Computational Physics

Recommended Prerequisites

Those of the 3rd year (mechanics, Electromagnetism, Quantum Mechanics, Statistical Physics).

Teaching Methods

Practical teaching and learning in a Computational Physics Laboratory.

Learning Outcomes

The fundamental objectives of this course are indicated in the Dublin descriptors. In particular, it is intended that the student should be able to identify, implement and critically analyze a set of computational  methods to solve important problems in physics. The strategy involves the theoretical exposition of a broad set of methods, the computational work in the class and a system of evaluation based only in small projects work and respective reports (a final project has a free subject). These works should allow students to develop skills of research and individual work on solving advanced problems in Physics.

Work Placement(s)

No

Syllabus

0- Introduction to Computational Physics.
1- Numerical Integration (rectangular, trapezoid and Simpson rules) and error analysis. Monte Carlo method.
2- Projectiles with air resistance (integration of differential equations - Euler modified and 2nd order  Runge-Kutta) and the two-body problem of celestial mechanics.
3- Integration of the three body problem (one sun and two planets, and two suns and a planet) in celestial mechanics. Analysis of chaos.
4- Schroedinger Equation (numerical solution using 4th order Runge-Kutta). Zeros of a function of one variable: the bisection method.
5- Classical Molecular Dynamics: Verlet method for particles that interact according to a van der Waals potential with periodic boundary conditions. Means of Statistical Physics.
6- Laplace and Poisson equations.
7- Electrical discharges model.
8- Aggregation of aggregates.
9- Extremes of functions. Genetic algorithms .
10- Random walkers and Metropolis algoritm. Ising model.

Head Lecturer(s)

Helmut Wolters

Assessment Methods

Assessment
Project: 15.0%
Resolution Problems: 85.0%

Bibliography

Principalmente:

GOULD E TOBOCHICK, Introduction to Computer Simulation Methods in Physics, Addison Wesley.

Ver também:

HJORTH-JENSEN, M. Computational Physics. http://www.uio.no/studier/emner/matnat/fys/FYS3150/h11/undervisningsmateriale/Lecture%20Notes/lectures2011.pdf

PANG, Tao (2006). An Introduction to Computational Physics. Cambridge: Cambridge University Press.

ALLEN, M. P. and TILDESLEY, D. J. (1989). Computer Simulation of Liquids. Oxford: Clarendon Press.

FRENKEL, Daan and SMIT, Berend (2001). Understanding Molecular Simulation: From Algorithms to Applications. New York: Academic Press.

PRESS, William [et al.]. Numerical Recipes in F77/F90/C/C++: The Art of Scientific Computing, Cambridge: Cambridge University Press.