Computational Physics

Master “Erasmus Mundus”
in Nuclear Fusion Science and Engineering Physics

Academic year: 2013-2014

Timetable: 2nd semester

– Starts on March 28, 2014
– Fridays, 10:30-13:30, Aula Sum, Aula 16, Facultad de Ciencias Físicas, UCM

Syllabus of the 2nd part of the course

– Random and pseudo-random numbers.
– Statistics. Estimation. Least-squares method. chi^2. Errors and confidence levels.
– Molecular Dynamics Simulations. Statistical Mechanics. Constant energy. Constant temperature. Molecular systems. Long-range interactions. Langevin dynamics.
– Monte Carlo Methods and Simulation. Monte Carlo integration. Importance sampling. Ising model. Metropolis algorithm.
– Optimization Problems and Genetic Programming. Indirect and direct Methods. Hillclimbing. Genetic algorithms. Multi-objective optimization. Simulated annealing.
– Symbolic Computing. High-Performance Computing: Types definition. Problems with symbolic calculations. Pipelining. Parallelism.

Bibliography

– W.H. Press, S.A. Teukolsky, W.T Vetterling, B.P. Flannery, Numerical Recipes in Fortran: The Art of Scientific Computing.
– R.J. Barlow, Statistics: A Guide to the Use of Statistical Methods in the Physical Sciences (Wiley).
– J.M. Thijssen, Computational Physics (Cambridge University Press).
– D.E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley).
– K. Deb, Multi-objective Optimization using Evolutionary Algorithms (Wiley-VCH)
– Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs (Springer)

Lectures

1. Presentation

2. Random Numbers
Additional Material

3. Statistics: Estimation
Additional Material

4. Statistical Mechanics

5. Molecular Dynamics

6. Monte Carlo Integration

7. Metropolis Monte Carlo

8. Ising Model

9. Genetic Algorithms
Additional Material

Additional classroom material

The Linux Random Number Generator

Australian National University Quantum Random Number Generator

Notes on Random Numbers

Exercises

- Exercise 1: Random Numbers

- Exercise 2: Mudlit-dimensional integration of the volume of the Sphere with MC

Evaluation

- Exercise 1: Random Numbers (25%)
- Exercise 2: Sphere D-dimensional integration with MONTECARLO (25%)
- Presentation (50%)