Santa fe institute complex systems summer school 2003
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Santa Fe Institute Complex Systems Summer School 2003. Summer school activities. Lectures on ‘foundation’ topics: nonlinear dynamics, information theory, statistical mechanics, computational mechanics, agent-based modelling, adaptive computation

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Santa Fe Institute Complex Systems Summer School 2003

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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


Belousov-Zhabotinsky Reaction

Motion of a shaken hanging chain

A. Belmonte et al (1997) Journal de Physique II 7, 1425-1468.  

A Belmonte et al (2001) Physical Review Letters, 87, 114301


Foam coarsening

Faraday experiment


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 (t) 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


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