Tag Archives: control-based continuation

Postdoc position now available

3 year postdoc position available for 1 June 2017 start!

We seek a highly motivated Research Associate who is interested in working as part of a team at the interface between Engineering and Applied Mathematics to investigate new methods for exploring the nonlinear behaviour of engineered systems and to develop numerical continuation techniques for physical experiments.

Modern test methods for investigating the dynamics of engineered structures are inadequate for dealing with the presence of significant nonlinearity since they have largely been developed under the assumption of linear behaviour. In contrast, control-based continuation (CBC), a versatile non-parametric identification method, has been developed with nonlinearity in mind from the beginning. It has been demonstrated on simple experiments but now advances in underlying methodology are required to apply CBC to real-world experiments which have higher levels of measurement noise and many degrees of freedom. The versatility of CBC is such that, with these advances, it will also become relevant for researchers studying nonlinear systems in both engineering and other fields, such as in the biological sciences.

We are seeking a Research Associate to drive this research forward alongside researchers working on closely related problems from the Departments of Engineering Mathematics, Mechanical Engineering and Aerospace Engineering. Support will be readily available from the investigators David Barton, Simon Neild and Djamel Rezgui. More widely, you will be part of the Dynamics and Control research group and the Applied Nonlinear Mathematics research group both of which carry out cutting-edge research in a wide range of application areas.

CBC presently draws on a wide range of underlying areas including, but not limited to, dynamical systems and bifurcation theory, system identification, control theory and machine learning. Applicants are expected to have experience in at least one of these areas in addition to a first degree and preferably a PhD in Applied Mathematics/Physics/Engineering (or a closely related discipline).

Possible initial avenues of research include

  • Improving the robustness of CBC in the presence of noise using surrogate models. Gaussian processes have previously been investigated and may be useful.
  • Investigating the scaling up of CBC to many degree-of-freedom systems. Ideas from numerical continuation of PDE systems could yield insights.
  • Implementation of CBC on existing aerospace experiments for dynamic testing and wind tunnel testing.

The post is available from 1 June 2017 with funding available for up to three years.

To apply visit http://www.bristol.ac.uk/jobs/find/details.html?nPostingId=5644&nPostingTargetId=21245

Please direct any questions to David Barton, david.barton@bristol.ac.uk.

PhD studentship opportunities

Breaking news: PhD studentships (scholarships) available for UK and EU* students in the Department of Engineering Mathematics at the University of Bristol for immediate start.

Due to a number of students withdrawing for personal reasons, there are now several PhD studentships available that must be taken up by September 2016. I am looking for motivated and able  students who are interested in doing research at the intersection of Applied Mathematics and Engineering/Science (my interests are quite broad!). In particular, I have three different topics that I’m actively pursuing at the moment all of which feature numerical computation/numerical analysis:

  • Nonlinear dynamics of stochastic differential equations — I’m interested in investigating how the tools and concepts of nonlinear dynamics and bifurcation theory can be applied to stochastic differential equations arising from various application areas (e.g., neuroscience or climate science).
  • Control-based continuation — numerical continuation is a very effective tool for investigating the nonlinear behaviour and bifurcations of mathematical models, and control-based continuation is a means for applying this tool to physical experiments (engineered systems or, hopefully, biological systems) without the need for a mathematical model. Research in this area requires a very interesting mix of numerical analysis, control theory, system identification and the theory of stochastic processes (I don’t expect students to have a background in all of these subjects!).
  • Equation-free methods and agent-based modelling — equation-free methods are a means for obtaining a macroscopic model from microscopic simulations. They have been used for many physical processes previously and I am interested in how they can be extended to agent-based models, such as models of Zebrafish locomotion to investigate the dynamics of shoaling (Zebrafish are just one example).

I have also worked extensively with delay differential equations and, though I don’t have any active work in this area at the moment, I’m happy to solicit project suggestions in this area. All of these projects are very open ended and I’m happy to work with students to tailor the projects to their own interests.

There is no deadline for these studentships, though obviously it’s better to apply sooner rather than later. If you are interested, get in touch for more information.

* EU students are eligible provided they have been resident in the UK for at least 3 years. See the EPSRC website for more details.

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.