Lyapunov exponents and diffusion rates

A windtree model is an extremely simplified modelling of wind blowing in a planted forest. These models turn out to be very rich, and a lot of questions about them remain open.
Recently the speed of the wind in some of them have been linked with Lyapunov exponents introduced for translation surfaces in stata of quadratic differentials.
The speed in that matter being measured by a number called diffusion rate.

After giving an overview on the advances about these questions, I will define and present techniques to compute orbit closures for the action of the Teichmüller flow on translation surfaces in their moduli spaces. Which are one of the key objects to compute this speed.