| EPSRC Reference: |
GR/L17177/01 |
| Title: |
MODELLING OF LOCALIZED FOLDING IN GEOMECHANICS USING 4TH ORDER NONLINEAR PARABOLIC EQUATIONS |
| Principal Investigator: |
Hunt, Emeritus Professor G |
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| Department: |
Mathematical Sciences |
| Organisation: |
University of Bath |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
09 January 1997 |
Ends: |
08 January 2000 |
Value (£): |
114,474
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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 proposal is to determine and analyse appropriate models for a single elastic upper layer supported either on or within a visco-elastic medium, such models forming the basis of investigation into the folding of geological rock strata under tectonic compression. Preliminary studies indicate that even weakly nonlinear constitutive equations for the supporting medium herald qualitative changes in response. Specifically, localized structures are expected, while in the linear context periodicity is the norm. Modern analytical and numerical methodology will be applied to the sets of nonlinear PDEs and integro-differential equations that result, to find the most likely folding patterns over a range of timescales. Over short timescales the models simplify to a set of ordinary differential equations in space. We will determine corresponding localised behaviour by finding homoclinic solutions and using a combination of numerical and analytical tools to examine how these depend upon the system parameters and describe patterns of evolution from random initial data. We will then investigate the evolution of these localised structures over longer timescales using tools developed for studying metastable structures and pattern formation. We will also study the existence of self-similar behaviour in the evolution. The systems will be investigated numerically using an adaptive numerical method specifically designed for computing localised structures.
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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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| 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.bath.ac.uk |