Publications

Papers on:

Homogenization in random media and correctors

Waves in Random Media, Time-reversal, and Imaging

Inverse Problems

Macroscopic Models in Transport

Probabilistic representations / Monte Carlo

Numerical Analysis

Equations with Random Coefficients. Homogenization and Stochastic Limits

Homogenization and Corrector Theory for Linear Transport in Random Media (with W. Jing) , submitted

Homogenization with large spatial random potential, submitted

Convergence to SPDEs in Stratonovich form, to appear in Comm. Math. Phys., 2009

Central limits and homogenization in random media, (long version with more detailed proofs arXiv:0710.0363 ), Multiscale Model. Simul., 7(2), pp. 677-702, 2008

Random integrals and correctors in homogenization (with J. Garnier, S. Motsch, and V. Perrier), Asymptotic Analysis, 59(1-2), pp. 1-26, 2008

Homogenization in random media and effective medium theory for high frequency waves, Disc. Cont. Dyn. Syst. B, 8(2), pp. 473-492, 2007

High Frequency waves in Random Media. Applications to Detection, Imaging, and Time Reversal

Imaging using transport models for wave-wave correlations (with O. Pinaud), submitted

Asymptotics of the phase of the solutions of the random Schroedinger equation (with T. Komorowski and L. Ryzhik), submitted

Single scattering estimates for the scintillation function of waves in random media (with I. Langmore and O. Pinaud), submitted

Dynamics of wave scintillation in random media (with O. Pinaud), submitted

Self-averaging of kinetic models for waves in random media (with O. Pinaud), (Some errors corrected compared to printed version) Kinetic Related Models, 1(1), pp. 85-100, 2008

Inverse Problems in random media: a kinetic approach, J. Phys. Conf. Series, 124, 012001, 2008.

Transport-based imaging in random media (with K. Ren), SIAM J. Appl. Math., 68(6), pp. 1738-1762, 2008

Experimental validation of a transport-based imaging method in highly scattering environments (with L. Carin, D. Liu, and K. Ren), Inverse Problems , 26(3), pp. 2527-2539, 2007

Kinetic Models for Imaging in Random Media (with O. Pinaud), SIAM Multiscale Model. Simul. , 6(3), pp. 792-819, 2007

Electromagnetic Time-Reversal Imaging in Changing Media: Experiment and Analysis (with D. Liu, S. Vasudevan, J. Krolik, and L. Carin), IEEE Trans. Anten. and Prop., 55(2), pp. 344-354, 2007

Accuracy of transport models for waves in random media (with O. Pinaud), Wave Motion, 43(7), pp. 561-578, 2006

Wave field correlations in weakly mismatched random media (with L.Ryzhik), Stochastics & Dynamics, 6(3), pp. 301-328, 2006

Kinetics of scalar wave fields in random media, Wave Motion, 43, pp. 132-157, 2005

Time reversal based detection in random media (with O. Pinaud), Inverse Problems, 21(5), pp. 1593-1620, 2005

Stability of time reversed waves in changing media (with L.Ryzhik), Disc. Cont. Dyn. Syst. A , 12(5), pp. 793-815, 2005

Time Reversal in Changing Environment (with R.Verastegui), SIAM Multiscale Model. Simul. , 2(4), pp. 639-661, 2004

Time splitting for wave equations in random media (with L.Ryzhik), M2AN Math. Model. Numer. Anal. , 38(6), pp. 961-988, 2004

Time splitting for the Liouville equation in a random medium (with L.Ryzhik), Comm. Math. Sci. , 2(3), pp. 515-534, 2004

On the self-averaging of wave energy in random media, SIAM Multiscale Model. Simul. , 2(3), pp. 398-420, 2004

Self-averaging of Wigner transforms in random media (with T. Komorowski and L. Ryzhik), Comm. Math. Phys., 242(1-2), pp. 81-135, 2003

Time Reversal and refocusing in Random Media (with L.Ryzhik), SIAM J. Appl. Math., 63(5), pp. 1475-1498, 2003

Self-averaging in time reversal for the parabolic wave equation (with G. Papanicolaou and L. Ryzhik), Stochastics and Dynamics , 2(4), pp. 507-532, 2002

Radiative transport limit for the random Schroedinger equation (with G. Papanicolaou and L. Ryzhik) Nonlinearity, 15(2), pp. 513-529, 2002

Time Reversal for Classical Waves in Random Media (with L.Ryzhik), C. R. Acad. Sci. Paris, Serie I, 333, pp. 1041-1046, 2001

Capillary-gravity wave transport over spatially random drift (huge file!) (with T.Chou), Wave Motion, 35 , pp. 107-124, 2002

Wave transport for a scalar model of the Love waves (with L.Ryzhik), Wave Motion, 36, pp. 49-66, 2002

Wave transport along surfaces with random impedance (with V.Freilikher, G.Papanicolaou and L.Ryzhik), Phys. Rev. B, 62(10), pp. 6228-6240, 2000

Transport Theory for Acoustic Waves with Reflection and Transmission at Interfaces (with J.B.Keller, G.Papanicolaou and L.Ryzhik), Wave Motion, 30, pp. 303-327, 1999

Radiative Transport in a Periodic Structure (with A.Fannjiang, G.Papanicolaou and L.Ryzhik), Journal of Statistical Physics, 95, pp. 479-494, 1999

Diffusive Energy Scattering from Weakly Random Surfaces (with G.Papanicolaou and L.Ryzhik), Journal of Mathematical Physics, 40, pp. 4813-4827, 1999

Inverse Problems

Inverse Scattering and Acousto-Optic Imaging (with J.C. Schotland), submitted

Inverse Diffusion Theory of Photoacoustics (with G. Uhlmann), submitted

Inverse Transport Theory of Photoacoustics (with A. Jollivet and V. Jugnon), submitted

An accurate solver for forward and inverse transport (with F. Monard), submitted

Inverse Transport Theory and applications (review paper), Inverse Problems, 25, 055006, 2009

Time-dependent angularly averaged inverse transport (with A. Jollivet), to appear in Inverse Problems, 2009. (long version with additional proofs and results arXiv:0902.3432 )

Approximate stability in inverse transport (with A. Jollivet), to appear in the Proceedings of the Huangguoshu International Conference on Biomedical Imaging, 2009

Physics-based models for measurement correlations. Application to an inverse Sturm-Liouville problem (with K. Ren), Inverse Problems, 25, 053001, 2009.

Stability for time dependent inverse transport (with A. Jollivet), submitted

Small volume expansions for elliptic equations (with O. Pinaud), submitted

Stability estimates in stationary inverse transport (with A. Jollivet), Inverse Probl. Imaging, 2(4), pp. 427-454, 2008

Inverse transport from angularly averaged measurements and time harmonic isotropic sources, in Mathematical Methods in Biomedical Imaging and Intesity-Modulated Radiation Therapy, Ed. Y. Censor, M. Jiang, A.K. Louis, CRM Series, Scuola Normale Superiore Pisa, Italy, pp. 19-35, 2008

Inverse transport with isotropic sources and angularly averaged measurements , (with I. Langmore and F. Monard), Inverse Probl. Imaging, 2(1), pp. 23-42, 2008

Transport- and diffusion-based optical tomography in small domains: a comparative study, (with K. Ren and A. Hielscher), Applied Optics, 46(27), pp. 6669-6679, 2007

Inverse source problems in transport equations, (with A. Tamasan), SIAM J. Math. Anal., 39(1), pp. 57-76, 2007

Frequency Domain Optical Tomography Based on the Equation of Radiative Transfer, (with K. Ren and A. Hielscher), SIAM J. Sci. Comput., 28, pp. 1463-1489, 2006

Reconstruction of singular surfaces by shape sensitivity analysis and level set method (with K. Ren), Math. Models Methods Appl. Sci, 16(8), pp. 1347-1373, 2006

Ray Transforms in Hyperbolic Geometry, J. Math. Pures Appl., 84(10), pp. 1362-1392, 2005

Reconstructions in impedance and optical tomography with singular interfaces, Inverse Problems, 21(1), pp. 113-132, 2005

Atmospheric Concentration Profile Reconstructions from Radiation Measurements (with K. Ren), in Inverse Problems, 21(1), pp. 153-168, 2005

Fast numerical inversion of the attenuated Radon transform with full and partial measurements (with P. Moireau), Inverse Problems, 20(4), pp. 1137-1164, 2004

On the attenuated Radon transform with full and partial measurements, Inverse Problems, 20(2), pp. 399-418, 2004

On the reconstruction of diffusions using a single first-exit time distribution (with T. Chou), Inverse Problems, 20(4), pp. 1053-10066, 2004

Optical tomography of small volume absorbing inclusions, Inverse Problems, 19(2), pp. 371-386, 2003

Inverse problems for homogeneous transport equations. Part I: One-dimensional case, Inverse Problems, 16 , pp. 997-1011, 2000

Inverse problems for homogeneous transport equations. Part II: Multidimensional case, Inverse Problems, 16 , pp. 1013-1028, 2000

Macroscopic Models in Transport Theory

Radiative transfer equations with varying refractive index: a mathematical perspective, J. Opt. Soc. Am. A, 23(7), pp. 1639-1644, 2006

Transport approximations in partially diffusive media, Lecture Notes in Computational Science and Engineering; Ed. F. Graziani, Proceedings of the Computational Methods in Transport Workshop, Lake Tahoe, September 2004, 48, pp. 373-400, 2006

Generalized diffusion model in optical tomography with clear layers (with K. Ren), J. Opt. Soc. Amer. A, 20(12), pp. 2355-2364, 2003

Transport through diffusive and non-diffusive regions, embedded objects, and clear layers, SIAM J. Appl. Math., 62(5), pp. 1677-1697, 2002

Particle transport through scattering regions with clear layers and inclusions, J. Comp. Phys., 180(2), pp. 659-685, 2002

Coupling of transport and diffusion models in linear transport theory (with Y. Maday), M2AN Math. Model. Numer. Anal., 36(1), pp. 69-86, 2002

Homogenization and localization in locally periodic transport (with G. Allaire and V. Siess) ESAIM Contr. Op. Ca. Va., 8, pp. 1-20, 2002

Homogenization of a spectral equation with drift in linear transport, ESAIM Contr. Op. Ca. Va., 6(26), pp. 613-627, 2001

Diffusion Approximation of Radiative Transfer Equations in a Channel, Transport Theory and Statistical Physics, 30(2-3), 2001

Diffusion Approximation of Radiative Transfer Problems with Interfaces (with L.Ryzhik), SIAM, J. Appl. Math., 60(6), pp.1887-1912, 2000

Homogenization of the criticality spectral equation in neutron transport (with G. Allaire), M2AN Math. Model. Numer. Anal., 33(4), pp. 721-746, 1999

First-order Corrector for the Homogenization of the Criticality Eigenvalue Problem in the Even Parity Formulation of the Neutron Transport, SIAM J. Math. Anal., 30, pp. 1208-1240, 1999

Boundary Layer Analysis in the Homogenization of Neutron Transport Equations in a Cubic Domain, Asymptotic Analysis, 20(3-4), pp. 213-239, 1999

Probabilistic Representation of Radiative Transfer and Monte Carlo Methods

Probabilistic Theory of Transport Processes with Polarization (with G.Papanicolaou and L.Ryzhik), SIAM, J. Appl. Math., 60(5), pp.1639-1666, 2000

Polarization Effects of Seismic Waves on the Basis of Radiative Transport Theory (with M.Moscoso), Geophys. J. Int., 142(2), pp. 571-585, 2000

Theoretical and Numerical Analysis of Polarization for Time Dependent Radiative Transfer Equations (with M.Moscoso), Journal of Quantitative Spectroscopy and Radiative Transfer, 70(1), pp. 75-90, 2001

Radiative Transfer for Wave Propagation in Random Media. Monte Carlo Simulations of Seismic Waves (with M.Moscoso), in Mathematical and numerical aspects of wave propagation (Santiago de Compostela, 2000), pp. 559-563, SIAM, Philadelphia, PA, 2000

Numerical Analysis

Symplectic Parareal (with Q. Wu), Proceedings of DD17, 2008

Parallelization in time of (stochastic) ordinary differential equations, submitted

On the Convergence and the Stability of the Parareal Algorithm to solve Partial Differential Equations, Proceedings of DD15, Berlin, Vol. 40, LNCSE Series, Springer Verlag, Berlin, pp. 425-432, 2004

A "parareal" time discretization for non-linear PDE's with application to the pricing of an American put (with Y. Maday), Proceedings of the Workshop on Domain Decomposition, Zurich, Switzerland, LNCSE Series, Springer Verlag, 2001

Fourier Analysis of Diamond Discretization in Particle Transport, Calcolo, 38(3), pp. 141-172, 2001

Spatially Varying Discrete Ordinates Methods in XY-Geometry, Math. Models Meth. Appl. Sci., 10(9), pp. 1277-1303, 2000

Discrete Ordinates Methods in xy Geometry with Spatially Varying Angular Discretizations (with X. Warin) Nuclear Science and Engineering: 127(2), pp. 169-181, 1997

Guillaume Bal