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Details of Grant 

EPSRC Reference: EP/J009636/1
Title: Creating macroscale effective interfaces encapsulating microstructural physics
Principal Investigator: Pavliotis, Professor G
Other Investigators:
Craster, Professor R Parry, Professor AO
Researcher Co-Investigators:
Project Partners:
Department: Mathematics
Organisation: Imperial College London
Scheme: Standard Research
Starts: 01 October 2012 Ends: 31 March 2016 Value (£): 546,594
EPSRC Research Topic Classifications:
Continuum Mechanics Numerical Analysis
EPSRC Industrial Sector Classifications:
Related Grants:
Panel History:
Panel DatePanel NameOutcome
30 Jan 2012 Mathematics Prioritisation Panel Meeting January 2012 Announced
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).

Key Findings
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Potential use in non-academic contexts
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Impacts
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Summary
Date Materialised
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Project URL:  
Further Information:  
Organisation Website: http://www.imperial.ac.uk