Difference between revisions of "Simulationsmethoden I WS 09 10"
(→Scope) 
Tabatabaei (talk  contribs) (→Tutorials (U 108)) 

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;Type  ;Type  
−  :Lecture (2 SWS) and Tutorials (  +  :Lecture (2 SWS) and Tutorials (1 SWS) 
:  :  
;Lecturer  ;Lecturer  
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: Monday, 11:30 a.m.1 p.m., Room V27.03 (tentative),  +  :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 handsontutorials which will take place in the CIPPool 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 handsontutorials which will take place in the CIPPool 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.  
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The course intends to give an overview about modern simulation methods  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  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  +  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 
−  but rather try to cover a broad  
lecture will consist of:  lecture will consist of:  
−  1.Molecular Dynamics  +  '''1. Molecular Dynamics''' 
+  
The first problem that comes to mind when thinking about simulating  The first problem that comes to mind when thinking about simulating  
physics is solving Newtons equations of motion for some particles with  physics is solving Newtons equations of motion for some particles with  
Line 29:  Line 30:  
common numerical integrators. This approach quickly leads us to  common numerical integrators. This approach quickly leads us to  
Molecular Dynamics (MD) simulations. Many of the complex problems of  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.  properties, ensembles and the macroscopic observables.  
+  
The goal is to be able to set up and run real MD simulations for  The goal is to be able to set up and run real MD simulations for  
different ensembles and understand and interpret the output.  different ensembles and understand and interpret the output.  
−  2.Partial Differential Equations  +  '''2. Partial Differential Equations''' 
+  
Some of the most common physical problems today can be formulated with  Some of the most common physical problems today can be formulated with  
−  Partial Differential Equations (  +  Partial Differential Equations (PDEs). We want to think about what kinds 
of physical problems can be dealt with PDEs and what methods we  of physical problems can be dealt with PDEs and what methods we  
have to solve them numerically.  have to solve them numerically.  
+  
The goal is to get to know the problems you run into when solving these  The goal is to get to know the problems you run into when solving these  
simplelooking equations and to get an overview on the methods available.  simplelooking equations and to get an overview on the methods available.  
−  3.Quantum mechanical systems  +  '''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  +  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)HartreeFock, Density Functional Theory, and CarParrinelloMolecular dynamics. We also want to examine the possibilities to simulate the quantum chromodynamics PDEs on a lattice (lattice gauge theory). 
−  methods like (post)HartreeFock, Density Functional  +  
−  Theory, and CarParrinelloMolecular dynamics.  
The goal is to get an overview on the methods to treat quantum  The goal is to get an overview on the methods to treat quantum  
mechanical systems and know about some of the advantages and  mechanical systems and know about some of the advantages and  
−  disadvantages of each method.  +  disadvantages of each method. 
−  +  
−  +  '''4. Monte Carlo Simulations'''  
−  
Since their invention, the importance of Monte Carlo (MC) sampling has  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  grown constantly. Nowadays it is applied to a wide class of problems in modern  
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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  
−  +    
+  21.10.09  First steps with Linux and C  
+    
+  28.10.09  [[Equations of motion and integrators]]  
+    
+  11.11.09  [[Molecular Dynamics: LennardJones 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 CarloIsing model]]  
}  }  
Latest revision as of 14:30, 1 February 2010
Contents
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 handsontutorials which will take place in the CIPPool 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 simplelooking 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)HartreeFock, Density Functional Theory, and CarParrinelloMolecular 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 Isingmodel.
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 handin 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: LennardJones 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 CarloIsing model 
Recommended literature

Daan Frenkel and Berend Smit.
"Understanding Molecular Simulation".
Academic Press, San Diego, 2002.
[DOI] 
Mike P. Allen and Dominik J. Tildesley.
"Computer Simulation of Liquids".
Oxford Science Publications, Clarendon Press, Oxford, 1987.

D. C. Rapaport.
"The Art of Molecular Dynamics Simulation".
Cambridge University Press, 2004.

D. P. Landau and K. Binder.
"A guide to Monte Carlo Simulations in Statistical Physics".
Cambridge, 2005.

M. E. J. Newman and G. T. Barkema.
"Monte Carlo Methods in Statistical Physics".
Oxford University Press, 1999.
Available EBooks
D.P. Landau and K. Binder.