Simulation Methods in Physics I WS 2013

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	Simulating liquids
06.02.2014	Advanced simulation techniques