Simulationsmethoden I 10 11

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Simulationsmethoden in der Physik I

Simulation Methods in Physics I

Type
Lecture (2 SWS) and Tutorials (1 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

Majority vote was for English!

Lectures
Time: Thursdays, 11:30 - 13:00, Room V 57.06
Tutorials
Time: Wednesday, 17:00-18.30, 2 hours/(every other week)

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.

Note: students from the COMMAS master will have to attend tutorials every week.

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++).

Certificate Requirements:

1. Attendance of the exercise classes
2. Obtaining 50% of the possible marks in the hand-in exercises


There will be a final grade for the Module "Simulation Methods" (this module consists of both lectures, Sim I plus Sim II) determined at the end of lecture Simulation Methods II.

The final grade will be determined in the following way :

1. 50% comes from the marks for the hand-in exercises for both parts of the course (Simulation Methods in Physics I and II) Basis for the grade is the sum of all marks obtained in the tutorials in Sim I plus all accumulated marks of all tutorials in Sim II.

2. The other 50% will be determined in an oral examination performed at (or after) the end of the course Simulation Methods II (SS 2011).

NOTE: students from the COMMAS master will have to present, at the end of the course, a supplementary project (topic to be discussed with tutors).

Lecture

Date Subject
21.10.2010 Course Content, Organisation,Introduction
28.10.2010 Equation of Motion and simple Integrators for Classical MD
04.11.2010 Integrators cont., simple Potentials for Liquids
11.11.2010 LJ Units, Simple MD Program
18.11.2010 Stat Mech in a Nutshell, Observables in MD
25.11.2010 Observables in MD, Diffusion, Brownian motion, RDF
02.12.2010 Green-Kubo relations, temperature fluctuations in NVE ensemble
09.12.2010 Thermostats and different ensembles
16.12.2010 Finite differencing techniques, solving PDEs
23.12.2010
13.01.2011
20.01.2011
27.01.2011
03.02.2011
10.02.2011

Tutorials (U 108)

Obtaining extra points
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.
Scheduling of tutorials
Starting from the 2nd tutorial, they are scheduled every two weeks (see table below). In the week between the tutorials, the tutors will be available to help the students. Since participation is optional, it is recommended that the studendts notify the tutors that they are intending to come and seek their assistance.


Week Date Topic
1. 27.10.2010 T0: First steps with Linux and C
2. 3.11.2010 T1: Equations of motion and integrators
3. 10.11.2010 Optional (attendance not required)
4. 17.11.2010 T2: Molecular Dynamics: Lennard-Jones liquid
5. 24.11.2010 Optional (attendance not required)
6. 1.12.2010 T3: MD in NVE and NVT ensembles; implementing different thermostats
7. 8.12.2010 Optional (attendance not required)
8. 15.12.2010 T(4): The finite Difference and Finite element methods
9. 22.12.2010 Optional (attendance not required)
10. 12.1.2011 T5: Simple and importance sampling. Random walks.
11. 19.1.2011 Optional (attendance not required)
12. 26.1.2011 T6: Monte Carlo-Ising model
13. 2.2.2011 Optional (attendance not required)
14. 9.2.2011 Discussion of T6, end of the tutorials

Guidelines for submitting the homework

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 or alternatively as a paper printout. Handwritten reports will be accepted. Source code should always be sent via e-mail. 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.

Identical pieces of reports annihilate when submitted by different people producing anti-points for both. The amount of anti-points grows exponentially with the similarity. It is fine when you work together, but each part of the report has to be an original, not a copy from your neighbour.

Deadline
Approximately 10 days after the tutorial, but no later than Monday 8:00 of the week when the next worksheet is handed out. Reports on paper can be handed in personally until lunch break on Monday.
In case of special circumstances (illness, accident, ...) contact the tutor immediately via e-mail to agree on an alternative 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.
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


Useful online resources

  • Linux cheat sheet application_pdf.pnghere (53 KB)Info circle.png.
  • 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.