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 Di erential 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).