| EPSRC Reference: |
GR/L42377/01 |
| Title: |
MOVING BOUNDARIES WITH NON-MONOTONIC CURVATURE- DEPENDENT PROPAGATION SPEED |
| Principal Investigator: |
Dold, Professor J |
| Other Investigators: |
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| Department: |
Mathematics |
| Organisation: |
UMIST |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 October 1997 |
Ends: |
31 March 2001 |
Value (£): |
56,954
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| EPSRC Research Topic Classifications: |
| Non-linear Systems Mathematics |
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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A rich and novel range of nonlinear dynamical problems arises when as interface moves at a speed that depends non-monotonically on mean curvature. Problems of this nature can be predicted for certain flames near stoichiometry and in the meandering of rivers (other examples will be sought). Typically:- windows of anti-diffusive instability arise over certain ranges of curvature in the linearised problem, with well-posedness with respect to initial conditions surviving in spite of diffusivity becoming negative; steady solutions appear to separate into different phases of curvature; there appears to be some connection with phase-separation; but as yet little more seems to be known about the dynamics of this range of problems. The project will investigate fully nonlinear dynamics arising from non-monotonic curvature-dependence in the propagation of surfaces. Different forms of high-order regularisation will be studied relating to different applications. Asymptotically, weak regularisation is most significant where large changes in curvature arise, i.e. between different phases of curvature. The main outcome of the project will be a deeper understanding of both the dynamics associated with a novel form of nonlinear diffusion and its practical implications.
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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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