CHAOS: CLASSICAL AND QUANTUM - PROJECTS

Predrag Cvitanović, Roberto Artuso, Ronnie Mainieri, Gregor Tanner, Gábor Vattay, Niall Whelan and Andreas Wirzba

[ published projects | open projects | theses | course outlines ]

Project template

An optional LaTeX template for term projects, in Phys Rev E style format (11 nov 2003)
A hitchhiker's guide to LaTeX - RevTeX4 APS article template - a sample BibTeX references file - APS BibTeX style file (though imperfect) - a not so short introduction to LaTeX - optimize figure file size - APS style manual
(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)

Summer 2009

Reducing the state-space of the complex Lorenz flow: This project first reproduces results reported in the Siminos 2009 Ph.D. thesis, and then investigates various ways of `quotienting' the SO(2) symmetry of complex Lorenz flow, and reducing the dynamics to symmetry 4-dimensional reduced state-space. The project consists of my notes and exercises. The flow of the argument is in the classical Socratic dialogue mode; question, answer, question, ...; Rebecca Wilczak, at UM-D
project advisor: P. Cvitanović

Fall 2008

Armbruster-Guckenheimer-Holmes flow: In presence of continuous symmetries notion of `periodic orbits' needs to be generalized to the notion of `relative periodic orbits.' This flow has O(2) symmetry, so both equilbira and relative equlibiria (travelling waves), periodic and relative periodic orbits are expected. I'll go fishing for such, try to make sense of them.; Dominic Kohler, dominic.kohler [snail] gmx.de
project advisor: Evangelos Siminos
Is functional chaos in neural systems a pipedream?: It has become fashionable to report the existence of deterministic chaos in biophysical neuron models. This report revisits two biophysical papers reporting chaotic bursting activity in neuron models. Using cycle-expansion techniques, we determine whether these models do in fact produce chaotic oscillations and how these oscillations come to be. We investigate how likely chaos is to play a functional role in these simple neural circuits given the presence of large noise in the vast majority of biological systems.; Jon Newman, jnewman6 snail gatech point edu
project advisor: Astrid Prinz
An exploration of moderate Reynolds no. plane Couette turbulence: The channelflow code for determining unstable periodic orbits of moderate Reynolds number plane Couette turbulence is applied to turbulence simulations.; John R. Elton, gtg960p(at)gatech.edu
project advisor: John F. Gibson

Spring, Fall 2007

Weak magnetic diffusivity corrections to kinematic dynamo: A method of Cvitanović and Ott for dealing with magnetic diffusivity in kinematic dynamo is studied.; Richard Joh, ijoh3(at)gatech.edu
project advisor: Domenico Lippolis
Construction of Poincaré return maps for Rössler flow: Construction of Poincaré return maps for flows by coding the arc-length along a Poincaré section of the unstable manifold.
Matlab code - gallery of figures
see also: Radford Mitchell, Gabor Simon and Joachim Mathiessen projects; Arindam Basu, abasu3 [ at ] mail.gatech.edu
project advisors: Domenico Lippolis, J. Halcrow

Spring, Fall 2005

AFM trajectories: Java applet which presents a stroboscopic section of a tapping mode Atomic Force Microscope, alongside with the (x,y) space trajectories. The program simulates trajectories for given initial conditions and system parameters.; Siddhartha Kasivajhula, siddhartha [snail] gatech.edu
project advisor: Rytis Paškauskas
Nonlinear Tumbling in AFM Dynamical Mode Assembly: Figures: v0_3.4, abs_v, Poincaré.
Code: main.cpp,
see also: Tyson Shepard's project; William Mather, gte994m(at)mail.gatech.edu (15 mar 2005)
project advisor: Rytis Paškauskas
A study of the Rössler system: Using symbolic dynamics and kneading theory the admissible periodic orbits are determined, the topological zeta function is constructed and the topological entropy is found, and the leading Lyapunov exponent is estimate
Matlab code; Radford Mitchell, Jr. (15 mar 2005)
project advisor: Rytis Paškauskas
Penalty for straying from the True Path: Evangelos Siminos, gtg083n(at)mail.gatech.edu (15 mar 2005)
project advisor: Rytis Paškauskas
Chaotic dynamics of inertial particles in three-dimensional rotating flows: simulation of two particles; the movie (27 mar 2005); Cristian Escauriaza (27 mar 2005)
Localized Control of 1-Dimensional Perturbed Hydrogen Atom: Shu Huang, gtg098n(at)mail.gatech.edu (5 apr 2005)
project advisors: Cristel Chandre, Turgay Uzer

Spring, summer, fall 2004

Stochastic trace formula: briefest of descriptions (mar 2004)
Project: stochastic trace formula - chapter: Noise - from chapter: Quantization - from Appendix: Noise/quantum determinants (28 apr 2004); Wei Kang, gtg819j(at)prism.gatech.edu
Cranked oscillator: T. Uzer proposal; Ji Il Choi, gtg526i at prism.gatech.edu (29 apr 2004)
project advisor: Turgay Uzer
Mapping of the classical kinetic balance equations onto the Schrodinger equation: LaTeX - mathematica; Austin Collins , tex at ugcs.caltech.edu (26 jul 2004)
Extremal stochastic paths: Project proposal - RosslerDescent.java; James A. Corno, gtg519d at prism.gatech.edu (28 Apr 2004)
Implementation of a Pressure Poisson Equation method for Plane Couette Flow: Jonathan Halcrow, gte899j(at)prism.gatech.edu (13 dec 2004)
schedule | mathematical framework Johnston's matlab code | Johnston note (14 may 2004) chebyd.f | dgeevstuff.f | Johnston note - POISS2D.tar.gz (23 may 2004) | Johnston note - Johnston060904.tar.gz (9 jun 2004) |
A model of velocity dependence of atomic friction,: Bo Li, gt3159a at prism.gatech.edu (26 jul 2004)
Kuramoto-Sivashinsky weak turbulence, in the symmetry unrestricted space: Project proposal (P. Cvitanović); Huaming Li, gtg527i at prism.gatech.edu (? mar 2004)
project advisor: Yueheng Lan
Uniform approximations: Domenico Lippolis, gtg092n at prism.gatech.edu (? mar 2004); T. Bartsch, T. Uzer proposal; project advisor: Thomas Bartsch
Atoms diffusing in a plane electromagnetic standing wave(?): Dzmitry Matsukevich, gtg863k at mail.gatech.edu (4 apr 2004)
project advisor: Alex Kuzmich
A Brief Survey of Periodic Orbit Theory for Real and Complex Energies and Tunneling in a double well: Lina Merchan, gtg090n at mail.gatech.edu (26 jul 2004)
project advisors: Slaven Peles | Olivier Sigwarth | S Creagh's note (11 feb 2004) | N Whelan's note (11 feb 2004)
A very brief review of complex angular momentum techniques (12 dec 2004)
Looking for creeping complex orbits behind a hill (27 jul 2004): Jorge E. Millan, gtg089n at mail.gatech.edu
project advisor: Thomas Bartsch | Olivier Sigwarth
Modeling Atomic, Dynamical Friction Using an Inelastic Impact Oscillator (+ Linear Stability Matrix) Fall 2004 progress report: Outline - Schedule - Riedo parameters: 8 mar 2004, 20 nov 2003 - Tyson notes: 9 mar 2004, 24 mar 2004, Various figures
L. Matyas, R. Klages: Irregular diffusion in the bouncing ball billiard, nlin.CD/0211023 [abs, ps, pdf, other] :; Tyson Shepherd, gtg084n(at)mail.gatech.edu (26 jul 2004)
project advisors: Elisa Riedo, Robert Szoszkiewicz
Kuramoto-Sivashinsky weak turbulence: Evangelos Siminos, gtg083n(at)mail.gatech.edu (12 dec 2004)
project advisor: Yueheng Lan

Fall 2003

OGY method: Controlling a chaotic driven double pendulum: Matthew E. Cammack, gtg535j at prism.gatech.edu (11 dec 2003)
Chaotic magnetic spinner toy dynamics: Magnetron.java , Magnetron.java; James A. Corno, gtg519d at prism.gatech.edu (11 dec 2003)
project advisor: Greg Huber
Phase-Locking between the Seasonal and the ENSO cycles: Mason A Porter's advice
Lecture Notes on Nonlinear Vibrations, by Richard H. Rand
The dynamics of two coupled Van der Pol oscillators with delay coupling, S.A. Wirkus (Ph.D. Thesis 1999)
The dynamics of two coupled Van der Pol oscillators with delay coupling, S.A. Wirkus and R.H. Rand, Nonlinear Dynamics 30, 205 (2002); Carlos D. Hoyos, choyos at eas.gatech.edu (11 dec 2003)
advisor: Peter J. Webster, Georgia Tech
The two-disk pinball game in the gravity field: Wei (Willy) Kang, gtg819j at mail.gatech.edu (11 dec 2003)
Spatiotemporally periodic solutions by variational methods: Literature update
ks2.fig (Matlab source) - ks.for - ks.m - bifurcation tree figure; Mingtian Liang, gtg516i at prism.gatech.edu (11 dec 2003)
project advisor: Yueheng Lan
Two-level atom in the field of a plane electromagnetic standing wave: Dzmitry Matsukevich, gtg863k at mail.gatech.edu (11 dec 2003)
project advisor: Alex Kuzmich
Calculation of the diffusion coefficient in a double well: Lina Merchan, gtg090n at mail.gatech.edu (11 dec 2003)
project advisor: Slaven Peles
Studying a driven pendulum with a 1-d circle map: Jorge E. Millan, gtg089n at mail.gatech.edu (11 dec 2003)
project advisor: Slaven Peles
Diffusion of electrons through a quantum dot: fortran program; Igor A. Romanovsky, gtg531e at prism.gatech.edu (11 dec 2003)
Dynamic friction of an Atomic Force Microscope tip: Outline - Schedule - Riedo parameters; Tyson Shephard, gtg084n at mail.gatech.edu (9 mar 2004)
project advisor: Elisa Riedo
Quasihorizontal Chaotic Mixing of a Passive Tracer in Re-analysis of Wind Fields: Jonathon S. Wright, gtg386d at prism.gatech.edu (12 dec 2003)
advisor: Rong Fu
Convergence of cycle expansions in 1-d maps: Wei Zhang, gtg978b at mail.gatech.edu (11 dec 2003)
advisor: Carlos Sa de Melo

Fall 2001

Chaotic advection: Lakshmi Prasad Dasi, gte502q at prism.gatech.edu (11 dec 2001)
Staring at the Kuramoto-Sivashinsky equation , preliminary version: Andreas Handel, andreas.handel at gmx.net (11 jan 2002)
Synchronization Confessions of an experimentalist: Kapilanjan Krishan, gte306q at prism.gatech.edu (11 dec 2001)
Spatiotemporally periodic solutions by variational methods, gzipped tar file: Bo Li, gt3159a at prism.gatech.edu (11 dec 2001)
Defects in roll-hexagon patterns: Denis Semwogerere, gt7526a at prism.gatech.edu (11 dec 2001)
Charged pinball in magnetic field: Yin, Shuangy, gt6218a at prism.gatech.edu (21 dec 2001)

Fall 1999

The Diagonal Approximation and Beyond - Case study: The Spectral Two-Point Function: Kim Splittorf, split at nbi.dk (20 jan 2000)
Nonlinear dynamics of dispersion managed breathers in Gaussian Ansatz approximation: Rytis Paškauskas (2 feb 2000)
Mesoscopic chaos: Thorsten Hansen, thorsten at fys.ku.dk (26 jan 2000 - not available in electronic form)
Periodic orbit theory: A Study of the Rössler Attractor,: Joachim Mathiessen (20 jan 2000)
The spectrum of Helium obtained by periodic orbit theory: Nikola Lars Zivkovic Schou, nikola at 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.
Bifurcations in a nonlinear model of the baroreceptor-cardiac reflex: Sandeep Bhangoo
Non-linear aspects of human gait: Steve C. Miff, Brian Ruhe, and Pinata Hungspreugh (related to the work with Dr. Childress at the Rehabilitation Institute)

Fall 1998

Project: Deterministic diffusion, sawtooth: Termpaper, Peter Andresén, andresen at chaos.fys.dtu.dk [3 Feb 99]; Termpaper, Christian I. Mikkelsen, cmik at fys.ku.dk [12 Jun 99]

Project: Deterministic diffusion, zig-zag map: Termpaper, Jakob Kisbye Dreyer, kisbye at fys.ku.dk [3 Jun 99]

Winter 1998

Deterministic diffusion, zig-zag map: Lan Yueheng, Vadim Moroz
Deterministic diffusion, sawtooth: Khaled A Mahdi, k-mahdi at northwestern.edu; done as Mathematica notebook, 22 Mar 1998; See above projects for the solution.
Periodic orbit theory of linear response: Niels Søndergaard, nsonderg at nbi.dk [18 may 98]

Spring 1997

A list of projects for the course (8 May 1997- incomplete).
Sune Hørlück : A small investigation into the Soft Bunimovich Stadium. (may 1997)
Ultrashort Bunimovich Stadium: Vadim Moroz, v-moroz at northwestern.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)
Cardioid Billiard (not Webshaped): Alexander Erner (13 Jun 1997)

Fall 1997

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

Spring 1995

Colinear helium spectrum: Preben Bertelsen, pbertelsen at nbivax.nbi.dk (13 Oct 1995) - 300 KB
Helium spectrum, s-wave model: Kristian Schaadt, schaadt at nbivax.nbi.dk (13 Oct 1995) - 453 KB
Hard Bunimovich stadium, washbord diffusion: Jonas Lundbek Hansen, (23 aug 1995) - 235 KB
Soft (but not easy) Bunimovich stadium: Sune Horlyck, HORLYCK at nbivax.nbi.dk (8 sep 1995) - 544 KB
Kai's instructions for soft Bunimovich stadium, in Norwegian, 30 may 1995)
Spectrum of the Liouville operator: Niels Søndergaard, NSONDERG at nbivax.nbi.dk (30 aug 1995)

[ published projects | open projects | theses | course outlines ]

svn: $Author: predrag $ --- $Date: 2009-09-09 09:36:03 -0400 (Wed, 09 Sep 2009) $