Simulation Methods in Physics I WS 2013
Revision as of 14:47, 17 September 2013 by Olenz (talk  contribs) (Created page with "== Overview == ;Type :Lecture (2 SWS) and Tutorials (2 SWS) ;Lecturer :Prof. Dr. Maria Fyta (Lecture); Dr. Olaf Lenz, Bibek Adhikari, Elena Minina (Tutorials)...")
Overview
 Type
 Lecture (2 SWS) and Tutorials (2 SWS)
 Lecturer
 Prof. 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 (CIPPool 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 handsontutorials which will take place in the CIPPool 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 Isingmodel.
 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).