Mean-field theory of polynuclear surface growth

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Abstract
We study statistical properties of a continuum model of polynuclear surface growth on an infinite substrate. We develop a self-consistent mean-field theory which is solved to deduce the growth velocity and the extremal behaviour of the coverage. Numerical simulations show that this theory gives an improved approximation for the coverage compared to the previous linear recursion relations approach. Furthermore, these two approximations provide useful upper and lower bounds for a number of characteristics including the coverage, growth velocity and the width exponent.
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