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Dissertation
Spatio-temporal dynamics in systems driven far from equilibrium: lasers and fluids
Doctor of Philosophy (Ph.D.), Drexel University
1996
DOI:
https://doi.org/10.17918/00000446
Abstract
Two systems able to display spatio-temporal structures when driven far from equilibrium have been studied. The spatio-temporal structures appear when the systems undergo bifurcations and they are the manifestation of the symmetry breaking of some property. (a) A very simple fluid experiment shows the appearance of sources and sinks of traveling waves in a one dimensional setting. The emphasis has been in the interaction between sinks and sources. By measuring both the wavelength and frequency of the traveling waves as well as the velocity of sinks and sources it was possible to compare theory with experiment. In particular, the so-called kinematic formula for localized structures in a one dimensional system was verified for the first time to our knowledge. However, discrepancies between theory and experiment have also been found, thus suggesting that it is worth considering both additional measurements and the revision of some theoretical aspects. (b) A CO₂ laser experiment (main part of the thesis), in which a discharge tube with square cross section is used, displays two dimensional patterns in the plane perpendicular to the direction of propagation of the beam. We studied these patterns in three different ways: (i) Spatio-temporal structures in patterns of small to moderate Fresnel number were studied by means of bifurcation theory in the presence of a symmetry group. Two sequences of bifurcations were observed and afterwards identified by means of the Hopf Equivariant Theorem applied to the group D4. (ii) Time-averaged spatial structures in patterns covering the whole range of available Fresnel numbers were analyzed using a Biorthogonal Decomposition. It was found that all the patterns, regardless of their size, can be described in terms of a small number of modes (less than five). (iii) Time series for the laser intensities at isolated points in patterns of big Fresnel number were analyzed. Global models were built by means of a Time Delay Embedding Algorithm. It was found that a five dimensional embedding space is able to support the dynamics.
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Details
- Title
- Spatio-temporal dynamics in systems driven far from equilibrium
- Creators
- Roberto Fernando Alvarez
- Contributors
- Jorge Tredicce (Advisor)Robert Gilmore (Advisor) - Drexel University, Physics
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Number of pages
- xi, 204 pages
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Arts and Sciences; Physics; Drexel University
- Other Identifier
- 991014970322604721