Publications

- 1. (with W. Pfeffer) An invariant Riemann type integral defined by figures, Proc. Am. Math. Soc., vol. 120 (1994), pp. 849-854.
- (with G. Papanicolaou) Eddy viscosity of cellular flows,

J. Fluid Mech., vol. 446 (2001), pp. 173-198 - (with L. Berlyand) Error of the network approximation for densely packed composites with irregular geometry, SIAM J. Math. Anal., vol. 34 (2002), no. 2, pp. 385-408.
- Modulational stability of cellular flows, Nonlinearity, vol. 16 (2003), pp.1607-1639.
- (with L. Berlyand) Geometric patterns and effective conductivity of highly packed two-phase composites, in Homogenization 2001 L. Carbone and R. De Arcangelis Ed.(2003)
- 6. Eddy viscosity of cellular flows by upscaling, J. Comput. Phys., vol. 195 (2004), no. 1, pp. 341-354.
- (with L.Berlyand and Y.Gorb) Discrete network approximation for highly-packed composites with irregular geometry in three dimensions, Uppsala Proceedings in Multiscale Methods in Science and Engineering, Springer Lecture Notes(2005), pp.21-58.
- (with G.Papanicolaou and L.Ryzhik) Boundary layers for cellular flows at high Peclet numbers, Comm. Pure Appl. Math., vol.58 (2005), no. 7, pp. 867-922.
- (with A. Borodin) On a conjecture of Widom, J. Phys. A 39 (2006), no. 28, pp. 8895–8903.
- (with V. Rai and H. Pitsch) Efficient dynamic Monte Carlo algorithm for time-dependent catalytic surface chemistry, Phys. Rev. E, vol.74, 046707 (2006).
- 11. (with L. Ryzhik) Bounds on the speed of propagation of the KPP fronts in a cellular flow, Arch. Ration. Mech. Anal., vol. 184 (2007), no.1, pp. 23-48.
- (with P. Constantin and L. Ryzhik) Relaxation in reactive flows, Geom. Funct. Anal., vol. 18 (2008), no.4, pp. 1145-1167.
- (with L. Berlyand and O. Bruno) Rise of Correlations of Transformaton Strains in Random Polycrystals, SIAM J. Math. Anal., vol. 40 (2008), no.4, pp. 1550–1584.
- (with L. Berlyand and Y.Gorb) Fictitious Fluid Approach and Anomalous Blow-up of the Dissipation Rate in a 2D Model of Concentrated Suspensions, Arch. Ration. Mech. Anal., vol. 193(2009), no.3, pp. 585–622.
- A Discrete Network Approximation for Effective Conductivity of Non-ohmic High-constrast Composites, Commun. Math. Sci., vol. 7(2009), no.3, pp. 719–740.
- 16. (with H. Berestycki, A. Kiselev, and L. Ryzhik) The explosion problem in a flow, J. Anal. Math., vol. 110(2010), no.1, pp.31–65.
- (with G. Iyer, L. Ryzhik, and A. Zlatos) Exit times of diffusions with incompressible drift, SIAM J. Math. Anal., vol. 42(2010), no.6,

pp. 2484–2498. - (with Y.Gorb, and D. Nam) Numerical simulations of diffusion in cellular flows at high Peclet numbers , DCDS-B, vol. 51(2011), no.1, pp.75–92.
- (with J.Nolen) Homogenization of the G-equation with incompressible random drift in two dimensions, Commun. Math. Sci., vol. 9(2011), no.2, pp. 561–582.
- (with G.Iyer) The regularizing effects of resetting in a particle system for the Burgers’ equation, Ann. of Probability, vol. 39(2011), no.4, pp. 1468-1501.
- 21. (with T.Komorowski and L.Ryzhik) Evolution of Particle Separation in Slowly Decorrelating Velocity Fields, Commun. Math. Sci., vol. 10(2012), no.3, pp. 767–786.
- (with Y.Gorb) Blow up of Solutions to the p-Laplace Equation, SIAM Multiscale Model. Simul. vol 10(2012), no.3, pp. 727–743.
- (with M.Moscoso, G.Papanicolaou and L.Ryzhik) A differential equations approach to l_1-minimization with applications to

array imaging, Inverse Problems, vol 28(2012), no.10, 105001, 21 pp, included in the Inverse Problems 2012 Highlights Collection. - (with E.Lunasin, Z.Lin, A.Mazzucato and C.Doering) Optimal mixing and optimal stirring for fixed energy, fixed power or fixed palenstrophy flows, Journal of Mathemtical Physics, vol 53 (2012), no.11, 115611.
- (with L.Monsaingeon and J.-M.Roquejoffre) Traveling wave solutions of Advection-Diffusion Equations with Nonlinear Diffusion, Ann. Inst. H. Poincare, Anal. Non Lineaire, vol 30 (2013), no.4, pp.705-735.
- 26. (with G.Iyer, T.Komorowski and L.Ryzhik) From homogenization to averaging in cellular flows, Ann. Inst. H. Poincare, Anal. Non Lineaire, vol 31 (2014), no.5, pp.957–983.
- (with T.Komorowski and L.Ryzhik) Homogenization driven by a fractional Brownian motion: the shear layer case,SIAM Multiscale Model. Simul., Vol. 12 (2014), No. 2, pp. 440–457.
- On the Explosion Problem in a Ball, Commun. Math. Sci., Vol. 13 (2015), No. 4, pp. 1025–1032.
- (with M.Moscoso and G.Papanicolaou) Illumination strategies for intensity-only imaging, SIAM J. Imaging Sci. 8-3 (2015), pp. 1547-1573.
- (with G.Iyer) Anomalous diffusion in fast cellular flows at intermediate time scales,Probab. Theory Related Fields, Vol.164 (2016), No.3, pp. 707-740.
- 31. (with M.Moscoso and G.Papanicolaou) Coherent Imaging without Phases, SIAM J. Imaging Sci. 9-4 (2016), pp. 1689-1707.
- (with D.Burago and S.Ivanov) A survival guide for feeble fish, St. Petersburg Math. J.(Algebra i Analiz) 29 (2017), No.1, pp. 49-59.
- (with M.Moscoso, G.Papanicolaou and C.Tsogka) Multifrequency interferometric imaging with intensity-only measurements, SIAM J. Imaging Sci., 10-3 (2017), pp. 1005–1032.
- (with M.Hairer, G.Iyer, L.Koralov and Z.Pajor-Gyulai) A fractional kinetic process describing the intermediate time behaviour of cellular flows, Ann. of Probability, 46-2(2018), pp. 897-955.
- (with Karim Shikh-Khalil) A Stochastic Lagrangian particle system for the Navier-Stokes equations,Commun. Math. Sci., 16-3(2018), pp. 879–886.
- 36.(with M.Moscoso, G.Papanicolaou and C.Tsogka) Robust multifrequency imaging with MUSIC, Inverse Problems, 35(2019), 01500, 22pp.
- (with D.Burago and S.Ivanov) Feeble fish in time-dependent waters and homogenization of the G-equation,Comm. Pure Appl. Math., to appear.
- (with M.Moscoso, G.Papanicolaou and C.Tsogka) Synthetic aperture imaging with intensity-only data, IEEE Trans. Comput. Imag., vol. 6(2020), pp. 87-94.
- (with D.Kuzmin and O.Ahwadi) Random walk methods for Monte Carlo simulations of Brownian diffusion on a sphere, Appl. Math. Comput., 364(2020), 124670.
- (with M.Moscoso, G.Papanicolaou and C.Tsogka) Imaging with highly incomplete and corrupted data, Inverse Problems, 36(2020), 035010, 21pp.

Work supported by NSF grant DMS-1813943 “Reduced Models for Transport of Particles in Heterogeneous Media”, 2018-2021.