Week 13
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ChaosBook is a book in reverse |
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Group theory voodoo |
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Symmetry is your friend - overview |
- 25. Deterministic diffusion / 12 April 2022 /
- 26. Finite groups / 14 April 2022 /
- Homework 13
- Optional
Read sect. 28.2: A class of simple 1-dimensional dynamical systems where all transport coefficients can be evaluated analytically, by hand. Diffusion is a non-monotonic function of the local expansion rate, and it is non-gaussian, with a non-vanishing kurtosis. Perhaps the most fundamental diagnostic of deterministic chaos is the non-differentiable dependence of its transport coefficients on smooth variations of system parameters.
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Chapter 24 Deterministic diffusion |
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Deterministic diffusion so far - a review |
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Running orbits |
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Cycle formulas for averages |
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This is one weird formula! |
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Diffusion on a 1-dimensional lattice |
Finite groups. Cyclic groups of two and three elements. Symmetries of a triangle, six element group multiplication table. Matrix representations. Regular representations. This is standard material, not written up in ChaosBook, but necessary for the course. We liked Tinkham, chapter 2, or Dresselhaus chapters 1 and 2 (early version available as lecture notes).
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Finite groups - slides Kezhou Lu |
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Hard work builds character |
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The symmetry group of a propeller |
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Irreps of C3 |
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Rotation in the plane |
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Trace of evolution operator |
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?? |
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diffusion Due 26 April 2022 |
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Discussion forum for week 13 |
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| The deepest thing about chaos |
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Why does everybody write a book on Group Theory? |
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Challenge: can you quotient D6 symmetry? |