G.A. Pavliotis and A.M. Stuart, "Multiscale Methods: Averaging and Homogenization," Springer, 2008.

W. E, D. Liu, and E. Vanden-Eijnden, "Nested Stochastic Simulation Algorithm for Chemical Kinetic Systems with Disparate Rates," *J. Chemical Physics*,
**123**, 194107 (2005) *(8 pages)* .

X. Li and W. E, "Multiscale modeling of dynamics of solids at finite temperature," *J. Mech. Phys.
Solids*, accepted for publication.

W. E, B. Engquist, X. Li, W. Ren, E. Vanden-Eijnden, "The Heterogeneous Multiscale Method: A Review."

W. Ren and W. E, "Heterogeneous multiscale method for the modeling of
complex fluids and micro-fluidics," *J. Comput. Phys.*, in press.

W. E, D. Liu, and E. Vanden-Eijnden, "Analysis of Multiscale Methods for
Stochastic Dierential Equations," *Comm. on Pure and Applied Math.*, 1-48 (2003).

I. Fatkullin and E. Vanden-Eijnden, "A computational strategy for multiscale chaotic systems with applications to Lorenz 96 model," preprint.

W. E and X.T. Li, "Multiscale Modeling of Crystalline Solids," submitted to the Handbook of Computational Material Science.

P. B. Ming and X. Yue, "Numerical Methods for Multiscale Elliptic Problems."

W. E, X. Li, E. Vanden-Eijnden, "Some Recent Progress in Multiscale Modeling."

T. Li, E. Vanden-Eijnden, P. Zhang and W. E, "Stochastic
models of polymeric fluids at small Deborah number," submitted to *J.
Non-Newtonian Fluids*.

A. Abdulle and W. E, "Finite difference
heterogeneous multi-scale method for homogenization problems," *J. Comput. Phys.*, **191**, 18-39 (2003).

G. Pavliotis and A.M. Stuart, "White noise
limits for inertial particles in a random field," *SIAM J. Multiscale Modeling and Simulation***, 1**(4),
527-553 (2003).

L. T. Cheng and W. E, "The heterogeneous
multiscale method for interface dynamics," to appear in *Contemporary
Mathematics*: A Special Volume in Honour of Stan Osher, S. Y. Cheng, C. W.
Shu and T. Tang eds.

C. Muratov and W. E, "Theory
of phase separation kinetics in polymer-liquid crystal systems," *J.
Chem. Phys.*, **116**(11), 4723-4734 (2002).

W. E, "Analysis of the heterogeneous multiscale
method for ordinary differential equations," *Comm.
Math. Sci.*, **1**(3), 423-436 (2003).

W. E and B. Engquist, "The
heterogeneous multi-scale methods," *Comm. Math. Sci.*, **1**, 87-133 (2003).

W. E and B. Engquist, "The heterogeneous
multi-scale method for homogenization problems," submitted to *SIAM J. Multiscale
Modeling and Simulations*.

W. E and B. Engquist, "Multiscale Modeling
and Computation," *Notices of the AMS*, ** 50**(9), 1062-1070 (2003).

W. E, B. Engquist and Z. Huang, "Heterogeneous
multi-scale method -- a general methodology for multi-scale modeling,"
*Phys. Rev. B*, **67**(9), 092101 (2003).

W. E and Z. Huang, "Matching
conditions in atomistic-continuum modeling of materials," *Phys.
Rev. Lett.*, **87** (13), 135501 (2001).

W. E and Z. Huang, "A
dynamic atomistic-continuum method for the simulation of crystalline materials,"
*J. Comput. Phys.*, **182**, 234-261 (2002).

W. E, P. B. Ming and P. W. Zhang, "Analysis of the heterogeneous multiscale method for elliptic homogenization problems," preprint.

P. B. Ming and P. W. Zhang, "Analysis of the heterogeneous multiscale method for dynamic homogenization problems," preprint.

T. Schulze, P. Smereka and W. E, "Coupling
kinetic Monte-Carlo and continuum models with application to epitaxial growth,"
*J. Comput. Phys.*, **189**, 197-211 (2003).

E. Vanden-Eijnden, "Numerical
techniques for multiscale dynamical systems with stochastic effects,"
*Comm. Math. Sci.*, **1**(2), 385-391 (2003).