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Exponential sensitivity, and the amplification of randomness
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Classroom Contents
Chance and Chaos - How to Predict the Unpredictable by Jens Marklof
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- 1 WHEN: 4:00 pm to pm Sunday, 11 December 2022
- 2 Start
- 3 Introduction
- 4 Speaker Introduction
- 5 Chance and chaos: how to predict the unpredictable
- 6 KAAPI WITH KURIOSITY
- 7 The butterfly effect
- 8 Climate modelling and extreme weather prediction
- 9 The deterministic universe, chance and chaos
- 10 Unpredictability
- 11 Example: The fair coin toss
- 12 The perfect coin tosser
- 13 Let's do an experiment with dice!"
- 14 Kneading dough: a simple model for generating randomness
- 15 Step 1: Place test raisins in the dough.
- 16 Step 4: Continue repeating Steps 2 and 3.
- 17 Exponential sensitivity, and the amplification of randomness
- 18 A mathematical theorem
- 19 The grand challenge
- 20 Helpful chaos: Boltzmann's statistical mechanics
- 21 The Boltzmann gas:
- 22 The Lorentz gas
- 23 The Lorentz gas and Brownian motion
- 24 A typical Brownian path in three dimensional space.
- 25 Visibility in a forest
- 26 The Lorentz gas in a crystal
- 27 The distribution of free path lengths
- 28 Underpinning mathematics: ergodic theory and dynamical systems
- 29 Conclusions
- 30 Recommendations for further reading
- 31 Thank you
- 32 Q&A
