Seminar 21/10/16: Noise and dissipation on coadjoint orbits

Noise and dissipation on coadjoint orbits
Alexis Arnaudon
Imperial College London
Friday 21 October 2016
1pm, Blue Room, DIT Kevin Street


In this talk I will start by introducing a stochastic perturbation of mechanical systems with symmetries that is most compatible with the preservation of geometrical invariants, or conserved quantities. In order for interesting phenomenons to emerge in these systems, I will add a dissipative term that also preserves the geometrical structure of the equations. Having both noise and dissipation in these systems will allow me to make a thermodynamical interpretation of the expected solutions and introduce a notion of temperature. Another feature is the existence of the so-called random attractors, a building block in modern random dynamical systems theory, that I will present in some details, with helps of some numerical simulations. My main examples of such systems will be the free rigid body associated to the group of rotations, and the heavy top when this symmetry is broken and requires the theory of semi-direct products. I will discuss some numerical challenges associated to these stochastic processes, and, if time permits, another application of this methodology to landmark dynamics in image matching.

This is joint work with D. Holm and A. De Castro and is an arXiv paper with number 1601.02249