Publications
 1. (with W. Pfeffer) An invariant Riemann type integral defined by figures,
Proc. Am. Math. Soc., vol. 120 (1994), pp. 849854.
 (with G. Papanicolaou) Eddy viscosity of cellular flows,
J. Fluid Mech., vol. 446 (2001), pp. 173198
 (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. 385408.
 Modulational stability of cellular flows,
Nonlinearity, vol. 16 (2003), pp.16071639.
 (with L. Berlyand) Geometric patterns and
effective conductivity of highly packed twophase 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. 341354.
 (with L.Berlyand and Y.Gorb)
Discrete network approximation for highlypacked
composites with irregular geometry in three dimensions,
Uppsala Proceedings in Multiscale
Methods in Science and Engineering, Springer Lecture Notes(2005), pp.2158.
 (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. 867922
 (with A. Borodin)
On a conjecture of Widom
, J. Phys. A 39 (2006), no. 28, pp. 88958903.
 (with V. Rai and H. Pitsch)
Efficient dynamic Monte Carlo algorithm for timedependent 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. 2348.
 (with P. Constantin and L. Ryzhik) Relaxation in reactive flows, Geom. Funct. Anal., vol. 18 (2008), no.4, pp. 11451167.
 (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. 15501584.
 (with L. Berlyand and Y.Gorb) Fictitious Fluid Approach and Anomalous Blowup of the Dissipation Rate in a 2D Model of Concentrated Suspensions, Arch. Ration. Mech. Anal., vol. 193(2009), no.3, pp. 585622.
 A Discrete Network Approximation for Effective Conductivity of Nonohmic Highconstrast Composites, Commun. Math.
Sci., vol. 7(2009), no.3, pp. 719740.
 16. (with H. Berestycki, A. Kiselev, and L. Ryzhik) The explosion problem in a flow, J. Anal. Math., vol. 110(2010), no.1, pp.3165.
 (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.24842498.
 (with Y.Gorb, and D. Nam) Numerical simulations of diffusion in cellular flows at
high Peclet numbers , DCDSB, vol. 51(2011), no.1, pp.7592.
 (with J.Nolen) Homogenization of the Gequation with incompressible random drift in two dimensions, Commun. Math. Sci., vol. 9(2011), no.2, pp. 561582.
 (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. 14681501.
 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. 767786.
 (with Y.Gorb) Blow up of Solutions to the pLaplace Equation, SIAM Multiscale Model. Simul. vol 10(2012), no.3, pp. 727743.
 (with M.Moscoso, G.Papanicolaou and L.Ryzhik)
A differential equations approach to l_1minimization 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 AdvectionDiffusion Equations with Nonlinear Diffusion, Ann. Inst. H. Poincare, Anal. Non Lineaire, vol 30 (2013), no.4, pp.705735.
 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 intensityonly imaging, SIAM J. Imaging Sci. 83 (2015), pp. 15471573.
 (with G.Iyer) Anomalous diffusion in fast cellular
flows at intermediate time scales,
Probab. Theory Related Fields, Vol.164 (2016), No.3, pp. 707740.
 31. (with M.Moscoso and G.Papanicolaou) Coherent Imaging without Phases, SIAM J. Imaging Sci. 94 (2016), pp. 16891707.
 (with D.Burago and S.Ivanov) A survival guide for feeble fish, St. Petersburg Math. J.(Algebra i Analiz) 29 (2017), No.1, pp. 4959.
 (with M.Moscoso, G.Papanicolaou and C.Tsogka) Multifrequency interferometric
imaging with intensityonly measurements, SIAM J. Imaging Sci., 103 (2017),
pp. 10051032.
 (with M.Hairer, G.Iyer, L.Koralov and Z.PajorGyulai) A fractional kinetic process describing
the intermediate time behaviour of cellular flows, Ann. of Probability, 462(2018), pp. 897955.

(with Karim ShikhKhalil) A Stochastic Lagrangian particle system for the NavierStokes equations,
Commun. Math. Sci., 163(2018), pp. 879–886.
 36. (with D.Burago and S.Ivanov) Feeble fish in timedependent waters and homogenization of the Gequation,
submitted.
Book.
Reports.
GeLMA Algorithm.
Work supported by NSF grant DMS1813943
``Reduced Models for Transport of Particles in Heterogeneous Media'',
20182021.