Simulation Methods in Physics I WS 2013

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Lecture (2 SWS) and Tutorials (2 SWS)
JP Dr. Maria Fyta (Lecture); Dr. Olaf Lenz, Bibek Adhikari, Elena Minina (Tutorials)
Course language
Location and Time
Lecture: Thu, 11:30 - 13:00 (Seminar room ICP, Allmandring 3); Tutorials: Wed, 15:45-17:15 (Bibek), Fri, 15:45-17:15 (Elena) (CIP-Pool ICP, Allmandring 3)
We expect the participants to have basic knowledge in classical and statistical mechanics, thermodynamics, and partial differential equations, as well as knowledge of a programming language (Python or C).

The lecture is accompanied by hands-on-tutorials which will take place in the CIP-Pool of the ICP, Allmandring 3. They consist of practical exercises at the computer, like small programming tasks, simulations, visualization and data analysis. The tutorials build upon each other, therefore continuous attendance is expected.



The first part of the course intends to give an overview about modern simulation methods used in physics today. The lecture should introduce different approaches to simulate a physical systems. In this respect, rather a broad range of methods will be outlined than an exhaustive presentation of specific computational methods. Roughly, the lecture will consist of:

General overview
The first 2-3 weeks will be dedicated on the general common aspects of computer simulations, elements of statistical ensemble theory and elements of elasticity theory, which are essential in understanding and performing simulations.
Quantum Mechanics
An extensive presentation of quantum mechanical simulations will be given in the second part of this course. Here, a general overview of the ideas behind these kinds of simulations will be given.
Molecular Dynamics
A more extensive investigation of classical Molecular Dynamics (MD) simulations is planned. This includes the algorithm, the integrators, the thermostats, to name a few necessary to perform MD simulations.
In terms of the respective tutorials, the goal is to be able to set up and run real MD simulations for different ensembles and understand and interpret the output.
Monte Carlo Simulations
A part of the lecture will be dedicated on Monte Carlo (MC) methods and their algorithms. Specific examples, such as the Ising model will be studied.
Error Analysis
The way errors come into the simulations and how to estimate these will be outlined.<-!!Autocorrelation, Jackknifing, Bootstrapping-->
An important component of molecular simulations are the potentials or force fields chosen to model the interactions within the simulated system. The efficiency of the simulations is stongly dependent on this choice. To this purpose, various methods can be applied for obtaining efficient potentials for different methods. Here, representative examples will be outlined.
Simulation of liquids
Methods such as the lattice Boltzmann method and specific details on simulating liquids will be briefly given.
Advanced simulation techniques
In the end of the course, a short overview of other more advanced methods than the ones studied here will be presented. Examples include MC beyond the Metropolis algorithm, metadynamics or rare events sampling.


We expect the participants to have basic knowledge in quantum, classical and statistical mechanics, thermodynamics, electrodynamics, and partial differential equations, as well as knowledge of a programming language.

Certificate Requirements

1. Attendance of the exercise classes
2. Obtaining 50% of the possible marks in the hand-in exercises

There will be a final grade for the Module "Simulation Methods" (this module consists of both lectures, Sim I plus Sim II) determined at the end of lecture Simulation Methods II.

The final grade will be determined in the following way: There will be an oral examination performed at (or after) the end of the course Simulation Methods II (SS 2012).

Recommended literature

Useful online resources

From Theory to Algorithms, Lecture Notes, (2002).

  • Be careful when using Wikipedia as a resource. It may contain a lot of useful information, but also a lot of nonsense, because anyone can write it.

Course Material

Date Subject Resources
17.10.2013 Course Content, Introduction Lecture Notes (2.54 MB)Info circle.png
24.10.2013 Molecular Dynamics (Introduction, integrators) Lecture Notes (4.59 MB)Info circle.png
31.10.2013 Energy minimization, common features in computer simulations of particles Lecture Notes (8.91 MB)Info circle.png
07.11.2013 Basics of Stat Mech, ensembles, observables Lecture Notes (6.53 MB)Info circle.png
14.11.2013 More on StatMech, MD (thermostats/barostats;intro) Lecture Notes (4.94 MB)Info circle.png
21.11.2013 MD (thermostats) Lecture Notes (6.35 MB)Info circle.png
28.11.2013 MD (barostats), error analysis Lecture Notes (4.32 MB)Info circle.png
05.12.2013 Error analysis (cont.) (binning, jackknife analysis) Lecture Notes (2.63 MB)Info circle.png
12.12.2013 Introduction to Monte Carlo (MC) Lecture Notes (8.43 MB)Info circle.png
19.12.2013 MC (Metropolis algorithm), Introducing thesis projects @ ICP Lecture Notes (1.68 MB)Info circle.png
09.01.2014 MC (Ising model), phase transitions & critical phenomena Lecture Notes (6.04 MB)Info circle.png
16.01.2014 Langevin dynamics, Brownian dynamics Lecture Notes (5.52 MB)Info circle.png
23.01.2014 Interactions, biomolecular force-fields Lecture Notes (4.79 MB)Info circle.png
30.01.2014 Inter-atomic potentials for solid state systems, reactive potentials Lecture Notes (4.76 MB)Info circle.png
06.02.2014 Classical potentials for metals, snippets on coarse-graining and multi-scale simulations Lecture Notes (9.14 MB)Info circle.png


Location and Time


Worksheet 6: Ising Model and Finite Size Scaling

  • Deadline: Wednesday, 29 January 2014, 10:00
  • application_pdf.pngWorksheet 6 (225 KB)Info circle.png
  • tgz.pngtemplates.tar.gz (3 KB)Info circle.png - Archive that contains the files required for this worksheet.

Worksheet 5: Monte-Carlo

  • Deadline: Wednesday, 15 January 2014, 10:00
  • application_pdf.pngWorksheet 5 (217 KB)Info circle.png

Worksheet 4: Error Analysis and Langevin Thermostat

  • Deadline: Monday, 16 December 2013, 10:00
  • application_pdf.pngWorksheet 4 (233 KB)Info circle.png
  • tgz.pngtemplates.tar.gz (8.43 MB)Info circle.png - Archive that contains the files required in some tasks

Worksheet 3: Molecular Dynamics 2 and Observables

  • Deadline: Monday, 2 December 2013, 10:00
  • application_pdf.pngWorksheet 3 (319 KB)Info circle.png
  • tgz.pngtemplates.tar.gz (4 KB)Info circle.png - Archive that contains the files required in some tasks

Worksheet 2: Statistical Mechanics and Molecular Dynamics

Worksheet 1: Integrators

General Remarks

  • The tutorials take place in the CIP-Pool on the first floor of the ICP (Room 1.033, Allmandring 3).
  • For the tutorials, you will get a personal account for the ICP machines.
  • All material required for the tutorials can also be found on the ICP computers in the directory /group/sm/2013.
  • For the reports, we have a nice txt.pnglatex-template.tex (7 KB)Info circle.png.
  • You can do the exercises in the CIP-Pool when it is not occupied by another course. The pool is accessible on all days, except weekends and late evenings.
  • If you do the exercises in the CIP-Pool, all required software and tools are available.
  • If you want to do the exercises on your own computer, the following tools are required. All of these packages should be readily available from your OS distribution, if it is not Windows.
    • Python
    • The following Python packages:
      • IPython
      • NumPy
      • SciPy
      • matplotlib
    • A C compiler (e.g. GCC)
  • We only have experience with Unix/Linux machines. Although most tools will probably also work on Windows, we cannot guarantee it, and we can also not help you to get it running there.


  • The worksheets are to be solved in groups of two or three people. We will not accept hand-in-exercises that only have a single name on it.
  • A written report (between 5 and 10 pages) has to be handed in for each worksheet. We recommend to use LaTeX to prepare the report.
  • You have two weeks to prepare the report for each worksheet.
  • The report has to be sent to the tutor via email.
  • Most participants need 50% of the points in the hands-in exercises to be admitted to the oral examination (see [[#Examination|]] for details).

What happens in a tutorial

  • The tutorials take place every week.
  • You will receive the new worksheet on the days before the tutorial.
  • In the first tutorial after you received a worksheet, the solutions of the previous worksheet will be presented (see below) and the new worksheet will be discussed.
  • In the second tutorial after you received the worksheet, there is time to work on the exercises and to ask questions for the tutor.
  • You will have to hand in the reports on Monday after the second tutorial.
  • In the third tutorial after you received the worksheet, the solutions will be discussed:
    • The tutor will ask a team to present their solution.
    • The tutor will choose one of the members of the team to present each task.
    • This means that each team member should be able to present any task.
    • At the end of the term, everybody should have presented at least once.




  • Use the existing documentation of Python itself! To get help on the command print, use
 pydoc print
  • Or use the Web browser to read it. Start
 pydoc -p 4242
and visit the page http://localhost:4242


  • first of all, try to use
 pydoc numpy



Depending on the module that this lecture is part of, there are differences on how to get the credits for the module:

BSc/MSc Physik, Modul "Simulationsmethoden in der Physik" (36010) and Erasmus Mundus International Master FUSION-EP
  • Obtain 50% of the possible points in the hands-in excercises of this lecture and the second part of the lecture as a prerequisite for the examination (USL-V)
  • 60 min of oral examination (PL)
    • After the lecture "Simulation Methods in Physics II" in summer term (i.e. Summer 2013)
    • Contents: both lectures and the tutorials of "Simulation Methods in Physics I"
International MSc Physics, Elective Module "Simulation Techniques in Physics I, II" (240918-005)
  • Obtain 50% of the possible points in the tutorials of this lecture as a prerequisite for the examination
  • 30 min of oral examination (PL) about the lecture and the tutorials
BSc/MSc SimTech, Modul "Simulationsmethoden in der Physik für SimTech I" (40520)
  • Obtain 50% of the possible points in the hands-in excercises of this lecture as a prerequisite for the examination (USL-V)
  • 40 min of oral examination (PL) about the lecture and the tutorials
MSc Chemie, Modul "Simulationsmethoden in der Physik für Chemiker I" (35840)
  • The marks for the module are the marks obtained in the excercises (BSL)