| EPSRC Reference: |
EP/J010820/1 |
| Title: |
Control-based bifurcation analysis for experiments |
| Principal Investigator: |
Sieber, Dr J |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
Mathematical Sciences |
| Organisation: |
University of Exeter |
| Scheme: |
First Grant - Revised 2009 |
| Starts: |
01 July 2012 |
Ends: |
30 June 2014 |
Value (£): |
85,003
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| EPSRC Research Topic Classifications: |
| Non-linear Systems Mathematics |
Numerical Analysis |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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| Panel History: |
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Summary on Grant Application Form |
Many phenomena that are predicted to exist by mathematical theory
remain invisible in real life. Yet, mathematical theory also predicts
that these hidden phenomena determine our fate when real life is "on
the edge". For example, a small increase of wind strength can abruptly
cause a bridge cable to start swinging violently. Still more puzzling,
the bridge cable may continue to swing strongly even if the wind
strength decreases again. Mathematical theory reveals that the
mechanisms behind these striking sudden changes (often catastrophes
from the point of view of engineering) are universal: they apply to a
bridge cable as well as to an ocean current or a neuron. The observed
change is abrupt only because the missing link between the two
different visible behaviours is typically a phenomenon that is
unstable or too sensitive to be visible. This insight enables
engineers and scientists to predict, and avoid or control, sudden
changes whenever they can rely on a set of equations describing the
motion.
This research will develop a method, "control-based continuation",
that enables experimenters to observe unstable phenomena directly in
controlled laboratory experiments. Control-based continuation uses
control to convert the relation between experimental inputs and
outputs into an equation that can be solved computationally. Every
phenomenon that is natural in the uncontrolled experiment can be found
as a solution of this equation. Mechanical prototype experiments
(using, for example, pendula and beam-magnet arrangements) have shown
that the method is indeed feasible. This project aims to make
control-based continuation applicable to more complex experiments and
more complex phenomena.
The PI will collaborate with experimenters at the Technical University
of Denmark (Lyngby) who investigate vibrations in fast rotating
machinery.
One specific objective of the project is to develop and test the continuation
of the exact boundaries between stability and instability (so-called
bifurcations). Traditional computational methods for determining
bifurcations are not applicable to equations extracted from
measurements because they rely on the ability to solve the equation
with high accuracy (8-16 significant digits), which is not achievable
in most experiments.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.ex.ac.uk |