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| Title: | Bifurcation problems in chaotically stirred reaction-diffusion systems |
| Authors: | Menon, Shakti Narayana |
| Keywords: | bifurcation chaotic stirring reaction-diffusion nonperturbative autocatalytic bistable excitable media flame filament |
| Issue Date: | Jun-2008 |
| Publisher: | University of Sydney Faculty of Science. School of Mathematics and Statistics. |
| Abstract: | A detailed theoretical and numerical investigation of the behaviour of reactive systems under the influence of chaotic stirring is presented. These systems exhibit stationary solutions arising from the balance between chaotic advection and diffusion. Excessive stirring of such systems results in the termination of the reaction via a saddle-node bifurcation. The solution behaviour of these systems is analytically described using a recently developed nonperturbative, non-asymptotic variational method. This method involves fitting appropriate parameterised test functions to the solution, and also allows us to describe the bifurcations of these systems. This method is tested against numerical results obtained using a reduced one-dimensional reaction-advection-diffusion model. Four one- and two-component reactive systems with multiple homogeneous steady-states are analysed, namely autocatalytic, bistable, excitable and combustion systems. In addition to the generic stirring-induced saddle-node bifurcation, a rich and complex bifurcation scenario is observed in the excitable system. This includes a previously unreported region of bistability characterised by a hysteresis loop, a supercritical Hopf bifurcation and a saddle-node bifurcation arising from propagation failure. Results obtained with the nonperturbative method provide a good description of the bifurcations and solution behaviour in the various regimes of these chaotically stirred reaction-diffusion systems. |
| Description: | Doctor of Philosophy |
| URI: | http://hdl.handle.net/2123/3685 |
| Appears in Collections: | Sydney Digital Theses |
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