Simulation Methods in Physics I WS 2015/2016

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Overview

Type
Lecture (2 SWS) and Tutorials (2 SWS)
Lecturer
Prof. Dr. Christian Holm
Course language
English
Location and Time
Lecture: Thu, 14:00 - 15:30; ICP, Allmandring 3, Seminar Room (room 01.079)
Tutorials: Thu, 11:30 - 13:00 (Tutor: Michael Kuron) and Fri, 14:00 - 15:30 (Tutor: Johannes Zeman); ICP, Allmandring 3, CIP-Pool (room 01.033)
Prerequisites
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 and C).

The lecture is accompanied by hands-on tutorials which will take place in the CIP-Pool of the ICP, Allmandring 3 (room 01.033). They consist of practical exercises at the computer such as small programming tasks, simulations, visualization and data analysis. The tutorials build upon each other, therefore continuous attendance is expected.

Lecture

Scope

The first part of the course intends to give an overview about modern simulation methods used in physics today. The focus of the lecture will be to introduce different approaches to simulating a problem, hence we will not go too to deep into specific details but rather try to cover a broad range of methods. In more detail, the lecture will consist of:

Molecular Dynamics
The first problem that comes to mind when thinking about simulating physics is solving Newtons equations of motion for particles with given interactions. From that perspective, we first introduce the most common numerical integrators. This approach quickly leads us to Molecular Dynamics (MD) simulations. Many of the complex problems of practical importance require us to take a closer look at statistical properties, ensembles and the macroscopic observables.
The goal is to be able to set up and run real MD simulations for different ensembles and understand and interpret the output.
Error Analysis
Autocorrelation, Jackknifing, Bootstrapping
Monte Carlo Simulations
Since their invention, the importance of Monte Carlo (MC) sampling has grown constantly. Nowadays it is applied to a wide class of problems in modern computational physics. We want to present the general idea and theory behind MC simulations and show some more properties using simple toy models such as the Ising model.
Critical exponents
Finite-size scaling, universality concept, how to determine critical exponent with lattice spin models
If time permits
Short interlude on Lattice Gauge Theory
It is obvious that solving quantum mechanical systems analytically is not possible and we need numerical help. We also give a short outlook on how to simulate quantum chromodynamics on a lattice.

Course Material

Date Subject Resources
15.10.2015 Course Content, Organization, Introduction
22.10.2015 MD: Integrators
29.10.2015 Basics of Statistical Mechanics
05.11.2015 MD: Potentials, Units
12.11.2015 MD - continued
19.11.2015 PBC, cell-lists, Observables
26.11.2015 RDF, D, Brownian motion
03.12.2015 Green-Kubo, Langevin Dynamics, Thermostats
10.12.2015 Thermostats, Barostats
17.12.2015 Error Analysis
07.01.2016 Monte-Carlo Method
14.01.2016 Monte-Carlo and Critical Phenomena
21.01.2016 Finite Size Scaling
28.01.2016 Binder Parameters
04.02.2016 B.Sc. / M.Sc. thesis @ ICP: information & research topics

Script

A preliminary version of the script can be downloaded here (929 kB).

If you find any kind of mistake / error / typo / bad formatting / etc. in the script (you surely will!), please send an email to Johannes Zeman.

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.

Tutorials

Location and Time

  • The tutorials take place in the CIP-Pool on the first floor of the ICP (Room 01.033, Allmandring 3) on

Worksheets

Worksheet 6: Ising Model and Finite Size Scaling

Worksheet 5: Thermostats, Monte-Carlo

Worksheet 4: Error Analysis and Langevin Thermostat

Worksheet 3: Molecular Dynamics 2 and Observables

Worksheet 2: Statistical Mechanics and Molecular Dynamics

Worksheet 1: Integrators

Worksheet 0: First steps with Linux, Python, and C

General Remarks

  • 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/2015.
  • 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.

Hand-in-exercises

  • 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 using LaTeX to prepare the report.
  • You have two weeks to prepare the report for each worksheet.
  • The report has to be sent to your 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.
  • The new worksheet will be available for download 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.
  • 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.

Documentation

Linux

Python

  • 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

NumPy

  • first of all, try to use
 pydoc numpy

LaTeX

Examination

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 hand-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 2016)
    • Contents: both lectures and the excercises 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 hand-in excercises of this lecture as a prerequisite for the examination
  • 30 min of oral examination (PL) about the lecture and the excercises
BSc/MSc SimTech, Modul "Simulationsmethoden in der Physik für SimTech I" (40520)
  • Obtain 50% of the possible points in the hand-in excercises of this lecture as a prerequisite for the examination (USL-V)
  • 40 min of oral examination (PL) about the lecture and the excercises
MSc Chemie, Modul "Simulationsmethoden in der Physik für Chemiker I" (35840)
  • The marks for the module are the marks obtained in the excercises (BSL)