You are invited to join this year’s MAGIC launch lecture on Thursday 30 September at 16:00.
Please do attend if you are able to. Staff, students and researchers are all welcome.
To join please go to “This week” and select the “Join lecture” button which will appear shortly before the start of the lecture.
Please note you will you need to have set up a MAGIC Zoom account to join this live lecture – instructions on how to do this can be found in the "How to join a live lecture
" thread on the MAGIC General Forum.
Should you be unable to join on the day the lecture will be recorded and available to view at a later time.
MAGIC Launch Lecture Title: Thermalisation in weakly nonlinear chains
Speaker: Davide Proment (University of East Anglia)
Date: Thursday 30 September 2021 at 16:00 – 17:00
Abstract: I will present some theoretical results on the seminal $\alpha$-Fermi-Pasta-Ulam-Tsingou (FPUT) problem, that is a one-dimensional system formed N=16,32 and 64 masses connected by nonlinear quadratic springs.
The theoretical approach is based on resonant wave-wave interaction theory and wave turbulence theory.
Assuming the weakly nonlinear regime, the one originally considered by Fermi to model heat transport in crystals, I will show that the long time dynamics of the system is ruled by exact discrete wave resonances.
After giving a general introduction to the 1955 Fermi-Pasta-Ulam-Tsingou model, a system that inspired areas in mathematics and physics like integrable systems, ergodic theory, nonlinear waves, and statistical mechanics, I will discuss the main idea of the wave-wave interaction theory and wave turbulence theory.
I will show that the first non-trivial wave resonances correspond to six-wave interactions as solutions of Diophantine equations.
These interactions are responsible for the thermalisation process in the FPUT system and explain its extremely long time scale.
Numerical simulations supporting out theoretical predictions will be briefly discussed (based on the joint work with Miguel Onorato, Lara Vozella and Yuri V. L'vov entitled "A route to thermalisation in the $\alpha$-Fermi-Pasta-Ulam(-Tsingou) system", PNAS 112, 4208-4213, 2005)
I hope you will be able to join us.