Fermi-Pasta-Ulam Problem

Here are the set of notes I took during the project, as well as some results. Click here to access the full project and the codebase!

This project studies the thermalisation and recurrence of the Fermi-Pasta-Ulam (FPU) problem. Through numerically solving Hamilton's equations for the system using SymPy's Backwards Difference Formula (BDF), the flows and energies are found. Modal spectra and spectral energies are found via a Discrete Sine Transform (DST) and progress towards thermalisation is formally quantified using Shannon Entropy.  The solver predicts recurrence time to within 3.5% error of the original 1955 paper by Fermi, Pasta and Ulam.  (Aug 2025, Summer of Year 1)