Statistical mechanics of spin systems
Numerical simulations: Markov chains, Montecarlo alghoritms, Glauber and Kawaski dinamics. Cluster alghoritm.
Stochastic dynamics: Brownian motion, Langevin equation, Fokker-Plank equation.
Interacting particle systems: hydrodynamic limit, Onsager theory.
Stochastic Interacting particle systems: symmetric exclusion and Burgers equation.
Fluidodynamics: Euler, Navier-Stokes, Boussinesq equations. Incompressible limit.
Mean field theory out of equilibrium: Vlasov, Vlasov-Fokker-Plank equations, swarming e flocking.
The course is intended to provide and advanced background in Physics with knowledge of specialistic topics in the recent research, with specific attention to the Physices of Complex systems and Fluiddynamics. Among the learning outcomes is the advanced knowledge of numerical simulation techniques, deterministic and stochastic interacting particle systems,fluiddynamic equations. Skill to solve general problems in the aforementioned context.
KNOWLEDGE AND UNDERSTANDING:
The students are required to acquire a deep understanding of the topics presented in the course. A good knowleg of the state of the art is also required. The knowledge and ability of understanding is verified by means of oral exams.
APPLYING KNOWLEDGE AND UNDERSTANDING:
The students are required to identify the essential elements of a physical problem, possibly complex, within the material presented and construct suitable models based on appropiate approximations.