| EPSRC Reference: |
EP/D505402/1 |
| Title: |
Mathematical Analysis of Bernoulli Free Boundaries |
| Principal Investigator: |
Toland, Professor JF |
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| Department: |
Mathematical Sciences |
| Organisation: |
University of Bath |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 October 2005 |
Ends: |
31 July 2009 |
Value (£): |
214,309
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The best way to describe this to a 14 year old might be the following. Suppose you have a sealed vessel containing a fluid, water say, and that inside the vessel the fluid is in motion, although you can't see it through the walls of the container. Now suppose you could somehow peel away these walls. You can imagine that the fluid will now spill out of the container because there is nothing to hold it in. The question is this, can we imagine a case when the container walls are in fact doing nothing, and that the motion would be the same even if they were taken away? For which containers is this possible. Here is a simple example. Suppose water is flowing horizontally in a horizontal channel with a horizontal lid. Take away the lid and nothing happens, the lid was doing nothing.What we want to investigate here is the fact that there are very complicated lids (not just flat ones) for a horizontal channel which have the property that when you take them away the flow does not alter. Moreover this phenomenon arises in electrostatics and elsewhere - it is called a free boundary problem because the question is how to design a boundary that can be removed without affecting the flow. We are looking for a particular geometric shape with these properties.Having described the problem picturesquely, I would then explain that we are not dealing with a mechanical problem, but with an abstract mathematical problem that involves some quite sophisticated material. Happily the outcome, being general and somewhat abstracted, may be relevant beyond the mechanical description of the problem just given.
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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 |
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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.bath.ac.uk |