Simulationsmethoden I

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 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. Tutorials are split in two parts 2 hours each on Wednesdays 14.00-15.30 and on Thursdays 17.15-18.45.

Scope

The course will give an introduction to modern simulational techniques, like Monte-Carlo (MC) and Molecular dynamics (MD) simulations (on- and off-lattice), and how to solve non-linear PDEs like the Poisson-Boltzmann 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 hand-in exercises

Lecture

Date	Subject
21.4.	Initial informational meeting - Vorbesprechung
22.4.	Monte-Carlo 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 motion--Ising 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, multi-histogram 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 (Lennard-Jones system)

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"