Publications

• (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)
  
  
• 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).
  
  
• (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.
  
  
• (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.
  
  
• (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, to appear.
  
  
• (with G.Iyer, T.Komorowski and L.Ryzhik) From homogenization to averaging in cellular flows, Preprint.
  
  Book.
  Reports.
  GeLMA Algorithm.
  
  Work supported by NSF grant DMS-0908011 ``Waves and Fronts in Heterogeneous Media'', 2009-2013.