Simulation Methods in Physics I WS 2014

Overview

Type

Lecture (2 SWS) and Tutorials (2 SWS)

Lecturer

Prof. Dr. Christian Holm and Dr. Jens Smiatek

Course language

English

Location and Time

Lecture: Thu, 14:00 - 15:30; ICP, Allmandring 3, Seminar Room (room 01.079)

Tutorials: Wed 15:45-17:15 (Tutor: Florian Weik) and Wed 17:30-19:00 (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 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	Resources
16.10.2014	Course Content, Organization, Introduction
23.10.2014	MD: Integrators	Lecture Notes (8.46 MB)
30.10.2014	Basics of Statistical Mechanics	Lecture Notes (4.22 MB)
06.11.2014	MD: Potentials, Units	Lecture Notes (2.49 MB)
13.11.2014	MD - continued	Lecture Notes (2.83 MB)
20.11.2014	PBC, cell-lists, Observables	Lecture Notes (3.12 MB)
27.11.2014	RDF, D, Brownian motion	Lecture Notes (1.7 MB), Brownian Motion (1.69 MB)
04.12.2014	Green-Kubo, Langevin Dynamics Thermostats, Barostats	Lecture Notes (3.63 MB)
11.12.2014	Error Analysis	Lecture Notes (3.91 MB)
18.12.2014	Bachelor thesis @ ICP: information & research topics	Bachelor topics presentation (5.26 MB)
08.1.2015	Thermostats	Lecture Notes (3.41 MB)
15.01.2015	Monte-Carlo Method	Lecture Notes (4.62 MB)
22.01.2015	Monte-Carlo and Critical Phenomena	Lecture Notes (1.35 MB)
29.01.2015	Finite Size Scaling	Lecture Notes (2.76 MB)
05.02.2015	Binder Parameters	Lecture Notes (3.88 MB)
12.02.2015	Lattice QCD	Lecture Notes (1.73 MB)

Script

To be reviewed

Recommended literature

• Daan Frenkel, Berend Smit.
  Understanding Molecular Simulation: From Algorithms to Applications.
  Part of Computational Science, volume 1. Edition 2.
  Academic Press, San Diego, 2002. ISBN: 978-0-12-267351-1.
  [DOI]
• Mike P. Allen, Dominik J. Tildesley.
  Computer Simulation of Liquids.
  Part of Oxford Science Publications. Edition 1.
  Clarendon Press, Oxford, 1987.
  
• D. C. Rapaport.
  The Art of Molecular Dynamics Simulation.
  Edition 2.
  Cambridge University Press, 2004. ISBN: 9780511816581.
  [DOI]
• D. P. Landau, K. Binder.
  A guide to Monte Carlo Simulations in Statistical Physics.
  Edition second edition.
  Cambridge, 2005.
  
• M. E. J. Newman, G. T. Barkema.
  Monte Carlo Methods in Statistical Physics.
  Edition 2002 edition.
  Oxford University Press, 1999.
  

Useful online resources

• Thermostats: Philippe H. Hünenberger, Thermostat Algorithms for Molecular Dynamics Simulations, Adv. Polym. Sci. (2005) 173:105–149.

• Error analysis: W. Janke, Statistical Analysis of Simulations:Data Correlations and Error Estimation, Quantum Simulations of Complex Many-Body Systems:

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

• Introduction to Molecular Simulation and Statistical Thermodynamics (pdf textbook from TU Delft)

• University of Virginia, Introduction to atomistic simulations

• 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
  • Wed 15:45-17:15 (Tutor: Florian Weik)
  • Wed 17:30-19:00 (Tutor: Johannes Zeman)

Worksheets

Worksheet 6: Ising Model and Finite Size Scaling

• Deadline: February 09, 2015, 10:00 a.m.
• Worksheet 6 (225 KB)
• templates.tar.gz (3 KB) - Archive containing the files required for this worksheet.

Worksheet 5: Thermostats, Monte-Carlo

• Deadline: January 26, 2015, 10:00 a.m.
• Worksheet 5 (229 KB)

Worksheet 4: Error Analysis and Langevin Thermostat

• Deadline: January 12, 2015, 10:00 a.m.
• Worksheet 4 (233 KB)
• templates.tar.gz (8.63 MB) - Archive containing the files required for this worksheet.

Worksheet 3: Molecular Dynamics 2 and Observables

• Deadline: December 08, 2014, 10:00 a.m.
• Worksheet 3 (326 KB)
• templates.tar.gz (4 KB) - Archive containing the files required for this worksheet.

Worksheet 2: Statistical Mechanics and Molecular Dynamics

• Deadline: November 17, 2014, 10:00 a.m.
• Worksheet 2 (332 KB)
• templates.tar.gz (10 KB) - Archive containing the files required in some tasks

Worksheet 1: Integrators

• Deadline: November 3, 2014, 10:00 a.m.
• Worksheet 1 (288 KB)
• solar_system.pkl.gz (496 bytes) - Archive containing the files required in some tasks
• cannonball_template.png (70 KB) - Python program template as an image
• latex-template.tex (7 KB) - LaTeX template for the report

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/2014.
• For the reports, we have a nice latex-template.tex (7 KB).
• 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.
• 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

• Linux Cheat Sheet (2.27 MB) (source (42 KB)) - the most important linux commands on a single page

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

• http://python.org/doc/ - the official Python documentation (including tutorials etc.)
• Byte_of_Python.pdf (546 KB) - the free eBook "A byte of Python" [1], also available in German[2]

NumPy

• first of all, try to use

 pydoc numpy

• http://numpy.scipy.org/ - the homepage of NumPy contains a lot of documentation
• Script of the lecture "Physik auf dem Computer" (German) (3.42 MB) - Numerics in Python, using Numpy

LaTeX

• The Not So Short Introduction to LaTeX
• List of documentation of the LaTeX project

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 2015)
  • 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)