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, 14.00-15.30 and 17:00-18.30, Room V27.U104

The lecture is accompanied by hands-on-tutorials which will take place in the CIP-Pool 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.

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 simple-looking 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-)Hartree-Fock, Density Functional Theory, and Car-Parrinello-Molecular 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 Ising-model.

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 hand-in 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)
20.10.2011	Course Content, Organisation,Introduction
27.10.2011	Equation of Motion and simple Integrators for Classical MD
03.11.2011	Integrators cont., simple Potentials for Liquids
10.11.2011	LJ Units, Simple MD Program
17.11.2011	Stat Mech in a Nutshell, Observables in MD
24.11.2011	Observables in MD, Diffusion, Brownian motion, RDF
01.12.2011	Green-Kubo relations, temperature fluctuations in NVE ensemble
08.12.2011	Thermostats and different ensembles
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 two-week 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.	26.10.2010	T0: First steps with Linux and C Worksheet for T0 (341 KB) T0 from last year	Peter Košovan
2.	2.11.2010	Discussion of T0 T1: Equations of motion and integrators Worksheet is being updated. We make it available soon before the tutorial T1 from last year	Peter Košovan
3.	9.11.2010	Working on problems from T1	Peter Košovan
4.	16.11.2010	Discussion of T1 T2: Molecular Dynamics: Lennard-Jones liquid Worksheet is being updated. We make it available before the tutorial. T2 from last year	Peter Košovan
5.	23.11.2010	Working on problems from T2	Peter Košovan
6.	30.11.2010	Discussion of T2 T3: MD in NVE and NVT ensembles; implementing different thermostats Worksheet is being updated. We make it available before the tutorial. T3 from last year	Marcello Sega
7.	7.12.2010	Working on problems from T3	Peter Košovan
8.	14.12.2010	Discussion of T3 T4: The finite Difference and Finite element methods Worksheet is being updated. We make it available before the tutorial. T4 from last year	Marcello Sega
9.	21.12.2010	Working on problems from T4	Marcello Sega
10.	11.1.2011	Discussion of T4 T5: Simple and importance sampling. Random walks. Worksheet is being updated. We make it available before the tutorial. T5 from last year	Marcello Sega
11.	18.1.2011	Working on problems from T5	Marcello Sega
12.	25.1.2011	Discussion of T5 T6: Monte Carlo-Ising model Worksheet is being updated. We make it available before the tutorial. T6 from last year	Peter Košovan
13.	1.2.2011	Working on problems from T6	Peter Košovan
14.	8.2.2011	Discussion of T6, end of the tutorials	Peter Košovan Marcello Sega

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 e-mail as a single pdf document. Submission of handwritten reports is discouraged, but will also be accepted. Source code should always be sent via e-mail 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 e-mail 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 re-run.; 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 y-scales 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, 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

Linux cheat sheet here (53 KB)

Computer basics lectures (in german)

E-book: 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)

Introduction to Molecular Simulation and Statistical Thermodynamics

Becareful when using Wiki-type of resources. They may contain a lot of useful information, but also a lot of nonsense, because anyone can write into them.