The hidden causes of volatile behaviour around non-smooth events

The hidden causes of volatile behaviour around non-smooth events

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There are three things vital to a good understanding of a system: analysis, simulation, and experiment. Finding agreement between these three might be difficult if a system is very large and complex, if it is very noisy, or if it contains nonsmooth events (like impact, switches, or discontinuous parameters). Obviously a large complex system might also be noisy. Less obviously, a small and simple system might appear noisy because it is nonsmooth.  I will be presenting a new way to study such nonsmooth events, and insights into why they make systems behave erratically and unpredictably. 

Physical models have difficulty peering inside non-smooth events, like impacts, because they involve complicated details on a small scale that seems remote from the large-scale behaviour we are often interested in. Using mathematical ideas from nonlinear dynamics we can actually peer inside such events, and in doing so we often find localized instabilities, hidden away on tiny scales, but with large-scale effects on behaviour. They are understandable as a novel kind of nonlinearity. 

What we find is that non-smooth events often create small-scale instability that can be mistaken for large-scale noise or complexity. While not surprising in itself, it does give us a way to study the instability, how and why it happens, how it can be analysed and simulated, and hopefully bring our models closer to what we see experimentally. 

Dr Mike Jeffrey, Faculty of Engineering, University of Bristol
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Centre for Applied Dynamics Research and School of Engineering
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