https://github.com/jqhoogland/slm

Exercises for the Statistical Physics of Soft and Living Matter
https://github.com/jqhoogland/slm

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Exercises for the Statistical Physics of Soft and Living Matter

• Host: GitHub
• URL: https://github.com/jqhoogland/slm
• Owner: jqhoogland
• Created: 2021-01-17T18:29:58.000Z (about 4 years ago)
• Default Branch: master
• Last Pushed: 2021-01-17T19:07:47.000Z (about 4 years ago)
• Last Synced: 2024-11-19T18:55:05.501Z (2 months ago)
• Language: Jupyter Notebook
• Size: 9.13 MB
• Stars: 0
• Watchers: 2
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# SLM

Exercises from a course in my Masters: the Statistical Physics of Soft and Living Matter

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Also contains my first (and only) attempt at taking [notes in markdown](/notes-md) live while reading a textbook (Steven Strogatz's *Nonlinear Dynamics and Chaos*).

And a [final project](/why_ML_works.pdf) (on why neural networks are so powerful) I co-wrote with classmate Karel Zijp. This includes code to run reservoir neural networks (aka echo networks): [Jupyter notebook](/reservoir_computing_chaos.ipynb), [Python module](/reservoir_computer.py).

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*From the [course catalogue](https://coursecatalogue.uva.nl/xmlpages/page/2020-2021-en/search-course/course/79791):*

## Objectives

- Understand and apply a wide variety of statistical analysis tools to soft matter and biophysics problems.

- Describe the interplay between theoretical and experimental soft matter and biophysics. 

- Understand the relation between the intricacy and complexity of biophysical and soft matter systems and the scientific methodology employed in their investigation.

## Contents

We will review (and, where necessary, introduce) the following topics:

- random walks, central limit theorem, first passage processes, Levy flights, extreme value statistics, correlated variables.

- Brownian motion and Langevin dynamics

- Fokker-Planck equation: derivation and application

- linear response near equilibrium, fluctuation-dissipation relations

- probabilities at 2nd-order: singular value decomposition and principal component analysis 

- attractors & bifurcations: fixed points, limit cycles and chaos

-  linear stability analysis

- probabilities at higher order: entropy and information theory

Contemporary research directions will be explored through group projects and motivated with particular analysis techniques. Group projects will culminate in short presentations towards the end of the course. While our focus is theoretical we will also emphasize important connections to modern experimental research. Students should expect exercises that involve numerical simulations and analysis.

## Recommended prior knowledge

- linear algebra

- equilibrium statistical mechanics

- programming proficiency

- numerical integration of ordinary differential equation