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RG methods may potentially be useful for studying turbulence, but their use is not restricted to turbulence alone. Many problems in non-linear growth and directed polymers are related to the Burgers equation (a simplified Navier-Stokes equation) by straightforward transformations. The KPZ equation is one such, and was originally introduced in 1986 by Kardar, Parisi and Zhang [Phys. Rev. Lett. 56 889 (1986)] by allowing growth to proceed in a direction perpendicular to the surface. It is the simplest equation to capture the essential properties of directedness, and non-linearity, as well as locality and the stochastic nature of the growth. The KPZ equation has already been subject to study by the RG techniques of Forster, Nelson and Stephen in hydrodynamics [Phys. Rev. A 16 732 (1977)] and the various scaling exponents usually exhibited in non-linear growth phenomena and phase transitions, have all been investigated by, for example, Medina, Hwa, Kardar and Zhang [Phys. Rev. A 39 3053 (1989)]. Preliminary study is therefore being done into what use the conditional averaging procedures that have been developed here can have in addressing non-linear growth problems governed by the KPZ equation. An alternative, conservative equation (which has shift symmetry), proposed by McComb and Pandya [J. Phys. A 29 L629 (1996)], and which seems to remain unstudied, may also be a fruitful area for exploration. Group contacts: |             
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