Über diesen Kurs
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Ca. 54 Stunden zum Abschließen

Englisch

Untertitel: Englisch

100 % online

Beginnen Sie sofort und lernen Sie in Ihrem eigenen Tempo.

Flexible Fristen

Setzen Sie Fristen gemäß Ihrem Zeitplan zurück.

Ca. 54 Stunden zum Abschließen

Englisch

Untertitel: Englisch

Lehrplan - Was Sie in diesem Kurs lernen werden

Woche
1
1 Stunde zum Abschließen

Monte Carlo algorithms (Direct sampling, Markov-chain sampling)

Dear students, welcome to the first week of Statistical Mechanics: Algorithms and Computations! <br> Here are a few details about the structure of the course: For each week, a lecture and a tutorial videos will be presented, together with a downloadable copy of all the relevant python programs mentioned in the videos. Some in-video questions and practice quizzes will help you to review the material, with no effect on the final grade. A mandatory peer-graded assignment is also present, for weeks from 1 to 9, and it will expand on the lectures' topics, letting you reach a deeper understanding. The nine peer-graded assignments will make up for 50% of the grade, while the other half will come from a final exam, after the last lecture. <br> In this first week, we will learn about algorithms by playing with a pebble on the Monte Carlo beach and at the Monaco heliport. In the tutorial we will use the 3x3 pebble game to understand the essential concepts of Monte Carlo techniques (detailed balance, irreducibility, and a-periodicity), and meet the celebrated Metropolis algorithm. Finally, the homework session will let you understand some useful aspects of Markov-chain Monte Carlo, related to convergence and error estimations.

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3 Videos (Gesamt 62 min), 2 Lektüren, 2 Quiz
3 Videos
Tutorial 1: Exponential convergence and the 3x3 pebble game32m
Homework Session 1: From the one-half rule to the bunching method1m
2 Lektüren
Python programs and references10m
Errata (Lecture 1)10m
1 praktische Übung
Practice quiz 1: spotting a correct algorithm4m
Woche
2
1 Stunde zum Abschließen

Hard disks: From Classical Mechanics to Statistical Mechanics

In Week 2, you will get in touch with the hard-disk model, which was first simulated by Molecular Dynamics in the 1950's. We will describe the difference between direct sampling and Markov-chain sampling, and also study the connection of Monte Carlo and Molecular Dynamics algorithms, that is, the interface between Newtonian mechanics and statistical mechanics. The tutorial includes classical concepts from statistical physics (partition function, virial expansion, ...), and the homework session will show that the equiprobability principle might be more subtle than expected.

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3 Videos (Gesamt 71 min), 1 Lektüre, 2 Quiz
3 Videos
Tutorial 2: Equiprobability, partition functions, and virial expansions for hard disks32m
Homework Session 2: Paradoxes of hard-disk simulations in a box2m
1 Lektüre
Python programs and references10m
1 praktische Übung
Practice quiz 2: spotting a correct algorithm (continued)4m
Woche
3
1 Stunde zum Abschließen

Entropic interactions and phase transitions

After the hard disks of Week 2, in Week 3 we switch to clothe-pins aligned on a washing line. This is a great model to learn about the entropic interactions, coming only from statistical-mechanics considerations. In the tutorial you will see an example of a typical situation: Having an exact solution often corresponds to finding a perfect algorithm to sample configurations. Finally, in the homework session we will go back to hard disks, and get a simple evidence of the transition between a liquid and a solid, for a two-dimensional system.

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3 Videos (Gesamt 62 min), 2 Lektüren, 2 Quiz
3 Videos
Tutorial 3: Algorithms, exact solutions, thermodynamic limit31m
Homework Session 3: Two-dimensional liquids and solids2m
2 Lektüren
Python programs and references10m
Errata (Tutorial 3)10m
1 praktische Übung
Practice quiz 3: Spotting a correct algorithm (continued)4m
Woche
4
1 Stunde zum Abschließen

Sampling and integration

In Week 4 we will deepen our understanding of sampling, and its connection with integration, and this will allow us to introduce another pillar of statistical mechanics (after the equiprobability principle): the Maxwell and Boltzmann distributions of velocities and energies. In the homework session, we will push the limits of sampling until we can compute the integral of a sphere... in 200 dimensions!

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3 Videos (Gesamt 69 min), 1 Lektüre, 2 Quiz
3 Videos
Tutorial 4: Sampling discrete and one-dimensional distributions34m
Homework Session 4: Sampling and integration in high dimensions2m
1 Lektüre
Python programs and references10m
1 praktische Übung
Practice quiz 4: four disks in a box6m
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Top reviews from Statistical Mechanics: Algorithms and Computations

von KLSep 23rd 2017

Excellent and enthusiastic lectures and tutorials covering a number of topics. Much of the learning took place in the assignments where the concepts were applied and various points were illustrated.

von MHMar 8th 2018

I really enjoyed the course. The only problem was that I was using python 3+ and the programs were written with python 2+. There are some minor differences but I figured the them easily.

Dozent

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Werner Krauth

Directeur de recherches au CNRS
Department of physics

Über École normale supérieure

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