Simulationsmethoden I

Overview

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 English, wie gewünscht

Time and Room

Lecture times: Mo:11:30-13:00 Thu: 9:45- 11:15
Tutorials: will be fixed during first week

The course will give an introduction to the computational tools that are used in soft matter science, like Monte-Carlo (MC) and Molecular dynamics (MD) simulations (on- and off-lattice), Poisson-Boltzmann theory (and extensions).

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++).

Lecture and tutorials

The lecture is accompanied by hands-on-tutorials which will be held in the ICP CIP- pool. They consist of practical excercises at the computer, like small programming tasks, simulations, visualisation and data analysis.

The tutorials build on each other, therefore continous attendance is expected.

The dates of the tutorials will be scheduled in the first lecture.

Lecture

Date	Subject
20.4.	Vorbesprechung
23.4.	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
27.4.	2D Random walks (RW) and Self-avoiding random walks (SAW)--Ising model I (Phase transitions, Critical phenomena, Finite size scaling)
30.4.	2D Ising model II (Reweighting, Cluster Algorithm)
4.5.	Error Analysis (Binning, Jackknife, ...)
7.5.	Molecular Dynamics I (Velocity Verlet algorithm, Reduced units, Langevin thermostat, Potentials, Forces, Atomistic force fields)
11.5.	Molecular Dynamics II
14.5.	Long range interactions (Direct sum, Ewald summation, P3M, Fast Multipole method) This pdf file long_range_lecture.pdf (216 KB) contains surely too many details, but I will walk you through in class. In case you like to have some more background material, here is a review article by A. Arnold and me about this topic (arnold05a.pdf ())
14.5.	Continuation of long range lecture, beginning of How to simulate Polymers and Polyelectrolytes.
18.5.	Continuation on How to simulate Polymers and Polyelectrolytes and background of Poisson-Boltzmann Theory.
25.5.	Introduction to the Project work: charged infinite rods in ionic solution-comparison to PB theory. CompMethods.pdf (1.65 MB) A good background reading is the thesis of M. Deserno thesis_deserno.pdf (3.57 MB)
28.5.	last lecture of Simulationsmethoden I

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.