| EPSRC Reference: |
EP/J001740/1 |
| Title: |
Coherent structures in non-local active-dissipative equations: theory and computations |
| Principal Investigator: |
Tseluiko, Dr D |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
Mathematical Sciences |
| Organisation: |
Loughborough University |
| Scheme: |
First Grant - Revised 2009 |
| Starts: |
20 December 2012 |
Ends: |
19 December 2014 |
Value (£): |
100,681
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| EPSRC Research Topic Classifications: |
| Continuum Mechanics |
Non-linear Systems Mathematics |
| Numerical Analysis |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The aim of the proposed research is to analyse coherent structures for non-local active-dissipative partial differential equations (PDEs). Such equations are characterised by the presence of mechanisms of instability (energy production) and stability (energy dissipation). In addition, such equations contain non-local terms that cannot be expressed as polynomials or functions of the solution to be found and its derivatives. The solutions of active-dissipative equations are often characterised by a particular spatial and temporal behaviour, e.g. by space, time or space-time localised structures, the so-called coherent structures. The study of such structures has received a lot of attention over recent years due to their importance in hydrodynamics, nonlinear optics, chemical-reaction theory and mathematical biology. Despite recent developments in the theory of such structures for 'local' equations, coherent-structures interaction in non-local active-dissipative equations has not been developed as of yet and new mathematical techniques need to be introduced. The proposed research is a decisive step towards the understanding of the formation and interaction of coherent structures for such non-local equations with the ultimate goal to advance the understanding of non-local effects in PDEs, which is important both from the theoretical point of view and for numerous practical applications. The research is particularly timely because of its relevance to a wide range of industrial devices that utilise thin liquid films in the presence of various external effects and complexities. Examples include cooling systems, falling-film chemical reactors, compact reflux condensers and microfluidic devices.
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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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| 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.lboro.ac.uk |