santa fe institute complex systems summer school 2003
TRANSCRIPT
Santa Fe InstituteComplex Systems Summer School
2003
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
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
Faraday experiment
Foam coarsening
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
Lorenz equations
Periodic and strange attractors
Malkus waterwheel
Equations of Motion
Mass change in each cup:
Torque balance for wheel:
Angle change for each cup:
Simulated mass time series
Angular velocity
Lorenz equations time series
Waterwheel equations time series
Model-data comparison
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
Reconstructed waterwheel attractors(simulation data)
Reconstructed Lorenz attractors
Reconstructed attractors from model and measured time series
Acknowledgments
• Andrew Belmonte, Department of Mathematics, Pennsylvania State University
• Ray Goldstein, Physics Department, University of Arizona