Simulation Methods in Physics I WS 2012
Contents
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, CIPPool
 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 handsontutorials which will take place in the CIPPool 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 Isingmodel.
 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  MDPotentials,Units  Lecture Notes (547 kB) 
22.11.2012  MDcont  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  MonteCarlo Method  Lecture Notes (316 kB) 
17.01.2013  MonteCarlo 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
 Script of lectures 1,2 and 3 (1.72 MB)  including all lectures until November 8th, 2012
 Script of lecture 4 (336 kB)  November 15th, 2012
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
 Thursday, 14:00  15:00, Olaf Lenz
 Friday, 8:00  9:30, Jens Smiatek
Worksheets
Worksheet 6: Ising Model and Finite Size Scaling
 Deadline: Tuesday (!) 5th February 2013, 10:00
 Worksheet 6 (221 KB) (last update Jan 30)
 templates.tar.gz (3 KB) (last update Jan 31)  Archive that contains the files required for this worksheet.
 solution.tar.gz (5 KB)  Archive that contains the sample solution
Worksheet 5: MonteCarlo
 Deadline: 24 January 2013, 10:00
 Worksheet 5 (216 KB) (last update Jan 16)
 solution.tar.gz (2 KB)  Archive that contains the sample solution
Worksheet 4: Error Analysis and Langevin Thermostat
 Deadline: 10 January 2013, 10:00
 Worksheet 4 (239 KB) (last update Dec 14)
 templates.tar.gz (8.43 MB)  Archive that contains the files required for this worksheet.
 solution.tar.gz (4.56 MB)  Archive that contains the sample solution
Worksheet 3: Molecular Dynamics 2 and Observables
 Deadline: 13 December 2012, 10:00
 Worksheet 3 (319 KB) (last update Dec 5)
 templates.tar.gz (4 KB) (last update Dec 5)  Archive that contains the files required for this worksheet.
 solution.tar.gz (5 KB)  Archive that contains the sample solution
Worksheet 2: Statistical Mechanics and Molecular Dynamics
 Deadline: 27 November 2012, 10:00
 Worksheet 2 (329 KB)
 template.tar.gz (5 KB)  Archive that contains the files required in some tasks
 latextemplate.tex (7 KB)  LaTeXtemplate for the report
 solution.tar.gz (203 KB)  Archive that contains the sample solution
Worksheet 1: Integrators
 Deadline: 13 November 2012, 10:00
 Worksheet 1 (285 KB)
 solar_system.tar.gz (585 bytes)  Archive that contains the files required in some tasks
 cannonball_template.png (114 KB)  Python program template as an image
 latextemplate.tex (7 KB)  LaTeXtemplate for the report
 solution.tar.gz (3 KB)  Archive that contains the sample solution
General Remarks
 The tutorials take place in the CIPPool 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 CIPPool 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 CIPPool, 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.
Handinexercises
 The worksheets are to be solved in groups of two or three people. We will not accept handinexercises 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 handsin 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) (3.24 MB)  Numerics in Python, using 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 FUSIONEP

 Obtain 50% of the possible points in the handsin excercises of this lecture and the second part of the lecture as a prerequisite for the examination (USLV)
 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" (240918005)

 Obtain 50% of the possible points in the handsin 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 handsin excercises of this lecture as a prerequisite for the examination (USLV)
 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)