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Mathematician Tries to Solve Wave Equations

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UCLA professor Terence Tao.

University of California, Los Angeles professor Terence Tao is using computers to determine whether wave equations can "exhibit blowup."

Credit: Reed Hutchinson/UCLA

University of California, Los Angeles professor Terence Tao is using computers to help him solve a tricky mathematical question: whether wave equations, also known as partial differential equations (PDEs), which describe the behavior of waves of everything from water to sound to light, can explode, or "exhibit blowup."

Tao notes this is the opposite of when a stone is thrown into a pond, generating waves. "Imagine a whole bunch of ripples in concentric circles converging to a single point and exploding," he says. Tao says his work relates to the concept of "rogue waves," where unexpected, large oscillations can emerge in a PDE when it is run over a long period of time. Tao studies this effect by using computers to run dozens of PDEs covering a wide range of possible scenarios, from basic physics up to and including every type of fluid in every conceivable situation.

Tao says his work could have useful applications in predicting weather events or natural disasters such as earthquakes, but the research's true utility will likely only be apparent in retrospect, noting, "in pure mathematics, we never really know where the applications are going to show up when working on foundational issues."

From National Science Foundation
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