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Chaos: Classical and Quantum - published projects

Daniel Borrero-Echeverry, Keith M. Carroll, and Bryce Robbins

Cartography of high-dimensional flows (graduate course project, Spring 2012)
Predrag Cvitanović, Daniel Borrero-Echeverry, Keith M. Carroll, Bryce Robbins, and Evangelos Siminos
Cartography of high-dimensional flows: A visual guide to sections and slices
Chaos 14, 739 (2012) [ arXiv.org:1209.4915 ]

Stefan Froehlich

Reducing continuous symmetries with linear slice (undergraduate research project, Summer and Fall 2010) [ pdf file ]
When a dynamical system has a continuous symmetry, it is possible to exploit this symmetry to reduce the system to an equivalent simpler system. One method for doing this is Cartan's method of slices. In this paper we investigate how the method of slices can be applied to linear subspaces.
Winner, the Georgia Tech SAIC Student Paper Competition
publication:
pdf Stefan Froehlich and Predrag Cvitanović
Reduction of continuous symmetries of chaotic flows by the method of slices
Comm. Nonlinear Sci. and Numerical Simulation , (2011) [ arXiv:1101.3037 ]
Vakhtang Putkaradze

A method for finding periodic orbits (course term paper, 29 apr 1996) [ ps.gz ]
  • Fig 1 , Fig 2 , Fig 3 , Fig 4
  • numerical routines for finding periodic orbits, zeros of Fredholms, data files...
  • periodic orbits data, used in the article for finding periodic orbits, zeros of Fredholms, data files...
  • Local Structures in Extended Systems (PhD thesis 1997). [ HTML ]
    Vachtang decided to apply the ChaosBook technology to his Ph D research with his adviser T. Bohr: spatiotemporal chaos in Kuramoto-Sivashinsky system. Joining forces with F. Chrisitansen, this course project not only became a part of Vachtang's thesis and lead to a publication, but was also a seed to the still ongoing research program in turbulence.
    publication:
    pdf Predrag Cvitanović, F. Christiansen and V. Putkaradze
    Hopf's last hope: spatiotemporal chaos in terms of unstable recurrent patterns
    Nonlinearity 10, 50 (1997) [ ps.gz ]

    Marc W. Slutzky

    Extraction of unstable periodic orbits from noisy data (19 oct 1998) [ ps.gz ]
    Marc wove cycles into a very broad-front attack on epylepsy; with his adviser D.J. Mogul he prepared rat hipocampal preparations, kept them alive, poked them with electrods, collected and analyzed numerically the neurnal interburst intervals, and with P. Cvitanovic he developed now methods for describing instability in systems where noise is comparable with the putative nonlinear dynamics, and measures like Lyapunov exponents make no sense.This project became a major part of Mark's thesis and lead to a series of publications, and is still an ongoing research program.
    publications:
    pdf Marc W. Slutzky, Predrag Cvitanović and David J. Mogul
    Deterministic chaos and noise in three in vitro hippocampal models of epilepsy
    Annals of Biomedical Engineering 29, 607 (2001).
    pdf Marc W. Slutzky, Predrag Cvitanović and David J. Mogul
    Manipulating epileptiform bursting in the rat hippocampus using chaos control and adaptive techniques
    IEEE Transactions on Biomedical Engineering 50, 559 (2001).
    pdf Marc W. Slutzky, Predrag Cvitanović and David J. Mogul
    Identification of determinism in noisy neuronal systems
    J. Neuroscience Methods 118, 153 (2002)

    Kim Hansen, Juri Rolf

    Sum rules Kim Hansen's Copenhangen University 3rd year physics undergraduate project, in danish, (10 May 1995) [ ps.gz ]
    Infintely many sum rules Kim Hansen addition, (14 July 95) [ ps.gz ]
    Kim's undergraduate term project was to read a draft of a Cvitanovic - Vattay paper and understand it. His interpretation was so original that reading it P. Cvitanovic saw it lead not only to the sum rules already in the paper, but an infinity of new sum rules over periodic orbits. He sent Kim back to write an addendum, and incorporated Kim's ideas into the final version of the paper. Kim decided to become an experimentalist.
    Comparison between cycle expansion and adjoint equations Juri Rolf (11 feb 1997) [ ps.gz ]
    Rereading the same draft of a Cvitanovic - Vattay paper, in this project J. Rolf proposed new conjectures for an infinite family of nontrivial spectral determinants, also incorporeted into the final publication
    publication:
    pdf Predrag Cvitanović, Kim Hansen, Juri Rolf and Gabor Vattay
    Beyond periodic orbit theory
    Nonlinearity 11, 1209 (1998) [ ps.gz ]

    Gabor Simon

    Chaotic Radial Oscillations of a Harmonically Forced Gas Bubble, Parametric Dependence and Consequences for Sonoluminescence (2 feb 2000) [ ps.gz ]
    After reading the theoretical papers related to the sonoluminescence experiment that he was carrying out with his adviser M.T. Levinsen, Gabor applied the periodic theory to a calculation of the mean light intensity emited by a chaotic sonoluminescent bubble. This is probably still one of the cutest applications of the periodic theory to a physical experiment (other than applications to quantum systems).
    publication:
    pdf G. Simon, Predrag Cvitanović, M.T. Levinsen, I. Csabai and Á. Horváth
    Periodic orbit theory applied to a chaotically oscillating gas bubble in water
    Nonlinearity 15, 25 (2002)

    Sune F. Nielsen

    4-disk resonances (20 Jan 1997) [ ps.gz ]
    The skills developed in executing this project made it possible to test Per Dahlqvist's ideas.
    publication:
    pdf Sune F. Nielsen, Per Dahlqvist and Predrag Cvitanović
    Periodic orbit sum rules for billiards: Accelerating cycle expansions
    J. Phys. A 32, 6757 (1999) [ ps.gz , chao-dyn/9901001 , working notes ]

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