Difference between revisions of "Simulation Methods in Physics I WS 2013"

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=== Scope ===
 
=== 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:
+
The first part of the course intends to give an overview about modern simulation methods used in physics today. The lecture should introduce different approaches to simulate a physical systems. In this respect, rather a broad range of methods will be outlined than an exhaustive presentation of specific computational methods. Roughly, the lecture will consist of:
 +
 
 +
; General overview
 +
: The first 2-3 weeks will be dedicated on the general common aspects of computer simulations, elements of statistical ensemble theory and elements of elasticity theory, which are essential in understanding and performing simulations.
 +
 
 +
; Quantum Mechanics
 +
: An extensive presentation of quantum mechanical simulations will be given in the second part of this course. Here, a general overview of the ideas behind these kinds of simulations will be given.
  
 
; Molecular Dynamics
 
; 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.
+
: A more extensive investigation of classical Molecular Dynamics (MD) simulations is planned. This includes the algorithm, the integrators, the thermostats, to name a few necessary to perform MD simulations.
−
:The goal is to be able to set up and run real MD simulations for different ensembles and understand and interpret the output.
+
<!--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.-->
 +
:In terms of the respective tutorials, the goal is to be able to set up and run real MD simulations for different ensembles and understand and interpret the output.
 +
 
 +
; Monte Carlo Simulations
 +
: A part of the lecture will be dedicated on Monte Carlo (MC) methods and their algorithms. Specific examples, such as the Ising model will be studied.
 +
<!-- 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.-->
  
 
; Error Analysis
 
; Error Analysis
−
:Autocorrelation, Jackknifing, Bootstrapping
+
:The way errors come into the simulations and how to estimate these will be outlined.<-!!Autocorrelation, Jackknifing, Bootstrapping-->
 +
 
 +
; Potentials
 +
: An important component of molecular simulations are the potentials or force fields chosen to model the interactions within the simulated system. The efficiency of the simulations is stongly dependent on this choice. To this purpose, various methods can be applied for obtaining efficient potentials for different methods. Here, representative examples will be outlined.
 +
<!--; 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).-->
 +
 
 +
; Simulation of liquids
 +
: Methods such as the lattice Boltzmann method and specific details on simulating liquids will be briefly given.
 +
 
 +
; Advanced simulation techniques
 +
: In the end of the course, a short overview of other more advanced methods than the ones studied here will be presented. Examples include MC beyond the Metropolis algorithm, metadynamics or rare events sampling.
 +
 
 +
=== Prerequisites ===
 +
We expect the participants to have basic knowledge in quantum, classical and statistical mechanics, thermodynamics, electrodynamics, and partial differential equations, as well as knowledge of a programming language.
 +
 
 +
=== Certificate Requirements ===
 +
:1. Attendance of the exercise classes
 +
:2. Obtaining 50% of the possible marks in the hand-in exercises
 +
 
 +
There will be a final grade for the Module "Simulation Methods" (this module consists of both lectures, Sim I plus Sim II) determined at the end of lecture Simulation Methods II.
 +
 
 +
The final grade will be determined in the following way: There will be an oral examination performed at (or after) the end of the course Simulation Methods II (SS 2012).
 +
 
 +
=== Recommended literature ===
 +
<bibentry>frenkel02b,allen87a,rapaport04a,landau05a,newman99a,thijssen07,tuckerman10</bibentry>
 +
=== Useful online resources ===
 +
* Roethlisberger, Tavernarelli, EPFL, Lausanne, 2011: [http://lcbcpc21.epfl.ch/Group_members/ivano/bachelor.pdf Introduction to electronic structure methods.]
 +
 
 +
* Linux cheat sheet {{Download|Sim_Meth_I_T0_cheat_sheet_10_11.pdf|here}}.
 +
 
 +
* A good and freely available book about using Linux: [http://writers.fultus.com/garrels/ebooks/Machtelt_Garrels_Introduction_to_Linux_3nd_Ed.pdf Introduction to Linux by M. Garrels]
 +
 
 +
* [http://t16web.lanl.gov/Kawano/gnuplot/index-e.html Not so frequently asked questions about GNUPLOT]
 +
 
 +
* [http://homepage.tudelft.nl/v9k6y/imsst/index.html Introduction to Molecular Simulation and Statistical Thermodynamics (pdf textbook from TU Delft)]
  
−
; Monte Carlo Simulations
+
* [http://www.filibeto.org/sun/lib/development/shell/intr_to_bash_scr.html Short introduction to shell scripting (bash)]
−
: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.
+
 
 +
* [http://tldp.org/LDP/abs/html/ A more detailed introduction to bash scripting]
  
−
; Short interlude on Quantum Mechanical Systems
+
* [http://people.virginia.edu/~lz2n/mse627/notes/Intro.pdf University of Virginia, Introduction to atomistic simulations]
−
: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).
 
  
 +
* Be careful when using Wikipedia as a resource. It may contain a lot of useful information, but also a lot of nonsense, because anyone can write it.
 
=== Course Material ===
 
=== Course Material ===
  
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|-
 
|-
−
|12.12.2013 || Monte Carlo (MC) introduction ||  
+
|12.12.2013 || Introduction to Monte Carlo (MC) ||  
  
 
|-
 
|-
Line 83: Line 130:
 
|-
 
|-
  
−
|06.02.2014 || Advanced simulation techniques <!--Elements on thermodynamic integration, free-energy calculations, metadynamics-->||
+
|06.02.2014 || Advanced simulation techniques <!--Elements on thermodynamic integration, free-energy calculations, metadynamics--> ||
 +
|}
 +
 
 +
== 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) and Erasmus Mundus International Master FUSION-EP:
 +
:* Obtain 50% of the possible points in the hands-in excercises of this lecture as well as for the first part of the lecture as a prerequisite for the examination (USL-V)
 +
:* 60 min of oral examination (PL)
 +
:** After the lecture (i.e. Summer 2013)
 +
:** Contents: both lectures and the excercises of "Simulation Methods in Physics I"
 +
; International MSc Physics, Elective Module "Simulation Techniques in Physics II" (240918-005):
 +
:* Obtain 50% of the possible points in the hands-in excercises of this lecture as a prerequisite for the examination
 +
:* 30 min of oral examination (PL) about the lecture and the excercises
 +
; BSc/MSc SimTech, Modul "Simulationsmethoden in der Physik für SimTech II" (?????):
 +
:* 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 II" (?????):
 +
:* The marks for the module are the marks obtained in the excercises (BSL)

Revision as of 10:06, 19 September 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 lecture should introduce different approaches to simulate a physical systems. In this respect, rather a broad range of methods will be outlined than an exhaustive presentation of specific computational methods. Roughly, the lecture will consist of:

General overview
The first 2-3 weeks will be dedicated on the general common aspects of computer simulations, elements of statistical ensemble theory and elements of elasticity theory, which are essential in understanding and performing simulations.
Quantum Mechanics
An extensive presentation of quantum mechanical simulations will be given in the second part of this course. Here, a general overview of the ideas behind these kinds of simulations will be given.
Molecular Dynamics
A more extensive investigation of classical Molecular Dynamics (MD) simulations is planned. This includes the algorithm, the integrators, the thermostats, to name a few necessary to perform MD simulations.
In terms of the respective tutorials, the goal is to be able to set up and run real MD simulations for different ensembles and understand and interpret the output.
Monte Carlo Simulations
A part of the lecture will be dedicated on Monte Carlo (MC) methods and their algorithms. Specific examples, such as the Ising model will be studied.
Error Analysis
The way errors come into the simulations and how to estimate these will be outlined.<-!!Autocorrelation, Jackknifing, Bootstrapping-->
Potentials
An important component of molecular simulations are the potentials or force fields chosen to model the interactions within the simulated system. The efficiency of the simulations is stongly dependent on this choice. To this purpose, various methods can be applied for obtaining efficient potentials for different methods. Here, representative examples will be outlined.
Simulation of liquids
Methods such as the lattice Boltzmann method and specific details on simulating liquids will be briefly given.
Advanced simulation techniques
In the end of the course, a short overview of other more advanced methods than the ones studied here will be presented. Examples include MC beyond the Metropolis algorithm, metadynamics or rare events sampling.

Prerequisites

We expect the participants to have basic knowledge in quantum, classical and statistical mechanics, thermodynamics, electrodynamics, and partial differential equations, as well as knowledge of a programming language.

Certificate Requirements

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

There will be a final grade for the Module "Simulation Methods" (this module consists of both lectures, Sim I plus Sim II) determined at the end of lecture Simulation Methods II.

The final grade will be determined in the following way: There will be an oral examination performed at (or after) the end of the course Simulation Methods II (SS 2012).

Recommended literature

  • Daan Frenkel, Berend Smit.
    Understanding Molecular Simulation: From Algorithms to Applications.
    Part of Computational Science, volume 1. Edition 2.
    Academic Press, San Diego, 2002. ISBN: 978-0-12-267351-1.
    [DOI]
  • Mike P. Allen, Dominik J. Tildesley.
    Computer Simulation of Liquids.
    Part of Oxford Science Publications. Edition 1.
    Clarendon Press, Oxford, 1987.
  • D. C. Rapaport.
    The Art of Molecular Dynamics Simulation.
    Edition 2.
    Cambridge University Press, 2004. ISBN: 9780511816581.
    [DOI]
  • D. P. Landau, K. Binder.
    A guide to Monte Carlo Simulations in Statistical Physics.
    Edition second edition.
    Cambridge, 2005.
  • M. E. J. Newman, G. T. Barkema.
    Monte Carlo Methods in Statistical Physics.
    Edition 2002 edition.
    Oxford University Press, 1999.

Useful online resources

  • Linux cheat sheet application_pdf.pnghere (53 KB)Info circle.png.
  • Be careful when using Wikipedia as a resource. It may contain a lot of useful information, but also a lot of nonsense, because anyone can write it.

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 Introduction to Monte Carlo (MC)
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

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) and Erasmus Mundus International Master FUSION-EP
  • Obtain 50% of the possible points in the hands-in excercises of this lecture as well as for the first part of the lecture as a prerequisite for the examination (USL-V)
  • 60 min of oral examination (PL)
    • After the lecture (i.e. Summer 2013)
    • Contents: both lectures and the excercises of "Simulation Methods in Physics I"
International MSc Physics, Elective Module "Simulation Techniques in Physics II" (240918-005)
  • Obtain 50% of the possible points in the hands-in excercises of this lecture as a prerequisite for the examination
  • 30 min of oral examination (PL) about the lecture and the excercises
BSc/MSc SimTech, Modul "Simulationsmethoden in der Physik für SimTech II" (?????)
  • 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 II" (?????)
  • The marks for the module are the marks obtained in the excercises (BSL)
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