Resarch

Publications:

WAVES IN RANDOM MEDIA
" 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.
" 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.
" precursor	Fractional precursors in random media, [.pdf,] J. Garnier and K. S\o lna, Waves in Random and Complex Meida, 20, 122-155, 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, 67-72, 2010.
" 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.
" 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.
" 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.
" 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.
" 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.
" coupled paraxial	Random backscattering in the parabolic scaling, [.pdf,] J. Garnier and K. S\o lna, J. Stat. Phys., 131, 445-486, 2008.
" 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.
" 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.
" 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.
" 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.
" 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.
" 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.
" 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.
" 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.
" 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.
" time-reversal	Focusing of time-reversed reflections. [.pdf,] K. Solna. Waves in Random Media, 12, 1-21, 2002.
" 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.
" 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.
" 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.
" 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, 66-77, 2003.
" 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.
" multi-scale	Acoustic pulse spreading in a random fractal. [.ps, .pdf, ] K. Solna. SIAM Journal of Applied Mathematics, V 63, 5, 1764-1788, 2003.
" 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
" 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 cross-correlations 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 68-19, 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 Multi-Sensor Adaptive Processing, edited by IEEE, 225-228, 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, 809-139, 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	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.
" 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.
" 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 ``field-field'' correlations in a random medium, [.pdf,] M. de Hoop and K. S\o lna, SIAM J. Appl. Math., 69, 909-932, 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, 1623-1632, 2007.
" 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.
" 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.
" SVD	A Direct Imaging Algorithm for Extended Targets. [.pdf,] S. Hou, K. Solna and H. Zhao. Inverse Problems, 22,4, 1151-1178, 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, 317-338, 2004.
MATHEMATICAL FINANCE
" 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.
" 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.
" 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.
" 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.
" 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.
" 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.
" 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.
" 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
" 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, 9-12, 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, 2064-2091, 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 well-logs. [.ps, .pdf, .ps.gz] K. Solna. Geophysics, V 66, 1605-1611, 2001.
" turbulence	Wavelet based estimation of Kolmogorov turbulence. [.ps, .pdf, .ps.gz] G. Papanicolaou and K. Solna. Accepted for publication in: Long-range Dependence: Theory and Applications. Editors P. Doukhan, G. Oppenmeim and M. S. Taqqu, 2002.
NUMERICAL ANALYSIS
" 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.
" 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.
" 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.
" 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.
" 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.
" 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.
PREPRINTS
" conductivity	Resolution and stability analysis in linearized conductivity and wave imaging. part I: Full aperture case. [.pdf,] H. Ammari, J. Garnier and K. Solna. Submitted 2011.
" wave propagation	Coupled wideangle wave approximations. [.pdf,] J. Garnier and K. Solna. Submitted 2011.
" imaging	Analysis of the multiple reflections by strong interfaces in random media. [.pdf,] M.V. de Hoop, J. Garnier and K. Solna. Submitted 2011.
" imaging	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. Submitted 2011.
" imaging	Scattering enabled retrival of Green's function from remotely incident wave packets using cross correlations. [.pdf,] M.V. de Hoop, J. Garnier, S.F. Holman and K. Solna. Submitted 2011.

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