Einladung zum Vortrag im Kolloquium
Dynamics and controllability of deformable bodies immersed in perfect and Stokes fluids
Dr. Alessandro Arsie
Department of Mathematics
University of Toledo
Toledo • MA • USA
Dienstag, 20. Juli 2010 · 16:00 Uhr
IST-Seminarraum 3.243 · Pfaffenwaldring 9 · Campus Stuttgart-Vaihingen
Modeling and understanding how deformable bodies and fluids interact is important not only from a theoretical point of view, but also for many applications, ranging from the design of optimal swimming strokes, submarine building, biological applications and energy harvesting using ocean tides.
In this talk it will be proved that in the case of perfect and Stokes fluids, the dynamical description of immersed deformable bodies is fully captured through a system of nonlinear ODEs. I will also show how natural control problems arise in this set-up, considering as control inputs some of the Langrangian coordinates describing the system. A geometric framework will be presented to analyze this kind of problems, and the issue of controllability will be related to the holonomy of an Ehresmann connection on a suitable bundle. Many examples will be presented and their controllability assessed. In particular, a proof of the controllability of a system investigated numerically by Valery Kozlov and collaborators will be presented.
This is joint work with Alberto Bressan (Penn State University, USA) and Franco Cardin (University of Padova, Italy).
Alessandro Arsie obtained a BSc (laurea) in Physics from the University of Padova and PhD in Mathematical Physics from the International School for Advanced Studies, Trieste. He hold post-doctoral appointments with the department of Mathematics at the University of Bologna, with the Laboratory for Information and Decision Systems at MIT and with the department of Mathematics at Penn State University. He is currently assistant professor of Mathematics at the University of Toledo, USA. His previous research interests were in algebraic geometry. His present research interests are in dynamical systems, with a focus on control systems and integrable systems, especially from a geometric point of view.