Master Thesis Defense by Cairu Duan

Title: Rare Events and Large Deviation Analysis in a Conceptual AMOC Model 

Abstract: 
This thesis investigates noise-induced transitions in multistable dynamical systems using Freidlin–Wentzell large deviation theory and numerical simulations. The most probable transition path, also known as the minimum action path (MAP), is computed in three systems: a one-dimensional double-well potential, a two-dimensional skewed potential, and the five-box model of the Atlantic Meridional Overturning Circulation (AMOC). For each system, MAPs are computed for various transition durations using a Monte Carlo method and compared to noisy transitions sampled using Adaptive Multilevel Splitting (AMS), a rare event sampling algorithm. It is found that when MAPs are computed using the mean transition time from AMS simulations, the resulting paths closely match the noisy trajectories in both spatial structure and time evolution. Furthermore, the results reveal that transition time, noise strength, and potential steepness are closely related and together determine whether the path avoids or crosses the saddle. In the AMOC model, it is found that the ON to OFF (collapse) and OFF to ON (recovery) transitions follow different paths. ON to OFF transitions begin with an initial increase in AMOC strength before collapsing to the OFF state, while OFF to ON transitions exhibit an overshoot in AMOC strength before stabilising at the ON state. These features become more pronounced as the allowed transition time increases. Furthermore, the point where the MAP crosses the basin boundary moves closer to the saddle point as the transition time increases. Lastly, the action values associated with ON to OFF transitions are lower than those for OFF to ON transitions, suggesting that collapse is more likely than recovery.

Supervisor: Peter Ditlevsen
Censor: Jens Olaf Pepke Petersen, DTU space