Kinetic theory and stochastic simulations
- Code: DT0601
- Unit Coordinator: Matteo Colangeli
- Programme: Double Degrees
- ECTS Credits: 6
- Semester: 1
- Year: 2
- Campus: University of L'Aquila
- Language: English
- Aims:
The course aims at offering an overview on the mathematical foundations of the classic kinetic theory of gases and on the derivation of the equations of fluid dynamics. Some basic notions on the theory of Markov Chains will be reviewed and some techniques of Monte Carlo simulations will be discussed. Such techniques will be then used in the development of a numerical project: the simulation of the 2D Ising model.
- Content:
Liouville Equation in the phase space; BBGKY Hierarchy; Boltzmann Equation for hard spheres and generalizations; H-Theorem; Kinetic models; Derivation of hydrodynamic laws; Kac ring model; Markov Chain Monte Carlo; Metropolis and heat bath algorithms; phase transitions in the 2D Ising model.
- Pre-requisites:
Basic notions of Mathematical Analysis and of Probability Theory
- Reading list:
Carlo Cercignani, The Boltzmann equation and its Applications, Springer‐Verlag 1988.
Neal Madras, Lectures on Monte Carlo Methods, American Mathematical Society, 2002.
