Computational Physics
Prerequisiti
None, although some foreknowledge of numerical analysis and coding practice (Fortran, C, C++, Matlab, Mathematica, Python, Julia...) will help. Some basic knowledge of physics will also facilitate the learning task.
Programma
In this Course, we shall illustrate the main computational methods which permit to simulate and analyse the behaviour of a wide range of problems in science and engineering, mostly but not exclusively involving fluids, soft matter, biophysics, classical and quantum waves. Special attention will be paid to the modelling/programming techniques involved in the simulation of complex systems, as well as to methods to analyse simulation data and extract knowledge therefrom.
1. Grid methods for classical and quantum fields
(a) Basics of grid-discretization
(b) Finite Difference Method for linear PDE's (transport phenomena)
(c) Finite Difference Method for nonlinear PDE's ( fluids and waves)
(d) Brief intro to Finite Volume and Finite Element methods
2. Mesoscale methods
(a) Lattice Boltzmann for Fluids
(b) Lattice Boltzmann for Soft Matter
(c) Numerical solution of Fokker-Planck equations
(d) Stochastic Particle Methods
3. Data analysis and machine learning
(a) Rudiments of Machine Learning
(b) Time-series and probability distribution functions
(c) Analysis of turbulent signals
Obiettivi formativi
At the completion of the course, the student is expected to be able to:
1. Employ and develop concepts and methods for the large scale simulations of the dynamic behaviour of complex systems, as well as the corresponding data analysis techniques.
2. Read the current literature and appreciate the various approaches to large-scale simulation of scientic and engineering applications
3. Choose and code the most appropriate computational techniques for modelling and data-analysing complex problems in physics, engineering biology and also social sciences.
4. Contribute to research projects involving the simulation and data analysis of complex natural and social systems.
Riferimenti bibliografici
- P. Moin, Fundamentals of Engineering Analysis, Cambridge U.P., 2001 (https://www.amazon.com/Fundamentals-Engineering-Numerical-Analysis-Parviz/dp/0521711231)
- T. Pang, Computational Physics, Cambridge Univ. Press, 2006, (https://www.amazon.it/Introduction-Computational-Physics-Tao-Pang/dp/0521825695/ref=tmm_hrd_swatch_0?_encoding=UTF8&qid=1565251184&sr=8-1-fkmr0)
- S. Succi, The lattice Boltzmann Equation for complex states of owing matters, Oxford Univ. Press, 2018 (https://global.oup.com/academic/product/the-lattice-boltzmann-equation-9780199592357?cc = it&lang = en&)
- Y. Abu-Mostafa et al, Learning from Data, 2012 (https://www.goodreads.com/book/show/15706459-learning-from-data)