Simulationsmethoden I
Overview
Simulationsmethoden in der Physik I:Simulation Methods in Physics I
 Type
 Lecture (2 SWS) and Tutorials (2 SWS)
 The course will take place during the first 6 weeks of the semester with 4 hours per week lectures, and 4 hours tutorial
 Lecturer
 Prof. Dr. Christian Holm (Lecture) and Joan Josep Cerdà, Fatemeh Tabatabaei, Nadezhda Gribova (Tutorials)
 Course language
 Deutsch oder Englisch, wie gewünscht German or English, by vote
 Time and Room
 Lecture times: Tue 11.30  13.00 in V57.04 and Wed 9.45  11.15 in V57.02
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. Tutorials are split in two parts 2 hours each on Wednesdays 14.0015.30 and on Thursdays 17.1518.45.
Scope
The course will give an introduction to modern simulational techniques, like MonteCarlo (MC) and Molecular dynamics (MD) simulations (on and offlattice), and how to solve nonlinear PDEs like the PoissonBoltzmann equation.
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 

21.4.  Initial informational meeting  Vorbesprechung 
22.4.  MonteCarlo integration/simulation (Simple vs. Importance sampling)
Look at Zuse's Z3 computer from 1941: Z3 and read something about the first big US computer at Los Alamos Evolving from Calculators to Computers 
28.4.  Random walks and Browninan motionIsing model, Theoretical foundations of Monte Carlo 
29.4.  Study of phase transitions, critical phenomena, critical exponents 
5.5.  Finite size scaling theory

6.5.  Reweighting, multihistogram and tempering methods 
12.5.  Error Analysis (Binning, Jackknife, ...)

13.5.  Random number generators, Cluster Algorithms 
19.5.  Molecular Dynamics I (Velocity Verlet algorithm, Reduced units, Langevin thermostat, Potentials, Forces, Atomistic force fields) 
20.5.  Molecular Dynamics II 
26.5.  Molecular Dynamics III 
27.5.  MD IV, last lecture of Simulationsmethoden I

Tutorials (U 108)
Date  Subject 

29.4. and 30.4  Simple and important sampling. Random walks. 
6.5. and 7.5  2D Ising model I 
13.5. and 14.5  2D Ising model II 
20.5. and 21.5  Error analysis 
27.5. and 28.5  Molecular Dynamics (LennardJones system) 
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.