UIB
Universitat de les
Illes Balears
Master in
Physics______________________________________________
COURSE DESCRIPTION
2006-2007 Academic Year
Technical information
Course
Course title: Stochastic Simulation Methods
Course code: a cumplimentar por el Centro de Tecnologías de la Información
Type of course: Optional
Level of course: Postgraduate
Year of study: First, second
Semester: First
Calendar: Mondays, 3.30 p.m. to 5.30 p.m. and Wednesdays, 10.30 a.m. to 11.30 a.m.
Language of instruction: Catalan/Spanish. English reading comprehension skills are
required. The course may be given in English, depending on the students enrolled.
Lecturers
Supervising lecturer
Name: Raúl Toral Garcés
Other lecturers
Name: Pere Colet Rafecas
Contact: raul@imedea.uib.es
Contact: pere@imedea.uib.es
Prerequisites
A bachelor’s degree in science
Number of ECTS credits 5
Number of classroom hours: 35
Independent study hours: 90
Description
Monte Carlo integration. Variance reduction methods. Random variable generation.
Markov chains. Dynamic methods: thermal bath and the metropolis approach.
Applications: phase changes, chemical reactions, population dynamics, nanotransport.
Stochastic optimisation. Stochastic differential equations. Molecular dynamics. Hybrid
methods.
Course competences
Specific
1. Have a grasp of the foundation of the Monte Carlo integration
2. Understand random number generators
3. Model processes with random components
4. Critically analyse and select the best numerical algorithm for simulating models
5. Approach and solve optimisation problems practically
Generic
1. Understand and express meaning in the languages of physics, mathematics and
programming
2. Apply theoretical and practical knowledge to problem solving
3. Apply information technologies
4. Be conversant with techniques for writing and publicly presenting individual and
research work
5. Initiate individual research in the field
Course contents
Concepts in probability: Random variables. Series of random variables. Law of large numbers.
Conditional probability.
- Introduction to Monte Carlo integration methods: Hit-or-miss methods. Sampling methods.
Variance reduction techniques. Biased and unbiased estimators.
- Uniform random number generation in (0,1). Random and pseudorandom numbers.
Generating congruence. Shift-back-register generators. Verifying random numbers.
- Random numbers with other probability density functions: Change and composition of
variables. Gaussian distribution. Numerical inversion. Rejection methods.
- Dynamic methods: Introduction. Markov series. Stationary probability in dynamical systems.
The Metropolis Algorithm. Thermal bath. Statistical Errors Statistics. Thermalisation.
- Acceleration methods: Clustering algorithm and extrapolation techniques.
- Molecular dynamics. Numerical integration in motion equations. Time reversibility and the
main properties in symplectic algorithms.
- Introduction to stochastic differential equations. The Langevin equation. Mathematical
properties of Gaussian white noise. Determinist dynamics compared to stochastic dynamics.
Numerical resolution: The Heun and Runge-Kutta methods. Coloured noise. The hybrid
Monte Carlo method and Gaussian acceleration.
- Applications according to student interest in the fields of phase changes (equilibrium,
kinetics, calculating phase diagrams), radiation-matter interactions, chemical reactions
(Gillespie method), cellular transport, neuronal behaviour, epidemic propagation, game theory
and other problems in the fields of economics and sociology.
Methodology and student workload
Subject-related
Teaching
competences
method
1, 2, 3, 4, 5
Classroom
sessions
3, 4,5,6,7
Practical classes
7,9
9,10
10
Tutorial
Presentation
Group work
Seminar
1, 2, 3, 4, 5
3,4,5,6,7
7,9
8,9
Theoretical study
Practical study
Theoretical work
Practical work
Type of group
Medium-sized
groups
Medium-sized
groups
Small
Medium-sized
groups
Medium-sized
groups
Student hours
20
Teaching staff
hours
20
10
10
2
1
2
1
2
2
50
15
15
10
Ten percent of course activities are distance-learning classes (e-learning)
Assessment instruments, criteria and learning agreement
Assessment criteria
1. Acquisition and/or fulfilment of course-specific competences
2. On-going student interest and participation throughout the course
Assessment instruments
1. Presentation of work (e.g., based on course material or the reproduction of a published
scientific study). Student-proposed problems of interest in specific fields.
2. On-going evaluation of participation in practical classes, efficiency and clarity in
programming algorithms, presentation of group work, etc.
Grading criteria
1. 50% of the grade: Presentation of programs and theoretical developments
2. 50% of the grade: Presentation of work, problem solving in practical classes
Assessment based on a learning agreement: No (enlace al contrato)
Independent study material and recommended reading
Material available on the Internet and photocopies given out by lecturers
Bibliography, resources and annexes
1- Monte-Carlo Methods, vol. 1: Basics, M. Kalos and P. Whitlock, John Wiley and Sons
(1986).
2- Computer Simulation Methods in Theoretical Physics, D. Heermann, Springer Verlag (1986).
3- Numerical Solution of Stochastic Differential Equations, P. E. Kloeden, E. Platen, Springer
(1992).
4- Simulation and the Monte-Carlo Method, R. Rubinstein, John Wiley and Sons (1981).
5- Distribution Sampling for Computer Simulation}, T. Lewis, Lexington Books (1975).
6- Computer Simulation of Liquids}, M.P. Allen and D.J. Tildesley, Clarendon Press (1987).
7- D.E. Knuth, The Art of Scientific Programming, vol. 1: Semi-numerical Algorithms,
Addison-Wesley (1981).
8- Mathematical Biology, James D. Murray, Springer, 3rd ed. 2002.
9- Probability, Random Variables and Stochastic Processes, A. Papoulis, McGraw-Hill (1984).
10- Probability and Random Processes, G.R. Grimmett, D.R. Stirzaker, Oxford Science
Pub.(1985).
11- Stochastic Processes in Physics and Chemistry, N.G. van Kampen, North-Holland (1987).
12- Third Granada Lectures in Computational Physics, J. Marro, P. L. Garrido, eds. Springer
(1995).
Link to the course teaching guide