The phenomenon of spiral wave propagation in Belousov-Zhabotinsky media is a remarkable example of self-organisation. This distinctive waveform arises in a variety of excitable systems. The primary objective of the work described in this thesis is the construction and analysis of deterministic reaction-diffusion models in terms of partial differential equations, to explain the local and global geometry of the spiral pattern. The secondary objective is to design experiments that enable observation and recording of evolving chemical waves in three dimensional Belousov-Zhabotinsky media. A mathematical formulation of the one dimensional A-w system based on a hierarchy of trial phase functions is introduced. A Schr8dinger type boundary value problem in an eigen sub-domain is established; an algebraic formula for the wave number spectrum and an analytical representation for the concentration amplitude are derived. This formulation suggests a piece-wise linear approach to X-w systems in higher dimensions. The concentrations are expressible in terms of real combinations of solutions to the Helmholtz equation with complex wave number and the solutions are matched by using continuity, differentiability and threshold conditions. A detailed analysis of the existence of solutions to piece-wise linear A-w systems in two dimensions is presented; existence is demonstrated by solving the matching equations. A stability analysis completes the discussion. Plots of the concentration contours characterised by the matching parameters are included. These contours simulate the cross-section of the scroll wave observed in experiments carried out in three dimensional media. The experimental design allows direct observation of undistorted three dimensional chemical waves in situ. The kinematics, dynamics and transformations of a variety of three dimensional scroll-based structures are recorded. The dominant waveforms are simple scroll waves. In addition, transient but significant events such as fission of a complex structure are recorded.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:354887 |
| Date | January 1984 |
| Creators | Welsh, Brian J. |
| Publisher | Glasgow Caledonian University |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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