Simulation Methods in Physics I WS 2012

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Overview

Type
Lecture (2 SWS) and Tutorials (2 SWS)
Lecturer
Prof. Dr. Christian Holm (Lecture); Dr. Olaf Lenz and Dr. Jens Smiatek (Tutorials)
Course language
English
Location and Time
Lecture: Thu, 11:30 - 13:00; ICP, Allmandring 3, Seminarroom 1
Tutorials: Thu, 14:00 - 15:30 and Fri, 8:00 - 9:30; ICP, Allmandring 3, CIP-Pool
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 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.

Lecture

Scope

The first part of the course intends to give an overview about modern simulation methods used in physics today. The stress of the lecture will be to introduce different approaches to simulate 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 some 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 like the Ising-model.
Short interlude on Quantum Mechanical Systems
It is obvious that solving quantum mechanical systems analytically is not possible and we need numerical help. We also want to examine the possibilities to simulate the quantum chromodynamics PDEs on a lattice (lattice gauge theory).

Course Material

Date Subject Ressources
18.10.2012 Course Content, Organisation, Introduction Slides (1.66 MB)
25.10.2012 MD: Integrators Lecture Notes (244 kB)
01.11.2012 Holiday
08.11.2012 Basics of Stat Mech Lecture Notes (384 kB)
15.11.2012 MD-Potentials,Units Lecture Notes (547 kB)
22.11.2012 MD-cont Lecture Notes (219 kB)
29.11.2012 Observables Lecture Notes (425 kB)
06.12.2012 Langevin Dynamics Lecture Notes (163 kB) Brownian motion slides (1.54 MB)
13.12.2012 Error analysis Lecture Notes (250 kB)
10.01.2013 Monte-Carlo Method Lecture Notes (316 kB)
17.01.2013 Monte-Carlo and Critical Phenomena Lecture Notes (228 kB)
24.01.2013 Finite Size Scaling Lecture Notes (214 kB)
31.01.2013 Binder parameters Lecture Notes (304 kB)

Script

Please note that the lecture notes are currently under development. Errors may be included. If you find errors, please contact Jens Smiatek.

Tutorials

Location and Time

Worksheets

Worksheet 6: Ising Model and Finite Size Scaling

  • Deadline: Tuesday (!) 5th February 2013, 10:00
  • application_pdf.pngWorksheet 6 (221 KB)Info circle.png (last update Jan 30)
  • tgz.pngtemplates.tar.gz (3 KB)Info circle.png (last update Jan 31) - Archive that contains the files required for this worksheet.
  • tgz.pngsolution.tar.gz (5 KB)Info circle.png - Archive that contains the sample solution

Worksheet 5: Monte-Carlo

  • Deadline: 24 January 2013, 10:00
  • application_pdf.pngWorksheet 5 (216 KB)Info circle.png (last update Jan 16)
  • tgz.pngsolution.tar.gz (2 KB)Info circle.png - Archive that contains the sample solution

Worksheet 4: Error Analysis and Langevin Thermostat

  • Deadline: 10 January 2013, 10:00
  • application_pdf.pngWorksheet 4 (239 KB)Info circle.png (last update Dec 14)
  • tgz.pngtemplates.tar.gz (8.43 MB)Info circle.png - Archive that contains the files required for this worksheet.
  • tgz.pngsolution.tar.gz (4.56 MB)Info circle.png - Archive that contains the sample solution

Worksheet 3: Molecular Dynamics 2 and Observables

  • Deadline: 13 December 2012, 10:00
  • application_pdf.pngWorksheet 3 (319 KB)Info circle.png (last update Dec 5)
  • tgz.pngtemplates.tar.gz (4 KB)Info circle.png (last update Dec 5) - Archive that contains the files required for this worksheet.
  • tgz.pngsolution.tar.gz (5 KB)Info circle.png - Archive that contains the sample solution

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.
  • 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 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.

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 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 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 hands-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 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 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)