| EPSRC Reference: |
GR/L06119/01 |
| Title: |
HYPERELLIPTIC ABELIAN FUNCTIONS AND JOSEPHSON JUNCTIONS |
| Principal Investigator: |
Eilbeck, Professor J |
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| Department: |
S of Mathematical and Computer Sciences |
| Organisation: |
Heriot-Watt University |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
17 December 1996 |
Ends: |
16 December 1998 |
Value (£): |
6,400
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| EPSRC Research Topic Classifications: |
| Non-linear Systems Mathematics |
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Summary on Grant Application Form |
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The research concerns the use of finite gap integration methods, based on Riemann surfaces theory, theta functions etc. One branch of this theory, the study and applications of abelian hyperelliptic functions, has been unjustly neglected. We plan to develop this theory and apply it to outstanding problems in the theory of Josephson Junctions. Enolskii has already made some progress in developing the abelian function theory, but substantial amounts requires to be done, in combination with sophisticated computer algebra systems. For example, addition theorems, which will play a key role in the theory, are required. In the Josephson junction applications, we plan to use the new theory to come up with a more comprehensive theory for the volt-ampere characteristics (VAC) of the junction, which present methods are unable to explain. For example, we hope to prove that the complicated singular structure of the VAC arises due to singularities of the moduli space of corresponding algebraic curves. We hope to be aided in this work by a well-qualified research assistant, Alistair Macintyre from Durham, whose position will be the subject of a separate grant application.
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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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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.hw.ac.uk |