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How Partial Differential Equations Are Saving Lives

January 14, 2013

Friday morning, exactly as predicted, the first flakes of snow began to fall near my house in Coventry, Conn. The millions of us who live in the Northeast Corridor were prepared for a potentially record-breaking blizzard, and over the next 24 hours we watched that blizzard do exactly what the forecasters had predicted.

Accounting for Hurricane Sandy, this was the second time in the past six months that forecasters predicted catastrophic events with astonishing accuracy, saving lives and preventing even more devastating property damage. I think it appropriate to celebrate their achievements. I therefore propose creating a new holiday, to be celebrated every year on Feb. 8, the anniversary of this storm, and to be called National Numerical Solutions to the Navier-Stokes Partial Differential Equations Day.

The Navier-Stokes partial differential equations, named after their discoverers, the 19th-century mathematicians George Gabriel Stokes and Claude-Louis Navier, govern the motion of a general fluid. Although one can write the equations very compactly using modern mathematical notation, they contain within them the full range of turbulent behavior that occurs in moving fluids, in settings as varied as airflow over a wing, water waves on a beach, and, of course, the weather.

The complexity of the Navier-Stokes equations means that one cannot hope to write down solutions for them. Instead, scientists and engineers use computer programs to construct approximations to solutions; the “European Model” that has been cited recently in weather forecasts is such a computer program.

While there is no question that such a model is an interdisciplinary triumph, with physicists, engineers, computer scientists, statisticians, a whole range of environmental scientists, and mathematicians working together to collect data, write code, and test the output of the model against reality, without the Navier-Stokes equations there would be no place to begin.

Read more posts by Jeremy Teitelbaum, dean of the College of Liberal Arts and Sciences, on his blog.

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