Dear Colleagues,
We would like to invite you to the following (double) SPASS seminar, jointly organized by UniPi, SNS, UniFi and UniSi (abstracts below):
Some recent developments in wave turbulence theory by *Gigliola Staffilani* (MIT)
Homogeneous and heterogeneous nucleation in the three-state Blume-Capel model by* Vanessa Jacquier* (University of Utrecht)
The seminars will take place on *TUE, 12.9.2023* respectively at *14:00 CET and 15:00 CET *in Aula Seminari, Dipartimento di Matematica, University of Pisa and streamed online at the link below.
The organizers, A. Agazzi, G. Bet, A. Caraceni, F. Grotto, G. Zanco https://sites.google.com/unipi.it/spass https://www.google.com/url?q=https://sites.google.com/unipi.it/spass&source=gmail-imap&ust=1665669490000000&usg=AOvVaw07o0tKOUGmZjDDF2Ta7pQY
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Some recent developments in wave turbulence theory
Abstract: In this talk I will present two different approaches in the study of wave turbulence theory. The first, introduced by Bourgain, consists in analyzing the long time behavior of high Sobolev norms for the defocusing, cubic NLS equation on 2D tori (periodic solutions). In this context I will emphasize how the rationality or irrationality of the torus affects the analysis. The second approach deals with the rigorous derivation of the 3-wave kinetic equation from a weakly nonlinear multidimensional KdV type equation.
Homogeneous and heterogeneous nucleation in the three-state Blume-Capel model
Abstract: We study the metastable behavior of the stochastic Blume–Capel model evolving according to the Glauber dynamics with zero boundary conditions. We will show that, due to the three–state character of the Blume–Capel model, the metastability scenario proven for periodic boundary conditions changes deeply when different boundary conditions are considered. The Hamiltonian of the Blume–Capel model depends on the magnetic field h and the chemical potential λ. We study the heuristic in the whole region λ,h > 0, where the chemical potential term equally favors minus and plus spins with respect to zeroes and the magnetic field favors pluses and disadvantages minuses with respect to the zeroes, and we compare our results with the Blume-Capel model with periodic boundary conditions. Then, we analyze in detail the region λ>h > 0. In this region, we identify the unique metastable state -1, we compute the energy barrier from -1 to the stable state +1, and we find an estimate for the asymptotic behavior of the transition time from the metastable to the stable state as β->∞, where β is the inverse of the temperature.