [.pdf,]
Daniel V. Alfaro and K. Solna. Communications in Mathematical Sciences, 6, 331-360, 2008.

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two-frequency
Time reversal of Parabolic Waves and Two-Frequency Wigner Distribution [.pdf,]
A. Fannjiang and K. Solna. Discrete and Continuous Dynamical Systems, 6, 4, 783-802, 2006.

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superresolution
Superresolution and Duality for Time-reversal of Waves in Random Media, [.pdf,]
A. Fannjiang and K. Solna. Physics Letters A, V 352, 1-2, 22-29, 2005.

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time-reversal
Propagation and time-reversal of wave beams in atmospheric turbulence, [.pdf,]
A. Fannjiang and K. Solna, SIAM Journal on Multiscale Modeling and Simulation, 3, 3, 522-558, 2005.

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time-reversal
Time Reversal Super Resolution in Randomly Layered Media. [.pdf,]
J.P. Fouque, J. Garnier and K. Solna. Wave Motion, 42,238-260,2006.

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time-reversal
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, 191-288, 2005.

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time-reversal
Focusing of time-reversed reflections. [.pdf,]
K. Solna. Waves in Random Media, 12, 1-21, 2002.

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time-reversal
The parabolic wave approximation and time reversal. [.ps, .pdf, ]
G. Papanicolaou, L. Ryzhik and K. Solna. Matematica Contemporanea, V 23, 139-160, 2002.

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time-reversal
Statistical stability in time reversal. [.ps, .pdf, ]
G. Papanicolaou, L. Ryzhik and K. Solna. SIAM Journal of Applied Mathematics, V 64, 1133-1155, 2004.

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time-reversal
Time-reversal aperture enhancement. [.ps, .pdf, ]
J. P. Fouque and K. Solna. SIAM Journal on Multiscale Modeling and Simulation, V 1, 4, 609-629, 2003.

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

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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, 66-77, 2003.

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multi-scale
Scaling limits for wave beams in atmospheric turbulence. [.pdf]
A. Fannjiang and K. Solna. Stochastics and Dynamics, V 4, 1, 135-151, 2004.

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multi-scale
Acoustic pulse spreading in a random fractal. [.ps, .pdf, ]
K. Solna. SIAM Journal of Applied Mathematics, V 63, 5, 1764-1788, 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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super-resolution
Medium induced resolution enhancement for broadband imaging, [.pdf,]
H. Ammari, J. Garnier, J. de Rosny, and K. Solna, Inverse Problems, 30:8, 085006, 2014.

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RMT
Applications of random matrix theory for sensor array imaging with measurement noise [.pdf,]
J. Garnier and K. Solna. Random Matrices MSRI Publications, 65, 223-246, 2014.

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

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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, 1704-722, 2013.

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noise blending
Imaging with Noise Blending [.pdf,]
M. de Hoop, E. Fedrizzi, J. Garnier and K. Solna. In ``Multi-Scale and High-Contrast PDE: From Modelling, to Mathematical Analysis, to Inversion'', Proceedings of the AMS, Editors H. Ammari, Y. Capdeboscq and H. Kang, 105-124, 2012.

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conductivity
Resolution and stability analysis in full-aperture linearized conductivity and wave imaging [.pdf,]
H. Ammari, J. Garnier and K. Solna. Proceedings of the AMS, 141, 3431-3446, 2013.

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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, 493-522, 2013.

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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, 343:8-9, 526-532, 2011.

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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.

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

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

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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.

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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 68-19, 2011.

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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 Multi-Sensor Adaptive Processing, edited by IEEE, 225-228, December 2009.

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

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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, 809-139, 2010.

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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.

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segmentation
Expectation-Maximization Algorithm with Local Adaptivity, [.pdf,]
Shingyu Leung, Gang Liang, Knut S\o lna and Hongkai Zhao, Siam Journal on Imaging Sciences, 2 [3], 834-857, 2009.

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multi-tone
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, 227-238, 2009.

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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.

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passive imaging
Estimating a Green's function from ``field-field'' correlations in a random medium, [.pdf,]
M. de Hoop and K. S\o lna, SIAM J. Appl. Math., 69, 909-932, 2009.

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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.

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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, 1623-1632, 2007.

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incoherent
Imaging of a Dissipative layer in a random Medium Using a Time-reversal Method. [.pdf,]
J.P. Fouque, J. Garnier A. Nachbin and K. Solna. Proceedings MC2QMC, Juan-les-Pins, 2004.

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far-field
A Direct Imaging Method Using Far Field Data. [.pdf,]
S. Hou, K. Solna and H. Zhao. Inverse Problems, 22, 4, 1151-1178, 2006.

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SVD
A Direct Imaging Algorithm for Extended Targets. [.pdf,]
S. Hou, K. Solna and H. Zhao. Inverse Problems, 22,4, 1151-1178, 2006.

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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, 317-338, 2004.

MATHEMATICAL FINANCE
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turbulent markets
Correction to Black-Scholes formula due to fractional stochastic volatility. [.pdf,]
J. Garnier and K. Solna, submitted to SIAM J. Finan. Math., 2015.

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portfolio
Three l1 based nonconvex methods in constructing sparse mean reverting portfolios. [.pdf,]
X. Long, K. Solna and J. Xin, submitted to Journal of Scientific Computing, 2015.

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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, 1956-1978, 2009.

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fixed-income
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, 215-242, 2008.

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credit-risk
Stochastic Volatility Effects on Defaultable Bonds, [.pdf,]
J. P. Fouque, K. R. Sircar and K. Solna. Applied Mathematical Finance, 13, 3, 215-244, 2006.

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multi-scale
Maturity Cycles in Implied Volatility. [.ps, .pdf,]
J. P. Fouque, G. Papanicolaou, K. R. Sircar and K. Solna. Finance and Stochastics, V 8, 4, 451-477, 2004.

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multi-scale
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, 22-42, 2003.

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estimation
Short time-scale in S&P500 volatility. [.ps, .pdf,]
J. P. Fouque, G. Papanicolaou, K. R. Sircar and K. Solna. Journal of Computational Finance, V 6, 4, 1-24, 2003.

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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, 1648-1665, 2003.

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

COMPOSITES/COMPLEX MEDIA
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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.

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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, 9-12, 2000.

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group velocity
Can mixing materials make electromagnetic signals travel faster? [.pdf]
K. Solna and G. Milton. SIAM Journal of Applied Mathematics, V 62, 6, 2064-2091, 2002.

ESTIMATION
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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.

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geophysics
Estimation of pulse shaping for well-logs. [.ps, .pdf, .ps.gz]
K. Solna. Geophysics, V 66, 1605-1611, 2001.

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

NUMERICAL ANALYSIS
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Foldy Lax
A generalized Foldy-Lax formulation, [.pdf,]
K. Huang, K. S\o lna and H. Zhao, J. of Computational Physics, 229, 4544-4553, 2010.

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paraxial backscattering
A Two-way Paraxial System for Simulation of Wave Backscattering by a Random Medium, [.pdf,]
J. Garnier and K. S\o lna, J. of Computational Physics, 20, 3307-3325, 2009.

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wave propagation
Analysis of wave propagation in 1D inhomogeneous media. [.pdf,]
P. Guidotti, J. Lambers and K. Numerical Functional Analysis and Optimization, 27, 1, 25-55, 2006.

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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, 448-464, 2006.

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wave propagation
Coupled Parabolic Equations for Wave Propagation. [.pdf,]
K. Huang, K. Solna and H. Zhao, Methods and Applications of Analysis, 11, 3, 399-412, 2004.

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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, 1-19, 2001.



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