Mathematical research furthers filmmaking, thanks to derivatives

Author: Madeline Schlehuber

Fb Postdoc Spotlight Ziyao Xu 1

In the scenes of some of our favorite movies, actors battle oceans’ waves, set sail, and enjoy beautiful, powerful scenes of stunning water. Postdoctoral research fellow Ziyao Xu shared a secret: that technology is only possible because of complex math.

“Many (scenes in) fancy scientific movies and pictures are obtained from numerical simulations, so actually in some movies the water is not real. It's a simulation from a computer, so we study this kind of matter,” said Xu, who works in the Department of Applied and Computational Mathematics and Statistics (ACMS).

With the help of mathematicians who study fluid dynamics using numerical analyses, Xu advances work on data about how water flows through different substances and scenarios, simulating these situations using models. Then, with these more precise assessments on the flow of water (or other fluids), film technology can better represent water without getting their cameras up-close and personal with actual oceans or water sources. To keep up with increasingly convincing technology and animation, accurate and efficient mathematical modeling and numerical simulation for water or fluid movement is crucial.

Xu is in his first year as a postdoctoral researcher after receiving his doctorate in applied mathematics. So far, in addition to his research, he enjoys teaching students. “I am currently teaching dynamical systems this semester… it is related to my research, but simpler, because it involves fewer derivatives,” he said. Xu explains that these scenarios may be simpler, “but they require more mathematical tools, so it isn’t necessarily easier.”

Using differential equations in his research can help relate to other situations, such as efficiency in natural gas extraction and how the pressure of water distributes underground, he said. This kind of analysis can lead to better predictions in production rates of petroleum, which is one topic Xu is currently studying.

As a postdoctoral fellow in the department, Xu will be working and researching at Notre Dame for the next three years, where he is excited to collaborate with others on advancing their research.