[an error occurred while processing this directive] - PROJECTS

[ published projectsopen projectstheses course outlines ]

link 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)

Spring 2014

Quantum Walkers
There is a life after PhD. Applying ChaosBook to the study of walkers? Should be possible.
Marc Fleury, marcf999[snail]gmail.com gatech.edu
project advisor: A. Knowledge
Cocyles and Fibered Rotations of the Torus
We will present many definitions.
Mikel J. De Viana XXX[snail]gmail.com gatech.edu
project advisor: Rafael de la Llave
Periodic Orbit Theory of Linear Response - A Numerical Study
It has been shown that the variation of the billiard expectation value in the parameter has a simple representation in terms of the (zeta) mean cycle and mean cycle period. However, a numerical computation of the dynamical averages has not yet been carried out for the linear response theory. We compute numerical averages of (interesting observables) for (model system) with (spatial perturbation), and compare the results to the linear order averages.
Benjamin McInroe, McInroe [snail] gatech.edu
project advisor: P. Cvitanović
A continuum elastic model of thermal fluctuation a protein: fat cigar approach
The project is based on a section from a manuscript in preparation. We approach a problem having to do with protein regulation by calculating the change in the equilibrium fluctuation correlations of the protein's shape due to the attachment of some small biomolecule. Some properties of fluctuation correlations are derived in a scalar and vector elastic setting. I show how the presence of gauge symmetries modifies the problem.
Michael S. Dimitriyev, michael.dimitriyev[snail] physics.gatech.edu
project advisor: P. M. Goldbart
State Space Partitions of Stochastic Chaotic Maps
The finest resolution that can be achieved in any real chaotic system is limited by the presence of noise. This noise can be used to define neighborhoods of the deterministic periodic orbits using the local eigenfunctions of the Fokker-Planck operator and its adjoint. We extend the work of D. Lippolis to include hyperbolic periodic orbits. The dynamics along the stable and unstable directions are separated. The neighborhoods on the stable and unstable manifolds can be defined in the same way as the neighborhoods for entirely stable or entirely unstable orbits. The neighborhoods are then returned to the original coordinates. The Fokker-Planck evolution can be described as finite Markov transition graph between these neighborhoods. Its spectral determinant is used to calculate the time averages of observables. We apply this technique to calculate long time observables of the Lozi map. (This project was completed as the GaTech Undergraduate Research Option Thesis)
Jeffrey M. Heninger, jeffrey.heninger [snail] gatech.edu
project advisor: P. Cvitanović
Thermoacoustic Instability
Thermoacoustic coupling is the interaction between acoustic pressure oscillations and the heat release dynamics that occurs in an acoustic field. Thermoacoustic instabilities can give rise to high amplitude pressure oscillations which can lead to flame blowout, structural damage etc [1].
To study this problem, a Rijke tube model will be used due to its simplicity.
[1] Zinn, B.T., Lieuwen, T.C., 'Combustion instabilities: basic concepts', Progress in Aeronautics and Astronautics, AIAA, 2005

Alexandre Damião, damiao [snail] gatech.edu
project advisor: Annonymous
Implementation of "chaos rules" to a periodic Lorentz gas for a successful calculation of observable transport properties.
In order to show how standard methods of chaotic dynamics work, we pick a simple, intuitively understandable system, which still can be used to model some real systems. As an example of such system we take a periodic Lorentz gas modeled as a lattice of hard spheres and calculate average transport properties of a classical particle propagating through the gas.
Pavel Svetlichnyy, psvetlichny3 [snail] gatech.edu
project advisor: P. Cvitanović
Symbolic dynamics, periodic and running orbits for hexagonal Lorentz gas
(abstarct to be written)
Tingnan Zhang, tingnan.zhang [snail] gmail.com
project advisor: Daniel I. Goldman
Stationary nonequilibrium ensembles for thermostated systems
My research involves studying what happens when a system of particles interacting through the "Kac collision", a stochastic process, is driven out of equilibrium. Some relevant questions are the existence and uniqueness of a steady state, convergence, and properties. Thus, I would like to study the applications of dynamical systems theory, and in particular the periodic orbit theory that we covered in the course, to understanding non-equilibrium steady states in statistical mechanics.
Ranjini Vaidyanathan, rvaidyanathan6 [snail] gatech.edu
project advisor: F. Bonetto
Dots, Lines, and Spirals (Oh My!)
Reaction diffusion systems present unique opportunities for the investigation of spatiotemporal chaos, arising as the governing equations in a number of open physical, chemical, and biological systems. In this work, we state a general form of the reaction diffusion system, enumerate the symmetries of the equation, and derive an equation for the flow on a symmetry-reduced manifold. Finally, we restate the central thesis motivating the efforts toward the "freezing" of equivariant partial differential equations, exploiting local symmetry for dynamical reduction.
C. D. Marcotte, XXX [snail] gatech.edu
project advisor: R. Grigoriev
Chaotic Regime Power Generation of a Bistable Piezomagnetoelastic Bimorph Energy Harvester
Piezoelectric cantilever bimorphs are a well-studied type of energy harvesting device, wherein a cantilever oscillator is tuned to resonate at the dominant frequency of an ambient vibration source. Little analysis has been done of the chaotic moderate forcing behavior. The study that has been done has relied solely on numerical simulation. This paper exploit the symmetry reduction and cycle expansion techniques to predict the average power generation of such an energy harvester in the chaotic regime.
Stephen Leadenham, sleadenham [snail] gatech.edu
project advisor: Annonymous
Biological oscillators
My research is based on the dynamics of the heart, so I am interested in biological oscillators in general. Biological oscillators can be chaotic, so I believe it is connected nicely to the topics we study in class. I will examine the mathematical side to oscillators and look at the systems' symmetries and chaotic dynamics.
Diana Chen, dchen87 [snail] gatech.edu
project advisor: F. Fenton, Richard Gray
Symmetry reduction of one-dimensional Kuramoto-Sivashinsky equation
One-dimensional Kuramoto-Sivashinsky equation on a periodic domain has three different symmetry: Galilean invariance, reflection symmetry and transnational invariance. Numerically, Kuramoto-Sivashinsky equation could be transformed into Fourier space and Galilean invariance could be quotiented out by setting the zeroth Fourier mode zero. Also, transnational symmetry in configuration space corresponds to rotational invariance in Fourier state space. For a lot of physically related problems, such as local physical dimension and shadowing periodic orbits, symmetries should be quotiented out in the first place. The problem with Kuramoto-Sivashinsky equation is that reflection and transnational invariance do not commute, so different order of quotienting out these two symmetries will generate different results.
Xiong Ding, xding [snail] gatech.edu
project advisor: P. Cvitanović
An Introduction to Chaos: The Rössler System
This note is intended as a short introduction to chaos in dynamical systems for advanced undergraduate and beginning graduate students. Knowledge of calculus, linear algebra and ODEs is assumed; some familiarity with measure theory and numerical methods is an asset, but is not necessary. In the first part we introduce deterministic dynamics from an abstract point of view and state a number of foundational results. Both ODEs and maps will be used to illustrate these and provide concrete examples. We follow this by studying chaos by investigating the dynamics some simple systems, the main one being the Rössler system. This example will be used as a way to introduce symbolic dynamics and to explore the dynamical zeta function.
Daniel Bernucci, dbernucci3 [snail] math.gatech.edu
project advisor: Annonymous
Vortices in Toroidal Bose-Einstein Condensates
Investigate vortices in a toroidal Bose-Einstein Condensate (BEC) with a rotating barrier.
Michael Krygier, XXX [snail] gatech.edu
project advisor: R. Grigoriev
Nonlinear behavior and analysis of vortex breakdown region and stagnation / flame stabilization point in swirl stabilized jets
In swirling, annular jets the flow field consists of a central vortex breakdown region, two shear layers, and an annular fluid jet. The vortex breakdown bubble, a region of highly turbulent recirculating flow in the center of the flowfield, is the result of a global instability of the swirling jet. High centrifugal forces push fluid outwards, creating a region of low pressure in the center of the flow, enabling fluid to reverse direction and move upstream. The furthest point upstream in which this reverse fluid can reach is the flame stabilization point, identified as the point in the spatial domain where there is a zero net axial velocity. This issue is made exciting when the flow is then transversely acoustically excited. This causes precession of the vortex breakdown region / "bubble" as well as axial bouncing in time. All of these dynamics influence the location of the flame stabilization point as the combustor operates. I intend to utilize Poincare sections, return maps, etc to elucidate the complex dynamics of the stabilization point motion.
Nick Magina, narthurm [snail] gatech.edu
project advisor: Tim Lieuwen
Dynamics of perturbation to gait limit cycles
Animal gaits may be characterized by limit cycles. During idealized steady-state locomotion each limb repeats the same motion with each stride, and state variables (velocities, angles, positions, etc.)describing the system are periodic in time. Perturbations to the 6-legged cockroach's alternating tripod gait have been described in the context of limit cycles and the stability of the state variables used to characterize the gait. The eigenvectors and values of the variables describe whether that variable will return to the periodic orbit on its own and how quickly it returns/diverges. This could give insight into which variables one might expect more active neurological control to correct and which can be corrected via more passive means. (Full, 2002)
Full, R. J., T. Kubow, J. Schmitt, P. Holmes, D. Koditschek. Quantifying dynamic stability and maneuverability in legged locomotion. Integ. and Comp. Biol.,42:149-157. (2002)

Perrin Schiebel, pschiebel3 [snail] gatech.edu
project advisor: Annonymous
Defocusing Wave Package in Quantum Billiard Collision
This project is a humble extension of Fig. 8.4 of ChaosBook. It's defocusing of a beam of nearby trajectories at a billiard collision. It's easily imagined to be about evolution of some Gaussian wake package. The sigma of the Gaussian distribution is expected to grow.
Wenbin Wei, wwb203 [snail] gatech.edu
project advisor: P. Cvitanović
A review of the Hénon map and its physical interpretation
The Hénon map is one of the simplest two-dimensional mappings exhibiting chaotic behavior. Even though the Hénon map is introduced mathematically as a model problem and has no particular physical import of itself, links between certain harmonic oscillators and "Hénon-like" maps have been found. To get a better understanding of the Hénon map, we review the dynamic properties of the Hénon map including its fixed points, stability and periodic orbits, and discuss its physical interpretation.
Haoran Wen, hrwen [snail] gatech.edu
project advisor: Annonymous
Food chain chaos redux
The Rosenzweig-Macarthur model of trophic interactions between three layers is an example of an ecological model displaying chaos. Mathematician B. Deng enlightened the ecological world in a series of papers that illustrated various mechanisms for the establishment of chaos within this model. I will choose one of his routes to chaos and attempt to discover symmetries, partition the space and calculate properties of the dynamics such as the topological entropy.
Bradford Taylor, btaylor40 [snail] gatech.edu
project advisor: P. Cvitanović
Barkley Model of reaction Diffusion Equation
A report on Barkley model of reaction diffusion PDEs and their simplified PDEs. This involves introduction to reaction diffusion systems equations, derivation of Barkley model by analysis of solutions of the PDEs and preserving the symmetry and bifurcation properties of PDEs into ODEs. Next I carry out symmetry reduction on the Barkley Model and what came out in a discussion of wash n fold study group about multiple symmetries.
Kamal Sharma, ksharma41 [snail] gatech.edu
project advisor: P. Cvitanović

Fall 2013

Understanding the production of photons from vacuum fluctuations via the dynamical Casimir effect
Recent developments in industry have pushed technology to the point where vacuum fluctuations matter at a practical level. Nanomachines and semiconductors are two such applications where there is a need to understand the Casimir Effect and how to use it when possible and avoid it when necessary. This requires an understanding of what is happening at a fundamental level. To the observer naive to Quantum Field Theory, there is no particular reason to think there should be a force in these limits. The following is a presentation of the background of the subject culminating with a discussion of the most recent observation of photons perturbed from the vacuum by a superconducting quantum interference device.
Gable M. Wadsworth, gwadsworth3 [snail] gatech.edu
Introduction to Gribov Ambiguity
In order to get correct predictions from non-Abelian field theories, which are susceptible to large number of gauge copies, we need to choose a representative of each gauge orbit. Some new methods and mathematical tricks have been explored but none have given a consistent recipe for selection of the representatives of these equivalence classes. However, if approximations are made in a clever manner, some of the methods can give us practically usable results.
Kamal Sharma, ksharma41 [snail] gatech.edu
project advisor: P. Cvitanović

Spring 2012

Cartography of high-dimensional flows: A visual guide to sections and slices
Predrag Cvitanović, Daniel Borrero-Echeverry, Keith M. Carroll, Bryce Robbins, and Evangelos Siminos
Chaos 14, 739 (2012); arXiv.org:1209.4915
Optimal resolution of state space in chaotic hyperbolic 2-dimensional maps
Methods for partitioning two dimensional state spaces are outlined using ``Knead and Fold'' type maps. Periodic orbits are found for these maps and the evolution of noise along these cycles is examined using the Fokker-Planck operator.
Gable M. Wadsworth and Daniel T. Kovari, gwadsworth3 [snail] gatech.edu
project advisor: P. Cvitanović
Towards reducing continuous symmetry of baroclinic flows
We introduce the physics and present some of the nonlinear theory methods that might be used to analyze baroclinic flows.
Sebastian Ortega Arango, sortega [snail] gatech.edu
project advisor: P. Cvitanović
A review of return maps for Rössler and the complex Lorenz
The methods of computing return maps and periodic solutions are reviewed for the Rössler system, and then applied to the Complex Lorenz equations
Keith M. Carroll, kcarroll3 [snail] gatech.edu
project advisor: P. Cvitanović
A survey of spiral wave studies: Dynamics and symmetries
I survey the nonlinear dynamics of spiral waves studies by Barkley and Biktashev et al. which respectively focus on spiral wave meander and group-orbit symmetry reduction.
Luis E. Saldana, lsaldana6 [snail] gatech.edu
project advisor: P. Cvitanović

Summer, Fall 2010

Reducing continuous symmetries with linear slice
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.
Stefan Froehlich, sfroehlich3 [snail] gmail.com
Submitted to the Georgia Tech SAIC Student Paper Competition (12 oct 2010)
related publication
project advisor: P. Cvitanović

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
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 equilibria and relative equilibria (travelling waves), periodic and relative periodic orbits are expected. I went looking for such, tried 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 Mathiesen 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, weikang(at)pku.edu.cn
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

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 Mathiesen (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
                        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)

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