The Fermi-Pasta-Ulam Experiment

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

The Fermi–Pasta–Ulam problem is named after the pioneering numerical experiments realized by Enrico Fermi, John Pasta, and Stanislaw Ulam in 1955 using the Los Alamos MANIAC computer. Based on the Debye theory of crystals, they considered a system of particles of mass connected by harmonic springs, but introduced a quadratic nonlinear term. They expected ergodic behavior, but to their surprise, observed recurrent behavior. The continuum limit of the model is the Korteweg–de Vries nonlinear partial differential equation.

Contributed by: Enrique Zeleny (August 2012)
Open content licensed under CC BY-NC-SA



The equations of motion are


where is the displacement of particle from its equilibrium position. The first factor represents Hooke's law, and the term containing represents the nonlinear force.


[1] T. Dauxois and S. Ruffo. "Fermi–Pasta–Ulam Nonlinear Lattice Oscillations." Scholarpedia, 3(8):5538. (Aug 24, 2012) _lattice _oscillations.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.