Simulation Methods in Physics I 11 12
 Type
 Lecture (2 SWS) and Tutorials (2 SWS)
 Lecturer
 Prof. Dr. Christian Holm (Lecture); Marcello Sega and Peter Košovan (Tutorials)
 Course language
 Deutsch oder Englisch, wie gewünscht  German or English, by vote
 Lectures
 Time: Thursdays, 11:30  13:00, Room V 57.06
 Tutorials
 Time: Wednesday afternoon, 14.0015.30 and 17:3019.00, Room V27.U104
The lecture is accompanied by handsontutorials which will take place in the CIPPool of the ICP, Pfaffenwaldring 27, U 108. They consist of practical exercises at the computer, like small programming tasks, simulations, visualization and data analysis. The tutorials build on each other, therefore continuous attendance is expected.
Contents
Scope
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:
1. 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.
2. Partial Differential Equations
Some of the most common physical problems today can be formulated with Partial Differential Equations (PDEs). We want to think about what kinds of physical problems can be dealt with PDEs and what methods we have to solve them numerically.
The goal is to get to know the problems you run into when solving these simplelooking equations and to get an overview on the methods available.
3. Quantum mechanical systems
It is obvious that solving quantum mechanical systems analytically is not possible and we need numerical help. We want to introduce various methods like (post)HartreeFock, Density Functional Theory, and CarParrinelloMolecular dynamics. We also want to examine the possibilities to simulate the quantum chromodynamics PDEs on a lattice (lattice gauge theory).
The goal is to get an overview on the methods to treat quantum mechanical systems and know about some of the advantages and disadvantages of each method.
4. 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.
Prerequisites
We expect the participants to have basic knowledge in classical and statistical mechanics, thermodynamics, electrodynamics, and partial differential equations, as well as knowledge of a programming language (preferably C or C++).
Prerequisites for the examination
 Attendance of the exercise classes
 Obtaining 50% of the possible marks in the handin exercises
(In German: USL V )
There will be a final grade for the Module "Simulation Methods" (this module consists of both lectures, Sim I plus Sim II and the exercise of Simulation Methods I) determined at the end of lecture Simulation Methods II. The grade will be determined in the following way : There is an oral examination (60 minutes) performed at (or after) the end of the course Simulation Methods II (SS 2012), where the dates are to be settled with the lecturer.
People taking other modules where this course is part of should contact the lecturer for optional other examinations.
Lecture
Date  Topics (subject may change during the course)  Downloads 

20.10.2011  Course Content, Organisation,Introduction  Lecture Notes 20.10.2011 
27.10.2011  Equation of Motion and simple Integrators for Classical MD  Lecture Notes 27.10.2011 
03.11.2011  Integrators cont., simple Potentials for Liquids, LJ Units  Lecture Notes 03.11.2011 
10.11.2011  Stat Mech in a Nutshell, efficiency considerations, Simple MD Program  Lecture Notes 10.11.2011 
17.11.2011  Observables in MD  Lecture Notes 17.11.2011 
24.11.2011  Diffusion, Brownian motion, RDF  Lecture Notes 24.11.2011 
01.12.2011  GreenKubo relations, temperature fluctuations in NVE ensemble  Lecture Notes 01.12.2011 Presentation 01.12.2011 
08.12.2011  Thermostats and different ensembles  Lecture Notes 08.12.2011 
15.12.2011  Finite differencing techniques, solving PDEs  
22.12.2011  Overview over research topics at the ICP  
12.01.2012  Introduction to Monte Carlo Methods, Metropolis Alg.  
19.01.2012  Phase transitions, critical phenomena  
26.01.2012  Finite Size Scaling  
02.02.2012  Error Analysis  
09.02.2012  Single particle Quantum Mechanics 
Tutorials (U 104)
 Scheduling of tutorials
 First tutorial is an introductory one and does not contain any graded homework. Starting from the second tutorial, a new worksheet is handed out every second week. The following week is dedicated to working on problems related to the last worksheet. Homework in the form of a report should be sent to the tutors before the next worksheet is handed out. The twoweek cycle ends with the discussion of results of the previous worksheet and handing out a new one.
Week  Date  Topic and files to download  Responsible tutor 

1.  26.10.2011  T0: First steps with Linux and C

Peter Košovan 
2.  2.11.2011  Discussion of T0
T1: Equations of motion and integrators

Peter Košovan 
3.  9.11.2011  Working on problems from T1  Peter Košovan 
4.  16.11.2011  Discussion of T1
T2: Molecular Dynamics: LennardJones liquid

Peter Košovan 
5.  23.11.2011  Working on problems from T2  Peter Košovan 
6.  30.11.2011  Discussion of T2
T3: MD in NVE and NVT ensembles; implementing different thermostats

Marcello Sega 
7.  7.12.2011  Working on problems from T3  Peter Košovan 
8.  14.12.2011  Discussion of T3
T4: The finite Difference and Finite element methods

Marcello Sega 
9.  21.12.2011  Working on problems from T4  Marcello Sega 
10.  11.1.2012  Discussion of T4
T5: Simple and importance sampling. Random walks.

Marcello Sega 
11.  18.1.2012  Working on problems from T5  Marcello Sega 
12.  25.1.2012  Discussion of T5
T6: Monte CarloIsing model

Peter Košovan 
13.  1.2.2012  Working on problems from T6  Peter Košovan 
14.  8.2.2012  Discussion of T6, end of the tutorials  Peter Košovan 
Assessment of the tutorials
Each task within the tutorial is assigned a given number of points. In total, every tutorial comprises 10 points. This means that there is a total maximum of 60 points and 30 are required to pass.
 Obtaining extra points
 Most tutorials contain some extra tasks. These constitute bonus points. typically there are two bonus points per worksheet.
 First person who identifies a bug in the code provided by the tutors gets an extra point and one additional extra point if he/she can fix the bug. Same applies to finding a mistake in the worksheets which significantly changes the meaning. We are also thankful for pointing out misprints but these are not awarded extra points.
 If you have a brilliant idea about an extra task which could be done in addition to what is requested in the worksheet, first ask the tutor to approve it. He will also tell you how many points you can get for it.
Guidelines for submitting the reports
Homework for the tutorials should be submitted in the form of a report. It has to be submitted via email as a single pdf document. Submission of handwritten reports is discouraged, but will also be accepted. Source code should always be sent via email in a separate file, if needed. If the code concerns only a few lines, it may be a part of the report. Reports clearly not meeting these requirements may be rejected without evaluation.
Reports obviously copied from someone else will be rejected without evaluation. It is encouraged to help each other and discuss your results, but each report has to be an original work.
If you have a technical problem on the CIP pool computers, e.g. a missing program or library or something else which does not allow you to perform a certain task, ask the tutor for assistance.
If you are not able for any reason to get the expected results, you should at least describe in the report your attempts to obtain them and/or to understand the origin of the problem. Saying in your report "I was not able to run program XXX, therefore I do not provide answer to Task YY." will not be accepted.
In your communications by email, always send the message to both tutors.
 Deadline
 Every other Monday morning, that is, two days before the next task is handed out.
 A delayed submission is penalized 1 point for each day of the delay.
 The deadline can be postponed if there is a good reason, but it must be decided together with the tutors during the last tutorial before the deadline. The tutor has a right to accept or reject the request and will announce it to all students.
 In case of special circumstances (illness, accident, ...) contact the tutors immediately via email to agree on an individual deadline.
 Text of the report
 Has to contain author name, student ID and date.
 Should be subdivided into sections, each section being clearly related to one task of the homework.
 Must be written in sentences, not points like in a presentation.
 All conclusions must be explained and when appropriate, supported by data (plots, tables). In case a derivation is required, all intermediate steps have to be clearly understandable or explained in the text.
 For each simulation, it has to be clear, what were the input parameters, so that it can be rerun.
 There is no upper or lower size limit on the report. Use common sense.
 Figures and plots
 Each figure has to have a number and a caption or title saying what is in the figure.
 In text, refer to figures by the number or title, so that it is clear which figure you are referring to.
 Each plot has to have labels on axes with font size comparable to other text. Plots without labels will not be considered.
 Data points should fill a major part of plot area. The point size, x and yscales have to be chosen appropriately so that all important features can be seen.
 All figures have to be included in the report. Figures sent as separate files will not be considered.
 You may optionally provide the data files. If there is a problem in your work, it may help the tutor understand where you made a mistake.
 Source files
 Remember that someone has to read your code, understand it and check that it is correct.
 Provide all files in which you made changes!
 Use variables with intuitively understandable names. If not, at least put a comment saying what it means.
 If the code is more complex, add comments to it. Especially to parts which may not be easy to read.
 We recommend that you indent your code for better readability.
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
 Linux cheat sheet here (53 KB)
 Ebook: D.P. Landau and K. Binder: A guide to Monte Carlo Simulations in Statistical Physics
 A good and freely available book about using Linux: Introduction to Linux by M. Garrels
 Not so frequently asked questions about GNUPLOT (Often used by myself as a cheat sheet)
 Becareful when using Wikitype of resources. They may contain a lot of useful information, but also a lot of nonsense, because anyone can write into them.