Monte Carlo-simuloinnit / Monte Carlo simulations

Basics of Monte Carlo Simulations / Monte Carlo simulointien perusteet, 530006

Monte Carlo Simulations in Physics / Monte Carlo simuloinnit fysiikassa, 530153

Timetable part II: Monte Carlo Simulations in Physics

Mon 12.3	Lecture 1	Thu 15.3	-
Mon 19.3	Lecture 2	Thu 22.3	Lecture 3
Mon 26.3	Exercise 1	Thu 29.3	-
Mon 2.4	Lecture 4	Thu 5.4	Lecture 5
Mon 9.4	Holiday	Thu 12.4	Exercise 2
Mon 16.4	Lecture 6	Thu 19.4	Exercise 3
Mon 23.4	-	Thu 26.4	Lecture 7
Mon 30.4	Consultation	Thu 3.5	Exercise 4
Mon 14.5	Exam, Phy. E207

Grading: 50% exercises, 50% exam

The Exam - 14.05, PHYSICUM E207, 10:00-14:00

The admission to the exam after the course requires 25% of all the exercise points.

List of students who are allowed to attend to the exam

013305912

013752727

013983114

013712880

013326577

013311168

012073559

013463676

013456353

013580177

013326836

013709738

013758970

013470025

013598318

013861249

013461788

013865973

012607404

013861252

If you fail the course, in accordance with the department rules, you have the right to try again at a departmental exam only if you have at least 25% of the total points (exercises+exam).

Lectures. Part 1.

1. Monte Carlo Methods: Introduction [PDF 4up]

2. Monte Carlo Methods: Generation of Random Numbers [PDF 4up]

2a. Monte Carlo Methods: Generation of Random Numbers (cont'd) [PDF 4up]

3. Monte Carlo Methods: Generation of Non-Uniform Random Numbers [PDF 4up]

4. Monte Carlo Methods: Quasi-random Numbers [PDF 4up]

5. Monte Carlo Methods: Monte Carlo Integration [PDF 4up]

5b. Monte Carlo Methods: Markov Chain Sampling [PDF 4up]

6. Monte Carlo Methods: MC Data Analysis [PDF 4up]

6b. Monte Carlo Data Analysis: Simulation of Underlying Physical Process [PDF 4up]

7. Cellular Automata [PDF 4up]

Lectures. Part 2.

1. Random walks [PDF 4up]

2. Kinetic Monte Carlo [PDF 4up]

2a. Lattice Kinetic Monte Carlo [PDF 4up]

3. Simulation of thermodynamic ensembles [PDF 4up]

4. Simulated annealing [PDF 4up]

Exercises

To be handed in by email to the course assistant, konstantin.avchachovhelsinki.fi

[PDF] Exercise 1: Random walks. Xorshift RNG. Python script

[PDF] Exercise 2: Kinetic Monte Carlo

[PDF] Exercise 3: The Ising model

[PDF] Exercise 4: Simulated annealing. Data file 20cities.dat

Exercise solutions

Students' points

List of course contents: Basics of MC. Part 1

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. Part 2

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
- Ising model
- 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

Course description. Part 2

Lecturing time: Spring 2012: Mon 10-12, Thu 10-12. First lecture Monday 12.03.

Place: Kiihdytinlab room 115

Lecturer: Dr. Flyura Djurabekova

Assistant: M.Sc. Konstantin Avchaciov

Extent of course: 5 credits

Duration: 8 weeks

Normal year to be taken: Specialization phase, third year and up.

Prerequisites: Mathematics. Knowledge of the Fortran, C programming language.

Language: English.

Exercises

Programming and mathematical exercises are given during the course, but not every week. They are graded by the assistant. For the more demanding exercises, more than one 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 (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 one of these is not necessary for the course.