Simulationsmethoden I 10 11

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

Lectures

Time: Thursday, hh.mm = hh.mm, Room V27.xx (tentative),

Tutorials

Ttime: To be decided yet, Room U 108 (Pfaffenwaldring 27)

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++).

Certificate Requirements:

1. Attendance of the exercise classes

2. Obtaining 50% of the possible marks in the hand-in exercises

Lecture

Date	Subject
21.10.2010	Contents, introduction, organisation

Tutorials (U 108)

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 tutor that

they are intending to come and seek his assistance.

Handing in the solutions

Approximately 10 days after the tutorial, but no later than Monday 8:00 before the next tutorial. Preferably via e-mail (Text answers and plots in PDF, source code as text files). Alternatively, solutions can be also handed in on paper.

Week	Date	Topic
1.	28.10.2010	T0: First steps with Linux and C
2.	4.11.2010	T1: Equations of motion and integrators
3.	11.11.2010	Optional (attendance not required)
4.	18.11.2010	T2: Molecular Dynamics: Lennard-Jones liquid
5.	25.11.2010	Optional (attendance not required)
6.	2.12.2010	T3: MD in NVE and NVT ensembles; implementing different thermostats
7.	9.12.2010	Optional (attendance not required)
8.	16.12.2010	T(4+5): The finite Difference and Finite element methods Numerical Solution of the Schroedinger Equation
9.	23.12.2010	Optional (attendance not required)
10.	6.1.2011	Holiday
11.	13.1.2011	T6: Simple and importance sampling. Random walks.
12.	20.1.2011	Optional (attendance not required)
13.	27.1.2011	T7: Monte Carlo-Ising model
14.	3.2.2011	Optional (attendance not required)
15.	10.2.2011	Discussion of T7, end of the tutorials

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.
  

Available E-Books

D.P. Landau and K. Binder.

"A guide to Monte Carlo Simulations in Statistical Physics"