# Simulation Methods in Physics I WS 2013

## Contents

## Overview

- Type
- Lecture (2 SWS) and Tutorials (2 SWS)
- Lecturer
- JP Dr. Maria Fyta (Lecture); Dr. Olaf Lenz, Bibek Adhikari, Elena Minina (Tutorials)
- Course language
- English
- Location and Time
- Lecture: Thu, 11:30 - 13:00 (Seminar room ICP, Allmandring 3); Tutorials: tba (CIP-Pool ICP, Allmandring 3)
- Prerequisites
- We expect the participants to have basic knowledge in classical and statistical mechanics, thermodynamics, and partial differential equations, as well as knowledge of a programming language (Python or C).

The lecture is accompanied by hands-on-tutorials which will take place in the CIP-Pool of the ICP, Allmandring 3. They consist of practical exercises at the computer, like small programming tasks, simulations, visualization and data analysis. The tutorials build upon each other, therefore continuous attendance is expected.

## Lecture

### Scope

The first part of 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:

- 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.

- Error Analysis
- Autocorrelation, Jackknifing, Bootstrapping

- 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.

- Short interlude on Quantum Mechanical Systems
- It is obvious that solving quantum mechanical systems analytically is not possible and we need numerical help. We also want to examine the possibilities to simulate the quantum chromodynamics PDEs on a lattice (lattice gauge theory).

### Course Material

Date | Subject | Resources |
---|---|---|

17.10.2013 | Course Content, Introduction | |

24.10.2013 | Introduction to quantum-mechanical methods | |

31.10.2013 | Common features in computer simulations (boundary conditions, long-range interactions, finite size effects, etc.) | |

07.11.2013 | Basics of Stat Mech, ensembles, observables | |

14.11.2013 | Elements of elasticity theory | |

21.11.2013 | Introduction to Molecular Dynamics (MD) | |

28.11.2013 | MD (integrators, Liouville formulation, Lyapunov instability) | |

05.12.2013 | MD (thermostats/barostats) | |

12.12.2013 | Monte Carlo (MC) introduction | |

19.12.2013 | MC (examples - Ising model, beyond Metropolis) | |

09.01.2014 | Building potentials | |

16.01.2014 | Langevin dynamics, Brownian dynamics | |

23.01.2014 | Error analysis | |

30.01.2014 | Elements on thermodynamic integration, free-energy calculations, metadynamics | |

06.02.2014 | Advanced simulation techniques |