EPSRC Reference: 
EP/J010820/1 
Title: 
Controlbased bifurcation analysis for experiments 
Principal Investigator: 
Sieber, Dr J 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Mathematical Sciences 
Organisation: 
University of Exeter 
Scheme: 
First Grant  Revised 2009 
Starts: 
01 July 2012 
Ends: 
30 June 2014 
Value (£): 
85,003

EPSRC Research Topic Classifications: 
Nonlinear Systems Mathematics 
Numerical Analysis 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 

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, "controlbased continuation",
that enables experimenters to observe unstable phenomena directly in
controlled laboratory experiments. Controlbased 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 beammagnet arrangements) have shown
that the method is indeed feasible. This project aims to make
controlbased 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 (socalled
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 (816 significant digits), which is not achievable
in most experiments.

Key Findings 
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Potential use in nonacademic contexts 
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Impacts 
Description 
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Summary 

Date Materialised 


Sectors submitted by the Researcher 
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Project URL: 

Further Information: 

Organisation Website: 
http://www.ex.ac.uk 