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Details of Grant 

EPSRC Reference: EP/N028457/1
Title: Interacting Particle Systems and Stochastic PDEs
Principal Investigator: Joseph, Dr M
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: Probability and Statistics
Organisation: University of Sheffield
Scheme: First Grant - Revised 2009
Starts: 01 May 2016 Ends: 30 April 2018 Value (£): 93,564
EPSRC Research Topic Classifications:
Mathematical Analysis
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
02 Mar 2016 EPSRC Mathematics Prioritisation Panel Meeting March 2016 Announced
Summary on Grant Application Form
The heat equation is a mathematical equation used to describe the flow of heat through a purely conducting substance. This equation and many variations of it have been studied for around two hundred years, and the mathematical theory is now well developed. Over the last few decades mathematicians and physicists have been interested in the more realistic stochastic heat equation which considers the effect of having impurities randomly scattered in the medium. Certain transformations of this equation are also used to describe many other physical phenomena, for example motion of a turbulent fluid, deposition of snow and bacterial growth.

Although many advances have been made in our understanding of the stochastic heat equation, much more remains to be discovered. One of the goals of this proposal is to describe features of this equation for a wide class of impurities in the medium. The proposal also looks into ways of approximating this equation so that one can simulate the equation on a computer, which in turn will give us further intuition on its behaviour. We shall also explore connections of this equation to other systems exhibiting randomness.
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Organisation Website: http://www.shef.ac.uk