Systematic experimental exploration of bifurcations with noninvasive control

One of the things I’ll be doing on this new website is highlighting some of my papers, past and present. This paper is one I’m particularly pleased with as it showcases what you can do when you link numerical methods (computer algorithms) with a physical experiment in real-time.

Normally to investigate the behaviour of a system or structure (e.g., an aerofoil) you would build a mathematical model of the system, then validate it (hopefully! lots of people skip this step) and then investigate it using some of the sophisticated mathematical tools we have for analysis. This paper looks at how we can throw out the model building step and use those same sophisticated mathematical tools directly on the original physical experiment. OK, there are a few constraints (we must have quite a bit of control over the experiment) but it does mean that we can be sure that the behaviour we see is real and not just because the model is wrong.

This paper looks at a very simple physical example, namely an energy harvester but it demonstrates the principle nicely.

Reference: Systematic experimental exploration of bifurcations with noninvasive control, David A.W. Barton and Jan Sieber, Physical Review E 87 2013, 052916. DOI: 10.1103/PhysRevE.87.052916. Preprint (open access): arXiv 1209.3713.

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