Fermi-Pasta-Ulam problem پراسهی ِ فرمی-پستا-اولام parâse-ye Fermi-Pasta-Ulam
*Fr.: expérience Fermi-Pasta-Ulam*
A computer experiment that was aimed to study the
→ *thermalization* process of a
→ *solid*.
In other words, the goal was to see whether there is an
approximate → *equipartition of energy*
in the system, which would mean that the motion is
→ *chaotic*.
Using computer simulation, Fermi-Pasta-Ulam studied the behavior of
a chain of 64 mass particles connected by → *nonlinear*
springs.
In fact, they were looking for a theoretical physics problem
suitable for an investigation with one of the very first computers,
the he MANIAC (Mathematical Analyzer, Numerical Integrator and
Computer). They decided to study how a → *crystal*
evolves toward → *thermal equilibrium*
by simulating a chain of particles,
linked by a quadratic interaction potential, but also by a weak
nonlinear interaction.
Fermi-Pasta-Ulam assumed that if the interaction in the chain
were nonlinear,
then an exchange of energy among the normal modes would occur, and
this would bring forth the equipartition of energy, i.e. the
thermalization.
Contrary to expectations, the energy revealed no tendency toward
equipartition. The system had a simple quasi-periodic behavior,
and no → *chaoticity*
was observed. This result, known as the Fermi-Pasta-Ulam paradox,
shows that → *nonlinearity*
is not enough to guarantee the equipartition of energy
(see, e.g., Dauxois et al., 2005, Eur. J. Phys., 26, S3). E. Fermi, J. Pasta, S. Ulam, 1955,
Los Alamos report LA-1940; → *problem*. |