Cari colleghi,
vi ricordo che *domani giovedì 12 Settembre, ore 18:00, in Aula Magna**,
*si terrà il seguente colloquio del Dipartimento di Matematica. Il
colloquio è aperto a tutti e sarà preceduto come da consueto da un
rinfresco a partire dalle ore 17:30. Siete tutti invitati a partecipare.
Speaker: *Klas Modin* (University of Gothenburg)
Title: *Statistical mechanics, 2-D fluids, and structure-preserving
numerics*
Abstract:
In a 1949 paper, the Norwegian American genius Lars Onsager demonstrated
that Boltzmann’s theory of statistical mechanics provides insights to
the long-time behavior of 2-D fluids described by Euler's equations. The
key notion is to “approximate” the fluid by a finite number of
interacting point vortices. Since these are governed by Hamiltonian
dynamics, the framework of statistical mechanics provides a
characterization of the long-time asymptotic behavior. The approach
successfully predicts clustering of equally signed vortices, which is
part of Onsager’s legacy. Nevertheless, and as Onsager proclaimed in his
paper, the point vortex approximation is highly non-regular and might
therefore be poor. Furthermore, statistical mechanics assumes
ergodicity, which fails for 2-D Euler. In this talk, I will present
another finite-dimensional approximation of 2-D Euler due to Vladimir
Zeitlin. Unlike point vortices, Zeitlin’s model gives smooth
approximations. It thereby renders a refinement of Onsager’s statistical
approach, and, together with a symplectic numerical time-integration
scheme, provides a structure preserving numerical method. Simulations
using this method suggest compelling connections between 2-D Euler and
integrability of low-dimensional Hamiltonian systems with symmetry. The
work is joint with Milo Viviani.
Saluti,
Dario Trevisan