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Multi-Turing instabilities & spontaneous patterns in discrete nonlinear systems : Simplicity and complexity, cavities and counterpropagation

Bostock, C, Christian, JM, Leite, AB, McDonald, GS and Huang, JG 2015, Multi-Turing instabilities & spontaneous patterns in discrete nonlinear systems : Simplicity and complexity, cavities and counterpropagation , in: 12th International Conference on the Mathematical and Numerical Aspects of Wave Propagation, 21- 25 June 2015, Karlsruhe, Germany. (In Press)

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Abstract

Alan Turing's profound insight into morphogenesis, published in 1952, has provided the cornerstone for understanding the origin of pattern and form in Nature. When the uniform states of a nonlinear reaction-diffusion system are sufficiently stressed, arbitrarily-small disturbances can drive spontaneous self-organization into simple patterns with finite amplitude. Emergent structures have a universal quality (including hexagons, honeycombs, squares, stripes, rings, spirals, vortices), and they are characterized by a single dominant scalelength that is associated with the most-unstable Fourier component. In this paper, we extend Turing's ideas to three wave-based discrete nonlinear optical models with a wide range of boundary conditions. In each case, the susceptibility of the uniform states to symmetry-breaking fluctuations is addressed and we predict a threshold instability spectrum for static patterns that comprises a multiple-minimum structure. These Turing systems are also studied numerically, and we uncover examples of simple and complex (i.e., fractal, or multi-scale) pattern formation.

Item Type: Conference or Workshop Item (Paper)
Themes: Energy
Subjects outside of the University Themes
Schools: Schools > School of Computing, Science and Engineering > Salford Innovation Research Centre (SIRC)
Refereed: Yes
Related URLs:
Funders: University of Salford
Depositing User: JM Christian
Date Deposited: 07 Jul 2015 14:57
Last Modified: 29 Oct 2015 00:09
URI: http://usir.salford.ac.uk/id/eprint/35371

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