Following on from the SERC Nonlinear Systems Initiative (NLS), the UK's Engineering and Physical Sciences Reasearch Council (EPSRC) in 1992 lauched a five-year Applied Nonlinear Mathematics (ANM) Programme, with the aim of supporting and encouraging genuinely interdisciplinary and collaborative research. It is intended as the means by which the results of the NLS are extended and taken up outside mathematics and transferred into otheracademic disciplines and industry.
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CHAOS THEORY: The occurrence of chaotic behaviour has been observed in mechanical, physico-chemical and biological systems. Chaos theory establishes the parameter regimes in which this behaviour occurs, thus allowing it to be avoided or exploited. Active areas of research include control of chaos and chaotic synchronisation.
NONLINEAR TIME-SERIES: Apparently random time-series may have an underlying deterministic origin. Nonlinear time-series analysis allows this to be revealed leading to improved predictions and providing a diagnostic tool to identify the dominant physical processes.
SOLITON THEORY: Solitons exist as waves in solids and in fluids, in problems where coherent and persistent finite amplitude features are expected. They arise in solid state electronic devices, protein molecules, nerve impulse propagation, laser dynamics and signal transmission lines.
BIFURCATION ANALYSIS: Is concerned with the determination of qualitative changes in behaviour of systems. It has a relevance to problems of stability of structures under load, ignition or explosion in chemical processes and transition from laminar to turbulent flows in fluids.
MIXING: Some chaotic flows are very good at mixing fluids, or at distributing particle suspensions uniformly - this has important spin-off for the process industry, for design of heat exchange devices and for pollutant dispersion.
PREDICTION: Methods of nonlinear time-series analysis can extract deterministric structure from a time-series (if it exists). This leads tomuch better prediction (eg weather forecasting) and control of complex engineering systems.
OSCILLATIONS: Nonlinear vibration theory is employed in modelling the large amplitude motion of structures such as suspension bridges and large cylindrical shells, in the design of dynamic vibration absorbers and in the control of wheel squeal.
COMMUNICATIONS: Nonlinear diffusion induced disorder is employed in theproduction of opto-electronic components, such as solid state wave-guides and lasers. Soliton theory is applied in the development of telecommunication techniques in fibre optic cables.
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Last Updated: 8th May 1996.