(Stine code: 63-740 and 63-745)
During the first semester we will focus on the treatment of nonlinearity. We will follow a number of examples in which nonlinearity appears in fluid dynamics as well as in simple models of climate, atmosphere and ocean dynamics (but not only). Central concepts will be bifurcations, periodic orbits and stability.
During the second semester we will instead study the raising of chaos. The approach will be predominantly geometric. Applications will be on predictability, transition to turbulence, Lagrangian dynamics, stirring and mixing and nonlinear stability (but not only).
PhD students, post-doctoral researchers and professors from any discipline (politics, philosophy, literature, etc), as well and non-academic people, are more than welcome to attend too.
- S.H. Strogatz, "Nonlinear dynamics and chaos", Westview Press
- J. Guckenheimer and P. Holmes, "Nonlinear oscillations, dynamical systems, and bifurcations of vector fields", Springer
During the second semester I will give a short introduction to Lagrangian and Hamiltonian dynamical systems. These are described in:
- G. Badin and F. Crisciani, 2018: "Variational Formulation of Fluid and Geophysical Fluid Dynamics - Mechanics, Symmetries and Conservation Laws -", Springer, DOI: 10.1007/978-3-319-59695-2 (order/download it on Springer's book webpage: here)
- First semester: An oral exam, with questions/exercises at the board. PhD students will get credits simply by attending at least 80% of the theoretical classes.
- Second semester: A review/project/experiment for the summer semester (early start is encouraged) followed by an oral exam.
- Possible experiments:
- Double and/or forced and/or magnetic pendulum
- Experiments on synchronization of chaos (example: two metronomes on a moving base)
- Experiments on chaos using electric circuits/chemical reactions
- Chaotic waterwheel
- Throughout the entire first and second semesters:
- 2012-2013: A Photo (or video) contest of natural fractals/patterns/synchronization.
- 2014-2015: It looks like that in 2014-2015 El-Nino will emerge. We will then try to integrate the lectures with the analysis of low-dimensional, chaotic models of El Nino. UPDATE: of course at the end El Nino didn't appear. We will then move the thematic project to the future.
- 2015-2016: El Nino is finally here...