Resarch

Publications:

WAVES IN RANDOM MEDIA
" Long Range Media	Paraxial wave propagation in random media with long-range correlations. [.pdf,] L. Borcea, J. Garnier and K. Solna, SIAM Journal of Applied Mathematics, 83(1), 2023.
" Partly Coherent	Partially Coherent Electromagnetic Beam Propagation in Random Media. [.pdf,] J. Garnier and K. Solna, Accepted in Waves in Random and Complex Media, 2022.
" Radiative Transfer	System of radiative transfer equations for coupled surface and body waves. [.pdf,] J. Garnier and K. Solna, Z. Angew. Math. Phys. (ZAMP), 73, 177, 2022.
" Memory Effect	Speckle Memory Effect in the Frequency Domain and Stability in Time-Reversal Experiments. [.pdf,] J. Garnier and K. Solna, SIAM J. Multiscale Model. Simul., 21(1), 2023.
" Sintillation	Scintillation of Partially Coherent Light in Time Varying Complex Media. [.pdf,] J. Garnier and K. Solna, J. Opt. Soc. Am. A , 22(8), 1309-1322, 2022.
" Surface waves	Onset of energy equipartition among surface and body waves. [PRSA,] L. Borcea, J. Garnier and K. Solna, Proceedings of the Royal Society A, 2246, 2021.
" beam	Beam Propagation in Random Media with Applications to Imaging and Communication. [.pdf,] J. Garnier and K. Solna, Abstract Oberwolfach, 2020.
" scintillation	Beaming Through Turbulence. [.pdf,] J. Garnier and K. Solna, OSA Technical Digest, paper PTh2D.4, 2019.
" focusing	Focusing waves through a randomly scattering medium in the white-noise paraxial regime. [.pdf,] J. Garnier and K. Solna, SIAM Journal of Applied Mathematics, 77:2, pp. 500-519, 2 DOI:10.1137/16M1087266, 2017.
" turbulent waveguide	Wave Propagation in Random Waveguides with Long-Range Correlations. [.pdf,] C. Gomez and K. Solna, Communication in Mathematical Sciences, 16:6, 1557-1596, 2019.
" 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.
" 4th wave moment	Fourth-moment Analysis for Wave Propagation in the White-Noise Paraxial Regime. [.pdf,] J. Garnier and K. Solna, Arch. Rat. Mech. Anal., 220, 37-81, 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, 265-300, 2016.
" hyperbolic system	White-Noise Paraxial Approximation for a General Random Hyperbolic System. [.pdf,] J. Garnier and K. Solna, SIAM J. Multiscale Model. Simul., 13:3, 1022-1060, 2015.
" 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.
" 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.
" precursor	Precursors for Waves in Random Media. [.pdf,] G. Bal, O. Pinaud, L. Ryzhik and K. Solna. Wave Motion, 51, 1237-1253, 2014.
" scintillation	Scintillation in the White-Noise Paraxial Regime. [.pdf,] J. Garnier and K. Solna. Communications in PDE, 39, 626-650, 2014.
" wide angle	Coupled wideangle wave approximations. [.pdf,] J. Garnier and K. Solna. SIAM Multiscale Model. Simul., 10:1, 217-244, 2012.
" 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.
" long-range	A general framework for waves in random media with long-range correlations, [.pdf,] R. Marty and K. Solna, Ann. Applied Probability, 21, 115-139, 2011.
" pressure release	Wave transmission through random layering with pressure release boundary conditions, [.pdf,] J. Garnier and K. Solna, SIAM J. on Multiscale Modeling and Simulation, 8, 912-943, 2010.
" precursor	Fractional precursors in random media, [.pdf,] J. Garnier and K. Solna, 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. Solna, J. Acoust. Soc. Am., 127, 67-72, 2010.
" enhanced backscattering	Scaling limits for wave pulse transmission and reflection operators, [.pdf,] J. Garnier and K. Solna, Wave Motion, 2, 122-143, 2009.
" elastic waves	Parabolic and white-noise approximations for elastic waves in random media, [.pdf,] J. Garnier and K. Solna, Wave Motion, 46, 237-254, 2009.
" el mag	Paraxial Coupling of Electromagnetic Waves in Random Media, [.pdf,] J. Garnier and K. Solna, 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. Solna, 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. Solna, SIAM J. on Multiscale Modeling and Simulation, 7, 1302-1324, 2009.
" coupled paraxial	Random backscattering in the parabolic scaling, [.pdf,] J. Garnier and K. Solna, J. Stat. Phys., 131, 445-486, 2008.
" waveguide	Effective transport equations and enhanced backscattering in random waveguides. [.pdf,] J. Garnier and K. Solna, 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. [.pdf, ] G. Papanicolaou, L. Ryzhik and K. Solna. Matematica Contemporanea, V 23, 139-160, 2002.
" time-reversal	Statistical stability in time reversal. [.pdf, ] G. Papanicolaou, L. Ryzhik and K. Solna. SIAM Journal of Applied Mathematics, V 64, 1133-1155, 2004.
" time-reversal	Time-reversal aperture enhancement. [.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. [.pdf, ] A. Nachbin and K. Solna. Proceeding, XX CILAMCE, Sao Paulo, 1999.
" shallow water	Apparent diffusion due to mountain microstructure in shallow waters. [.pdf, ] 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. [.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.
" local layering	Stable spreading of acoustic pulses due to laminated microstructure. [.pdf,] K. Solna, thesis, 1998.
IMAGING
" learning	Conditional score-based diffusion models for Bayesian inference in infinite dimensions. [.pdf,] L. Baldassari, A. Siahkoohi, J. Garnier, Knut S\o lna and M. De Hoop, arXiv:2305.19147v1, 2023.
" multiplexing	Multiplexing schemes for optical communication through atmospheric turbulence. [.pdf,] L. Borcea, J. Garnier and K. Solna, J. Opt. Soc. Am. A 37(5), 720-730, 2020.
" enhanced backscattering	Enhanced Backscattering of a partially coherent field from an anisotropic random lossy medium, [.pdf,] J. Garnier and K. Solna, Discrete and continuous dynamical systems series B, doi:10.3934/dcdsb.2020158 accepted 2020.
" moving medium	Sound propagation in a weakly turbulent flow in a waveguide. [.pdf,] L. Borcea, J. Garnier and K. Solna, SIAM J. Appl. Math., 79:6, 2663-2687, 2019.
" moving medium	Wave propagation and imaging in moving random media. [.pdf,] L. Borcea, J. Garnier and K. Solna, SIAM J. Multiscale Model. Simul., 31, 31-67, 2019.
" speckle imaging	Non-invasive imaging through random media. [.pdf,] J. Garier and K. Solna, SIAM Journal of Applied Mathematics, 78:6, 3296-3315, 2018.
" speckle imaging	Imaging through a scattering medium by speckle intensity correlations. [.pdf,] J. Garier and K. Solna, Inverse Problems 34:9, 094003, 2018.
" 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, 665-710, 2017.
" daylight imaging	Global acoustic daylight imaging in a stratified Earth-like model. [.pdf,] M.V. de Hoop, J. Garnier and K. Solna, Inverse Problems, 43:1, 2018.
" 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.
" 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.
" 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, 1704-722, 2013.
" 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.
" 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.
" 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.
" 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.
" Extended targets	Multistatic imaging of extended targets, [.pdf,] H. Ammari, J. Garnier, H. Kang, M. Lim and K. Solna, SIAM J. Imaging Science, 5:2,564-600, 2011.
" Passive Kirchhoff	Filtered Kirchhoff migration of cross-correlations of ambient noise signals, [.pdf,] J. Garnier and K. Solna, Inverse Problems, 5, 371-390, 2011.
" passive imaging	Background velocity estimation by cross correlations of ambient noise signals in radiative transport regime, [.pdf,] J. Garnier and K. Solna, Comm. Math. Sci., 9:3, 743-766, 2011.
" detection	A statistical approach to target detection and localization in the prescence of noise, [.pdf,] H. Ammari, J. Garnier and K. Solna, Waves in Random and Complex Media, 22:1, 4-65, 2011.
" detection	Imaging Schemes for perfectly conducting cracks, [.pdf,] H. Ammari, J. Garnier, H. Kang, W.K. Park and K. Solna, SIAM Journal on Applied mathematics, 71 68-19, 2011.
" passive imaging	Passive imaging and detection in cluttered media, [.pdf,] J. Garnier and K. Solna, 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. Solna, In: Mathematical and Statistical methods for Imaging, AMS, 2011.
" passive imaging	Cross correlation and deconvolution of noise signals in randomly layered media, [.pdf,] J. Garnier and K. Solna, 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. Solna, Inverse Problems, 25, 045005, 2009.
" segmentation	Expectation-Maximization Algorithm with Local Adaptivity, [.pdf,] Shingyu Leung, Gang Liang, Knut Solna 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. Solna, 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. Solna, 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
" turbulent market	Implied Volatility Structure in Turbulent and Long-memory Markets, Accepted in . [.pdf,] J. Garier and K. Solna, Frontiers in Applied Mathematics and Statistics, 2020.
" bitcoin	Chaos and Order in the Bitcoin Market. [.pdf,] J. Garier and K. Solna, Physica A, 524,708-721, 2019.
" chaos	Emergence of Turbulent Epochs in Oil Prices. [.pdf,] J. Garier and K. Solna, Chaos, Solitons \& Fractals, 22, 281-292, 2019.
" oil-data	A Time-Frequency Analysis of Oil Price Data. [.pdf,] J. Garier and K. Solna, Prisme N 33, 2017.
" hedging	Optimal hedging under fast-varying stochastic volatility [.pdf,] J. Garier and K. Solna, SIAM Jornal of Financial Mathematics, 11:1, 274-325, 2020.
" turbulent markets	Option pricing under fast-varying and rough stochastic volatility. [.pdf,] J. Garnier and K. Solna, Annals of Finance, accepted 2018.
" turbulent markets	Option pricing under fast-varying long-memory stochastic volatility. [.pdf,] J. Garnier and K. Solna, Mathematical Finance, accepted 2018.
" turbulent markets	Correction to Black-Scholes formula due to fractional stochastic volatility. [.pdf,] J. Garnier and K. Solna, SIAM J. Finan. Math., 8:1, 560-588, 2017.
" portfolio	Three l1 based nonconvex methods in constructing sparse mean reverting portfolios. [.pdf,] X. Long, K. Solna and J. Xin, Journal of Scientific Computing, 75:2, 2017.
" credit	Multiname and Multiscale Default Modeling, [.pdf,] J.P. Fouque, R. Sircar and K. Solna, 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. Solna, 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. [.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. [.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. [.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. [.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. [.pdf, ] 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. erratum [.pdf]
ESTIMATION
" local turbulence	Characterization of local turbulence in magnetic confinement devices, [.pdf,] M. Rajkovic, M. Skoric, K. Solna and G. Antar, Nucl. Fusion, 48, 024016, 2008.
" geophysics	Estimation of pulse shaping for well-logs. [.pdf, ] K. Solna. Geophysics, V 66, 1605-1611, 2001.
" turbulence	Wavelet based estimation of Kolmogorov turbulence. [.pdf, ] G. Papanicolaou and K. Solna. In: Long-range Dependence: Theory and Applications. Editors P. Doukhan, G. Oppenmeim and M. S. Taqqu, 2002.
" turbulence	Segmentation independent estimates of turbulence parameters. [.pdf, ] G. Papanicolaou, D. Washburn and K. Solna. Airborne laser advanced technology. Editors T. Steiner and P. Merritt, SPIE, V 3381, 256 - 267, 1998.
" turbulence	Robust Analysis of Aerothermal Data. [.pdf, ] G. Papanicolaou, C. Rino, V. Kruger and K. Solna. Vista Research Technical Report No. 2096 TM-98-001, 1998.
" global warming	Time-Trend Estimation for a Geographic Region. [.pdf, ] K. Solna and P. Switzer. Journal of the American Statistical Association, V 91, 577 - 589, 1996.
NUMERICAL ANALYSIS
" Foldy Lax	A generalized Foldy-Lax formulation, [.pdf,] K. Huang, K. Solna 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. Solna, 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. [.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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