Simulation Methods in Physics I WS 2020/2021

Overview

Type

Lecture (2 SWS) and Tutorials (2 SWS)

Lecturer

Prof. Dr. Christian Holm

Course language

English

Location and Time

Lecture: Thu, 14:00–15:30; online: via webex

Tutorials: TBA (Samuel Tovey); TBA (Christoph Lohrmann)

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 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.

Course material

All course material (general info, lecture recordings, worksheets, ...) will be distributed via ILIAS (you join the ILIAS groups upon registration through C@MPUS)

Lecture

Scope

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

Course Material

	Date	Subject	Resources	Remarks
1	2020-11-05	Organization, Introduction, MD Basics	Slides
2	2020-11-12	Integrators Chaos, LJ-Potential, Units	Lecture Notes
3	2020-11-19	Basics of Statistical Mechanics	Lecture Notes
4	2020-11-26	PBC, cell-lists, simple MD	Lecture Notes
5	2020-12-03	Observables, Brownian Motion, Diffusion	Lecture Notes
6	2020-12-10	Diffusion, Green-Kubo, Langevin Dynamics	Lecture Notes
7	2020-12-17	Thermostats part 1	Lecture Notes
8	2021-01-07	Error analysis	Lecture Notes
9	2021-01-14	Thermostat part2 + Intro Monte Carlo	Lecture Notes
10	2021-01-21	Monte-Carlo Method and critical phenomena	Lecture Notes
11	2021-01-28	Critical Exponents	Lecture Notes
12	2021-02-04	Finite Size Scaling	Lecture Notes
13	2021-02-11	Reweighting	Lecture Notes

Script

A preliminary version of the script can be downloaded here (929 kB).

If you find any kind of mistake / error / typo / bad formatting / etc. in the script, please send an email to Christoph Lohrmann or Samuel Tovey.

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.
  

We recommend that you search the university library for ebook versions of these books

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

• Introduction to Molecular Simulation and Statistical Thermodynamics (pdf textbook from TU Delft)

Tutorials

General Remarks

• For the tutorials, you will get a personal account for the ICP machines.
• For the reports, we have a nice LaTeX template (7 KB).

Hand-in-exercises

• 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 (Samuel Tovey or Christoph Lohrmann).
• Each task within the tutorial is assigned a given number of points. Each student should have 50 % of the points from each tutorial as a prerequisite for the oral examination.

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.

Getting ready for the exercises

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

• The Not So Short Introduction to LaTeX
• Documentation list of the LaTeX project

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

OpenSUSE Linux

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

Windows

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).

Examination

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.

C++ Course

The Computer Science department is offering a week-long C++ course at the end of this semester. We recommend all students that plan on participating the Advanced Simulation Methods lecture in winter semester 2020 to take this course. We also recommend it to all students that are considering doing a master's or bachelor's thesis at the ICP. Current bachelor students might be able to take this course as Schlüsselqualifikation – but please contact the organizing Professor beforehand to ensure that this is actually the case. Master students will be able to take this course as One Course (2 SWS) in an Application Field of Simulation Methods as part of the Fortgeschrittene Simulationsmethoden (Schwerpunkt) module, pending a change of the Modulhandbuch. Note that even current bachelor students can already take the course in 2020 if they intend to enroll in the master programme (starting in fall 2021) and take Advanced Simulation Methods (in summer 2022). All students will need to present their "Schein" at the Advanced Simulation Methods exam in order to prove that they successfully participated in the C++ course and completed all required exercises.