Molei Tao joined Georgia Tech’s School of Mathematics in 2014. Prior to joining Georgia Tech, he held the prestigious postdoctoral position of Courant Instructor in the Courant Institute of Mathematical Sciences at New York University. He obtained his PhD in Control & Dynamical Systems with a minor in Physics from California Institute of Technology. His research interests center around the analysis, numerics, and control of multiscale stochastic mechanical systems.
Explain some of the energy-related applications of your work.
One of my research areas is to characterize how microscopic dynamics effectively contribute to macroscopic behaviors. An example application is the harvest of energy contained in fast or small oscillations. A quantitative understanding of whether accumulative effects can be obtained from the interaction of such oscillations with the designed device is essential. Similar ideas extrapolate to, for instance, unconventional means of energy transfer and system control as well. It is also important to characterize how noise and uncertainty affect the aforementioned processes, and this is why my investigations in stochastic systems are relevant too.
What have you found most interesting/challenging in your exploration of this area?
Two aspects are intertwined. The first, more on the mathematical side, is nonlinearity. The existence of multiple scales, perturbations from noise, and intrinsic structures in the system of interest (such as symplecticity and conservation laws), by themselves, can be handled. However, when mixed with nonlinearity, the difficulty is exponentiated. Without theoretical studies, even purely numerical investigations are infeasible in many situations. The second, this time on the practical side, is on modeling. The art lies in an appropriate amount of abstraction and simplification, such that the model maximizes its predictive powers, and yet is somehow approachable -- this is why these two aspects cannot be viewed individually.
Other related research interests or projects?
I work with nonlinear systems with multiple scales, randomness, and geometric structures. Even though that it is a lot of adjectives, such systems are everywhere. I will just give two examples that I have been interested in. The first one is on a large scale, coarsely described as dynamical astrophysics. For instance, to find a habitable (to life forms similar to terrestrial ones) planet other than Earth, understanding long-term nonlinear interactions among objects in its stellar system is vital. Of course, that candidate planet has to be at an appropriate distance from its host star, but it is also important that its orbit doesn’t slowly get perturbed into an eccentric ellipse, which will mean glacial winter or sizzling summer (should I also mention more violent scenarios, in which the planet collides with another major object, being thrown out of its stellar system, or gets slingshot towards its star?) The second example is a small scale one, which is molecular dynamics. Even without invoking quantum mechanics, it is intriguing enough how biomolecules, in a noisy environment, accomplish structural changes which could take ~1E-3 seconds, by coordinating small scale dynamics such as bond oscillations with periods of ~1E-15 seconds.
If you were not teaching/conducting research, what would you be doing?
House husband, financial industry, programmer (or pro gamer?)