The Fermi Pasta Ulam Problem

Chandra, Nitish Kumar (2021) The Fermi Pasta Ulam Problem. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS Dissertation of Nitish Kumar Chandra (16MS122)) 16MS122_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (7MB)

Abstract

The Fermi Pasta Ulam problem consists of a chain of particles which are connected with nonlinear oscillators. In this work, we implement the 4th Yoshida integrator to observe quasi-periodic behavior leading to recurrences and super-recurrences in �-FPU model. We then study energy sharing in � + � FPU model for N = 124 and N = 1023 at small energy density. We characterize the dynamics of different physical systems like Lorenz model, a dissipative system and Henon-Heiles potential, a conservative Hamiltonian system using lyapunov exponents. We implement the Wolf’s algorithm in �-FPU model to calculate the lyapunov spectrum and analyze its dynamics. We then investigate, how lyapunov exponents scale on changing the nonlinear parameter � and the energy of the system when the first energy mode of the system is excited.

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