Selected Publications

• Radiative Transfer of Waves
  • PHASESPACEMODELSFORSTOCHASTICNONLINEARPARABOLIC WAVES: WAVESPREADANDSINGULARITY
  • Radiative Transport in a Periodic Structure
    J. Stat. Phys. 95:1-2 (1999), pp.479-494. (with G. Bal, G.C Papanicolaou L. Ryzhik)
  • Radiative Transfer of Sound Waves in a Random Flow: Turbulent Scattering, Straining and Mode-Coupling
    SIAM J. Appl. Math. (In press) (with L. Ryzhik).
  • High Frequency Behavior of the Focusing Nonlinear Schroedinger Equation with Random Inhomogeneities
    SIAM J. Appl. Math. (with S. Jin and G. C. Papanicolaou)
• Convection-Enhanced Diffusion
  • Convection Enhanced Diffusion for Periodic Flows.
    SIAM J. Appl. Math. 54:2(1994), pp. 333-408. (with G.C. Papanicolaou)
  • Convection Enhanced Diffusion for Random Flows
    J. Stat. Phys 88:5-6(1997), pp. 1033-76 (with G.C. Papanicolaou)
• Noise-Induced Dissipation and Homogenization
  • Time Scales in Noisy Conservative Systems
    Lec. Notes Phys 450 (1995), pp. 124-139.
  • Time Scales in Homogenization of Periodic Flows with Vanishing Molecular Diffusion
    J. Diff. Eq. (In press)
  • Noise-Induced Dissipation in discrete time conservative systems
    
• Homogenization and Turbulent Diffusion
  • Diffusion in Turbulence
    Probab. Th. Rel. Fields 105 (1996), pp. 279-334. (with G.C. Papanicolaou)
  • A Martingale Approach to Homogenization of Unbounded Random Flows
    Ann. Probab. 25:4(1997), pp. 1872--1894 (with T. Komorowski)
  • Boundary Value Problems with Unbounded Random Flows
    J. Diff. Eq. 143:2 (1998), pp. 327--359.
  • An Invariance Principle for Diffusion in Turbulence
    Ann. Probab. 27:2 (1999), pp. 751-781. (with T. Komorowski).
  • Turbulent Diffusion in Markovian Flows
    Ann. Appl. Probab. 9:3 (1999), pp. 591-610. (with T. Komorowski).
  • Invariance Principle for a Diffusion in a Markov Field
    Bull. Pol. Acad. Sci. 49(1) (2001). (with T. Komorowski)
  • Diffusive and Non-diffusive limits for Transport in Non-Mixing Flows
    SIAM J. Appl. Math. (to appear) (with T. Komorowski)
  • Diffusions in Long-Range Correlated Ornstein-Uhlenbeck Flows
    submitted (with T. Komorowski)
• Anomalous Transport and Phase Diagram
  • Anomalous Diffusion in Random Flows
    IMA Math Appl. 99 (1998), pp. 81-99.
  • Phase Diagram for Turbulent Transport
    Physica D Vol. 136, Nos. 1-2, pp. 145-174. Erratum Physica D 157(2001), pp. 166-168
  • Limit Theorems for Motions in a Flow with a Nonzero Drift
    Bull. Pol. Acad. Sci. 47:4 (1999), pp. 393-413. (with T. Komorowski)
  • Taylor-Kubo Formula for Turbulent Diffusion in a Non-Mixing Flow with Long-Range Correlation
    Bull. Pol. Acad. Sci. 48 (3)(2000), pp 253-275 (with T. Komorowski).
• Trajectory Correlations
  • Evolution of Trajectory Correlations in Steady Random Flows
    Proc. Symp. Appl. Math. 54(1998), pp. 105-130. (with L. Ryzhik and G.C. Papanicolao)
• Fractional Brownian Motion
  • Fractional Brownian Motion Limit for Turbulent Transport
    Ann. Appl. Probab. (In press) (with T. Komorowski).
  • Fractional Brownian Motions and Enhanced Diffusion in a Unidirectional Wave-like Turbulence.
    J. Stat. Phys. 100:5/6(2000), pp. 1071-1095. (with T. Komorowski)
• Motion in Flows with Kolmogorov-type Spectrum
  • Lagrangian Dynamics for a Passive Tracer in a Class of Gaussian Markovian Flows
    Stoch. Proc. Appl. (in press).
• Cracks Problems in Strain-Gradient Theory
  • Gradient Elasticity Solution for a Mode III Crack in a Functionally Graded Materials
    Materials Science Forum Vols. 308-311 (1999), pp. 971-976. (with G.H. Paulino and Y.-S. Chan)
  • The Crack Problem for Nonhomogeneous Materials Under Antiplane Shear Loading --- A Displacement Based Formulation
    Int. J. Solids Structures 38:17 (2001), pp. 2989-3005. (with Y.-S. Chan and G. H. Paulino).
  • Integral Equations with Hypersingular Kernels -- Theory and Applications to Fracture Mechanics
    Int. J. Num. Meth. Eng. (In press) (with Y-S. Chan and G.H. Paulino)
  • Strain Gradient Elasticity for Mode III Cracks: A Hypersingular Integrodifferential Equation Approach
    SIAM J. Appl. Math. (in press) (with Y.-S. Chan and G. Paulino).
  • Gradient Elasticity Theory for Mode III Fracture in Functionally Graded Materials -- Part I.
    J. Appl. Mech. (In press) (with Y.-S. Chan and G. Paulino)