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Santa Fe InstituteComplex Systems Summer School
2003
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Summer school activities
• Lectures on ‘foundation’ topics: nonlinear dynamics, information theory, statistical mechanics, computational mechanics, agent-based modelling, adaptive computation
• Lectures on specific application areas: RNA folding, economic game theory, emergent engineering
• Experimental laboratory
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A Belmonte et al (2001) Physical Review Letters, 87, 114301
A. Belmonte et al (1997) Journal de Physique II 7, 1425-1468.
Belousov-Zhabotinsky Reaction
Motion of a shaken hanging chain
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Faraday experiment
Foam coarsening
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Chaos you can play in:the Malkus Waterwheel
Aaron Clauset, Nicky Grigg, May Tan Lim, Erin Miller
Santa Fe Institute Complex Systems Summer School
June 2003
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Lorenz equations
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Periodic and strange attractors
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Malkus waterwheel
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Equations of Motion
Mass change in each cup:
Torque balance for wheel:
Angle change for each cup:
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Simulated mass time series
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Angular velocity
Lorenz equations time series
Waterwheel equations time series
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Model-data comparison
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Phase space reconstruction
• Delay coordinate embedding requires a delay time () and an embedding dimension (dE)
• Delay time from first minimum in average mutual information function
• Embedding dimension from false nearest neighbours analysis
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Reconstructed waterwheel attractors(simulation data)
Reconstructed Lorenz attractors
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Reconstructed attractors from model and measured time series
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Acknowledgments
• Andrew Belmonte, Department of Mathematics, Pennsylvania State University
• Ray Goldstein, Physics Department, University of Arizona