Difference between revisions of "Simulationsmethoden I WS 09 10"

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;Type
 
;Type
:Lecture (2 SWS) and Tutorials (2 SWS)
+
:Lecture (2 SWS) and Tutorials (1 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
 
;Lecturer
 
:Prof. Dr. [[Christian Holm]] (Lecture) and  [[Joan Josep Cerdà]], [[Fatemeh Tabatabaei]],  [[Nadezhda Gribova]] (Tutorials)
 
:Prof. Dr. [[Christian Holm]] (Lecture) and  [[Joan Josep Cerdà]], [[Fatemeh Tabatabaei]],  [[Nadezhda Gribova]] (Tutorials)
Line 10: Line 10:
 
:Deutsch oder Englisch, wie gewünscht- German or English, by vote
 
:Deutsch oder Englisch, wie gewünscht- German or English, by vote
 
;Time and Room
 
;Time and Room
:Lecture times: Wed. 11.30 - 13.00 in V57.04 and Wed 9.45 - 11.15 in V57.02  <br/>
+
:Lecture times: Monday, 11:30 a.m.-1 p.m., Room V27.03 (tentative),
 +
:Tutorial times: Wednesday, 3:30 p.m.-5:30 p.m., Room U 108 (Pfaffenwaldring 27)
 
The lecture is accompanied by hands-on-tutorials which will take place in the CIP-Pool of the ICP, Pfaffenwaldring 27, U 108. They consist of practical exercises at the computer, like small programming tasks, simulations, visualization and data analysis.
 
The lecture is accompanied by hands-on-tutorials which will take place in the CIP-Pool of the ICP, Pfaffenwaldring 27, U 108. They consist of practical exercises at the computer, like small programming tasks, simulations, visualization and data analysis.
 
The tutorials build on each other, therefore continuous attendance is expected.
 
The tutorials build on each other, therefore continuous attendance is expected.
Tutorials will be hold on:  Time to be announced.
+
Tutorials will be hold on:  Time to be negotiated during the first meeting on October 19.
  
 
==Scope==
 
==Scope==
The course will give an introduction to modern simulational techniques, like Monte-Carlo (MC) and Molecular dynamics (MD) simulations (on- and off-lattice).
+
 
 +
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:
 +
 
 +
'''1. 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.
 +
 
 +
'''2. Partial Differential Equations'''
 +
 
 +
Some of the most common physical problems today can be formulated with
 +
Partial Differential Equations (PDEs). We want to think about what kinds
 +
of physical problems can be dealt with PDEs and what methods we
 +
have to solve them numerically.
 +
 
 +
The goal is to get to know the problems you run into when solving these
 +
simple-looking equations and to get an overview on the methods available.
 +
 
 +
'''3. Quantum mechanical systems'''
 +
 
 +
It is obvious that solving quantum mechanical systems analytically is not possible and we need numerical help. We want to introduce various methods like (post-)Hartree-Fock,  Density Functional Theory, and Car-Parrinello-Molecular dynamics. We also want to examine the possibilities to simulate the quantum chromodynamics PDEs on a lattice (lattice gauge theory).
 +
 
 +
The goal is to get an overview on the methods to treat quantum
 +
mechanical systems and know about some of the advantages and
 +
disadvantages of each method.
 +
 
 +
'''4. 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.
  
 
== Prerequisites ==
 
== Prerequisites ==
Line 29: Line 73:
 
|-valign="top"
 
|-valign="top"
 
!Date !! Subject
 
!Date !! Subject
 
+
|-
 +
| 19.10.09 || Contents, introduction, organisation
  
 
|}
 
|}
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|-valign="top"
 
|-valign="top"
 
!Date !! Subject
 
!Date !! Subject
 
+
|-
|-valign="top"
+
|21.10.09 || First steps with Linux and C
! 29.4. and 30.4
+
|-
| Simple and important sampling. Random walks.
+
|28.10.09 || [[Equations of motion and integrators]]
 
+
|-
|-valign="top"
+
|11.11.09 || [[Molecular Dynamics: Lennard-Jones liquid]]
! 6.5. and 7.5
+
|-
| 2D Ising model I
+
|25.11.09 || [[MD in NVE and NVT ensembles; implementing different thermostats]]
 
+
|-
|-valign="top"
+
|09.12.09 || [[The finite Difference and Finite element methods]]
! 13.5. and 14.5
+
|-
| 2D Ising model II
+
|23.12.09 || [[Numerical Solution of the Schroedinger Equation]]
 
+
|-
|-valign="top"
+
|20.01.09 || [[Simple and important sampling. Random walks.]]
! 20.5. and 21.5
+
|-
| Error analysis
+
|04.02.09 || [[Monte Carlo-Ising model]]
 
 
|-valign="top"
 
! 27.5. and 28.5
 
| Molecular Dynamics (Lennard-Jones system)
 
 
|}
 
|}
  

Latest revision as of 13:30, 1 February 2010

Overview

Simulationsmethoden in der Physik I:Simulation Methods in Physics I

Type
Lecture (2 SWS) and Tutorials (1 SWS)
Lecturer
Prof. Dr. Christian Holm (Lecture) and Joan Josep Cerdà, Fatemeh Tabatabaei, Nadezhda Gribova (Tutorials)
Course language
Deutsch oder Englisch, wie gewünscht- German or English, by vote
Time and Room
Lecture times: Monday, 11:30 a.m.-1 p.m., Room V27.03 (tentative),
Tutorial times: Wednesday, 3:30 p.m.-5:30 p.m., Room U 108 (Pfaffenwaldring 27)

The lecture is accompanied by hands-on-tutorials which will take place in the CIP-Pool of the ICP, Pfaffenwaldring 27, U 108. They consist of practical exercises at the computer, like small programming tasks, simulations, visualization and data analysis. The tutorials build on each other, therefore continuous attendance is expected. Tutorials will be hold on: Time to be negotiated during the first meeting on October 19.

Scope

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:

1. 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.

2. Partial Differential Equations

Some of the most common physical problems today can be formulated with Partial Differential Equations (PDEs). We want to think about what kinds of physical problems can be dealt with PDEs and what methods we have to solve them numerically.

The goal is to get to know the problems you run into when solving these simple-looking equations and to get an overview on the methods available.

3. Quantum mechanical systems

It is obvious that solving quantum mechanical systems analytically is not possible and we need numerical help. We want to introduce various methods like (post-)Hartree-Fock, Density Functional Theory, and Car-Parrinello-Molecular dynamics. We also want to examine the possibilities to simulate the quantum chromodynamics PDEs on a lattice (lattice gauge theory).

The goal is to get an overview on the methods to treat quantum mechanical systems and know about some of the advantages and disadvantages of each method.

4. 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.

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++).

Certificate Requirements:

1. Attendance of the exercise classes
2. Obtaining 50% of the possible marks in the hand-in exercises

Lecture

Date Subject
19.10.09 Contents, introduction, organisation

Tutorials (U 108)

Date Subject
21.10.09 First steps with Linux and C
28.10.09 Equations of motion and integrators
11.11.09 Molecular Dynamics: Lennard-Jones liquid
25.11.09 MD in NVE and NVT ensembles; implementing different thermostats
09.12.09 The finite Difference and Finite element methods
23.12.09 Numerical Solution of the Schroedinger Equation
20.01.09 Simple and important sampling. Random walks.
04.02.09 Monte Carlo-Ising model

Recommended literature


Available E-Books

D.P. Landau and K. Binder.

"A guide to Monte Carlo Simulations in Statistical Physics"