Professor Weinan E

WEINAN E
Professor, Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton, NJ 08544-1000 U.S.A. Phone: (609)258-3683 ~ Fax: (609)258-1735 weinan@princeton.edu	Curriculum Vitae Research Interests/Papers Publications Courses Reviews/Perspectives

Research Interests/Papers:

The Heterogeneous Multi-Scale Method (PS, PDF), submitted to Proceeding of ICCM 2001.
The Heterogeneous Multi-Scale Methods(PS), Comm. Math. Sci., in press
Matching Conditions in Atomistic-Continuum Modeling of Materials(PDF), Phys. Rev. Lett, vol. 87, No. 13, 135501, 2001.
A Dynamic Atomistic-Continuum Method for the Simulation of Crystalline Materials(PDF, PS), J. Comput. Phys. in press.
Coupling Kinetic Monte Carlo and Continuum Models with Applications to Epitaxial Growth(PS), submitted to J. Comput. Phys.
The Heterogeneous Multi-Scale Method for Homogenization Problems (PS).

String Method for the Study of Rare Events (PS ), submitted to Phys. Rev. B.
Probing Multi-Scale Energy Landscapes Using the String Method (PS ), submitted to Phys. Rev. Lett.
Energy Landscapes and Rare Events (PS ), ICM report, 2002.

Gibbsian Dynamics and Ergodicity for the Stochastically Forced Navier-Stokes Equation (PS ).
Ergodicity for the Navier-Stokes Equation with Degenerate Random Forcing: Finite Dimensional Approximation (PS ).
Gibbsian Dynamics and Invariant Measures for Stochastic Dissipative PDEs (PS ).
Statistical Theory for the Stochastic Burgers Equation in the Inviscid Limit (PS, PDF)
Invariant Measures for Burgers Equation with Stochastic Forcing (PS, PDF)
PDFs for the Random Forced Burgers Equation (PS, PDF)
PDFs for Velocity and Velocity Gradients in Burgers Turbulence (PS, PDF)
Asymptotic Theory for the Probability Density Functions in Burgers Turbulence (PS, PDF)
Another Note on Forced Burgers Turbulence (PS, PDF)
Generalized Flows, Intrinsic Stochasticity, and Turbulent Transport (PS, PDF)

Numerical Solutions for the Landau-Lifshitz Equations (PS, PDF)
A Gauss-Seidel Projection Method for Micromagnetics Simulations (PS, PDF), J. Comput. Phys., vol. 171, 357-372 (2001).
Effective Dynamics for Ferromagnetic Thin Films (PS, PDF), J. Appl. Phys., vol. 90, No. 4, 370-373 (2001).

Projection Method I: Convergence and Numerical Boundary Layers (PS, PDF)
Projection Method II: Godunov-Ryabenki Analysis (PS, PDF)
Projection Method with Spatial Discretizations (PS, PDF)
Vorticity Boundary Condition and Related Issues for Finite Difference Schemes (PS, PDF)
Essentially Compact Schemes for Unsteady Viscous Incompressible Flows (PS, PDF)
Finite Difference Methods for 3D Viscous Incompressible Flows in the Vorticity-Vector Potential Formulation on Non-Staggered Grids (PS, PDF)
Finite Difference Schemes for Incompressible Flows in the Velocity - Impulse Density Formulation (PS, PDF
Simple Finite Element Method in Vorticity Formulation for Incompressible Flows (PS, PDF)
Gauge Finite Element Method for Incompressible Flows (PS, PDF)

Nonlinear Continuum Theory of Smectic A Liquid Crystals (PS, PDF)
Dynamics of Filaments during the Isotropic - Smectic A Phase Transition (PS, PDF)
Thermodynamically Driven Incompressible Fluid Mixtures (PS, PDF)
Phase Separation of Incompressible Systems

Onsager's Conjecture on the Energy Conservation for Solutions of Euler's Equation (PS, PDF)

APC 518: Applied Stochastic Analysis and Methods

Boundary Layer Theory and the Zero-Viscosity Limit of the Navier-Stokes Equation (PS, PDF)
Numerical Methods for Viscous Incompressible Flows: Some Recent Advances (PS, PDF)
Recent Results on Mathematical & Statistical Hydrodynamics (PS, PDF)
Stochastic PDEs in Turbulence Theory (PS, PDF)
Mathematics and Sciences (PS), written for the Beijing Intelligencer, 2002.
Stochastic Hydrodynamics (PS), in ``Current Development in Mathematics'', 2001.
Selected Problems in Material Sciences (PS), in ``Mathematics Unlimited, 2001 and Beyond'', Engquist and Schmid Editors.