Publications of Albert Fannjiang

Turbulent Transport and Homogenization

Relative diffusion and small-scale behaviors of scalar field in rough turbulent velocities
1. Invariance Principle for Inertial-Scale Behavior of Scalar Field in Kolmogorov-type Turbulence
  Physica D, 179: 3-4 (2003), pp. 161-182.
2. Convergence of Passive Scalars in Ornstein-Uhlenbeck Flows to Kraichnan's Model
  Journal of Statistical Physics 114:1/2 (2004), 115-135.
3. Lagrangian Dynamics for a Passive Tracer in a Class of Gaussian Markovian Flows
  Stoch. Proc. Appl. 97 (2002), pp. 171-198 (with T. Komorowski and S. Peszat).
4. Evolution of Trajectory Correlations in Steady Random Flows
  Proc. Symp. Appl. Math. 54(1998), pp. 105-130. (with L. Ryzhik and G.C. Papanicolao)
Convection-Enhanced Diffusion
1. Convection Enhanced Diffusion for Periodic Flows.
  SIAM J. Appl. Math. 54:2(1994), pp. 333-408. (with G.C. Papanicolaou)
2. Convection Enhanced Diffusion for Random Flows
  J. Stat. Phys 88:5-6(1997), pp. 1033-76 (with G.C. Papanicolaou)
Homogenization and Turbulent Diffusion
1. Diffusion in Turbulence
  Probab. Th. Rel. Fields 105 (1996), pp. 279-334. (with G.C. Papanicolaou)
2. A Martingale Approach to Homogenization of Unbounded Random Flows
  Ann. Probab. 25:4(1997), pp. 1872--1894 (with T. Komorowski)
3. Boundary Value Problems with Unbounded Random Flows
  J. Diff. Eq. 143:2 (1998), pp. 327--359.
4. An Invariance Principle for Diffusion in Turbulence
  Ann. Probab. 27:2 (1999), pp. 751-781. (with T. Komorowski).
5. Turbulent Diffusion in Markovian Flows
  Ann. Appl. Probab. 9:3 (1999), pp. 591-610. (with T. Komorowski).
6. Invariance Principle for a Diffusion in a Markov Field
  Bull. Pol. Acad. Sci. 49(1) (2001). (with T. Komorowski)
7. Diffusive and Non-diffusive limits for Transport in Non-Mixing Flows
  SIAM J. Appl. Math. 62:3(2002), pp. 909-923 (with T. Komorowski)
8. Diffusions in Long-Range Correlated Ornstein-Uhlenbeck Flows
  Electronic Journal of Probability 7(2002), 20 (with T. Komorowski)
Anomalous Transport and Phase Diagram
1. Anomalous Diffusion in Random Flows
  IMA Math Appl. 99 (1998), pp. 81-99.
2. Phase Diagram for Turbulent Transport
  Physica D Vol. 136, Nos. 1-2, pp. 145-174. Erratum Physica D 157(2001), pp. 166-168
3. Limit Theorems for Motions in a Flow with a Nonzero Drift
  Bull. Pol. Acad. Sci. 47:4 (1999), pp. 393-413. (with T. Komorowski)
4. 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).
Fractional Brownian Motion
1. Fractional Brownian Motion Limit for Turbulent Transport
  Ann. Appl. Probab. 10:4 (2000), pp. 1100-1120. (with T. Komorowski).
2. 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)
3. Frozen Path Approximation for Turbulent Diffusion and Fractional Brownian Motion in Random Flows.
  SIAM Journal on Applied Mathematics, 63:6(2003), pp. 2042-2062 (with T. Komorowski).

Imaging and Communications

Multi-frequency imaging of multiple targets in Rician fading channels: stability and resolution
Inverse Problems 23 (2007) 1801-1819 (with Mike Yan).
Broadband Resolution Analysis for Imaging with Measurement Noise
Journal of Optical Society of America A, Vol. 24 (2007) pp. 1623-1632 (with Knut Solna)
Information Transfer in Disordered Media by Broadband Time Reversal: Stability, Resolution and Capacity
Nonlinearity 19 (2006) 2425-2439.
Time Reversal Communication in Rayleigh Fading Broadcast Channels with Pinholes
Physics Letters A Vol 353/5 (2006) pp 389-397

Propagation and Time Reversal in Random Media

Mutual Coherence of Polarized Light in Disordered Media: Two-Frequency Method Extended
Journal of Physics A: Math and Theor. 40 No 45 (9 November 2007) 13667-13683
Two-Frequency Radiative Transfer. II: Maxwell Equations in Random Dielectrics
Journal of Optical Society of America A Vol. 24, Issue 12, pp. 3680-3690, 2007.
Space-frequency correlation of classical waves in disordered media: high-frequency and small-scale asymptotics
Europhysics Letters Vol 80 (2007) 14005.
Two-frequency radiative transfer and asymptotic solution.
Journal of Optical Society of America A Vol. 24 (2007), pp. 2248-2256
Self-Averaging Scaling Limits of Two-Frequency Wigner Distribution for Random Paraxial Waves
J. Phys. A: Math. Theor. 40 (2007) 5025-5044.
Radiative transfer limit of two-frequency Wigner distribution for random parabolic waves: An exact solution
Comptes Rendus Physique Volume 8, Issue 2 , March 2007, Pages 267-271
Time Reversal of Parabolic Waves and Two-Frequency Wigner Distribution (with K. Solna)
Discrete and Continuous Time Dynamical Systems. Volume 6, 2006, Pages: 783 -- 802
Superresolution and Duality for Time-Reversal of Waves in Random Media
Physics Letters A Vol 352:1-2 (2005), pp. 22-29.(with K. Solna)
White-Noise and Geometrical Optics Limits of Wigner-Moyal Equation for Wave Beams in Turbulent Media II. Two-Frequency Wigner Distribution Formulation.
Journal of Statistical Physics 120 (2005), 543-586.
Self-Averaging Radiative Transfer for Parabolic Waves
Comptes rendus de l'Académie des sciences- Mathematics Volume 342, Issue 2, 15 January 2006, Pages 109-114
Parabolic approximation, radiative transfer and time reversal
Journal of Physics: Conf. Ser. 7 (2005) 121-137.
Propagation and Time-reversal of Wave Beams in Atmospheric Turbulence
SIAM Multiscale Modeling and Simulation 3:3 (2005), pp. 522-558 (with K. Solna).
Self-Averaging Scaling Limits for Random Parabolic Waves
Archives of Rational Mechanics and Analysis 175:3 (2005), pp. 343 - 387
White-Noise and Geometrical Optics Limits of Wigner-Moyal Equation for Wave Beams in Turbulent Media.
Communications in Mathematical Physics. 254:2 (2005), pp. 289-322.
Scaling limits for laser beam propagation in atmospheric turbulence
Stochastics and Dynamics 4:1(2004), pp. 135-150 (with K. Solna).
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. 61:5(2001), pp. 1545-1577 (with L. Ryzhik).

Random Nonlinear Waves

Phase space models for stochastic nonlinear parabolic waves: wave spread and collapse
Journal of Physics A.: Math. Gen. Vol 39 (2006), 11383-11398.

Nonlinear Schr\"odinger Equation with a White-Noise Potential: Phase-space Approach to Spread and Singularity
Physica D, Volume 212, Issues 3-4, 2005, Pages 195-204. e-print:http://arxiv.org/abs/nlin/0503059

Quenching of Reaction by Cellular Flows
Geometrical and Functional Analysis, 16 (2006) 40-69 (with A. Kiselev and L. Ryzhik)

High Frequency Behavior of the Focusing Nonlinear Schroedinger Equation with Random Inhomogeneities
SIAM J. Appl. Math. 63(2003), pp. 1328-1358. (with S. Jin and G. C. Papanicolaou)

Classical and Quantum Chaos with Noise

Relaxation Time of Quantized Toral Maps
Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 7 (2006), no. 1, 161--198. (with S. Nonnenmacher and L. Wolowski).
Dissipation time and decay of correlations
Nonlinearity 17 (July 2004) 1481-1508 (with S. Nonnenmacher and L. Wolowski).
Noise-Induced Dissipation in discrete time conservative systems
Journal of Statistical Physics, 113:112 (2003), pp. 335-378 (with L. Wolowski).
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. 179(2002), pp. 433-455.

Gradient Elasticity and Fracture

Finite part integrals and hypersingular kernels Dynamics of Continuous, Discrete and Impulsive Systems A 14 (S2) 264-269 (2007). (with Y.-S. Chan, G. Paulino and B.-F. Feng ).
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
International Journal of Engineering Science 41:7(2003), pp. 683-720 (with Y-S. Chan and G.H. Paulino)
Strain Gradient Elasticity for Anti-Plane Shear Cracks: A Hypersingular Integrodifferential Equation Approach
SIAM Journal on Applied Mathematics 62:3(2002), pp. 1066-1091 (with Y.-S. Chan and G.H. Paulino).
Gradient Elasticity Theory for Mode I Crack in Functionally Graded Materials
Ceramic Transactions 114(2001), pp. 731-738. (with Y.-S. Chan and G. H. Paulino).
Gradient Elasticity Theory for Mode III Fracture in Functionally Graded Materials -- Part I: Crack Perpendicular to the Material Gradient.
ASME Journal of Applied Mechanics, 70:4(2003), pp. 531-542 (with Y.-S. Chan and G.H. Paulino).
Gradient Elasticity Theory for Mode III Fracture in Functionally Graded Materials -- Part II: Crack parallel to the Material Gradation.
ASME Journal of Applied Mechanics 75:6 (2008) 061015 (with Y.-S. Chan and G.H. Paulino).
Change of Constitutive Relations Due to Interaction between Strain-Gradient Effect and Material Gradation
ASME Journal of Applied Mechanics -- September 2006 -- Volume 73, Issue 5, pp. 871-875 (with Y.-S. Chan and G.H. Paulino)

Non-Math Writings

Einstein's religious thought
Oversea Campus Magazine, No. 62, December, 2003.
You can also download the article and the (unpublished) footnotes from OCM's page
in traditional and simplified Chinese.
Spinoza's view on religion
Oversea Campus Magazine, No. 63, February, 2004.
Karl Rahner's `` God of my prayer''
Oversea Campus Magazine, No. 68, December 2005.
A brief history of Fannjiangs and my birth place