MATR323 Basics of Monte Carlo Simulations, 5 cr
||Basics of Monte Carlo Simulations
||Basics of Monte
||Can be taken more than once||no
||Master's Programme in Materials Research
Master's Programme in Materials Research is responsible for the course.
Modules where the course belongs to:
- MATR300 Advanced Studies in Materials Research.
- Study Track in Computational Materials Physics
- Study Track in Medical Physics and Biophysics
- PAP300 Advanced Studies in Particle Physics and Astrophysical Sciences.
- Study Track in Astrophysical Sciences
- Study Track in Particle Physics and Cosmology
- TCM300 Advanced Studies in Theoretical and Computational Methods
The course is available to students from other degree programmes.
The course can be taken at any time, when it is available.
The course is given annually during the third teaching period (spring term).
After completion the course you will be able:
- Generate uniform and non-uniform random numbers by using different methods
- Apply pseudo- and quasirandom numbers for different tasks
- Perform Monte Carlo integration of multidimensional functions
- Estimate the statistical error of the mean for different methods
- Generate the synthetic data to improve on estimation of the average and the error of the mean
- Improve the convergence of the Monte Carlo integration result using different methods
- Create your own Game of life by using the Cellular automata principle
The attendance of the lectures is recommended. Returning home completed exercises is mandatory. The exercises are aimed to test the programming skills of students. These will contribute equalliy to the final grade of the exam along with the answers to the exam questions.
The programming skills are mandatory. Basic knowledge of probability theory is recommended.
|Recommended optional studies
Monte Carlo in Physics
Uniform random numbers
- Pseudo-Random Number Generators (RNG):
- linear algorithms: congruential and generalised feedback shift register(GFSR)
- non-linear algorithms: developments of congruential and twisted GFSR and Mersenne Twister RNG
- Stratified methods
- Quasi- RNG
Non-uniform random numbers
- Inversion, hit and miss and combined methods
- Markov chain
Monte Carlo integration, improving convergence of the Monte Carlo integration
Analysis of Monte Carlo integration result: estimation of the error of the mean
Generation of synthetic data to improve the analysis
Cellular automata and self-organized critical phenomena
|Study materials and literature
- Lecture notes and Supplementary material
- Numerical Recipes in C,
- The art of scientific computing, 2nd edition
- W.H. Press, S.A. Teukolsky, W.T.Vetterling, B.P.Flannery
|Activities and teaching methods in support of learning
Exercises are designed to help students to understand better the material of the course. Regular programming will help to implement the received knowledge during the course in practice.
|Assessment practices and criteria
The final exam is held in form of answering theoretical questions in form of essays, however, the grade for the exercises performed during the course give 50% of the total weight.
Current and future instruction
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