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- 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)

- 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
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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).

- (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.
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- (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,
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- (with Y.Gorb, and D. Nam) Numerical simulations of diffusion in cellular flows at
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- (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.

- (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
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- (with E.Lunasin, Z.Lin, A.Mazzucato and C.Doering)
Optimal mixing and optimal
stirring for fixed energy, fixed power or fixed palenstrophy flows,
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- (with
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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.

- (with
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From homogenization to averaging in cellular flows,
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- (with
T.Komorowski and L.Ryzhik)
Homogenization driven by a fractional Brownian motion: the shear
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- On the Explosion Problem in a Ball, Commun. Math.
Sci., Vol. 13 (2015), No. 4, pp. 1025–1032.

- (with G.Iyer) Anomalous diffusion in fast cellular
flows at intermediate time scales,
Probab. Theory Related Fields, DOI 10.1007/s00440-015-0617-9 (2015), 35 pages.

- (with M.Moscoso and G.Papanicolaou) Illumination strategies for intensity-only imaging, SIAM J. Imaging Sci. 8-3 (2015), pp. 1547-1573.

Book.

Reports.

GeLMA Algorithm.

Work supported by NSF grant DMS-0908011 ``Waves and Fronts in Heterogeneous Media'', 2009-2013.