| EPSRC Reference: |
EP/J009636/1 |
| Title: |
Creating macroscale effective interfaces encapsulating microstructural physics |
| Principal Investigator: |
Pavliotis, Professor G |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
Mathematics |
| Organisation: |
Imperial College London |
| Scheme: |
Standard Research |
| Starts: |
01 October 2012 |
Ends: |
31 March 2016 |
Value (£): |
546,594
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| EPSRC Research Topic Classifications: |
| Continuum Mechanics |
Numerical Analysis |
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| EPSRC Industrial Sector Classifications: |
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| Panel History: |
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Summary on Grant Application Form |
This proposal seeks funding for a comprehensive three year research
program into
methodologies for modeling microscale interfacial phenomena on the macroscale
level. A fundamental question stretching across many disciplines is:
Given a microstructured interface
can it be replaced by an effective ``averaged'' boundary condition
entirely posed upon a macroscale. If so, can it accurately reproduce the physical
effects created by the microstructure? Can this effective boundary condition be
derived rigorously, rather than in some ad-hoc fashion, and what are
the limitations in so doing?
The proposal aims to answer these questions, with the goal of being
able to accurately and efficiently predict complex physical behaviour
in three apparently unconnected
fields: in wave propagation for surface Rayleigh-Bloch
waves and for the reflection of waves from designer structured
surfaces, in the statistical mechanics of phase transitions on
micropatterned surfaces, and in modeling diffusions through
structured domains. These fields all share a complex structured
interface and the generic overarching Mathematical approach we propose will lead to effective
boundary conditions
encapsulating the dominant microscale Physics; this will represent a
considerable advance in each of these areas.
The primary Mathematical approach will be based around
Homogenization theory utilizing the discrepancy in lengthscales to
create asymptotics from multiple scales analysis. Homogenization is conventionally
used when the bulk material has short-scale fluctuations and the
solution varies on a long-scale, its use for
interfaces is much less well explored.
Importantly we also aim to enhance the
range of validity of homogenization theory away from long-wave,
quasi-static, regimes to ones that can vary on the same scale as
the microstructure. This analytical work will be complemented by
detailed
numerical simulations that will act to verify the efficacy of the
developed interfacial models. The work will be undertaken by a team
from the Mathematics Department at Imperial College London
with complementary skills and strengths: Pavliotis (Homogenization
theory, stochastic processes), Parry (Statistical mechanics, phase
transitions) and Craster (Wave propagation, homogenization, fluid mechanics).
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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.imperial.ac.uk |