13 aug 2003

Chaos: Classical and Quantum - projects

HMV
[ Term projectsThesesUndergraduate projectsCourse outlines ]

(For inspiration, look at any of the projects on the this homepage, or use one of them as the starting point for your own project)

Published projects


link
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 ]

    link
    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)

    link
    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 ]

    link
    Gabor Simon (Budapest)

    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)

    link
    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 ]



    Fall 2001
    Chaotic advection
    Lakshmi Prasad Dasi, gte502q@prism.gatech.edu (11 dec 2001)

    Staring at the Kuramoto-Sivashinsky equation , preliminary version
    Andreas Handel, andreas.handel@gmx.net (11 jan 2002)

    Synchronization
    Confessions of an experimentalist
    Kapilanjan Krishan, gte306q@prism.gatech.edu (11 dec 2001)

    Spatiotemporally periodic solutions by variational methods, gzipped tar file
    Bo Li, gt3159a@prism.gatech.edu (11 dec 2001)

    Classical Xe in E cross B
    Rytis Paskauskas, gte203x@prism.gatech.edu (11 dec 2001)

    Defects in roll-hexagon patterns
    Denis Semwogerere, gt7526a@prism.gatech.edu (11 dec 2001)

    3-disk pinball game with gravitational field, and the corresponding diffusion problem
    Er-Yi Shang, gte513x@prism.gatech.edu (11 dec 2001)

    Multimode laser with optical feedback
    Jianfei Shao, gte303q@prism.gatech.edu (11 dec 2001)

    Anomalous transport for a Hamiltonian system
    Elena Shchekinova, gte232g@prism.gatech.edu (11 dec 2001)

    Logarithmically slow anomalous diffusion in a 1-d system
    Su, Xiaohua, gte456x@prism.gatech.edu (11 dec 2001)

    N-body 2-dimensional rigid diatomic molecular fluid
    Alfred Ganson Walters III, gt4277b@prism.gatech.edu (not delivered)

    Charged pinball in magnetic field
    Yin, Shuangy, gt6218a@prism.gatech.edu (21 dec 2001)

    3 atoms in Lennard-Jones potential
    Zhang, Wenxian AKA Wingham, gte893w@prism.gatech.edu (11 dec 2001)



    Projects still open
    Spatiotemporally periodic solutions by variational methods, gzipped tar file
    Your Name Here, Your@email.here
    A nonlinear optics project, by Greg Luther
    Your Name Here, Your@email.here
    (for a solution to this problem, click here)


    Fall 1999
    The Diagonal Approximation and Beyond - Case study: The Spectral Two-Point Function
    Kim Splittorf, split@nbi.dk (20 jan 2000)
    Nonlinear dynamics of dispersion managed breathers in Gaussian Ansatz approximation
    Rytis Paskauskas, rytis@fys.ku.dk (2 feb 2000)
    Mesoscopic chaos
    Thorsten Hansen, thorsten@fys.ku.dk (26 jan 2000 - not available in electronic form)
    Periodic orbit theory: A Study of the Rossler Attractor,
    Joachim Mathiessen, joachim@fys.ku.dk (20 jan 2000)
    The spectrum of Helium obtained by periodic orbit theory
    Nikola Lars Zivkovic Schou, nikola@fys.ku.dk (31 jan 2000)



    Spring 1999
    1-week project: Turbulence, and what to do about it?
    in either pdf (447 Kb) or gzipped postscript (1.8 Mb) format. The exam involves analysis of a dynamical system (fixed points, stability, bifurcations) and numerical experimentation with integration of a set of differential equations describing the system.
    (none of the rest available in electronic form)
    Nonlinear dynamic and chaotic motions in two-degree of freedom robots
    Prasun Choudhury, prasun@lims.mech.nwu.edu, Caizhen Liu, cz-liu@nwu.edu
    A stochastic model of granular mixing
    Jim Gilchrist, jim@chem-eng.nwu.edu
    Chaos in mixing of viscous fluids
    Nitin Jain, n-jain1@nwu.edu
    Underactuated planar robot
    Brian Miller, bemiller@nwu.edu
    Nonlinear spin-echo amplification phenomenon in magnetic resonance
    Nan-Kuei Chen, nch525@hecky.acns.nwu.edu
    Bifurcations in a nonlinear model of the baroreceptor-cardiac reflex
    Sandeep Bhangoo, s-bhangoo@nwu.edu
    Non-linear aspects of human gait
    Steve C. Miff, scm767@hecky.acns.nwu.edu, Brian Ruhe, b-ruhe@nwu.edu, and Pinata Hungspreugh, p-hungspreugs@nwu.edu (related to the work with Dr. Childress at the Rehabilitation Institute)


    Fall 1998
    Project: Deterministic diffusion, sawtooth
    Termpaper, Peter Andresén, andresen@chaos.fys.dtu.dk [3 Feb 99]
    Termpaper, Christian I. Mikkelsen, cmik@fys.ku.dk [12 Jun 99]
    Project: Deterministic diffusion, zig-zag map
    Termpaper, Jakob Kisbye Dreyer, kisbye@fys.ku.dk [3 Jun 99]


    Winter 1998
    Deterministic diffusion, zig-zag map
    Lan Yueheng, y-lan@nwu.edu
    Vadim Moroz, v-moroz@nwu.edu
    Solution [29 sep 98]
    Deterministic diffusion, sawtooth
    Khaled A Mahdi, k-mahdi@nwu.edu
    done as Mathematica notebook, 22 Mar 1998
    See above projects for the solution.
    Periodic orbit theory of linear response
    Niels Søndergaard, nsonderg@nbi.dk [18 may 98]


    Spring 1997
    A list of projects for the course (8 May 1997- incomplete).
    Ultrashort Bunimovich Stadium
    Vadim Moroz, v-moroz@nwu.edu (not available as of 29 Jun 1997)
    Hopf's last hope for B.&D. model of solidification
    (continuation of Hopf's last hope: spatiotemporal chaos in terms of unstable recurrent patterns)
    Vladimir (Volodia) Ajaev, vaj103@casbah.acns.nwu.edu (not available as of 28 Jun 1997)
    Cardioid Billiard (not Webshaped)
    Alexander Erner, sascha@snowmass.phys.nwu.edu (13 Jun 1997)


    Fall 1996
    A list of projects for the course (26 Nov 1996 - incomplete). Sune, Kasper, Jakob, Niels and Juri
                            Sune             Kasper     Jakob   Niels    and    Juri
    Dissociation of hydrogen in external magnetic field (Mathematica input files)
    Kasper Juel Eriksen kasper@fys.ku.dk (3 Mar 1997)
    Lyapunov exponent for products of random matrices
    Jakob Langgaard Nielsen, langgard@alf.nbi.dk (6 Feb 1997)


    Spring 1995
    A list of projects for the course (31 May 1995)
    Colinear helium spectrum
    Preben Bertelsen, pbertelsen@nbivax.nbi.dk (13 Oct 1995) - 300 KB
    Helium spectrum, s-wave model
    Kristian Schaadt, schaadt@nbivax.nbi.dk (13 Oct 1995) - 453 KB
    Hard Bunimovich stadium, washbord diffusion
    Jonas Lundbek Hansen, lundbek@kaos.nbi.dk (23 aug 1995) - 235 KB
    Soft (but not easy) Bunimovich stadium
    Sune Horlyck, HORLYCK@nbivax.nbi.dk (8 sep 1995) - 544 KB
    Spectrum of the Liouville operator
    Niels Søndergaard, NSONDERG@nbivax.nbi.dk (30 aug 1995)

    Undergraduate projects

    Hopf's last hope
    Wave chaos

    Small projects

    J. Meiss' list of projects

    Habilitation theses

    Ph.D. theses

    M. Sci. theses

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    DasBuch