Difference between revisions of "Simulation Methods in Physics I WS 2014"
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+  <!{{Infobox<b>On January 28, 2015, tutorial 1 (with Florian) is shifted from 17:45 to 19:00 and will take place together with tutorial 2</b>}}>  
+  <!{{Infobox<b>NO tutorial on Wednesday, December 10, 2014</b>}}  
+  {{Infobox<b>The deadline for worksheet 3 has been shifted by one week to Dec 8, 2014, 10:00 a.m.</b>}}>  
== Overview ==  == Overview ==  
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:Lecture (2 SWS) and Tutorials (2 SWS)  :Lecture (2 SWS) and Tutorials (2 SWS)  
;Lecturer  ;Lecturer  
−  :Prof. Dr. [[Christian Holm]]  +  :Prof. Dr. [[Christian Holm]] and Dr. [[Jens Smiatek]] 
;Course language  ;Course language  
:English  :English  
;Location and Time  ;Location and Time  
−  :'''Lecture''': Thu,  +  :'''Lecture''': Thu, 14:00  15:30; ICP, Allmandring 3, Seminar Room (room 01.079) 
−  :'''Tutorials''':  +  :'''Tutorials''': Wed 15:4517:15 (Tutor: [[Florian Weik]]) and Wed 17:3019:00 (Tutor: [[Johannes Zeman]]); ICP, Allmandring 3, CIPPool (room 01.033) 
; Prerequisites  ; 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  +  : 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 handsontutorials which will take place in the CIPPool of the ICP, Allmandring 3 (room 01.033). They consist of practical exercises at the computer  +  The lecture is accompanied by handsontutorials which will take place in the CIPPool 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.  The tutorials build upon each other, therefore continuous attendance is expected.  
−  +  
== Lecture ==  == Lecture ==  
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−  16.10.2014  Course Content, Organization, Introduction  <!{{DownloadExt/teaching/2012wssim_methods/slides01.pdfSlides}}>  +  16.10.2014  Course Content, Organization, Introduction <!{{DownloadExt/teaching/2012wssim_methods/slides01.pdfSlides}}> 
    
−  23.10.2014  MD: Integrators   +  23.10.2014  MD: Integrators  {{DownloadExt/teaching/2014wssim_methods/lecture02_notes.pdfLecture Notes}} 
    
−  30.10.2014  Basics of Statistical Mechanics   +  30.10.2014  Basics of Statistical Mechanics  {{DownloadExt/teaching/2014wssim_methods/lecture03_notes.pdfLecture Notes}} 
    
−  06.11.2014  MD: Potentials, Units   +  06.11.2014  MD: Potentials, Units  {{DownloadExt/teaching/2014wssim_methods/lecture04_notes.pdfLecture Notes}} 
    
−  13.11.2014  MD  continued   +  13.11.2014  MD  continued  {{DownloadExt/teaching/2014wssim_methods/lecture05_notes.pdfLecture Notes}} 
    
−  20.11.2014  Observables   +  20.11.2014  PBC, celllists, Observables  {{DownloadExt/teaching/2014wssim_methods/lecture06_notes.pdfLecture Notes}} 
    
−  27.11.2014   +  27.11.2014  RDF, D, Brownian motion  {{DownloadExt/teaching/2014wssim_methods/lecture07_notes.pdfLecture Notes}}, {{DownloadExt/teaching/2014wssim_methods/simulating_brownian_motion.pdfBrownian Motion}} 
    
−  04.12.2014   +  04.12.2014  GreenKubo, Langevin Dynamics Thermostats, Barostats  {{DownloadExt/teaching/2014wssim_methods/lecture08_notes.pdfLecture Notes}} 
    
−  11.12.2014   +  11.12.2014  Error Analysis  {{DownloadExt/teaching/2014wssim_methods/lecture09_notes.pdfLecture Notes}} 
    
−  18.12.2014   +  18.12.2014  Bachelor thesis @ ICP: information & research topics  {{DownloadExt/teaching/2014wssim_methods/lecture10_bachelor_topics_slides_2014.pdfBachelor topics presentation}} 
    
−  08.  +  08.1.2015  Thermostats  {{DownloadExt/teaching/2014wssim_methods/lecture11_notes.pdfLecture Notes}} 
    
−  15.01.2015   +  15.01.2015  MonteCarlo Method  {{DownloadExt/teaching/2014wssim_methods/lecture12_notes.pdfLecture Notes}} 
    
−  22.01.2015   +  22.01.2015  MonteCarlo and Critical Phenomena  {{DownloadExt/teaching/2014wssim_methods/lecture13_notes.pdfLecture Notes}} 
    
−  29.01.2015   +  29.01.2015  Finite Size Scaling  {{DownloadExt/teaching/2014wssim_methods/lecture14_notes.pdfLecture Notes}} 
    
−  05.02.2015   +  05.02.2015  Binder Parameters  {{DownloadExt/teaching/2014wssim_methods/lecture15_notes.pdfLecture Notes}} 
    
−  12.02.2015   +  12.02.2015  Lattice QCD  {{DownloadExt/teaching/2014wssim_methods/lecture16_notes.pdfLecture Notes}} 
}  }  
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>  >  
To be reviewed  To be reviewed  
+  
+  === Recommended literature ===  
+  <bibentry>frenkel02b,allen87a,rapaport04a,landau05a,newman99a,thijssen07,tuckerman10</bibentry>  
+  === Useful online resources ===  
+  <!* Roethlisberger, Tavernarelli, EPFL, Lausanne, 2011: [http://lcbcpc21.epfl.ch/Group_members/ivano/bachelor.pdf Introduction to electronic structure methods.]>  
+  
+  * Thermostats: Philippe H. Hünenberger, [http://link.springer.com/chapter/10.1007%2Fb99427 <i>Thermostat Algorithms for Molecular Dynamics Simulations</i>], Adv. Polym. Sci. (2005) 173:105–149.  
+  
+  * Error analysis: W. Janke, [http://www.google.de/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CDkQFjAA&url=http%3A%2F%2Fwww.physik.unileipzig.de%2F~janke%2FPaper%2Fnic10_423_2002.pdf&ei=CwXUtDyPITUtAb50YC4CA&usg=AFQjCNFAtjE76HIMKIjlATNqo_r3R_O0yw&bvm=bv.57155469,d.Yms&cad=rja <i>Statistical Analysis of Simulations:Data Correlations and Error Estimation</i>], Quantum Simulations of Complex ManyBody Systems:  
+  From Theory to Algorithms, Lecture Notes, (2002).  
+  
+  * [http://homepage.tudelft.nl/v9k6y/imsst/index.html Introduction to Molecular Simulation and Statistical Thermodynamics (pdf textbook from TU Delft)]  
+  
+  * [http://people.virginia.edu/~lz2n/mse627/notes/Intro.pdf 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 ==  == Tutorials ==  
=== Location and Time ===  === Location and Time ===  
−  * The tutorials take place in the CIPPool on the first floor of the ICP (Room 01.033, Allmandring 3)  +  * The tutorials take place in the CIPPool on the first floor of the ICP (Room 01.033, Allmandring 3) on 
−  *  +  ** Wed 15:4517:15 (Tutor: [[Florian Weik]]) 
−  +  ** Wed 17:3019:00 (Tutor: [[Johannes Zeman]])  
−  *  
=== Worksheets ===  === Worksheets ===  
+  ==== Worksheet 6: Ising Model and Finite Size Scaling ====  
+  * Deadline: '''February 09, 2015, 10:00 a.m.'''  
+  * {{DownloadWS_2014_SM1_worksheet6.pdfWorksheet 6}}  
+  * {{DownloadWS_2014_SM1_WS6_templates.tar.gztemplates.tar.gztgz}}  Archive containing the files required for this worksheet.  
<!  <!  
−  +  * {{DownloadWS_2014_SM1_WS6_solution.tar.gzsolution.tar.gztgz}}  Archive containing the sample solution  
−  +  >  
−  * {{Download  +  ==== Worksheet 5: Thermostats, MonteCarlo ==== 
−  +  * Deadline: '''January 26, 2015, 10:00 a.m.'''  
−  +  * {{DownloadWS_2014_SM1_worksheet5.pdfWorksheet 5}}  
−  +  <!  
−  ==== Worksheet 5: MonteCarlo ====  +  * {{DownloadWS_2014_SM1_WS5_solution.tar.gzsolution.tar.gztgz}}  Archive containing the sample solution 
−  * Deadline: '''  +  > 
−  * {{Download  
−  * {{Download  
==== Worksheet 4: Error Analysis and Langevin Thermostat ====  ==== Worksheet 4: Error Analysis and Langevin Thermostat ====  
−  * Deadline: '''  +  * Deadline: '''January 12, 2015, 10:00 a.m.''' 
−  * {{Download  +  * {{DownloadWS_2014_SM1_worksheet4.pdfWorksheet 4}} 
−  * {{Download  +  * {{DownloadWS_2014_SM1_WS4_templates.tar.gztemplates.tar.gztgz}}  Archive containing the files required for this worksheet. 
−  * {{Download  +  <! 
+  * {{DownloadWS_2014_SM1_WS4_solution.tar.gzsolution.tar.gztgz}}  Archive containing the sample solution  
+  >  
==== Worksheet 3: Molecular Dynamics 2 and Observables ====  ==== Worksheet 3: Molecular Dynamics 2 and Observables ====  
−  * Deadline: '''  +  * Deadline: '''December 08, 2014, 10:00 a.m.''' 
−  * {{Download  +  * {{DownloadWS_2014_SM1_worksheet3.pdfWorksheet 3}} 
−  * {{Download  +  * {{DownloadWS_2014_SM1_WS3_templates.tar.gztemplates.tar.gztgz}}  Archive containing the files required for this worksheet. 
−  * {{Download  +  <! 
+  * {{DownloadWS_2014_SM1_WS3_solution.tar.gzsolution.tar.gztgz}}  Archive containing the sample solution  
+  >  
==== Worksheet 2: Statistical Mechanics and Molecular Dynamics ====  ==== Worksheet 2: Statistical Mechanics and Molecular Dynamics ====  
−  * Deadline: '''  +  * Deadline: '''November 17, 2014, 10:00 a.m.''' 
−  * {{Download  +  * {{DownloadWS_2014_SM1_worksheet2.pdfWorksheet 2}} 
−  * {{Download  +  * {{DownloadWS_2014_SM1_WS2_templates.tar.gztemplates.tar.gztgz}}  Archive containing the files required in some tasks 
−  +  <!  
−  * {{Download  +  * {{DownloadWS_2014_SM1_WS2_solution.tar.gzsolution.tar.gztgz}}  Archive containing the sample solution 
>  >  
==== Worksheet 1: Integrators ====  ==== Worksheet 1: Integrators ====  
−  +  * Deadline: '''November 3, 2014, 10:00 a.m.'''  
+  * {{DownloadWS_2014_SM1_worksheet1.pdfWorksheet 1pdf}}  
+  * {{DownloadWS_2014_SM1_solar_system.pkl.gzsolar_system.pkl.gztgz}}  Archive containing the files required in some tasks  
+  * {{DownloadWS_2014_SM1_cannonball_template.pngcannonball_template.png}}  Python program template as an image  
+  * {{Downloadlatextemplate.texlatextemplate.textxt}}  LaTeX template for the report  
<!  <!  
−  +  * {{DownloadWS_2014_SM1_WS1_solution.tar.gzsolution.tar.gztgz}}  Archive containing the sample solution  
−  * {{Download  
−  
−  
−  
−  
>  >  
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* For the tutorials, you will get a [[ICP Unix Accounts for Studentspersonal account for the ICP machines]].  * For the tutorials, you will get a [[ICP Unix Accounts for Studentspersonal account for the ICP machines]].  
+  * All material required for the tutorials can also be found on the ICP computers in the directory <code>/group/sm/2014</code>.  
+  * For the reports, we have a nice {{Downloadlatextemplate.texlatextemplate.textxt}}.  
* You can do the exercises in the CIPPool when it is not [[CIP Pool Occupancyoccupied by another course]]. The pool is accessible on all days, except weekends and late evenings.  * You can do the exercises in the CIPPool when it is not [[CIP Pool Occupancyoccupied 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 do the exercises in the CIPPool, all required software and tools are available.  
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* You have two weeks to prepare the report for each worksheet.  * You have two weeks to prepare the report for each worksheet.  
* The report has to be sent to your tutor via email.  * The report has to be sent to your 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).  +  * Most participants need 50% of the points in the handsin exercises to be admitted to the oral examination (see [[#ExaminationExamination]] for details). 
=== What happens in a tutorial ===  === What happens in a tutorial ===  
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:and visit the page http://localhost:4242  :and visit the page http://localhost:4242  
* http://python.org/doc/  the official Python documentation (including tutorials etc.)  * http://python.org/doc/  the official Python documentation (including tutorials etc.)  
−  * {{DownloadByte_of_Python.pdf}}  the free eBook "A byte of Python" [http://www.swaroopch.com/notes/python/], also available in German[http://abopgerman.berlios  +  * {{DownloadByte_of_Python.pdf}}  the free eBook "A byte of Python" [http://www.swaroopch.com/notes/python/], also available in German[http://sourceforge.net/projects/abopgerman.berlios/] 
==== NumPy ====  ==== NumPy ====  
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pydoc numpy  pydoc numpy  
* http://numpy.scipy.org/  the homepage of NumPy contains a lot of documentation  * http://numpy.scipy.org/  the homepage of NumPy contains a lot of documentation  
−  * {{Download  +  * {{DownloadSS_2014_PadC.pdfScript of the lecture "Physik auf dem Computer" (German)}}  Numerics in Python, using Numpy 
==== LaTeX ====  ==== LaTeX ==== 
Latest revision as of 15:55, 13 April 2015
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 15:4517:15 (Tutor: Florian Weik) and Wed 17:3019:00 (Tutor: Johannes Zeman); ICP, Allmandring 3, CIPPool (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 handsontutorials which will take place in the CIPPool 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, celllists, 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  GreenKubo, 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  MonteCarlo Method  Lecture Notes (4.62 MB) 
22.01.2015  MonteCarlo 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 and Berend Smit.
"Understanding Molecular Simulation".
Academic Press, San Diego, 2002.
[DOI] 
Mike P. Allen and Dominik J. Tildesley.
"Computer Simulation of Liquids".
Oxford Science Publications, Clarendon Press, Oxford, 1987.

D. C. Rapaport.
"The Art of Molecular Dynamics Simulation".
Cambridge University Press, 2004.

D. P. Landau and K. Binder.
"A guide to Monte Carlo Simulations in Statistical Physics".
Cambridge, 2005.

M. E. J. Newman and G. T. Barkema.
"Monte Carlo Methods in Statistical Physics".
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 ManyBody Systems:
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 CIPPool on the first floor of the ICP (Room 01.033, Allmandring 3) on
 Wed 15:4517:15 (Tutor: Florian Weik)
 Wed 17:3019:00 (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, MonteCarlo
 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
 latextemplate.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 latextemplate.tex (7 KB).
 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 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 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) (3.42 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 2015)
 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)