Resarch

Publications:

WAVES IN RANDOM MEDIA
" 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.
" local layering	Coupled paraxial wave equation in random media in the white-noise regime. [.pdf,] J. Garnier and K. Solna. Submitted to Annals of Applied Probability, 2007.
" long range	Acoustic waves in long range random media, [.pdf,] R. Marty and K. Solna. Submitted, 2007.
" 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. Submitted 2007.
" 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.
IMAGING
" estimation	Background velocity estimation with cross correlations of incoherent waves in the parabolic scaling. [.pdf,] J. Garnier and K. Solna, Submitted to Inverse Problems 2008.
" resolution	Broadband Resolution Analysis for Imaging with Measurement Noise. [.pdf,] A. Fannjiang and K. Solna. Journal of the Acoustic Society A, To appear 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. Submitted 2007.
" 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 estimation
" 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
" 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.
NUMERICAL ANALYSIS
" 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.
ESTIMATION
" 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.
" turbulence	Segmentation independent estimates of turbulence parameters. [.ps, .pdf, .ps.gz] G. Papanicolaou, D. Washburn and K. Solna. Airborne laser advanced technology. Editors T. Steiner and P. Merritt, SPIE, V 3381, 256 - 267, 1998.
" global warming	Time-Trend Estimation for a Geographic Region. [.ps, .pdf, .ps.gz] K. Solna and P. Switzer. Journal of the American Statistical Association, V 91, 577 - 589, 1996.

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