Courant Institute NYU, New York NY 10012, USA
mtao at cims dot nyu dot edu
Welcome to my homepage! I'm a Courant Instructor in Courant Institute of Mathematical Sciences, New York University.
My interests in applied math lie at the intersection of differential equations and dynamical systems, probability, and geometry. Example topics include: (1) the analysis and numerics of multiscale systems, and their applications; (2) geometric mechanics and structure-preserving integrators; (3) rare events and sampling for physical and statistical purposes; (4) theory of uncertainty quantification and engineering applications.
Non-intrusive and structure preserving multiscale integration of stiff ODEs, SDEs and Hamiltonian systems with hidden slow dynamics via flow averaging. With H. Owhadi and J.E. Marsden. SIAM Multiscale Model. Simul. (2010) Vol. 8, 1269-1324.
inverted pendulum movie ; propane molecule movie
Space-time FLAVORS: finite difference, multisymplectic, and pseudospectral integrators for multiscale PDEs. With H. Owhadi and J.E. Marsden. Dynamics of PDEs. (2011) Vol. 8, 21-46.
low-resolution small sized preprint
From efficient symplectic exponentiation of matrices to symplectic integration of high-dimensional Hamiltonian systems with slowly varying quadratic stiff potentials. With H. Owhadi and J.E. Marsden. Appl. Math. Res. Express. (2011) Num. 2, 242-280.
An additional preprint on the error analysis of a stochastic extension of impulse methods is available at http://arxiv.org/abs/1006.4657
Evaluation of a wave vector frequency domain method for nonlinear wave propagation. With Y. Jing and G. Clement. J. Acous. Soc. Am. (2011) 129 (1) 32-46.
Control of a model of DNA division via parametric resonance. With W-S. Koon, H. Owhadi, and T. Yanao. Chaos (2013) 23 013117.
Variational integrators for electric circuits. With S. Ober-Bloebaum, M. Cheng, H. Owhadi, and J.E. Marsden. J. Comput. Phys. (2013) 242 (1) 498-530.
Symplectic, linearly-implicit and stable integrators with applications to fast symplectic simulations of constrained dynamics. With H. Owhadi and J.E. Marsden. Preprint at http://arxiv.org/abs/1103.4645
pendulum chain movie; toy water cluster at constant temperature movie