Simulation Methods in Physics I WS 2020/2021
- Lecture (2 SWS) and Tutorials (2 SWS)
- Prof. Dr. Christian Holm
- Course language
- Location and Time
- Lecture: Thu, 14:00–15:30; online: via webex
- Tutorials: TBA (Samuel Tovey); TBA (Christoph Lohrmann)
- 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 hands-on tutorials which will take place via webex (details will follow). 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 first part of the course intends to give an overview about modern simulation methods used in physics today. The focus of the lecture will be to introduce different approaches to simulating 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 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 such as the Ising model.
- Critical exponents in second order phase transitions
- Finite-size scaling, universality concept, how to determine critical exponent with lattice spin models
A preliminary version of the script can be downloaded here (929 kB).
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 Many-Body Systems:
From Theory to Algorithms, Lecture Notes, (2002).
- Reweighing: W. Janke, Histograms and all that, Computer Simulations of Surfaces and Interfaces, pp 137-157, Springer book
- Monte Carlo Simulations: W. Janke, Monte Carlo, Monte Carlo Simulations of Spin Systems, Computational Physics pp 10-43
- 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.
- For the tutorials, you will get a personal account for the ICP machines.
- For the reports, we have a nice latex-template.tex (7 KB).
- You can do the exercises in the CIP-Pool 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 on ICP machines, 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.
- The following Python packages:
- 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.
- The worksheets are to be solved in groups of two or three people. We will not accept hand-in-exercises 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.
- Participants need 50 % of the points of the hands-in exercises on each worksheet to be admitted to the oral examination (see Examination for details).
What happens in a tutorial
- The tutorials take place every week.
- The new worksheet will be available for download 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.
- 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.
- Use the existing documentation of Python itself! To get help on the command
- 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" , also available in German
- first of all, try to use
- 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
Running Python on your own computer
If you want to solve the problems on your own computer, you need to install Python along with a few extensions. This works differently depending on your operating system.
Debian und Ubuntu Linux
sudo apt-get update sudo apt-get install python3 python3-numpy python3-scipy \ python3-matplotlib ipython ipython-notebook gcc g++ mkdir -p ~/.config/matplotlib echo 'backend: TkAgg' > ~/.config/matplotlib/matplotlibrc
sudo zypper install python python-numpy python-scipy \ python-matplotlib IPython gcc python-Cython mkdir -p ~/.config/matplotlib echo 'backend: TkAgg' > ~/.config/matplotlib/matplotlibrc
Mac OS X
First, install the C compiler:
xcode-select --install xcodebuild -license accept
Now download and install MacPorts. Next, you can install the Python packages.
sudo port selfupdate sudo port install python36 py36-numpy py36-scipy \ py36-matplotlib py36-ipython py36-jupyter sudo port select python python36 sudo port select ipython py36-ipython
For Windows, we recommend Anaconda Python, an all-in-one package that includes all required Python modules.
For the worksheets that use Cython, you will also need to install a compatible C compiler. If you chose Python 2.7, that is Visual Studio 2008 Express Edition plus, if you are running 64-bit Windows, the Windows SDK 2008 (in the installer, select "Installation Options", "Developer Tools", "Visual C++ Compilers", "Install the Visual C++ 9.0 Compilers). If you chose Python 3.5 or 3.6, you need Visual Studio 2015 Community Edition (in the installer, select "Custom" and on the next page, select "Common Tools for Visual C++ 2015" in the "Programming Languages" category and uncheck all the other components that we do not need).
Depending on the programme you are enrolled in, Simulation Methods is part of different modules that award different numbers of credits after different kinds of exams. Please have a look at File:SimMethModuleOverview.pdf, which also explains how you can take Advanced Simulation Methods.