Computer Exercises and Course Materials

James P. Sethna

for "Statistical Mechanics: Entropy, Order Parameters, and Complexity"

This site includes materials useful in some of the interactive exercises, and also hints for the computer exercises (available both for Mathematica and Python). For python, we recommend the Anaconda Scientific Python distribution. One useful additional step for speed when linear algebra is being done: set the environment variable MKL_NUM_THREADS (e.g., 'export MKL_NUM_THREADS=4' if you run bash, or 'setenv MKL_NUM_THREADS 4' if you run csh or tcsh), replacing '4' with some number <= the number of cores on your machine.

2024 Prelim
- P.1 'Rubber band dynamics I: Random walk'
  - Mathematica notebook, or pdf
  - Python notebook (download, run 'jupyter notebook', then select this file), or pdf
- P.2 'Rubber band dynamics II: Diffusion'
  - Mathematica notebook, or pdf
  - Python notebook (download, run 'jupyter notebook', then select this file), or pdf
- P.3 'Rubber band dynamics III: Free energy and statics'
  - Mathematica notebook, or pdf
  - Python notebook (download, run 'jupyter notebook', then select this file), or pdf
  Hints and other materials
  
  Second edition, then new exercises N###, then sloppy model exercises S###
  - 1.5 'Stirling and asymptotic series'
    - Mathematica notebook, or download pdf
    - Python notebook (download, run 'jupyter notebook', then select this file). View notebook directly.
  - 1.6 'Random matrix theory'
  - 1.7 'Six degrees of separation', Small world exercise hints
  - Molecular dynamics exercises: 2.4 'Perfume walk', 3.4 'Pressure computation', 4.1 'Equilibration', 6.1 'Exponential atmosphere', 10.2 'Pair distribution function and molecular dynamics', Molecular dynamics software
  - 2.5 'Generating random walks'
  - 2.10 'Polymers and random walks' Self-Avoiding Random Walk simulation (Java applet from BU)
  - 2.11 'Stocks, volatility, and diversification'
    - Data file SandPConstantDollars.dat.zip
    - Mathematica notebook, or download pdf
    - Python notebook (download, run 'jupyter notebook', then select this file). View notebook directly, or download pdf.
  - Percolation exercises: 2.13 'Building a percolation network', 12.12 'Percolation and universality' Percolation hints and writeup
  - 3.11 'Maxwell relations' MaxwellRelationsHandout
  - 4.3 'Invariant measures'
    - Mathematica notebook, or download pdf
    - Python notebook (download, run 'jupyter notebook', then select this file). View notebook directly, or download pdf.
  - 4.4 'Jupiter! and the KAM Theorem'
  - 4.9 "Jupiter's Red Spot"
  - 5.9 'Chaos, Lyapunov, and entropy increase'
    - Mathematica notebook, or download pdf
    - Python notebook (download, run 'jupyter notebook', then select this file). View notebook directly, or download pdf.
  - 5.12 'Rubber band'. (Bring rubber bands.)
  - 5.13 'How many shuffles?'. (Bring decks of cards.)
  - 5.16 'Fractal dimensions'
    - Mathematica notebook, or download pdf
    - Python notebook (download, run 'jupyter notebook', then select this file). View notebook directly, or download pdf.
  - 6.25 'Epidemics and zombies'
    - Mathematica notebook, or download pdf
    - Python notebook (download, run 'jupyter notebook', then select this file). View notebook directly, or download pdf.
  - 7.12 'Semiconductors': see "Semiconductors: The Big Picture"
  - 7.24 'Is sound a quasiparticle': see "Quasiparticles in Physics"
  - 7.27 'Heisenberg entanglement'
    - Mathematica notebook, or download pdf
    - Python notebook (download, run 'jupyter notebook', then select this file). View notebook directly, or download pdf.
  - Ising model exercises
    - 8.1 'The Ising model', 8.2 'Ising fluctuations and susceptibilities', 10.6 'Fluctuation-dissipation: Ising', 11.6 'Coarsening in the Ising model', 12.1 'Ising self-similarity', 12.3 'Scaling and coarsening', Bierbaum's Ising model code
    - 8.7 'Implementing Ising', 8.9 'Implementing Wolff', 11.4 'Nucleation in the Ising model', Ising Model Python exercises and hints for the Ising model
  - Systems Biology and Cellular Networks (start with the overview of reaction networks)
    - 8.10 'Stochastic Cells'
    - 8.11a 'The repressilator' Simple Repressilator
    - 8.11b 'The repressilator' Stochastic and Deterministic Repressilator
  - Avalanche models: 8.13 'Hysteresis and avalanches', 8.14 'Hysteresis algorithms', and 12.13 'Hysteresis and avalanches: scaling' Hysteresis and Avalanches simulation (Matt Kuntz's old windows binary; may not work)
  - 8.15 'NP-completeness and kSAT'
  - 8.22 'Metastability and Markov'
    - Mathematica notebook, or download pdf
    - Python notebook (download, run 'jupyter notebook', then select this file). View notebook directly, or download pdf.
  - 9.1 'Topological defects in nematic liquid crystals':
    - Nematic S=1/2 defect,
    - S=-1/2 defect, and
    - transition path in order parameter space
  - 9.10, 'Nematic order parameter half space': Projective plane for cutting and pasting. (Print it out double-sided. Bring scissors and tape.)
  - 9.11, 'Pentagonal order parameter':
    - Soccer ball flattened
    - Soccer ball cut-and-pasted.
    - (Bring soccer ball.)
  - 9.17, 'Fingerprints':
    - Arch
    - Loop
    - Whorl
    - Tented arch
    - Transmuting defects
  - 9.20, 'Defect entanglement': Demo video
  - 10.10 'Human correlations' Plot of subway riders, and matched grid graph for plotting correlations
  - 11.1 'Maxwell and van der Waals' van der Waals P-V plot
  - 11.7 'Origami microstructure'. (Bring scissors.)
    - Sheet patterned on one side
    - Origami Microstructure (not foldable in less than four dimensions)
    - Origami Microstructure first two levels (foldable in 3D)
    - Chen Wang's proof that further levels are not foldable in three dimensions.
  - 11.11 'What is it unstable to? Maxwell equal area construction figure
  - 12.9 'Period doubling'
    - Mathematica notebook, or download pdf
    - Python notebook (download, run 'jupyter notebook', then select this file). View notebook directly, or download pdf.
  - 12.14 'Crackling noises'
    - Crackling noises
    - Earthquakes in 1995
    - Magnetic Barkhausen noise (simulated with our model)
    - Paper crumpling
    - Fire
    - Rice Krispies^TM
  - 12.15 'Hearing the onset of chaos: Period doubling' (files courtesy of Erich Mueller)
    - Period doubling audio file
    - near the onset of chaos
    - and source mathematica file
  - 12.22 'Activated rates and the saddle-node transition'
    - Mathematica notebook, or download pdf
    - Python notebook (download, run 'jupyter notebook', then select this file). View notebook directly, or download pdf.
  - 12.23 'Biggest of bunch: Gumbel'
  - 12.30 'The onset of chaos: Full renormalization-group calculation'
    - Mathematica notebook, or download pdf
    - Python notebook (download, run 'jupyter notebook', then select this file). View notebook directly, or download pdf.
  - 12.32 'Conformal Invariance'
    - Mathematica notebook, or download pdf
    - Python notebook (download, run 'jupyter notebook', then select this file). View notebook directly, or download pdf.
    - Ising snapshot at the critical temperature
    - Ising snapshot at temperature T = 100
    - Ising snapshot at temperature T = 3
    - 2048x2048 Ising snapshot at the critical temperature
  - 12.33 'Pandemic'
    - Mathematica notebook, or download pdf
    - Python notebook (download, run 'jupyter notebook', then select this file). View notebook directly, or download pdf.
  - N1.3 'Accelerators vs. ergodicity'
    - Mathematica notebook, or download pdf
    - Python notebook (download, run 'jupyter notebook', then select this file). pdf.
  - N1.12 'Interpolation and free energies'
    - Mathematica notebook, or download pdf
    - Python notebook (download, run 'jupyter notebook', then select this file).
  - N1.17 'Nonabelian Defects' Evolution of the order parameter as one defect circles another.
  - N1.25 'Localization'
    - Mathematica notebook, or pdf
    - Python notebook (download, run 'jupyter notebook', then select this file), or pdf
  - S2.1 'Sloppy exponentials'
    - Mathematica notebook, or pdf
    - Python notebook (download, run 'jupyter notebook', then select this file), or pdf
  - S2.2 'Sloppy monomials'
    - Mathematica notebook, or pdf
    - Python notebook (download, run 'jupyter notebook', then select this file), or pdf
  - S3.1 'Plotting model manifolds'
    - Mathematica notebook, or pdf
    - Python notebook (download, run 'jupyter notebook', then select this file), or pdf
  - S3.2 'Monomial hyperribbons'
    - Mathematica notebook, or pdf
    - Python notebook (download, run 'jupyter notebook', then select this file), or pdf
  James P. Sethna, Christopher R. Myers.
  Last modified: January 19, 2024
  
  Statistical Mechanics: Entropy, Order Parameters, and Complexity Second Edition, available at Oxford University Press.

Computer Exercises and Course Materials

James P. Sethna

for "Statistical Mechanics: Entropy, Order Parameters, and Complexity"

Hints and other materials

Second edition, then new exercises N###, then sloppy model exercises S###