EPSRC Reference: 
EP/M028607/1 
Title: 
Effective properties of interface evolution in a random environment 
Principal Investigator: 
Dirr, Professor NP 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Sch of Mathematics 
Organisation: 
Cardiff University 
Scheme: 
Standard Research 
Starts: 
01 January 2016 
Ends: 
31 December 2018 
Value (£): 
202,479

EPSRC Research Topic Classifications: 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 
Panel Date  Panel Name  Outcome 
16 Jun 2015

EPSRC Mathematics Prioritisation Panel June 2015

Announced


Summary on Grant Application Form 
This is mathematical research connecting the analysis of partial differential equations (PDEs) and (applied) probability.
The main goal of this project is to derive macroscopic evolution laws for interfaces in heterogeneous, random environments, described on a small scale by nonlinear PDEs with random coefficients. In particular, we want to go beyond classical homogenisation in order to treat systems where a longrange collective behaviour emerges. A key aspect of this project is to establish a new link between analysis and probability, benefitting both fields, by working on problems motivated by applications.
It is motivated by the following situation:
With an interface is associated a scalar quantity called its energy (think e.g. of its area) which it tries to decrease, i.e., it performs a gradient flow. This energy is perturbed through obstacles or impurities on a very small scale, and driven by some largescale force. The impurities are random, i.e., we have information only on the probability of finding certain impurities in a certain place, not on their precise nature and location.
We are interested in the effective velocity and other qualitative properties of the interface on a large scale, much larger than the scale on which the perturbations vary. On that scale, the perturbations should average out, but the questions is:
What is the effective evolution law on a large scale, and what are the qualitative properties of the interface, e.g. on which scales does it look rough due to all the random heterogeneities? How does all this depend on the law of the impurities?
This is important because we are interested in the reaction of a system on the scale of our everyday life to an input on that scale. E.g. we would like to know how a piece of metal changes shape in a car crash, we are not interested in the position of each single atom, and we wouldn't be able to compute those anyway. But most realistic materials have some random structure on a fine scale.

Key Findings 
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Potential use in nonacademic contexts 
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Impacts 
Description 
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Summary 

Date Materialised 


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Project URL: 

Further Information: 

Organisation Website: 
http://www.cf.ac.uk 