Simulationsmethoden I 10 11
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 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, 11:30 = 13:00, Room V 57.06 (tentative),
 Tutorials
 Ttime: To be decided yet, Room U 108 (Pfaffenwaldring 27)
The lecture is accompanied by handsontutorials which will take place in the CIPPool 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 simplelooking 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)HartreeFock, Density Functional Theory, and CarParrinelloMolecular 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 Isingmodel.
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 handin 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 tutors that they are intending to come and seek their assistance.
 Handing in the solutions
 Approximately 10 days after the tutorial, but no later than Monday 8:00 before the next tutorial. Preferably via email (Text answers and plots in PDF, source code as text files). Alternatively, solutions can be also handed in on paper.
 Becareful  dates of the tutorials will certainly be adjusted yet!!!
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: LennardJones 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 CarloIsing model  
14.  3.2.2011  Optional (attendance not required)  
15.  10.2.2011  Discussion of T7, end of the tutorials 
Recommended literature

Daan Frenkel and Berend Smit.
"Understanding Molecular Simulation".
Academic Press, San Diego, 2002.
[DOI] 
Mike P. Allen and Dominik J. Tildesley.
"Computer Simulation of Liquids".
Oxford Science Publications, Clarendon Press, Oxford, 1987.

Rapaport, D. C..
"The Art of Molecular Dynamics Simulation".
Cambridge University Press, 2004.
[DOI] 
D. P. Landau and K. Binder.
"A guide to Monte Carlo Simulations in Statistical Physics".
Cambridge, 2005.

M. E. J. Newman and G. T. Barkema.
"Monte Carlo Methods in Statistical Physics".
Oxford University Press, 1999.
Available EBooks
D.P. Landau and K. Binder.