Simulation Methods in Physics I WS 2012

Overview

Type

Lecture (2 SWS) and Tutorials (2 SWS)

Lecturer

Prof. Dr. Christian Holm (Lecture); Dr. Olaf Lenz and Dr. Jens Smiatek (Tutorials)

Course language

English

Location and Time

Lecture: Thursdays, 11:30 - 13:00; ICP, Allmandring 3, Seminarroom 1

Tutorials: tbd; ICP, Allmandring 3, CIP-Pool

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.

Scope of the lecture

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).

Examination

Depending on the module that this lecture is part of, there are differences on how to get the credits for the module:

BSc/MSc Physik, Modul "Simulationsmethoden in der Physik" (36010)

• Obtain 50% of the possible points in the hands-in excercises of this lecture as a prerequisite for the examination (USL-V)
• 60 min of oral examination (PL)
  • After the lecture "Simulation Methods in Physics II" in summer term (i.e. Summer 2013)
  • Contents: both lectures and the excercises of "Simulation Methods in Physics I"

BSc/MSc SimTech, Modul "Simulationsmethoden in der Physik für SimTech I" (40520)

• Obtain 50% of the possible points in the hands-in excercises of this lecture as a prerequisite for the examination (USL-V)
• 40 min of oral examination (PL)
  • about the lecture and the excercises

MSc Chemie, Modul "Simulationsmethoden in der Physik für Chemiker I" (35840)

• Obtained marks from the excercises (BSL)