Monte Carlo-simuloinnit / Monte Carlo simulations
Monte Carlo-simuloinnit, 2+2 ov (4+4 op) / Monte Carlo simulations, 2+2 sw (4+4 op)
Huom. Vuodesta 2005 alkaen kurssi on jaettu kahteen osaan:
- 530119 Monte Carlo-simulointien perusteet, 2 ov, 4 op
- 530153 Monte Carlo-simuloinnit fysiikassa, 2 ov, 4 op
Edellinen on suunnattu kaikille matemaattis-luonnontieteellisille
tieteille, ja luennoidaan joka vuosi. Jälkimmäinen luennoidaan
joka toinen vuosi. Opintooppaassa 2005-2006 on virhe opintopisteiden
suhteen, oikea määrä on 4 op/osakurssi.
Course names in English:
- Basics of Monte Carlo simulations
- Monte Carlo simulations in physics
Kursnamn på svenska:
- Grunder för Monte Carlo-simuleringar
- Monte Carlo-simuleringar i fysik
Sisältökuvaus: osa 1
Opetusajankohta: kl. 2005 ti, to 10-12 (luennot
pääasiassa tiistaisin, laskuh. torstaisin) 18.1-10.3. Ensimmäinen
luento 18.1.
Paikka: Kiihdytinlaboratorion seminaarihuone (Pietari Kalmin katu 2)
Laajuus: 2 ov
Kesto: 7 viikkoa
Ajankohta opintojen ajoitusmallissa: cum laude tai erikoistumisvaihe
Esitiedot: Matematiikka.
Fortran-, C- tai java-kielen perusteiden tuntemus.
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Sisältö (osa 1):
Kurssilla käsitellään useilla luonnontieteen aloilla hyvin tärkeiden
Monte Carlo-simulointimenetelmien perusteita.
Kurssilla käsitellään
satunnaislukujen generointia eri jakaumissa,
Monte Carlo-integrointia ja sen virhelaskentaa, synteettisen
datan generointia sekä soluautomaatteja
Suoritustapa:
Lasku/ohjelmointiharjoitukset ja loppukoe.
Kirjallisuus:
Luentomonisteet.
Tukena voi käyttää useitakin kirjoja, kts. englanninkielinen osuus alla.
Kommentteja:
Kurssi pidetään englanniksi pyydettäessä.
Laskuharjoituksiin ja kokeisiin voi vastata suomeksi,
ruotsiksi, englanniksi tai saksaksi.
Description: part 1 "Basics of Monte Carlo simulations"
Lecturing time: spring 2005: Tue, Thu 10-12 (lectures primarily on Tuesday, exercises on Thursdays) 18.1-10.3. First lecture 18.1.
Place: Kiihdytinlaboratorion seminaarihuone (Pietari Kalmin katu 2)
Lecturer: Prof. Kai Nordlund
Extent of course: 2 sw
Duration: 7 weeks
Normal year to be taken: specialization phase, third year and up.
Prerequisites: Mathematics.
Knowledge of the Fortran, C or java programming language.
Language of instruction: English, or Finnish if
everyone understands Finnish. The exercises and exams can in any case
be solved in Finnish, Swedish, English or German.
Course description:
During the course we will give an introduction to the so called
Monte Carlo simulation methods which are very important in
many branches of modern science.
During the course we will discuss generation of random numbers,
Monte Carlo integration and its error estimates, synthetic
data generation and cellular automata.
Exercises
Programming and mathematical exercises are given during the
course, but not every week. They are graded by the lecturer
For the more demanding exercises more than 1 week of solution time
is given.
The programming exercises should be preferably solved in an
Unix environment, but also solutions written under
other environments in strict adherence to the Fortran90,
ANSI C or java standards (so that they can be compiled anywhere)
are acceptable.
Evaluation:
Exercises (50 %)
Final exam (50 %)
Literature:
Lecture notes.
Some parts of the material are well described in
- W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery,
Numerical Recipes in C; The Art of Scientific Computing,
Cambridge University Press, New York, second edition, 1995
- M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids,
Oxford University Press, Oxford, England, 1989
- Gould, Tobochnik: An Introduction to Computer Simulation Methods : Applications to Physical Systems, Harvey Gould, et al
but acquiring any of these is not necessary for the course.
Exam
The exam will be on Thu Mar 10, 2005, 14:00-18:00.
Lectures
About lecturing times, barring any further unforeseen events they will
be as follows for the rest of the course
Thu Feb 10 lecture 10-12
Tue Feb 15 no lecture (due to a fusion seminar)
Thu Feb 17 lecture
Tue Feb 22 lecture
Thu Feb 24 exercise session 2:
Tue Mar 1 lecture
Thu Mar 3 exercise session 3:
I will try to put out the lecture notes here at least one day before
the lecture. After the lecture I may still correct errors and put a
new version here 'for the record'.
1. General information = this web page.
(2. skipped)
[PDF] [PS 2up] [PS notes] [PS 4up] [PS 32up] 3. History, definition.
[PDF] [PS 2up] [PS notes] [PS 4up] [PS 32up] 4. Generating random numbers
[PDF] [PS 2up] [PS notes] [PS 4up] [PS 32up] 5. Monte Carlo integration
[PDF] [PS 2up] [PS notes] [PS 4up] [PS 32up] 6. MC data analysis
[PDF] [PS 2up] [PS notes] [PS 4up] [PS 32up] 11. Cellular automata
Exercises
To be handed in by email to the lecturer.
PDF PS Exercise 1: random number generators
PDF PS Exercise 2: nonuniform random numbers
PDF PS Exercise 3: MC integration, synthetic data
PDF PS Exercise X: Cellular automata (bonus)
Exercise solutions
Only solution codes are given here. To get the descriptions you have to
come to the exercise session.
1.2
1.3
1.4
1.5
2.1
2.2
2.3
2.4
Exercise points
Person 1 2 3 X Sum % of total
1 2 3 4 5 6 1 2 3 4 1 2 3 1
--------------- ----------- --------- ------ --- --- ----------
Max Maximus 4 6 6 6 6 4 12 6 6 12 6 6 12 0 92 0.5
Tero Laakso 4 6 6 5 7 - 15 6 6 11 6 6 9 9 96 0.521739
Santeri Paavolainen 4 6 6 6 6 4 12 6 5 11 6 0 12 15 99 0.538043
Martin Zumsande 4 6 6 5 6 4 12 5 5 12 6 6 0 17 94 0.51087
Otso Koskelo 4 3 6 0 6 0 - - - - - - - - 19 0.103261
Sauli Lehtimaki 4 6 6 5 6 3 10 3 6 12 6 6 10 17 100 0.543478
Mathias Osterberg 4 6 6 6 6 0 12 6 5 10 6 6 12 17 102 0.554348
Teemu Salmi - - 6 6 6 0 12 6 6 12 6 6 10 9 85 0.461957
Jenni Virtanen 4 6 6 6 6 0 12 5 6 12 6 6 10 - 85 0.461957
Simo Kilponen 4 6 6 5 6 4 12 0 5 10 -6 6 6 6 - 82 0.445652
Reijo Keskitalo 4 6 6 6 6 4 12 6 6 12 6 6 12 17 109 0.592391
Anders Wallin 4 6 6 6 6 4 12 6 5 10 6 6 10 15 102 0.554348
Ari Raunio 4 4 6 6 6 4 9 4 6 12 6 6 12 17 102 0.554348
Henri Moilanen - - - - - - - - - - - - - - 0 0
(-6 pistettä jos palautus toistamiseen reilusti myöhässä).
Final point scale:
%
----------
<25.0 i
<45.0 +
<50.0 1-
<56.0 1
<62.0 1+
<68.0 2-
<76.0 2
<82.0 2+
<88.0 3-
>=88.0 3
List of contents: "Basics of MC"
- Introduction (1/2 hours)
- Times, lectures, exercises
- Monte Carlo - introduction (1 hour)
- Definition
- History: first MC simulation
- Confusing terminology, and trying to avoid it
- Even most MD is sort of MC!
- List of some varieties of MC
- Generating random numbers (4 hours)
- Importance of doing this well
- Testing generators: 2D, MC simulation, etc...
- Generating a uniform distribution
- Generating non-uniform distributions
- Analytical approach
- von Neumann rejection method
- Special case: Gaussian distribution
- Generating points on a surface of a sphere: the infamous pitfall
- Non-random random numbers: these may sometimes be better
- Monte Carlo integration (2-3 hours)
- MC integration of many-dimensional functions
- When is this advantageous compared to a grid?
- Weight functions
- MC simulation of experimental data (2 hours)
- Quick-and-dirty: the bootstrap method
- Test: how good is this actually?
- Simulation of physical process
- Cellular automata (2-4 hours)
- Basic concepts
- Numerical rule schemes
- Applications: sand piles, forest fires etc.
List of contents: MC simulations in physics
- Random walks: introduction (2 hours)
- Drunken sailor in 1 and 2D
- Relation to diffusion
- Lattice gas
- Length of polymers
- Kinetic Monte Carlo (2 hours)
- Motion of activated objects
- Trivial and residence-time algorithm
- Lattice and non-lattice
- Example: defect migration in Si
- MC simulation of ensembles (4 hours)
- MC and statistical physics
- Simulating atomic systems
- Metropolis algorithm: NVT
- Demon algorithm: NVE
- NPT and muPT algorithms
- Calculating thermodynamic quantities
- Simulated annealing (1 hour)
- Basic idea: Metropolis + T lowering (as in metals annealing)
- example: Annealing a metal
- example: Traveling salesman problem
- Exercise: solve the salesman problem
Time permitting and according to attendees interests possibly also some of the following:
- Ising model (1-2 hours) ?
- Definition of problem, algorithm
- Computer code
- Solving equations (2-6 hours) ?
- Linear sets of equations
- Integral equations
- Quantum Monte Carlo ?
- Solving the Schrödinger equation
- Random walk QMC (see e.g. Gould-Tobochnik)
- Transport simulations (4-8 hours) ?
- Relation to radiation effects
- Simulating ionic collisions
Taustatietoa/Background information
Course material from 2002
Course material from 2004
A bit of history of random number generators
HISTORY OF MONTE CARLO METHOD by Sabri Pllana .
Also has nice Buffon's needle java applet.
History of Metropolis MC and MD: An Interview with Bernie Alder
Veikko Karimäen aiemman vastaavan kurssin materiaalia
Antti Kurosen aiemman vastaavan kurssin materiaalia
Duane Johnson (UIUC) lecture and refs. on KMC.
David Ceperleys note on QMC
Introduction to the Finite Element Method
More scientific introduction to the Finite Element Method
Ilpo Vattulainen: Studies of Random Numbers
The RANMAR generator
The Mersenne twister pages
HAVEGE: HArdware Volatile Entropy Genertator
Volume of n-Spheres
Ising model java applet (with good comments on science)
Cellular automata animations (CSC)
Game of life java applet
Xtoys as xtoys.tar package
Stephen Wolfram's book on CA's
Numerical recipes online
Gould and Tobochnik book:related material; see especially list of errors!
Article on euro coin diffusion, in Finnish
Rand Corp's one million random digits
Kai Nordlund