Details of Grant 

EPSRC Reference:	GR/K79307/01
Title:	STOCHASTIC DIFFERENTIAL EQUATIONS AND THE NON- EQUILIBRIUM POTENTIAL
Principal Investigator:	McKane, Professor A
Other Investigators:	Bray, Professor AJ
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Department:	Physics & Astronomy
Organisation:	Victoria University of Manchester, The
Scheme:	Standard Research (Pre-FEC)
Starts:	01 October 1996	Ends:	30 September 1999	Value (£):	224,569
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Summary on Grant Application Form
Non-equilibrium analogues of equilibrium thermodynamic potentials, such as the free energy, have been sought for many years. The most promising candidate arises from the path-integral formulation of stochastic differential equations. Our aim is to use the expertise which we have built up from using this concept over the last few years to further develop it when it is applied to the generic case which holds for most systems of physical interest. The proposed work is both analytical and numerical. In the former case we will use the deep analogies between the weak noise limit of the equations and an underlying Hamiltonian dynamics to predict general features that may arise and to develop an intuition to understand them. The possible description of state selection from an unstable state using only a few degrees of freedom, may allow us to use this technique to reduce stochastic partial differential equations to a deterministic dynamical system. The numerical work will initially consist of the solution of the equations of the underlying dynamics, building in the features uncovered in the analytic treatment. Later on in the project, the very promising approach in which the non-equilibrium potential is numerically minimised will be explored. An important part of the work is to promote this little known, but powerful tool to the community of scientists who work with stochastic differential equations.
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