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UEA mathematicians solve 60-year-old problem

University of East Anglia

A 60-year-old maths problem first put forward by Nobel laureate Enrico Fermi has been solved by researchers at the University of East Anglia, the Università degli Studi di Torino (Italy) and the Rensselaer Polytechnic Institute (US).

In 1955, a team of physicists, computer scientists and mathematicians led by Fermi used a computer for the first time to try and solve a numerical experiment.

The outcome of the experiment wasn't what they were expecting, and the complexity of the problem underpinned the then new field of non-linear physics and paved the way for six decades of new thinking.

Chaos theory, popularly referred to as the butterfly effect, is just one of the theories developed to try and solve the 'Fermi-Pasta-Ulam' problem.

Researchers at UEA looked to the oceans for inspiration and used what is known as wave turbulence theory to partially solve the problem.

Dr Davide Proment from UEA's School of Mathematics, said: "Enrico Fermi, John Pasta and Stanislaw Ulam outlined the first ever computer simulation for research purposes - of a one-dimensional vibrating nonlinear string.

"It was designed to mimic how heat is conducted into solids and the authors expected to observe that the heat energy would be equally distributed after a while.

"On the contrary, they reported a complicated recurrence phenomena which led to the development of new maths and physics theories over the last six decades.

"Various mathematical approaches have been put forward to understand the recurrence, now called FPU-recurrence, and explain the thermalization, which occurs only at incredibly large time scales.

"We borrowed ideas from a different mathematical topic called wave turbulence theory, which was developed and applies to wave systems like ocean or plasma waves.

"Thanks to this lateral approach, we partially answered the 60-year-old FPU problem. We were able to predict the long thermalization timescale knowing the initial conditions of the system. We also corroborated our theoretical result with extensive numerical simulations.

"This is an interesting example on how cross-fertilisation between different areas of maths and physics can be sometimes very successful."

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'Route to thermalization in the α-Fermi-Pasta-Ulam system' is published in the journal PNAS on March 24, 2015.

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