PHYSICS OF COMPLEX SYSTEMS AND LABORATORY
Academic year and teacher
If you can't find the course description that you're looking for in the above list,
please see the following instructions >>
- Versione italiana
- Academic year
- 2015/2016
- Teacher
- HUBERT FERDINAND RICHARD SIMMA
- Credits
- 6
- Didactic period
- Secondo Semestre
- SSD
- FIS/01
Training objectives
- The main goal of this course is to provide basic knowledge about different types of complex systems in the context of physics problems and to enable the students to analyze and interpret the properties of such systems by carrying out numerical simulations on a computer.
In particular, the course conveys
knowledge about different ways to define and analyze systems in terms of their states and dynamics
the ability to describe real physical system by abstract models
methods to qualitatively analyze, classify and predict the behavior of a system
practical scientific-computing techniques for the numerical simulation of complex systems on the computer
capability to implement such simulations efficiently, to analyze the results, and to estimate their precision Prerequisites
- Familiarity with basic concepts and methods provided in the elementary physics courses (classical mechanics, statistical physics, quantum mechanics) and basic knowledge of computational methods (numerical computations, programming in C)
Course programme
- Definition of systems through states and dynamics (discrete and contiguous states, degrees of freedom and dimensions, deterministic and stochastic dynamics)
Properties of dynamical systems and origins of complex phenomena (dynamical systems, bifurcations, fractals and chaos, ergodicity)
Techniques of numerical computer simulations (representations, integrators, Monte Carlo methods)
Examples and applications (cellular automata, chaotic maps, random number generators)
Basic concepts of probability theory and stochastic processes (random variables, probability distributions, random walk, stochastic calculus, Markov chains)
Methods and phenomena in the framework of statistical physics (diffusion, phase transitions, scaling, renormalization group)
Monte Carlo simulations of statistical systems (ideal gas, spin models)
Statistical data analysis (estimators, correlations and auto-correlations, fits) Didactic methods
- Lectures and practical exercises using the own computer
Learning assessment procedures
- Oral exam including the presentation of a small project carried out by the student and questions about topics treated during the course.
Reference texts
- D. Amit, V. Martin-Mayor, "Field Theory, the Renormalization Group, and Critical Phenomena"
L. Barone et al., "Scientific Programming"
J. Hale, H. Kocak, "Dynamics and Bifurcations"
K. Huang, "Statistical Mechanics"
