Localisation of energy in the FPUT- α system with variability and its chaotic behaviour. 

Localisation of energy in the FPUT- α system with variability and its chaotic behaviour. 

Fermi, Pasta, Ulam, and Tsingou studied one-dimensional lattices to model the crystal evolution towards thermal equilibrium. They expected to observe the equipartition of energy as predicted by the Boltzmann-Gibbs (BG) statistics due to nonlinearities in their model.

However, they noticed that almost all energy was back to its initial state after some period of steady state. This phenomenon, well-known as the FPUT recurrences, led to numerous discoveries in mathematics and physics. A recent study by Nelson et al. shows that if variability is incorporated in the FPUT system, it will limit the observance of recurrences. They numerically show that this variability can prevent recurrences in this system.

In this talk, we will discuss two-modes approximations in the normal mode coordinate to explain the localisation of energy for large enough variabilities. Moreover, we also investigate the chaotic behaviour of the FPUT-α system for different numbers of particles as we increase the variabilities by computing the maximum Lyapunov exponent and the SALI of this system.

Speaker

Zulkarnain, University of Essex.

How to attend

If not a member of the Dept. Mathematical Science at the University of Essex, you can register your interest in attending the seminar and request the Zoom’s meeting password by emailing Dr Jesus Martinez-Garcia (jesus.martinez-garcia@essex.ac.uk)